S uc u al and elec onic
p ope ies o ansi ion me al
nanoalloys and magne ic compounds
Genehmig e Abhandlung
zu E langung des akademischen G ades
eines Dok o s de Na u wissenscha en (D . e . na .)
im P omo ionsp og amm
Physik Weiche Ma e ie, Nich linea e Dynamik und Fes k¨o pe physik
de Bay eu he G aduie enschule ¨u Ma hema ik und Na u wissenscha en
on
Linn Leppe
gebo en in Chemni z
1. Gu ach e : P o . D . S ephan K¨ummel
2. Gu ach e : P o . D . Ma hias Schmid
3. Gu ach e : P o . D . Paul-Ge ha d Reinha d
Tag de Ein eichung: 28. Mai 2013
Tag des Kolloqiums: 5. Sep embe 2013
I migh be w ong
I could ha e swo n
I saw a ligh coming on
(Radiohead)
Abs ac
In ansi ion me al clus e s, po en ially p o i able echnological applica ions and ascina ing
undamen al ques ions a e closely connec ed. Bime allic nanoalloys, e.g., ha e become
inc easingly popula as hei pe o mance in ca alysis is o en supe io o hei pu e
coun e pa s. Exempla y o his a e gold-pla inum (Au-P ) nanoalloys ha ha e been
used as highly po en ca alys s in elec oca alysis and in a a ie y o oxida ion eac ions.
Howe e , he me e exis ence o Au-P nanoalloys is as onishing, as Au and P canno be
mixed in bulk o e a wide ange o composi ions. Fu he mo e, how a combina ion o
Au and P in nanoalloys esul s in hei special p ope ies has no ye been de e mined
conclusi ely.
I has been shown in empi ical simula ions and i s -p inciples densi y unc ional heo y
(DFT) calcula ions ha Au-P nanoalloys p e e ably a ange in a co e-shell mixing pa e n
wi h Au o ming a shell a ound a P co e. This is in con adic ion o many expe imen al
s udies ha epo he o ma ion o solid solu ions o Au and P . In he p esen wo k,
his seeming disc epancy is add essed by simula ing x- ay di ac ion pa e ns ha a e
expe imen ally used o cha ac e ize nanoalloys. I is shown ha he in e p e a ion o he
di ac ion pa e ns elies on ques ionable assump ions and he e o e does no su ice as a
de ini e cha ac e iza ion ool o Au-P nanoalloys.
To shed ligh on he special ca aly ic p ope ies o Au-P nanoalloys unde a he
di e en expe imen al condi ions, a ho ough in es iga ion o hei elec onic and s uc u al
p ope ies has been ca ied ou . I is ound ha ea u es a o able o ca alysis in Au-P
nanoalloys eme ge as a consequence o combining wo undamen al p ope ies: P con ibu es
a high densi y o s a es close o he Fe mi le el, which p omo es chemical ac i i y. Au
inc eases he s uc u al lexibili y o he Au-P sys em, which migh be bene icial o he
o ma ion o ac i e and elemen -speci ic binding si es as well as egene a ion o he ca alys
a e he eac ion.
Al hough DFT o e s an a ac i e comp omise be ween compu a ional e o and
accu acy o a heo e ical desc ip ion o Au-P nanoalloys, o he ansi ion me al compounds
se e ely challenge exis ing DFT app oxima ions. Manganese (Mn) doped silicon (Si) clus e s
ep esen an ideal model sys em o s udy he in e ac ion o a single magne ic impu i y
wi h a semiconduc ing hos bo h expe imen ally and heo e ically. The ansi ion om
exohed al (lowly coo dina ed) o endohed al (highly coo dina ed) doping ha occu s o Si
clus e s wi h mo e han en a oms, is accompanied by comple e quenching o he magne ic
momen o Mn. We show ha MnSi
+
11
, he smalles endohed al clus e ound in expe imen ,
su e s s ongly om a well-known gene al p oblem o mos DFT app oxima ions: he
sel -in e ac ion e o . Finally, a uni e sal co ela ion be ween magne ic momen and he
coo dina ion o he Mn dopan is es ablished ha can be gene alized o ex ended sys ems
and sugges s a ou e o s abilize he magne ic momen o bulk Mn-Si compounds.

Ku zda s ellung
In
¨
Ube gangsme allclus e n liegen gewinnb ingende echnische Anwendungen und undamen-
ale F agen o mals nah beieinande . Dime allische Nanolegie ungen e euen sich beispiel-
sweise g oße Belieb hei , weil sie in di e sen ka aly ischen Reak ionen den en sp ech-enden
einen Me allen ¨ube legen sind. Gold-Pla in (Au-P ) Nanolegie ungen wu den als ¨auße s
wi ksame Ka alysa o en in de Elek oka alyse und ¨u eine Reihe on Oxida ions eak ionen
iden i izie . Genau genommen is jedoch die bloße Exis enz diese Nanolegie ungen e -
s aunlich, da Au und P in ausgedehn en Sys emen kaum mischba sind. Bislang is zudem
nich kla , au welche Weise eine Kombina ion on Au und P in eine Nanolegie ung zu
speziellen Eigenscha en ¨uh .
In empi ischen Simula ionen und nich -empi ischen Dich e unk ional heo ie (DFT) Rech-
nungen konn e gezeig we den, dass Au-P Nanolegie ungen ein Au
Schale
P
Ke n
Mischungsmu-
s e be o zugen. Dies s eh im Wide sp uch zu expe imen ellen S udien, in denen homogen
gemisch e Clus e beobach e wu den. In de o liegenden A bei wi d diese scheinba e
Disk epanz du ch Simula ion on R¨on genbeugungsmus e n un e such . Es wi d gezeig ,
dass die ¨ubliche Auswe ung diese Beugungsmus e au meh deu igen Annahmen be uh
und somi nich zu alleinigen Cha ak e isie ung on Au-P Nanolegie ungen aus eich .
Um Au schluss ¨ube die hohe ka aly ische Ak i i ¨a on Au-P Nanolegie ungen zu
e langen, wu den ih e elek onischen und s uk u ellen Eigenscha en un e such . Es wi d
gezeig , dass sich die g¨uns igen Eigenscha en on Au-P Nanolegie ungen als Konsequenz
de Kombina ion zweie undamen ale Eigenscha en e geben k¨onnen: P ¨ag zu eine
hohen Zus andsdich e am Fe mini eau bei, welche ¨o de lich ¨u die chemische Ak i i ¨a
sein kann. Mi s eigendem Au-An eil s eig wiede um die s uk u elle Flexibili ¨a de Au-P
Sys eme. Dies kann ¨u die Bildung ak i e und elemen spezi ische Ka alysezen en sowie
zu Regene a ion des Ka alysa o s nach de Reak ion on Nu zen sein.
DFT bie e ¨u die Behandlung on Au-P Nanolegie ungen einen gu en Komp omiss
zwischen echne ischem Au wand und Genauigkei . Im zwei en Teil diese A bei geh es
jedoch um eine ande e
¨
Ube gangsme all e bindung, welche exis ie ende N¨ahe ungen de
DFT au eine ha e P obe s ell . Siliziumclus e (Si) do ie mi einem einzelnen Mangana om
(Mn) sind ein ideales Modellsys em um die F age zu un e suchen, wie eine magne ische
Ve un einigung mi einem halblei enden Wi sma e ial wechselwi k . De
¨
Ube gang on
exohed ale (nied ige Koo dina ion) zu endohed ale (hohe Koo dina ion) Do ie ung inde
¨u Clus e mi meh als zehn Si-A omen s a und wi d on eine komple en Ausl¨oschung
des magne ischen Momen s beglei e . In diese A bei wi d gezeig , dass MnSi
+
11
, de kleins e
expe imen ell iden i izie e endohed ale Clus e , besonde s s a k un e einem wohlbekann en
P oblem iele DFT N¨ahe ungen leide : dem Selbs wechselwi kungs ehle . Abschließend wi d
ein uni e selle Zusammenhang zwischen dem magne ischen Momen und de Koo dina ion
des Mn-Do ie a oms gezeig , de auch au Fes k¨o pe sys eme ¨ube agen we den kann.
Diese Zusammenhang e ¨o ne die M¨oglichkei das magne ische Momen on ausgedehn en
Mn-Si Ve bindungen zu s abilisie en.
Con en s
1 In oduc ion 1
2 Theo e ical and echnical amewo k 5
2.1 Founda ions o Densi y Func ional Theo y . . . . . . . . . . . . . . . . . . . 5
2.2 Exchange-co ela ion ene gy unc ionals . . . . . . . . . . . . . . . . . . . . 7
2.3 In e p e a ion o (gene alized) Kohn-Sham eigen alues . . . . . . . . . . . . 12
2.4 Pseudopo en ials ................................. 14
2.4.1 No m-conse ing pseudopo en ials . . . . . . . . . . . . . . . . . . . 15
2.4.2 Ene gy-adjus ed pseudopo en ials . . . . . . . . . . . . . . . . . . . . 16
2.4.3 P ojec o augmen ed wa es . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Me hods o geome y op imiza ion . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.1 Simula ed annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.2 The ”Big Bang” sea ch . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.3 The Nudged Elas ic Band me hod . . . . . . . . . . . . . . . . . . . 20
3 The bime allic e ec in Au-P and Au-Pd nanoalloys 23
3.1 Au-P and Au-Pd nanoalloys in ca alysis . . . . . . . . . . . . . . . . . . . . 23
3.2 Geome ic s uc u e and mixing pa e ns o Au-P nanoalloys . . . . . . . . 25
3.3 Au-P alloys and Vega d’s law on he nanoscale . . . . . . . . . . . . . . . . 27
3.4 The in e play be ween luxionali y and elec onic s uc u e . . . . . . . . . 34
3.4.1 Elec onic s uc u e o Au-P nanoalloys . . . . . . . . . . . . . . . . 35
3.4.2 Elec onic s uc u e o Au-Pd nanoalloys . . . . . . . . . . . . . . . 39
3.4.3 The ole o Au in Au-P nanoalloys . . . . . . . . . . . . . . . . . . . 41
3.4.4 Combining elec onic s uc u e and luxionali y . . . . . . . . . . . . 45
4 Magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s 47
4.1 Dilu e magne ic semiconduc o s . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 S ong co ela ion in Densi y Func ional Theo y . . . . . . . . . . . . . . . 49
4.3
A DFT-s udy o he magne ic- o-nonmagne ic ansi ion in Mn-doped Si-
clus e s ...................................... 52
5 Summa y and ou look 61
5.1 Summa y ..................................... 61
6 Chap e 2 — Theo e ical and echnical amewo k
he in e ac ion o he elec ons wi h all ex e nal po en ials and
ˆ
W
=
Pi<j w
(
ˆ i,ˆ j
) is he
elec on-elec on in e ac ion.
The Hohenbe g-Kohn heo em can be subsumed in wo s a emen s: Fi s , o a gi en
elec on-elec on in e ac ion
ˆ
W
he e is a one- o-one mapping be ween he ex e nal po en ial
ex
(up o a physically i ele an cons an ), he (non-degene a e) g ound s a e
|ψ0i
esul ing
om Sch ¨odinge ’s equa ion
ˆ
H|ψ0i
=
E0|ψ0i
and he g ound s a e densi y
n
(
).
|ψ0i
is a
unique unc ional o he g ound s a e densi y, hence e e y g ound s a e obse able, and
in pa icula he g ound s a e ene gy, is a densi y unc ional, oo. Second, using he
Raleigh-Ri z a ia ional p inciple one can ob ain he exac g ound s a e densi y and ene gy
co esponding o ex by minimizing he ene gy unc ional
E[n] = F[n] + Z ex ( )n( )d3 . (2.1)
F
[
n
] =
hψ
[
n
]
|ˆ
T
+
ˆ
W|ψ
[
n
]
i
is a uni e sal unc ional, i.e., i is independen o
ex
(
). This
p o ides a simple and exac e o mula ion o Sch ¨odinge ’s equa ion. Howe e , as Hohenbe g
and Kohn no ed al eady in 1964 [15]: “The majo pa o he complexi ies o he many-
elec on p oblem a e associa ed wi h he de e mina ion o he uni e sal unc ional F[n].”
The mos success ul app oach o de e mine
F
[
n
] was p oposed in 1965 by Kohn and
Sham [16], who e o mula ed he ene gy unc ional o a sys em o
N
in e ac ing elec ons as
E[n] = Ts[n] + EH[n] + Eex [n] + Exc[n],(2.2)
whe e
Ts
[
n
] is he kine ic ene gy o a sys em o
N
non-in e ac ing elec ons.
EH
[
n
] is he
classical elec os a ic Ha ee ene gy
EH=e2
2Z Z n( )n( 0)
| − 0|d3 d3 0(2.3)
and Eex [n] desc ibes he in e ac ion be ween he elec ons and he ex e nal po en ial
Eex [n] = Z ex ( )n( )d3 . (2.4)
Exc
[
n
], he exchange-co ela ion (xc) ene gy unc ional, is de ined as consis ing o e e y
con ibu ion no ea ed by EHand Ts, i.e.,
Exc =T−Ts+W−EH.(2.5)
He e,
T
is he ull kine ic ene gy o he in e ac ing elec on sys em and
W
is he elec on-
elec on in e ac ion ene gy. Minimiza ion o Eq.
(2.2)
wi h espec o
nσ
, he o al spin
densi y, and compa ison wi h he co esponding e m o a sys em o
N
non-in e ac ing
elec ons leads o he same g ound s a e densi y i he
N
non-in e ac ing elec ons a e
subjec o an e ec i e, local, mul iplica i e po en ial
KS
σ( ) = ex ( ) + H( ) + xc,σ( ),(2.6)
in which
H
is he Ha ee po en ial
H
=
e2Rn
(
0
)
/| − 0|d3 0
and
xc,σ
=
δExc/δnσ
he xc po en ial. Eq.
(2.6)
de ines he so-called KS po en ial. Rega ding he ques ion o

2.2. Exchange-co ela ion ene gy unc ionals 7
whe he such a po en ial exis s o all densi ies ( - ep esen abili y p oblem) he eade is
e e ed o Re . [17] and e e ences he ein. In mos p ac ically ele an cases he densi y
is - ep esen able. This means ha one can calcula e he g ound s a e densi y
n
(
) o
he many-elec on sys em in an ex e nal po en ial
ex
(
) by sol ing he Sch ¨odinge -like
one-pa icle equa ions
−¯h2
2m∇2+ KS
σ( )!ϕiσ( ) = εiσϕiσ( ),(2.7)
and summing o e all occupied KS o bi als, ϕiσ( ),
n( ) = X
σ=↑,↓
nσ( ) = X
σ=↑,↓
Nσ
X
i=1
iσ|ϕiσ( )|2.(2.8)
The sum o e all occupa ion numbe s iσ yields he o al numbe o elec ons
X
σ=↑,↓
Nσ
X
i=1
iσ =N. (2.9)
Equa ions
(2.6)
–
(2.8)
cons i u e he KS equa ions, ha ha e o be sol ed sel -consis en ly
in mos p ac ical applica ions o DFT.
The KS equa ions a e in p inciple an exac e o mula ion o he ull in e ac ing many-
body p oblem o quan um mechanics. Howe e , all exchange and co ela ion e ec s ha go
beyond he Ha ee ene gy EHand he non-in e ac ing kine ic ene gy Tsa e by de ini ion
(Eq.
(2.5)
) included in he xc ene gy
Exc
, which is in gene al no known exac ly. The mos
impo an app oxima ions o Exc a e discussed in he ollowing sec ion.
2.2 Exchange-co ela ion ene gy unc ionals
App oxima ions o he xc ene gy unc ional can oughly be di ided in o wo g oups: explici
and implici densi y unc ionals. Commonly used unc ional app oxima ions o he i s
kind a e he local densi y app oxima ion (LDA) and he gene alized g adien app oxima ion
(GGA). Func ionals o he second g oup do no explici ly depend on he densi y bu on
he o bi als, i.e., hey possess an implici dependence on he elec on densi y by i ue
o he Hohenbe g-Kohn heo em. P ominen examples a e so-called hyb id unc ionals
and ange-sepa a ed hyb id (RSH) unc ionals, me a-GGAs as well as he sel -in e ac ion
co ec ion (SIC). A ho ough discussion o he p ope ies and limi s o all unc ionals is
beyond he scope o his hesis. A comp ehensi e o e iew can be ound in Re . [18] and
e e ences he ein. Rele an app oxima ions o he p esen wo k a e desc ibed in he
ollowing.
8 Chap e 2 — Theo e ical and echnical amewo k
The LDA
1
is one o he mos o en used app oxima ions o
Exc
and was in oduced
al eady by Hohenbe g and Kohn [15]. I is based on he simple idea ha in a sys em in
which he elec on densi y a ies only slowly in space,
exc
, he xc ene gy pe elec on, is
app oxima ely equal o
ehom
xc
in he homogeneous elec on gas. One hen ob ains
Exc
by
in eg a ion o exc o e space. The exchange con ibu ion is exac ly known o be
ELDA
x[n] = −3e2
43
π1/3Zn( )4/3d3 . (2.10)
The co ela ion pa has been compu ed wi h high accu acy using Mon e-Ca lo me hods
[19]. Many widely used LDA ene gy unc ionals, e.g., he ones by Vosko, Wilke and Nusai
[20], Pe dew and Zunge [21] and Pe dew and Wang [22], a e based on pa ame iza ions o
hese ea ly Mon e-Ca lo calcula ions ex ended by known limi s and scaling laws de i ed
om he exac
Ehom
c
. The la ge numbe o sys ems o which he LDA leads o quali a i ely
easonable esul s
2
is su p ising aking in o accoun ha o mos sys ems he assump ion
o a nea ly homogeneous elec on densi y is an o e simpli ica ion. This can be a ionalized
by in oducing he concep o he xc hole
nxc
(
, 0
) =
ρ2
(
, 0
)
/n
(
)
−n
(
0
) wi h
ρ2
(
, 0
)
ep esen ing he elec on pai densi y. The xc hole has o obey he sum ule
Znxc( , 0)d3 =−1.(2.11)
The LDA’s xc hole sa is ies Eq.
(2.11)
e en in a he inhomogeneous si ua ions [23]. This
leads o a sub le e o cancella ion be ween he exchange and he co ela ion pa o
ELDA
xc
.
A sys ema ic way o imp o e on he LDA is o include no only in o ma ion abou he
elec on densi y a each poin
, bu also on he a e o i s spa ial a ia ion. Such GGA
unc ionals ha e he o m
EGGA
xc [n] = Z (n( ),∇n( ))d3 . (2.12)
The unc ion
(
n
(
)
,∇n
(
)) is cons uc ed ei he by ying o sa is y as many exac
cons ain s o he exac xc ene gy unc ional as possible (leading, e.g., o one o he mos
popula GGAs o Pe dew, Bu ke and E nze ho (PBE) [24] o by i ing o la ge se s o
es molecules (e.g., BLYP, consis ing o he exchange unc ional o Becke [25] and he
co ela ion unc ional o Lee, Yang and Pa [26]).
Al hough he LDA and he GGA pe o m sa is ac o ily in many p ac ical calcula ions,
hei ailu e in o he s is d ama ic. This quali a i ely inco ec beha io can in mos cases be
aced back o one common sou ce, he sel -in e ac ion e o (SIE) [21], which is a p oblem
ha was ecognized al eady in Thomas-Fe mi heo y [27, 28], an ances o o DFT. The
SIE is i ial o de ine in an one-elec on sys em wi h densi y
n1
, in which he e is no
elec on-elec on in e ac ion. He e, he exac xc ene gy (po en ial) and he Ha ee ene gy
1And he local spin densi y app oxima ion (LSDA) o spin-pola ized sys ems.
2
Al hough being a om chemical accu acy, which would equi e an e o o less han 0.04336 eV pe
pa icle as compa ed o he expe imen .
2.2. Exchange-co ela ion ene gy unc ionals 9
(po en ial) ha e o cancel each o he
EH[n1] + Exc[n1] = 0 (2.13)
H[n1]( ) + xc[n1]( )=0
by de ini ion. An app oxima e unc ional mus he e o e sa is y Eq.
(2.13)
in o de o be
ee o one-elec on sel -in e ac ion. This no ion can be ex ended o many-elec on sys ems
by iden i ying single elec ons wi h KS o bi al densi ies
niσ
=
iσ|ϕiσ|2
. Acco ding o
Pe dew and Zunge [21, 29] one can hen de ine he one-elec on SIE in a many-elec on
sys em as
eiσ =EH[niσ] + Exc[niσ,0].(2.14)
I
X
σ=↑,↓
Nσ
X
i=1
eiσ = 0 (2.15)
he app oxima e unc ional is conside ed ee o one-elec on sel -in e ac ion. This de ini ion
sugges s a s aigh o wa d way o co ec ing
Eapp ox
xc
o sel -in e ac ion by simply sub ac ing
he e oneous e ms om he app oxima e xc unc ional
ESIC
xc [n↑, n↓] = Eapp ox
xc [n↑, n↓]−X
σ=↑,↓
Nσ
X
i=1
(EH[niσ] + Eapp ox
xc [niσ,0]).(2.16)
This so-called sel -in e ac ion co ec ion (SIC) an example o an o bi al-dependen , implici
densi y unc ional. Two concep ual in icacies a e associa ed wi h such unc ionals. Fi s ,
he unc ional de i a i e
δExc/δnσ
canno be e alua ed as s aigh o wa dly as o explici
densi y unc ionals. One way o deal wi h his p oblem and a he same ime o s ay wi hin
he concep ual ealm o KS DFT, is o use a unc ional de i a i e chain ule
OEP
xc,σ =δExc[{ϕjτ }]
δnσ( )(2.17)
=X
α=↑,↓
Nα
X
i=1 ZδExc[{ϕjτ }]
δϕiα( 0)
δϕiα( 0)
δnσ( )d3 0+ c.c. (2.18)
=X
α,β=↑,↓
Nα
X
i=1 Z Z δExc[{ϕjτ }]
δϕiα( 0)
δϕiα( 0)
δ KS
β( 00)
δ KS
β( 00)
δnσ( )d3 0d3 00 + c.c.,(2.19)
whe e
α, β, σ
and
τ
deno e he spin pola iza ion and c.c. he complex conjuga e. F om his
exp ession one ob ains he op imized e ec i e po en ial (OEP) equa ion
Nσ
X
i=1
iσ Zϕ∗
iσ( 0)[ OEP
xc,σ ( 0)−uxc,iσ( 0)]GKS
iσ ( 0, )ϕiσ( )d3 0+ c.c. = 0 (2.20)
in which GKS
iσ ( 0, ) is he KS G een’s unc ion
GKS
iσ ( 0, ) = ∞
X
j=1
j6=i
ϕjσ( 0)ϕ∗
jσ( )
εiσ −εjσ
(2.21)
10 Chap e 2 — Theo e ical and echnical amewo k
and uxc,iσ( ) an o bi al speci ic po en ial
uxc,iσ( ) = 1
iσϕ∗
iσ( )
δExc[{ϕjτ }]
δϕiσ( ).(2.22)
The
xc,σ
ha sol es Eq.
(2.20)
is called he op imized e ec i e po en ial, as i yields he KS
o bi als ha minimize he o al ene gy. Fo p ac ical applica ions, a ull OEP calcula ion is
o en compu a ionally oo demanding, as Eq.
(2.20)
is an in eg al equa ion and con ains he
comple e se o occupied and unoccupied KS eigen alues. The app oxima ion o K iege , Li
and Ia a e (KLI) [30]
KLI
xc,σ( ) = 1
2nσ( )
Nσ
X
i=1 |ϕiσ( )|2[uxc,iσ( ) + (¯ KLI
xc,iσ −¯uxc,iσ)] + c.c. (2.23)
wi h
¯ KLI
xc,iσ =Zϕ∗
iσ( 0) KLI
xc,σ( 0)ϕiσ( 0)d3 0(2.24)
¯uxc,iσ =Zϕ∗
iσ( 0)uxc,iσ( 0)ϕiσ( 0)d3 0(2.25)
p o ides an al e na i e ha educes he compu a ional e o , bu can in many cases yield
esul s e y close o hose om a ull OEP calcula ion [18].
The second in icacy o o bi al-dependen unc ionals such as he SIC, is in ima ely
ela ed o he quan um mechanical na u e (indis inguishabili y) o he in e ac ing many-
elec on p oblem i sel : One-elec on o bi als a e an a i icial concep in oduced h ough
he KS ansa z and he KS o bi als a e in no way unique among o he o bi al se s ha also
sum up o he co ec g ound s a e densi y. This uni a y in a iance p oblem means ha
di e en OEP can be cons uc ed depending on he chosen o bi al se . A gene aliza ion
o he OEP me hod can be employed o deal wi h he uni a y in a iance p oblem ia a
densi y-conse ing uni a y ans o ma ion o he KS o bi als [31]. A de ailed discussion o
he OEP and app oxima ions o i can be ound in Re . [17] and [18]. The ambigui y o he
one-elec on o bi al se s also di ec ly a ec s he de ini ion o a SIE in many-elec on sys ems.
A emp s ha e been made o de ine a many-elec on SIE. The issue will be discussed in
Sec. 4.2. Eq.
(2.14)
is use ul e en wi hou ca ying ou an ac ual SIC calcula ion. I
p o ides a simple c i e ion o whe he he KS eigen alue spec um esul ing om a gi en
app oxima e xc unc ional is physically eliable (see discussion in Sec. 2.3 and a p ac ical
example in Sec. 4.3) [32, 33].
A second class o o bi al-dependen unc ionals a e me a-GGAs. They con ain he KS
kine ic ene gy densi y
τσ( ) = ¯h2
2m
Nσ
X
i=1
iσ|∇ϕiσ( )|2(2.26)
(and some imes e ms
∇2nσ
) and imp o e in some espec s upon semilocal unc ionals, e.g.,
hey in p inciple can achie e absence o he sel -co ela ion e o . Howe e , as comple e
sel -in e ac ion absence is no gua an eed by me a-GGAs, hey sha e concep ual di icul ies
2.2. Exchange-co ela ion ene gy unc ionals 11
wi h he LDA and GGA. An example o a me a-GGA ele an o he co ec desc ip ion
o he 2d-3d ansi ion in small Au-clus e anions [34] is he one by Tao, Pe dew, S a o e o
and Scuse ia [35].
Hyb id unc ionals a e among he mos o en used xc unc ional app oxima ions and ha e
become a a o i e ool o quan um chemis y. Such unc ionals a e cons uc ed o a ixed
ac ion o exac exchange
Eex
x
as well as semilocal exchange
Eapp ox
x
and co ela ion
Eapp ox
c3
.
The app oach was i s in oduced in 1993 by Becke [36], who p oposed a unc ional o m
Ehyb
xc =bEex
x+ (1 −b)Eapp ox
x+Eapp ox
c,(2.27)
in which Eex
xdeno es he Fock in eg al
Eex
x=−e2
2X
σ=↑,↓
Nσ
X
i,j=1
iσ jσ Z Z ϕ∗
iσ( )ϕ∗
jσ( 0)ϕjσ( )ϕiσ( 0)
| − 0|d3 d3 0.(2.28)
The pa ame e
b
is de e mined ei he by i ing o ex ensi e es se s o molecules o
a ionalized by i ue o he adiaba ic connec ion o malism [37, 38]. An example o he
la e app oach is he one-pa ame e hyb id PBE0, based on he PBE GGA [24] in which
b
= 0
.
25 [39]. Howe e , mos o oday’s hyb id unc ionals employ e en mo e pa ame e s,
he mos p ominen example being he 3-pa ame e B3LYP unc ional [40, 41], ha con ains
ac ions o he semilocal Becke unc ional [25] as
Eapp ox
x
, he GGA by Lee, Yang and Pa
[26] as Eapp ox
cand he LDA pa ame iza ion by Vosko, Wilke and Nusai [20].
Finally, I wan o men ion he ange-sepa a ed hyb ids (RSHs). The unde lying concep
o hese unc ionals is o sepa a e he elec on-elec on in e ac ion in o a long- ange and a
sho - ange pa ia
1
| − 0|=e (ω| − 0|)
| − 0|
| {z }
long ange
+1−e (ω| − 0|)
| − 0|
| {z }
sho ange
.(2.29)
The sc eening unc ion is o nume ical easons o en chosen as he e o unc ion and
ω
is an adjus able pa ame e ha de e mines a which leng h scale he sho - ange pa o
Eq.
(2.29)
decays o ze o and he long- ange pa becomes dominan . The long- ange pa
is gi en by he sc eened Fock in eg al, so ha one p ese es he ad an ages o employing
semilocal exchange a sho ange, while inco po a ing 100% o he non-local exac exchange
a long ange and hus ob ains he co ec asymp o ic beha io o he xc po en ial. Hence,
RSHs a e pa icula ly use ul o he desc ip ion o cha ge ans e exci a ions, bu hey can
also imp o e on g ound s a e p ope ies [42].
An example o such a unc ional is
ω
PBE, which is a RSH ha models he exchange hole
o he PBE GGA a sho ange [43]. The ange-sepa a ion pa ame e can be ob ained in
di e en ways: One can empi ically de e mine he alue o
ω
ha desc ibes he mochemis y
o cha ge ans e exci a ions bes . Howe e , e idence sugges s ha in ac conside ably
3
P io o hei o mal jus i ica ion ia he gene alized KS amewo k, hese unc ionals had been seen as
”hyb ids” be ween DFT and Ha ee-Fock.

12 Chap e 2 — Theo e ical and echnical amewo k
di e en ange-sepa a ion pa ame e s migh be necessa y depending on he pa icula
sys em and p ope ies o in e es . Ano he app oach is he e o e o une
ω
o each sys em
in such a way ha ce ain p ope ies o he exac unc ional (such as Eq.
(2.33)
in Sec. 2.3)
a e ul illed [44].
O bi al-dependen unc ionals can be used in conjunc ion wi h he OEP me hod as
explained abo e. The widely used hyb ids (and RSHs) a e p ac ically always implemen ed
in a way which lea es he g ounds o he KS amewo k. This second app oach is jus i ied
by he obse a ion ha i is possible o o mula e a so-called gene alized KS app oach
in which he in e ac ing
N
-elec on sys em is mapped on o ano he in e ac ing auxilia y
sys em, which can, howe e , s ill be ep esen ed by a single Sla e -de e minan [45].
2.3 In e p e a ion o (gene alized) Kohn-Sham eigen alues
Gi en hei s a us as me ely auxilia y quan i ies wi hin he KS amewo k, i migh be
su p ising ha he KS eigen alues should ca y any physical meaning a all. Howe e , he
success o DFT pa ly elies on he ac ha in an o e whelmingly la ge numbe o sys ems
he eigen alue spec a ag ee, apa om a shi o he comple e spec um, ema kably
well wi h expe imen ally ob ained quasipa icle ene gies. In he ea ly days o DFT his
ag eemen was ega ded acciden al. La e , G¨o ling could show ha KS eigen alue di e ences
ha e in ac a well-de ined physical meaning as exci a ion ene gies o ze o h o de in he
elec on-elec on in e ac ion [46]. The de i a ion is based on linking he in e ac ing ull
Hamil onian o he KS Hamil onian h ough
[ˆ
T+αˆ
W+ˆ
Vα]|ψα
ni=Eα
n|ψα
ni.(2.30)
The coupling cons an
α
c ea es a con inuous (adiaba ic) connec ion be ween he ully
in e ac ing
N
-elec on sys em wi h
α
= 1 and
ˆ
Vα=1
=
ˆ
Vex
and he non-in e ac ing KS
sys em wi h
α
= 0 and
ˆ
Vα=0
=
KS
[37, 38]. Using G¨o ling-Le y pe u ba ion heo y [47]
one can hen expand
Eα
n
in a Taylo se ies in
α
and show ha exci a ion ene gies can
igo ously be gained om g ound s a e DFT. In pa icula , he ze o h o de e m connec s
he quasipa icle exci a ion ene gies o KS eigen alue di e ences.
The p ac ical use ulness o G¨o ling’s inding o cou se depends on he quali y o his
ze o h o de app oxima ion. Chong e al. could show ha he ene ge ically highes lying
occupied KS le els can be in e p e ed as app oxima e, bu a he accu a e, elaxed e ical
ioniza ion po en ials, p o ided ha hey a e compu ed using a high-quali y xc po en ial
[48]. Al eady ea lie i was obse ed by Janak [49] ha
∂E
∂ iσ
=εiσ,(2.31)
whe e
iσ
is he ( ac ional) occupa ion o he
i
- h KS o bi al. A igo ous physical meaning,
howe e , can only be assigned o he highes occupied KS eigen alue
εHOMO
, which is
2.3. In e p e a ion o (gene alized) Kohn-Sham eigen alues 13
iden ical o minus he ioniza ion po en ial
I
(
N
) o he ully in e ac ing physical sys em.
This was p o ed by Almbladh and on Ba h [50] by de i ing di e en ial equa ions o he
quasipa icle ampli udes
Fn,σ( ) := hψN−1
n|ˆ
Ψσ( )|ψN
0i,(2.32)
whe e
ˆ
Ψσ
(
) is he elec on- ield ope a o which annihila es an elec on o spin
σ
a
and
ψN
n
a e he
N
-elec on eigens a es o he ull many-body Hamil onian. A close look a he
asymp o ic decay o his quasipa icle ampli ude shows ha he asymp o ically leading
ampli ude is ob ained o
n
= 0 and ha he densi y i sel is domina ed by
F0,σ
(
) o
| |→∞
. By compa ing his esul o he asymp o ic o m o he KS densi y, which is
domina ed by he mos weakly decaying KS o bi al, one a i es a he iden i y
εHOMO(N) = −I(N) = E(N)−E(N−1).(2.33)
Simila ly, one can show o he elec on a ini y
A
(
N
), i.e., he ene gy gained by b inging in
a pa icle om in ini y ha
εHOMO(N+ 1) = −A(N) = E(N+ 1) −E(N).(2.34)
E
(
N−
1)
, E
(
N
) and
E
(
N
+ 1) a e he ene gies o he
N−
1,
N
and
N
+ 1 elec on sys em,
espec i ely.
In p ac ical calcula ions one o en aces he p oblem o no knowing whe he he used
xc unc ional desc ibes he sys em o in e es accu a ely o no . As a ule o humb may
coun , ha in sys ems in which he uppe occupied KS o bi als a e localized on a simila
leng h scale, s anda d xc unc ionals esul in eigen alue spec a ha a e physically eliable
[21]. The SIE in such sys ems, ha can be e alua ed using Eq.
(2.14)
, a ec s all ele an
o bi als in he same way and he e o e only amoun s o a common shi o he eigen alue
spec um [32]. In sys ems in which he uppe o bi als di e in hei deg ee o localiza ion,
he spec um will be dis o ed as a esul o he SIE a ec ing he o bi als di e en ly. In
his sense, e alua ion o Eq.
(2.14)
can se e as a wa ning o sys ems ha a e s ongly
a ec ed by he SIE. No e, howe e , ha he ela ion be ween o bi al localiza ion and he
SIE is no i ial [51].
The close connec ion be ween he SIE and he eliabili y o an eigen alue spec um
sugges s ha sel -in e ac ion ee app oaches (in he sense o Eq.
(2.15)
) should yield good
ag eemen wi h expe imen in cases in which semilocal unc ionals ail and indeed his has
been shown o a numbe o sys ems (see e.g. Re . [32]). Howe e , hese app oaches a e
nume ically expensi e, especially in cases in which inding he ene ge ically mos a o able
posi ion o he nuclei poses addi ional p oblems (see Sec. 2.5). The commonly used hyb id
unc ionals can a leas pa ly cancel he SIE by employing a ac ion o exac exchange.
As men ioned ea lie , hyb id unc ionals a e ypically implemen ed in a GKS amewo k.
The GKS equa ions
−¯h2
2m∇2+ ex ( ) + H([n], ) + c,σ([n], b, )
+bˆ ex
x,σ[n] + (1 −b) x,σ([n], )ϕiσ( ) = εGKS
iσ ϕiσ( ),
(2.35)
14 Chap e 2 — Theo e ical and echnical amewo k
in which
ˆ ex
x,σ[n]ϕiσ( ) = −e2X
σ=↑,↓
Nσ
X
j=1 Zϕjσ( )ϕ∗
jσ( 0)
| − 0|ϕiσ( 0)d3 0(2.36)
deno es he non-local Fock ope a o , a e by cons uc ion exac , jus as he KS equa ions.
The esul ing eigen alues εGKS
iσ di e om he exac KS eigen alues by
b∆ x,σ,i =bhϕiσ( )|ˆ ex
x,σ[n]− x,σ([n], )|ϕiσ( )i,(2.37)
i one neglec s di e ences in he KS and GKS o bi als and he co ela ion po en ial [45].
As ∆
x,N
= 0 o he highes occupied GKS eigen alue, he ela ion
εGKS
HOMO
=
−I
(
N
) holds
also o he GKS case. The e is again no such equali y o all he o he GKS eigen alues.
Howe e , one can show ha including a ac ion o he non-local exchange mimics a pa ial
sel -in e ac ion co ec ion [52]. Consequen ly, GKS eigen alues ag ee well wi h expe imen al
esul s o many cases in which semilocal unc ionals ail.
2.4 Pseudopo en ials
The basic idea o eplacing he s ong Coulomb po en ial o he nucleus and he sc eening
e ec o he igh ly bound co e elec ons by an e ec i e co e po en ial (commonly e e ed
o as pseudopo en ial), has i s oo s in he simple no ion ha only he alence elec ons o
an a om de e mine i s chemical p ope ies.
The app oach was o iginally in oduced by Fe mi when he s udied low ene gy elec on
sca e ing om a oms [53]. In ac , he aim o he pseudopo en ial cons uc ion is o ind an
e ec i e po en ial ha mimics he sca e ing p ope ies o nucleus and co e elec ons eliably
o e a ce ain ene gy ange. The deg ees o eedom o pseudopo en ial gene a ion hen allow
o de ise hem in such a way as o minimize he compu a ional e o . Fi s ly, by educing he
numbe o elec ons ha ha e o be conside ed explici ly in he DFT calcula ion. Secondly,
because pseudopo en ials allow he nume ical desc ip ion o po en ials and o bi als on much
coa se g ids o wi h ewe plane wa e componen s han would be necessa y i he highly
oscilla o y s uc u e o he o bi als in he co e- egion had o be ep esen ed comple ely. In
he p esen hesis pseudopo en ials en e he s age a ye ano he poin . When one deals
wi h hea y-elemen ansi ion me al compounds such as Au and P , ela i is ic e ec s such
as spin-o bi coupling and he ela i is ic mass inc ease o elec ons in he co e egion a e
c ucial o he accu a e desc ip ion o he elec onic, and hus also he geome ic s uc u e
o he compounds [54]. Pseudopo en ials o e ways in which hese e ec s can be accoun ed
o implici ly.
An impo an concep unde lying mos pseudopo en ial gene a ion schemes is he
ozen-co e app oxima ion: The co e s a es, e alua ed in an all-elec on a omic e e ence
calcula ion, a e assumed no o change i in a di e en en i onmen , i.e., in a molecule o
solid. Fo his eason he adius o he co e egion
c
is a c ucial pa ame e de e mining
ans e abili y and accu acy o he pseudopo en ial.
2.4. Pseudopo en ials 15
2.4.1 No m-conse ing pseudopo en ials
The spi i o no m-conse a ion is o s a he cons uc ion o he pseudopo en ial om he
all-elec on o bi als ha s em om a sel -consis en solu ion o he adial KS equa ion
4
( o
a spin-unpola ized case)
−¯h2
2m
d2
d 2+¯h2l(l+ 1)
2m 2+ KS([n], )! Ril( ) = εil Ril( ),(2.38)
in which
Ril
=
ϕil
and
l
deno es he angula momen um quan um numbe . The pseudopo-
en ial has o ul ill ou p ope ies o be conside ed no m-conse ing: Fi s , all-elec on (AE)
and pseudo (PP) alence eigen alues mus ag ee o a chosen a omic e e ence con igu a ion.
Second, all-elec on and pseudo o bi als ag ee beyond a chosen co e adius
c
. Thi d, he
in eg a ed cha ge inside
c
o he all-elec on and he pseudo cha ge densi ies ag ee o each
alence s a e Z c
0|RPP
il ( )|2 2d =Z c
0|RAE
il |2 2d , (2.39)
as his ensu es ha he o al cha ge in he co e egion is conse ed. And las , he loga i hmic
de i a i es o he all-elec on and he pseudo o bi als and hei i s ene gy de i a i es
ag ee o
> c
[56]. The eedom ha is le in cons uc ing he pseudopo en ial can hen
be used o make i as smoo h as possible a he same ime ensu ing ans e abili y o as
many di e en chemical en i onmen s as possible. Di e en schemes o pseudopo en ial
gene a ion we e p oposed, e.g., by Bachele , Hamann and Schl¨u e [57] and by T oullie
and Ma ins [58].
By in e ing he adial KS equa ions one hen ob ains he sc eened pseudopo en ial
om he pseudo wa e unc ion
PP
sc eened,l =εl−¯h2
2m l(l+ 1)
2−1
RPP
l( )
d2
d 2[ RPP
l( )]!.(2.40)
In he las s ep he sc eening o he alence elec ons has o be emo ed o ob ain an
unsc eened (”ba e”) ionic pseudopo en ial
PP
ionic,l( ) = PP
sc eened,l( )− PP
H[n al]( )− PP
xc [n al( )] (2.41)
The esul ing pseudopo en ial di e s o e e y angula momen um componen
l
, i.e., he
e ec i e ex e nal po en ial in he KS equa ions is no local anymo e. A u he ans o ma-
ion sugges ed by Kleinman and Bylande b ings Eq.
(2.41)
in a sepa able non-local o m
ha educes compu a ion ime and s o age space. T oullie -Ma ins pseudopo en ials in
Kleinman-Bylande o m a e used h oughou his wo k o calcula ions on eal-space g ids
using a local e sion o he PARSEC p og am package [59], e.g., o he calcula ion o he
SIE o Mn-doped Si clus e s in Sec. 4.3.
4
I ela i is ic e ec s a e o be included one has o use Di ac’s o mula ion o he kine ic ene gy. The
Sch ¨odinge -like Eq.
(2.38)
is hen eplaced by a pai o coupled equa ions o mino and majo o bi al
componen s, which ou side he co e adius educe app oxima ely o a Sch ¨odinge - ype equa ion o he
majo o bi al componen [55].

3
The bime allic e ec in Au-P and
Au-Pd nanoalloys
3.1 Au-P and Au-Pd nanoalloys in ca alysis
Alloying o wo (o mo e) elemen s is a p omising ou e o enhance he ca aly ic ac i i y
o ansi ion me al NP and imp o e hei elemen -speci ic selec i i y [78]. Loosely based
on A is o le’s bon mo ha “ he whole is g ea e han he sum o i s pa s”, hese e ec s
a e equen ly dubbed syne gis ic. Au-P nanoalloys a e a p ominen example o a sys em
which exhibi s inc eased u no e a es in a a ie y o oxida ion eac ions [79–81] as
well as en icing p ope ies in elec oca aly ic applica ions [82–90] compa ed o hei pu e
coun e pa s. Au-P nanoalloys a e bene icial because hey educe he well-known p oblem
o ”poisoning” o P ca alys anodes used in di ec me hanol uel cells wi h s ongly adso bed
in e media e CO-species. Fu he mo e, inc eased u no e a es allow o ca y ou eac ions
a oom empe a u e and wi hou possibly oxic sol en s, hus causing less impac on he
en i onmen . Finally, by changing he Au-P composi ion one can une hei ca aly ic
p ope ies which makes Au-P nanoalloys po en ially use ul o many di e en ca aly ic
eac ions. When looking deepe in o hese p oblems, se e al puzzles appea .
The i s puzzle is he miscibili y o Au and P on he nanoscale. I is well known ha
he bulk phase diag am o Au-P alloys exhibi s a la ge miscibili y gap o a wide ange o
Au-P composi ions. In going o he nanoscale i has been epo ed ha Au-P NP can
o m ue solid solu ions. Such Au-P nanoalloys ha e, e.g., been syn hesized in he mally
e apo a ed a y amine ilms, whe e hey we e alloyed a low empe a u e [91], in sphe ical
polyelec oly e b ushes (SPBs) [80] and in ionic liquids by a spu e deposi ion echnique
24 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
[92]. O he g oups ha e ob ained s able Au-P nanoalloys by capping hem wi h hiola es
[82, 93] o by suppo ing hem on silica [79].
co e-shell andom laye ed
Figu e 3.1: Th ee possible miscibili y
pa e ns in bime allic NP. F om le o
igh : co e-shell, andomly mixed and lay-
e ed. O he pa e ns such as se e al lay-
e s/shells o an o de ed solid solu ion a e
possible.
Theo y, in con as , consis en ly p edic s a
Au
shell
-P
co e
mixing pa e n as ene ge ically mos
a o able [94–97]. An illus a ion o di e en mixing
pa e ns in NP is gi en in Fig. 3.1.
Theo e ical s udies o clus e s in he expe i-
men ally ele an size ange o se e al hund ed up
o housands o a oms ha e been based on semi-
empi ical MD simula ions and we e mos ly con-
ce ned wi h he mel ing beha iou o he Au-P
NP [98–101]. A global geome y op imiza ion using
a gene ic algo i hm wi h a semiempi ical Gup a-
many-body po en ial o Au-P clus e s wi h 2–100
a oms has been pe o med by Logsdail e al. [102]. Fi s -p inciples DFT s udies exis ed,
up o he beginning o his wo k, only o e y small clus e s wi h 2–13 a oms [103, 104].
Howe e , mo e ecen s udies on la ge clus e s (including one ha will b ie ly be p esen ed
in Sec. 3.2), ha e con i med ha Au-P NP p e e a co e-shell mixing pa e n [94–97]. This
seeming disc epancy o heo y and expe imen is subjec o Sec. 3.3.
The second Au-P nanoalloy puzzle is hei enhanced ca aly ic ac i i y as compa ed o
hei pu e coun e pa s. Conside ing he known bulk elec onic p ope ies o P and Au
1
i is no pe se clea , why a combina ion o P and Au should lead o enhanced ca aly ic
ac i i y a all (see also Sec. 3.4.1). Addi ionally, while i is known how he elec onic
s uc u e o Au changes upon going om he bulk o small NP [2], simila insigh s in o he
elec onic s uc u e o Au-P nanoalloys a e a e. Explana ions o he special p ope ies o
Au-P nanoalloys ha e been a emp ed in se e al s udies, mainly concen a ing on he local
elec onic s uc u e o P [85, 95, 104, 106]. A de ailed unde s anding o he concu ence o
Au and P leading o a o able ca aly ic p ope ies in a a ie y o di e en eac ions, i.e.,
independen o he ype o suppo o ma ix he NP a e immobilized in, possible sol en s
and di e en eac ion empe a u es, is lacking. Puzzle numbe wo will be subjec o Sec.
3.4.
Al hough elemen s om he P -g oup a e chemically simila , he abo e ma e s a e
sligh ly di e en o Au-Pd nanoalloys. The s uc u al cha ac e iza ion o Au-Pd NP is
much easie as compa ed o Au-P NP, as Au and Pd’s a omic numbe s a e su icien ly
di e en o allow o he use o high- esolu ion echniques, e.g., high-angle-annula -da k- ield
ansmission elec on mic oscopy [107]. Syne gis ic e ec s ha e been obse ed o Au-Pd
NP ca alys s in a a ie y o eac ions. Two ecen examples a e Au-Pd nanoalloys used o
elec oca aly ic H
2
O
2
p oduc ion [108] and o sol en - ee oxida ion o p ima y ca bon-
hyd ogen bonds [107]. As he ollowing sec ions will ocus p ima ily on Au-P nanoalloys, I
e e he eade o Re . [78] and e e ences he ein, o a summa y o s udies in which a
syne gis ic e ec o Au-Pd ca alys s was obse ed. Insigh s in o he elec onic s uc u e o
Au-Pd nanoalloys and hei impac on Au-Pd ca alysis a e discussed in Sec. 3.4.1.
1P esen ed in a nu shell in “Why gold is he nobles o all me als” by Hamme e al. in Re . [105].
3.2. Geome ic s uc u e and mixing pa e ns o Au-P nanoalloys 25
3.2 Geome ic s uc u e and mixing pa e ns o Au-P nanoalloys
This sec ion gi es a sho summa y o esul s ha a e discussed in de ail in Re . [109]. Mos
o he nanoalloy p ope ies ha will be iden i ied in he ollowing sec ions as being a o able
o ca aly ic ac i i y a e o a la ge ex end independen o he exac geome ic s uc u e o
he clus e s. S ill, ene ge ically low-lying Au-P isome s a e a well-chosen s a ing poin o
he s udy o hese p ope ies. In combined e o s o heo y and expe imen , he g ound
s a e s uc u e o many pu e neu al and cha ged Au clus e s has been de e mined. A
p ominen example a e Au
20
and Au
−
20
, whose g ound s a e s uc u e is a egula e ahed on
as e ealed by gas phase in a ed spec oscopy [110] and pho oelec on spec oscopy [68].
Au
20
is an excellen oy model o he p esen s udy as i ep esen s a cu ou o he cc
la ice in which bo h bulk Au and P c ys allize. Fu he mo e, many o he expe imen ally
obse ed Au-P nanoalloys ha e been shown o be la gely ace ed and bulk-like (e.g. [80]).
Figu e 3.2: The e a e h ee
symme y-inequi alen ways
how o eplace one Au a om in
he Au
20
e ahed on by a P
a om.
By sys ema ically eplacing Au by P a oms in Au
20
one
inds ha he ene ge ically lowes lying homo op is always
ha in which P is as highly coo dina ed as possible. In
going om Au
20
o Au
19
P
1
, as illus a ed in Fig. 3.2, he
ene ge ically lowes lying homo op is he one in which P
occupies a posi ion in he middle o one o he ou ace s.
As a esul o his g ow h pa e n a Au
shell
P
co e
s uc u e
eme ges na u ally. Tha he co e-shell mixing pa e n is no a
me e a i ac was es ed by compa ing homo ops and isome s
wi h ixed Au-P composi ion especially o s uc u al mo i s
o he han he a he special e ahed al s uc u e as well
as o la ge clus e s. The s abili y o a a ie y o s uc u es
was es ed using simula ed annealing (see Sec. 2.5). In
hese simula ions he clus e s we e hea ed o a empe a u e
o 600 K and subsequen ly slowly annealed. Impo an ly,
he co e-shell mixing pa e n emains s able h oughou he
en i e simula ion and can he e o e be ega ded as being s able e en a ele a ed empe a u es.
Fig. 3.3 shows, as an example, di e en Au20P 20 isome s om A o F wi h inc easing
o al ene gy. No e ha e en a comple e seg ega ion o he Au and he P componen
(C and D) is ene ge ically mo e a o able han he andom mixing pa e n (E and F).
Compu a ional de ails on he geome y op imiza ion and he accu acy o he used xc
unc ional and basis se s as well as s uc u es o e ahed al and amo phous Au
n
P
20−n
clus e s can be ound in Re . [109] and [94]. In his wo k, Au-P NP wi h
≈
1000 alence
elec ons, i.e., 60-a om clus e s, we e he la ges sys ems o which ull local geome y
op imiza ions we e pe o med. The Gup a po en ial based Au
30
P
30
s uc u e [102] was
used as a s a ing poin o hese calcula ions.
Howe e , conside ing ha expe imen ally ele an nanoca alys s ange be ween sizes o
26 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
1 and 4 nm, we need e en la ge sys ems o exclude ha he obse ed e ec s a e only due
o he compa ably small size o he clus e s.
A B C
D E F
Figu e 3.3: S uc u es a e named a e he
geome y ha se ed as a s a ing poin o
he geom y op imiza ion ei he “Gup a”
[102] o “Su on Chen” [111]. A: Gup a
co e-shell, B: Su on-Chen co e-shell, C:
Su on-Chen laye ed, D: Gup a laye ed, E:
Gup a andom, F: Su on-Chen andom.
Two s a egies we e used o o e come he com-
pu a ional limi a ions ha i s p inciples DFT cal-
cula ions ace o sys ems wi h signi ican ly mo e
han 1000 alence elec ons. Fi s ly, we cons uc ed
unca ed oc ahed al clus e s wi h closed a omic
shells, i.e., wi h 38, 201, 586 and 1289 a oms as illus-
a ed in Fig. 3.4 and op imized hem in empi ical
MD simula ions. These clus e s a e, analogously o
Au
20
, cu ou s o he cc la ice and a e used in he
s udies discussed in Sec. 3.3 and 3.4. Clus e s wi h
egula polyhed al s uc u es and closed a omic
shells a e some imes called “magic”, in analogy o
he magic elec on numbe s ha we e disco e ed
by Knigh e al. in 1984 in sodium clus e s [112].
This seminal disco e y igge ed he de elopmen o clus e physics much beyond he ealm
o he simple sphe ical jellium model which was used o explain he abundance o sodium
clus e s con aining 2, 8, 20, 40,... a oms. Elec onic shell closu e e ec s wi hin he jellium
model a e esponsible o he s abili y o hese clus e sizes in he simple alkali me als and
e en in Au clus e s, as hei 6ss a es o m a good ee elec on gas [2].
1 nm 2 nm
3 nm
4 nm
Figu e 3.4: T unca ed oc ahed a wi h
( om le o igh ) 38, 201, 586 and 1289
a oms. These a omic numbe s a e called
magic, because hey co espond o clus e s
ha ing only closed shells o a oms. The
app oxima e diame e s o hese clus e s
a e 1, 2, 3 and 4 nm.
Fo la ge clus e s he elec onic shell closu e
e ec is supe imposed by he closu e o a omic
shells, a p ominen example again being sodium
clus e s ha exhibi icosahed al shell closu es [113].
In sodium clus e s wi h a ew ens o a oms, elec-
onic and ionic shell closu e e ec s wo k oge he
in de e mining he s uc u e o he clus e s, while
o la ge clus e s, s a ing wi h Na
55
, ionic shell
closu e e ec s win o e elec onic ones esul ing in
nea -ly sphe ical clus e s [114]. Howe e , I wan o
s ess ha unca ed oc ahed al s uc u es migh
no be a s uc u al mo i ound in smalle Au clus-
e s. The impo an poin is ha hey a e ace ed
and cc-bulk-like, which makes hem a aluable model o he ca alys s obse ed expe imen-
ally.
A second app oach o ca alysis on Au-P NP is o model hem as pe iodic su ace slabs.
The mo i a ion o his is wo old: Fi s ly, much o he ca aly ic ac i i y o NP can be
a ibu ed o hei high su ace o olume a io. Secondly, a syne gis ic e ec o Au and P
has also been obse ed o bime allic su aces [115]. Au-P su aces a e s udied in Sec. 3.4.
In summa y, he ollowing Au-P s uc u es a e used in he p esen hesis o de e mine
s uc u al and elec onic p ope ies o Au-P sys ems: 20-a om e ahed al and amo phous
low-ene gy isome s, 40-a om and 60-a om s uc u es based on empi ical po en ials and ully
3.3. Au-P alloys and Vega d’s law on he nanoscale 27
op imized using DFT, unca ed oc ahed al model s uc u es wi h 38, 201, 586 and 1289
a oms o which di e en a angemen s o Au and P , e.g., in co e-shell and andom mixing
pa e ns can be cons uc ed, and inally bime allic su ace slabs.
3.3 Au-P alloys and Vega d’s law on he nanoscale
All esul s o his sec ion a e published in Re . [116]. In he p e ious wo sec ions I discussed
ha i s -p inciples DFT calcula ions con i m ha low-ene gy s uc u es o ee Au-P
clus e s indeed exhibi an Au
shell
P
co e
mixing pa e n and hus con i m he esul s o
semi-empi ical MD simula ions men ioned in Sec. 3.1. The seeming disc epancy be ween
heo y (co e-shell) and expe imen (solid solu ion) mus hus be sea ched o elsewhe e.
Figu e 3.5
: A ske ch o he i s wo
B agg peaks as ypically obse ed in
XRD measu emen s on Au-P NP.
F om hese di ac ion pa e ns i can
p esumably be in e ed ha he sys-
em unde s udy (blue line) is a ue
solid solu ion. The a ows indica e
he posi ion o he i s B agg peak.
pu e Au
pu e P
nanoalloy
(111)
(200)
B agg angle [2 ]
30 35 40 45 50
0
10
20
30
in ensi y [a b. uni s]
The nex s ep is o unde s and he assump ions ha unde lie he expe imen al cha ac-
e iza ion o Au-P NP. A p ominen cha ac e iza ion me hod is he use o x- ay di ac ion
(XRD) echniques. The esul ing di ac ion pa e ns a e ypically analyzed as ske ched
in Fig. 3.5. The o ange and black lines indica e he i s wo B agg peaks o pu e Au and
pu e P NP as obse ed in small angle x- ay sca e ing expe imen s. These peaks can
be indexed in o an cc- ype la ice. Fo each se o Mille indices (
hkl
) one can hen use
B agg’s equa ion
a
=
λ√h2+k2+l2
2 sin θ
o de e mine a la ice pa ame e
a
om he sca e ing
angle θ. He e, λis he wa e leng h o he incoming x- ays.
The same can be done o he di ac ion pa e n o he bime allic NP. Addi ionally,
depending on he expe imen al esolu ion, one can use he peak shape o de e mine, whe he
he sys em o in e es shows any sign o demixing o Au and P (in which case one would
expec dis inc peaks o he Au- and he P -phase) o whe he i o ms a eal alloy (only
one clea peak). The blue line in Fig. 3.5 would, ollowing his easoning, belong o a
andomly mixed Au-P NP.
Bulk alloys o en obey Vega d’s law [117], which s a es ha he la ice pa ame e o
a wo-componen alloy can be de e mined by linea ly in e pola ing be ween he la ice
pa ame e s o he wo componen s ha o m he alloy. Hence in an alloy ha consis s
o 50% o bo h elemen s, he a e age la ice pa ame e would be jus he a e age o he
la ice pa ame e s o bo h pu e c ys als. XRD cha ac e iza ion now e eals ha he la ice

28 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
pa ame e o Au-P NP goes linea ly wi h he Au-P a io as well. This inding is aken as
e idence ha Au-P NP o m ue alloys (see, e.g., Re . [80, 93]).
The ”Vega d-analysis” hus assumes i s ly ha a phase sepa a ion mus be isible in
he di ac ion pa e n, secondly ha Vega d’s law is alid and can be used o de e mine
he composi ion o he alloy and hi dly ha Vega d’s law is only alid o andomly mixed
alloys. By simula ing he XRD pa e ns o pu e Au and P , as well as o andomly mixed
and co e-shell NP one can hus es he alidi y o hese assump ions.
The sca e ing in ensi y Io an ensemble o a oms is gi en by Debye’s equa ion
I=X
mX
n
m n
sin kRmn
kRmn
,(3.1)
whe e
n
and
m
a e he o m ac o s o a oms
n
and
m
,
Rmn
=
|Rm−Rn|
is he dis ance
o wo a oms a posi ions Rmand Rnand k= 4πsin θ/λ is he wa e numbe .
Rmn
2θ
Figu e 3.6: A ske ch o he sca -
e ing o ligh a an ensemble o
andomly o ien ed a oms, whe e
he di e ence ec o
Rmn
=
Rm−Rn
is allowed o ake all
o ien a ions in space, i.e., all po-
si ions on he black ci cle wi h
equal p obabili y (adap ed om
[118]).
The gene al sca e ing equa ion
(3.1)
o a oms which a e
andomly o ien ed in space is easily de i ed by conside ing
ha one ob ains he sca e ed x- ay in ensi y by summing
o e he sca e ing ampli udes o x- ays sca e ed by di e en
a oms
I=X
m
me(2πi/λ)(s−s0)RmX
n
ne(−2πi/λ)(s−s0)Rn(3.2)
=X
mX
n
m ne(2πi/λ)(s−s0)Rmn ,
whe e
s
and
s0
a e he di ec ions o incoming and ou going
x- ays, as ske ched in Fig. 3.6.
Eq.
(3.2)
is o cou se alid o sca e ing on any ensemble
o a oms. We now assume ha his ensemble akes all
o ien a ions in space wi h equal p obabili y, i.e., ha
Rmn
ends a all poin s o he sphe e ske ched in Fig. 3.6 (in 2d)
wi h equal p obabili y. The spa ial a e age o he exponen ial
e m
he2πi/λ(s−s0)Rmn i
can wi h
k
= 4
πsin θ/λ
and (
s−
s0)Rmn = 2 sin θRmn cos φbe w i en as
heikRmn cos φi=1
4πR2
mn ZdAeikRmn cos φ
=1
4πR2
mn Z2π
0
dϕ Zπ
0
dφR2
mn sin φeikRmn cos φ
=sin kRmn
kRmn
,
and leads o Debye’s sca e ing equa ion 3.1.
Addi ionally, empe a u e e ec s ha cause a omic ib a ions independen om each
o he could be aken in o accoun by including a Debye-Walle ac o [119, 120] in he Debye
3.3. Au-P alloys and Vega d’s law on he nanoscale 29
Table 3.1
: A e age bond leng hs and
hei s anda d de ia ions o co e-shell
and andom Au
22
P
38
(37% Au) as
ob ained om DFT and MD op imiza-
ion.
DFT Au-Au [˚
A] Au-P [˚
A] P -P [˚
A]
co e-shell 2.88 ±0.03 2.85 ±0.03 2.76 ±0.05
andom 2.90 ±0.05 2.82 ±0.06 2.72 ±0.06
MD Au-Au [˚
A] Au-P [˚
A] P -P [˚
A]
co e-shell 2.74 ±0.03 2.70 ±0.04 2.69±0.04
andom 2.73 ±0.04 2.70 ±0.04 2.67 ±0.04
equa ion
(3.1)
. We do no include his ac o he e, as we will explici ly ake empe a u e
in o accoun by pe o ming MD simula ions a ele a ed empe a u es.
A easonable simula ion o XRD pa e ns equi es wo impo an condi ions o be
me . Fi s ly, he size o he NP needs o be be ween 3 and 4 nm o con o m wi h he
expe imen al size ange. Secondly, he in e a omic bond leng hs need o be ealis ic, as
hey a e he decisi e inpu o Eq.
(3.1)
. As al eady men ioned, hese equi emen s pose
se e e di icul ies o DFT, as compu a ional e o o bids o ea NP o such size, i.e.,
wi h mo e han 1000 Au and P a oms. On he o he hand, he eliabili y o bond leng h
es ima es is bes i a i s -p inciples me hod is used o geome y op imiza ion. We assess
his p oblem in he ollowing way. The 1289-a om unca ed oc ahed on as shown on he
igh hand side o Fig. 3.4 is used as a s a ing poin o geome y op imiza ion. A pu e Au
and P , a Au
shell
P
co e
wi h one and wo Au-shells (co esponding o he NP Au
484
P
805
and Au
830
P
459
espec i ely) and inally a andomly mixed NP wi h exac ly he same
Au-P a io as he co e-shell pa icle Au484P 805 we e cons uc ed based on he unca ed
oc ahed al geome y. The geome y op imiza ion o hese sys ems was ca ied ou using MD
simula ions, in which he po en ial ene gy was modelled by he many-body Su on-Chen
po en ial [121], ha has been employed success ully in simula ions o a a ie y o nanoalloys
[100, 122–124]. The Su on-Chen pa ame e s o he Au-P in e ac ion we e ob ained om
he pa ame e s o he Au-Au and P -P in e ac ion using a combina ion ule [100]. Each
sys em was i s elaxed a 1 K and subsequen ly p opaga ed o 500 ps a a empe a u e
o 300 K in a canonical ensemble using E ans’ he mos a [125] and acuum bounda y
condi ions. E e y 20 ps a s uc u e ”snapsho ”, yielding a se o a omic posi ions
{Rm}
,
was aken. These s uc u es we e hen op imized wi h a conjuga e g adien p ocedu e. Fo
each sys em he op imized geome y wi h he lowes ene gy was aken as he inal s uc u e
o u he analysis. All MD simula ions in his and Sec. 3.4.3 we e ca ied ou by Rod igo
Q. Albuque que using he DL-POLY p og am package [126].
The second pa o ou s a egy consis s o de e mining he Au-Au, P -P and Au-P
bond leng hs o DFT-op imized co e-shell and andom geome ies. We do no expec he
bond leng hs esuling om MD simula ions o equal he DFT bond leng h, because he
Su on-Chen pa ame e s a e i ed o bulk p ope ies and bulk bond leng hs a e ypically
sligh ly di e en om NP bond leng hs. Howe e , wha is decisi e he e is, ha he ela i e
di e ences be ween he Au-Au, P -P and Au-P bond leng hs esul ing om MD and DFT
op imiza ion, espec i ely, a e simila .
As one o he la ge sys ems whe e s uc u e op imiza ion wi h DFT is s ill possible
we chose he 60-a om clus e Au
22
P
38
. I s Au con en o abou 37% is simila o ha o
he 4 nm clus e Au
459
P
830
ha is he main ocus o ou s udy. We gene a ed s a ing
30 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
Au con en me hod Au-Au [˚
A] Au-P [˚
A] P -P [˚
A]
87 % DFT 2.87 ±0.02 2.83 ±0.03 2.72 ±0.02
MD 2.75 ±0.01 2.71 ±0.02 2.73 ±0.06
50 % DFT 2.87 ±0.08 2.83 ±0.05 2.65 ±0.05
MD 2.73 ±0.06 2.68 ±0.05 2.65 ±0.03
13 % DFT none 2.84 ±0.04 2.72 ±0.04
MD none 2.68 ±0.04 2.65 ±0.02
Table 3.2
: A e age bond
leng hs and s anda d de-
ia ions ob ained om
DFT and MD op imiza-
ion o andomly mixed
38-a omic clus e s wi h
di e en Au-P mixing
a ios.
s uc u es by aking he coo dina es om he 60-a omic clus e in Re . [102] and dis ibu ed
Au and P a oms once andomly and once in a P -co e Au-shell ashion o hese posi ions.
The s uc u es we e hen elaxed wi h DFT and MD sepa a ely. In he DFT calcula ions
he elaxa ion was ca ied ou wi hou any symme y cons ain s using a spli alence basis
se augmen ed by one pola iza ion unc ion (SVP). The use o la ge basis se s changes he
bond leng h by less han 2% [94] and does no a ec he ela i e dis ibu ion o he leng hs
o Au-Au, Au-P and P -P bonds.
Fo he op imized s uc u es we calcula ed he dis ance o e e y a om o i s i e nea es
neighbo s, a he same ime de e mining whe he hese bonds we e Au-Au, Au-P o P -P
bonds. The a e age Au-Au bond leng h was hen de ined by he a i hme ic mean o all
esul ing Au-Au dis ances. In he same way, Au-P and P -P bond leng hs we e calcula ed.
The esul s s ay quali a i ely he same i one somewha changes he a e aging p ocedu e,
e.g., using ou ins ead o i e nea es neighbo s.
Tab. 3.1 shows he a e age bond leng hs hus ob ained om DFT and MD o co e-shell
and o andomly mixed a ian s o Au
22
P
38
. The MD bond leng hs a e ound o be
consis en ly smalle han he DFT bond leng hs. Howe e , he ends wi h espec o
bond leng h di e ences a e simila . Fo bo h DFT and MD calcula ions he di e ences
be ween he a e age leng h o Au-Au bonds, Au-P bonds and P -P bonds ha one inds
in andomly mixed and co e-shell pa icles a e small. In all cases Au-Au bonds a e longes
and P -P bonds a e sho es , wi h Au-P alling in be ween.
In o de o also es he MD bond leng h dis ibu ion o a ace ed pa icle we chose
he smalles unca ed oc ahed on buil om 38 a oms. Alloy pa icles wi h Au con en s o
87 % (Au
33
P
5
), 50 % (Au
19
P
19
) and 13 % (Au
5
P
33
) we e gene a ed by dis ibu ing Au
and P a oms andomly o e he clus e . The s uc u es we e ene ge ically op imized as
desc ibed p e iously. Tab. 3.2 shows he esul ing a e age bond leng hs. We obse e again
ha he MD and DFT a e age bond leng hs a e no iden ical, wi h he MD bonds gene ally
being sho e han he DFT ones. Ye , again he ends a e he same in bo h DFT and
MD: Au-Au bonds a e he longes and P -P bonds a e he sho es , wi h Au-P bonds
alling in be ween. The one excep ion ha we ound is shown in Tab. 3.2 o 87 % Au,
whe e Au-P and P -P bonds in he MD a e qui e simila . We a ibu e his o he low P
concen a ion and small pa icle size. We also pe o med he same ype o analysis o he
20-a om e ahed al and amo phous s uc u es ha a e desc ibed in Re . [94]. The esul s
a e in line wi h he conclusions d awn o he 38-a om and 60-a om s uc u es shown abo e
and a e he e o e no epo ed in de ail he e.
We can now analyze he a e age bond leng hs o he Au
459
P
830
co e-shell and andomly
3.3. Au-P alloys and Vega d’s law on he nanoscale 31
mixed unca ed oc ahed on. In he co e-shell clus e he la ge P co e domina es he bond
leng h dis ibu ion, wi h an a e age P -P dis ance o 2.77
˚
A. The mean Au-Au dis ance in
he single Au shell is he same as he mean P -P bond leng h. This inding is eminiscen
o he la ice de o ma ion and ma ching ha one encoun e s when g owing single laye s
o one ma e ial on a subs a e wi h a di e en la ice pa ame e . The Au-P dis ance o
2.78
˚
A is sligh ly la ge , allowing he shell o w ap a ound he co e. The bond leng h mos
o en encoun e ed in he andomly mixed NP is one ha alls in be ween he Au-Au and
he P -P bond leng h, wi h Au-P bonds on a e age being 2.76
˚
A, Au-Au bonds 2.79
˚
A,
and P -P bonds 2.74 ˚
A.
a omic o m ac o
gold
pla inum
00.2 0.4 0.6 0.8 1.0 1.2
20
40
60
80
100
120
140
160
Figu e 3.7: A omic o m ac o s o Au and
P aken om Re . [127] and polynomial leas
squa e i s o he da a.
A e hese p elimina y conside a ions we
u n o simula ing he XRD pa e ns o he
NP using Eq.
(3.1)
wi h he incoming x- ays
ha ing a wa e leng h o
λ
=1.5
˚
A. The o m
ac o s o Au and P a e abula ed in Re . [127]
and i ed using a polynomial leas squa es i
o allow con inuous ep esen a ion o he da a
(see Fig. 3.7).
The op le panel in Fig. 3.8 shows he pa -
e n ha one ob ains om pu e Au o P NP
wi h 1289 a oms in o ange and black, espec-
i ely. The ed line shows he x- ay pa e n
o he co e-shell NP. As laid ou abo e he
expec a ion so a has been o ind sepa a e
peaks o his ype o s uc u e, as he Au and P componen a e sepa a ed. Ye , no
double-peak s uc u e is obse ed a all; he peak shapes o he di e en NP a e nea ly
iden ical. Ou i s impo an conclusion he e o e is ha a co e-shell s uc u e in NP does
no necessa ily lead o sepa a e x- ay peaks o he di e en componen s. The lowe le
panel shows he second impo an esul : The x- ay pa e n o he co e-shell NP (as abo e)
and he one o he andomly mixed NP a e e y simila . Co e-shell s uc u es may hus
be ha d o iden i y ia x- ay sca e ing.
Figu e 3.8
: Le : Calcu-
la ed XRD pa e n o pu e
Au, P , and co e-shell NP
( op) and co e-shell and an-
domly mixed NP (bo om).
Righ : View o he co e-
shell ( op) and andomly
mixed (bo om) NP (ou -
side and c oss sec ion).
in ensi y [a b.uni s]
pu e Au
pu e P
co e-shell
co e-shell
andom
30 35 40 45 50
50
100
150
250
200
50
100
150
250
200 co e-shell
andom
B agg angle [2 ]
Howe e , we now ake he analysis one s ep u he and go h ough he Vega d’s-law-
based analysis o he x- ay da a as explained abo e. Fo pu e NP he x- ay analysis leads
38 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
0
2
4
6
8
10
0 20 40 60 80 100
DOS a Fe mi le el/elec on [a b. uni s]
Au con en [%]
20 e a
20 amo phous
38 oc a
60 Gup a
40 Su on-Chen
Figu e 3.16: The DOS a he Fe mi le el (in eg a ion
h eshold de ined as -1 eV) as a unc ion o he Au
con en o 20-a om e ahed al and amo phous, 38-
a om unca ed oc ahed al and 40- and 60-a om
Gup a-po en ial clus e s.
We can now analyze he DOS a he
Fe mi le el o a a ie y o Au-P NP wi h
di e en o e all geome ies and mixing
pa e ns. Fig. 3.16 shows ha i inc eases
wi h inc easing P con en o 20-a om
e ahed al
5
and amo phous clus e s (co e-
shell), o 38-a om unca ed oc ahed a
( andom) and o 40- and 60-a om Gup a-
po en ial clus e s (co e-shell). Impo an -
ly, his end is independen o he speci ic
way in which Au and P a oms a e a -
anged in he clus e , i.e., he DOS a he
Fe mi le el inc eases bo h o co e-shell
and andomly mixed Au-P nanoalloys
wi h inc easing P con en . This inding
sugges s ha he binding ene gy be ween
Au-P nanoalloys and an adso ba e should
inc ease wi h inc easing P con en and ha a pu e P NP should bind adso ba es mos
s ongly o i s su ace. F om his pe spec i e, a ce ain Au-P a io could co espond o an
op imal binding ene gy in a speci ic eac ion in e ms o Saba ie ’s p inciple.
co e-shell laye ed
20 a oms
40 a oms
Figu e 3.17: Plo s o he highes occupied
molecula o bi al a
±
0.04
a−3/2
0
. Top:
o wo jus sligh ly di e en Au
10
P
10
clus e s. Bo om: Au
20
P
20
wi h co e-
shell and laye ed mixing pa e n, espec-
i ely.
A close look a he local elec onic s uc u e
e eals ha he addi ion o P is bene icial om
ye ano he pe spec i e. Fig. 3.17 shows isosu ace
plo s o he highes occupied KS o bi al (HOMO)
o se e al Au-P NP. The HOMO has physical el-
e ance as i asymp o ically domina es he densi y
and i s exponen ial decay is go e ned by he i s
ioniza ion po en ial, i.e., i ep esen s he spa ial
dis ibu ion o he ene ge ically highes lying pa
o he densi y. Fig. 3.17 e eals ha he spa ial
loca ion o he HOMO is closely ela ed o ha o
he P a oms. The wo Au
10
P
10
clus e s a he
op o Fig. 3.17 di e only in he posi ion o one P
a om ha si s wi hin he bo om ace on he le
side and is mo ed o he op co ne on he igh
side o Fig. 3.17. This sligh ea angemen esul s
in a ma ked change o he spa ial dis ibu ion o
he HOMO densi y. The same e ec can be seen
o he wo Au
20
P
20
homo ops a he bo om o Fig. 3.17 and all o he sys ems ha we
s udied. This has wo impo an consequences: Fi s ly, as he P con en inc eases, mo e
P a oms a e loca ed a he su ace o he clus e , so ha he HOMO can ex end away
5
No e, ha he Au
20
e ahed on is he only excep ion ha we ound o his obse a ion. We a ibu e
his de ia ion o he unusual elec onic s uc u e o Au20 [68].

3.4. The in e play be ween luxionali y and elec onic s uc u e 39
om he su ace. Secondly, he known impo ance o he su ace o ca aly ic p ocesses is
enhanced in Au-P nanoalloys, no only due o he inc eased su ace- o- olume a io on he
nanoscale, bu also because o he p esence o P , he many possible dis ibu ions o Au
and P on he su ace and he esul ing implica ions o he local elec onic s uc u e o he
sys em.
3.4.2 Elec onic s uc u e o Au-Pd nanoalloys
Au-Pd nanoalloys show an elec onic s uc u e e y simila o ha o Au-P nanoalloys.
The e is bu one poin equi ing special a en ion in small Au-Pd nanoalloys ha can be
neglec ed in Au-P NP: hei spin pola iza ion. Bulk Au and Pd a e no magne ic, bu
high magne ic momen s ha e been epo ed o small Pd clus e s [140]. We s a om
he bilaye ed g ound s a e o Pd
13
aken om Re . [140], s ep-by-s ep eplacing lowly-
coo dina ed Pd a oms by Au as sugges ed in Re . [141, 142]. The esul ing Au
n
Pd
13−n
(n=0-13) s uc u es we e hen locally elaxed.
0
2
4
6
8
10
12
0 20 40 60 80 100
DOS a Fe mi le el/elec on [a b. uni s]
Au con en [%]
13 bilaye
20 e a
38 ype 1
38 ype 2
Figu e 3.18: The DOS close o he Fe mi le el as
a unc ion o he Au con en o Au/Pd pa icles.
Fo all h ee sizes (13-a om, 20-a om and 38-a om)
he DOS dec eases wi h inc easing Au con en . Fo
he 38 a omic clus e s he DOS o wo di e en
s uc u e ypes is shown. The end is he same o
bo h ypes.
We allowed and checked o spin po-
la iza ion, e alua ing he o al ene gy o
di e en mul iplici ies. We ound ha o
he pu poses o his s udy he magne i-
za ion is no decisi e, as he DOS a he
Fe mi le el depends only e y li le on
he spin pola iza ion in he cases ha we
s udied. The in eg a ed DOS ypically
changes by less han 1% o mos s uc-
u es as a unc ion o magne iza ion, and
a ew pe cen a mos . Fo he sake o
comple eness, some magne iza ions a e,
howe e , epo ed in he ollowing. The
esul ing magne ic momen s a e 6
µB
o
Pd
13
, 3
µB
o Pd
12
Au
1
, 4
µB
o Pd
11
Au
2
and 2
µB
o Pd
9
Au
4
. Clus e s wi h la ge
Au con en s a e ei he single s o iple s
depending on whe he hei elec on num-
be is odd o e en. The DOS a he Fe mi
le el is hen de ined as o Au-P NP and shown in Fig. 3.18 as a unc ion o he pa icles’
composi ion ( ed diamonds). The ed inse depic s he s uc u e o Au
3
Pd
10
as an example.
F om he igu e one can clea ly d aw he conclusion ha again he DOS a he Fe mi edge
dec eases wi h inc easing Au amoun .
In o de o check whe he his beha io o he DOS is gene al we epea ed he p ocedu e
o la ge clus e s. Ou choice o u he es sys ems was mo i a ed by simila conside a ions
as in he case o Au-P NP. The expe imen al s udies a e conce ned wi h ela i ely la ge
pa icles ha show a bulk-like s uc u e [132]. The e o e, we also heo e ically ocus on
in es iga ing sys ems whe e a bulk-like geome y is a easonable s a ing poin . Fu he mo e,
as bulk Pd and Au a e no magne ic, and as he expe imen ally obse ed pa icles a e
40 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
bulk-like in hei s uc u e, i is a plausible assump ion ha magne ic e ec s a e no
impo an o explaining he ca aly ic p ope ies. In addi ion, ou s udy o he 13-a om
clus e s has shown ha he o al DOS is no e y sensi i e o he magne iza ion. The e o e,
we choose o ou ollowing in es iga ions always he elec onic con igu a ion ha has he
lowes spin pola iza ion (unde he condi ion ha he au bau p inciple is espec ed). F om
he jus desc ibed poin s o iew he Au
20
e ahed on is again a good s a ing poin o
he heo e ical in es iga ion. We eplaced Au by Pd as explained in Sec. 3.2 wi h P , again
obse ing he ule ha high-coo dina ion numbe si es a e ene ge ically a o able o Pd.
The o ange inse o Fig. 3.18 shows he s uc u e o Au
16
Pd
4
as an example and he DOS a
he Fe mi le el as a unc ion o he Au con en . Also in his case an inc ease wi h inc easing
amoun o Pd is obse ed o all mixed Au/Pd pa icles. This obse a ion does no depend
on he speci ic s uc u al mo i .
−3−2−1 0
densi y o s a es [a b. uni s]
[eV]
(a)
(b)
(c)
(d)
(e)
( )
Figu e 3.19: Righ : geome ic s uc u e and iso-
su ace plo o he HOMO o 38-a om pa icles.
F om op o bo om: (a) Au
19
Pd
19
, (b)-(d) 3
di e en s uc u es o Au
28
Pd
10
, (e) Au
30
Pd
8
,
( ) Au
32
Pd
6
. Whi e and blue a eas ep esen
nega i e and posi i e isosu ace alues o 0.04
a−3/2
0. Le : he DOS o each o he clus e s.
To demons a e his explici ly and o check
ano he clus e size we epea ed he p ocedu e
o he unca ed oc ahed al 38-a om clus e s.
We s udied wo lines o s uc u es wi h 38
a oms. In bo h o hem 6 Pd a oms o m
he co e (see black inse o Fig. 3.18), as his
is an ene ge ically a o ed a angemen . How-
e e , he wo lines di e in he posi ion o he
emaining “su ace” Pd a oms. The s uc u es
labeled “ ype 1” in Fig. 3.18 we e ob ained by
andomly eplacing su ace Au by Pd a oms.
In he s uc u es labeled “ ype 2” he su ace
Pd a oms we e placed such ha hey occupy
he in e io pa s o he ace s. In he li e a-
u e [141] hese la e con igu a ions ha e been
epo ed as being ene ge ically a o able. Ou
calcula ions con i m his inding as s uc u es
o ype 2 a e lowe by 0.08 eV o Au
30
Pd
8
and
0.83 eV o Au
28
Pd
10
han he co esponding
s uc u es o ype 1. We obse e ha all s uc-
u es ha e a he small HOMO-LUMO gaps,
which may be an indica ion o u he symme-
y b eaking being ene ge ically a o able. The
impo an inding is ha also in he 38-a om
ace ed cases bo h ypes o s uc u es show
he same end: he DOS a he Fe mi le el
inc eases wi h inc easing Pd con en . Again
his inding could imply ha , in e ms o Saba ie ’s p inciple, a ce ain Au-Pd a io migh
co espond o op imal adso ba e binding ene gies in a ce ain eac ion.
In he nex s ep, ollowing he same easoning as be o e, we in es iga e he ela ion
be ween he clus e s’ geome y and hei elec onic s uc u e. To his end we ake a close
3.4. The in e play be ween luxionali y and elec onic s uc u e 41
look a se e al o he ace ed 38-a om pa icles. The igh side o Fig. 3.19 shows om op
o bo om s uc u es and HOMO densi ies o Au
19
Pd
19
, h ee di e en Au
28
Pd
10
homo ops,
Au
30
Pd
8
and Au
32
Pd
6
. The le column depic s he occupied DOS wi h he espec i e
Fe mi le els aligned a 0 eV. The e ical line a -1 eV indica es he p e iously men ioned
in eg a ion ange.
The conclusions ha can be d awn om Fig. 3.19 a e a he simila o he Au-P NP
case: Fi s , he HOMO in each case is closely associa ed wi h he Pd a oms. Second, an
inc easing amoun o Pd b ings an inc easing numbe o Pd a oms o he su ace and hus
leads o a HOMO ha is dominan ly loca ed a he su ace o he clus e . This is clea ly
seen, e.g., when compa ing he HOMO ep esen a ion o Au
32
Pd
6
o he one o Au
19
Pd
19
and i indica es ha Pd a oms a he su ace a e likely o be a o able in e ms o he
pa icles’ ac i i y. Thi d, we ca e ully inspec h ee homo ops o Au
28
Pd
10
. S uc u e (b)
as sugges ed in he li e a u e [141] has he lowes o al ene gy, (d) is highe by 0.83 eV and
(c) by 1.64 eV. Independen o hese ene ge ic di e ences, he e is an impo an obse a ion
o be made in compa ing s uc u es (b)-(d): al hough he h ee geome ies a e o e all
a he simila , he di e ences be ween he HOMOs a e qui e no iceable. A mode a e change
in he geome y leads o a signi ican change o he ene ge ically high-lying pa o he
densi y. Thus, a speci ic a angemen o Au and Pd a oms a he su ace can lead o special
elec onic and hus chemical p ope ies.
3.4.3 The ole o Au in Au-P nanoalloys
In he spi i o Re . [131] and as explained in he in oduc o y pa ag aphs o Sec. 3.4 one
could specula e ha a syne gis ic e ec in Au-P nanoalloys o a speci ic eac ion could
in p inciple be explained by linking a ca aly ic desc ip o o his eac ion o he DOS a
he Fe mi le el. One could hen a gue ha he binding ene gy be ween Au-P NP and he
speci ic eac an s mus nei he be oo s ong no oo weak o he eac ion o ake place, in
compliance wi h Saba ie ’s p inciple. An op imal Au-P mixing a io would hen eme ge
om hese conside a ions. E en hough his poin o iew is pe ec ly legi ima e and has
led o aluable insigh s in o gas-phase ca alysis on su aces unde well-con olled condi ions,
i is no easily applicable in ou case as men ioned be o e. Howe e , as a syne gis ic e ec
is obse ed in many di e en eac ions wi h di e en ma ices and sol en s, we sugges ha
undamen al p ope ies o Au-P NP ha a e independen o he eac ion lead o he special
p ope ies o Au-P NP. Wi h he DOS a he Fe mi le el and he spa ial a angemen o
he HOMO densi y being de e mined by P as discussed ea lie , we now wan o ask he
ques ion which undamen al ca alysis- a o able p ope y is associa ed o Au.
He e, I wan o a gue ha his p ope y is he mobili y o a oms in he Au-P sys ems,
o he NP luxionali y. Fluxionali y has been ecognized o be o c ucial impo ance o
he ca aly ic ac i i y o clus e s and su aces [143]. I can be a p ime o he abili y o
s uc u ally adjus o eac an s, o m ac i e si es [144] and di ec ly in luences u no e a es
by a ec ing he ca alys s’ abili y o egene a e a e he eac ion. In o de o de e mine
how easy i is o a oms o ea ange in Au-P sys ems we pe o med wo ypes o s udies.
In he i s one we ake he pe spec i e ha wi h espec o ca aly ic ac i i y, he su ace
o he NP, which o ace ed NP is simila o a bulk su ace, is likely hei mos impo an
42 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
ini
fin
ini
finini
fin
ini
finini
fin
ini
fin
I. P /P II. P /P +Au III. Au/P
IV. Au/P +Au V. P /Au VI. Au/Au
Figu e 3.20
: Ske ch o he se up used o he
s udy o Au and P ada om sel -di usion om
a cc (ini) o a hcp ( in) hollow posi ion. The
sys ems we s udied we e: I. P ada om on pu e
P (111) su ace, II. P ada om on P (111) su -
ace wi h single Au a om in op su ace laye ,
III. Au ada om on pu e P (111), IV. Au ada om
on P (111) doped wi h Au, V. P ada om on
Au(111) and VI. Au ada om on Au(111).
pa . When eac an s app oach he su ace, he su ace may s uc u ally eac o o m
ac i e si es. The induc ion ime, i.e., he ime ha goes by be o e he eac ion s a s, seen
in NP ca alysis can be an indica ion o such p ocesses [80, 132, 145]. A canonical s ep in
su ace es uc u ing is he mo emen (di usion) o a oms on he su ace. The e o e, we
chose he heigh o he ba ie s o he di usion o Au and P ada oms on pu e and doped
P - and Au-su aces as a measu e o he su aces’ abili y o es uc u e. As an aside we
no e ha his line o hinking is also suppo ed by he obse a ion ha bime allic e ec s as
well play a ole in Au-P su aces [115] as men ioned be o e.
sys em Eads cc Eads hcp Eba ie
P /P 4.60 4.82 312
P /P +Au 4.61 4.76 287
Au/P 2.77 2.87 177
Au/P +Au 2.79 2.86 165
P /Au 4.05 4.15 143
Au/Au 2.50 2.56 115
Table 3.3
: Adso p ion ene gies (in eV) o P -
and Au-ada oms in pu e and doped P - and Au
su aces o he s a and he end posi ion o
each NEB calcula ion. Fo a de ini ion o he
di usion ba ie (in meV) see ex .
Fo calcula ing hese di usion ba ie s we ely on he NEB me hod (see Sec. 2.5). I
allows o de e mine he minimum ene gy pa h be ween a gi en ini ial and inal s a e. I his
minimum ene gy pa h goes h ough one o se e al maxima as a unc ion o he eac ion
coo dina e he la ges o hese ba ie s can be ega ded he a e-de e mining s ep o he
eac ion. Calcula ions we e ca ied ou wi h VASP using he PBE GGA [24] and employing
he PAW me hod o desc ibe he elec on-ion in e ac ion [64, 67] (see Sec. 2.4). Technical
de ails ega ding hese calcula ions can be ound in Appendix C. The cu o -ene gy o he
plane wa e basis se was se o 450 eV. Pu e and doped P and Au cc(111) su aces we e
modeled by 4-laye slabs con aining 4x4 a oms in each laye and being sepa a ed by 20
˚
A o
acuum. The bo om wo laye s we e held ixed a he P (Au) bulk equilib ium dis ance
o 3.977 (4.174)
˚
A, while he o he laye s we e allowed o ully elax. The B illouin-zone
in eg a ions we e pe o med using Monkho s -Pack k-poin meshes o 5x5x1 size. We
conside ed a di usion s ep om a cc o a hcp hollow si e o di e en combina ions o
su aces and ada oms, as depic ed in Fig. 3.20. In all cases he di usion ba ie was de ined
as he ene ge ic di e ence be ween he ansi ion s a e and he hcp adso p ion si e, his
being he la ges ene gy di e ence and hus de e mining he a e o his pa icula di usion
3.4. The in e play be ween luxionali y and elec onic s uc u e 43
s ep. In addi ion o he di usion ba ie s we de e mined he adso p ion ene gies (see
Tab. 3.3) o he ada oms a he cc and hcp hollow si e as
Eads =Eslab +Eada om −Eslab+ada om (3.7)
100
120
140
160
180
200
220
240
260
280
300
320
P /P P /P +Au Au/P Au/P +Au P /Au Au/Au
Sys em
Diffusion ba ie [meV]
Figu e 3.21: Ba ie o P - and Au-
ada om di usion on P -su aces wi h and
wi hou Au doping and on a pu e Au-
su ace. An explana ion o he no a ion
can be ound in Fig. 3.20.
Fig. 3.21 shows ha di usion o a P ada om
on a pu e P su ace has he highes ba ie o all
conside ed sys ems. This is in line wi h he P
ada om being mos s ongly adso bed o he pu e
P su ace. Ye , he inse ion o one Au a om in o
he P su ace lowe s he di usion ba ie by abou
25 meV. A simila e ec can be seen by compa ing
he di usion ba ie o an Au ada om on a pu e P
su ace and on a P su ace wi h one Au dopan . I
is pa icula ly in e es ing ha he di usion ba ie
dec eases e en mo e o a P ada om on a Au su -
ace. In his case he adso p ion ene gy is almos
as high as ha o P on P (111) leading one o
expec an equally high di usion ba ie . The acil-
i a ed su ace di usion on su aces wi h a highe
Au con en can he e o e no only be explained by
Au ada oms being mo e weakly bound o he su -
ace han P ada oms. We in e p e his inding
as an inc eased abili y o Au-alloyed P -su aces o
unde go s uc u al changes and hus as a highe
su ace luxionali y wi h inc easing Au-con en .
In he second ype o s udy ha we did in o de o show ha inc easing amoun s o Au
inc ease he a omic mobili y in Au-P NP we mo ed away om he su ace pe spec i e and
ega ded he NP as ini e clus e s. The luxionali y o small Au clus e s has ecen ly been
shown by ex ensi e scans o hei po en ial ene gy su aces [146]. This me hod, howe e , is
no easible o Au-P nanoalloys in he expe imen ally ele an size ange. The e o e, we
pe o med one nanosecond long MD simula ions o andomly mixed unca ed oc ahed al
clus e s (38, 201 and 586 a oms) and o 60-a om and 100-a om Gup a po en ial based
co e-shell clus e s o ob ain a measu e o he mobili y o he clus e a oms in e ms o hei
mean squa e displacemen (MSD)
hˆ 2i=*1
M
M
X
i=1
(Ri( )−Ri( = 0))2+,(3.8)
whe e
M
is he numbe o a oms in he clus e and
Ri
(
) is he posi ion o a om
i
a
ime
. The angle b acke s indica e a ime a e age. The MD simula ions we e done using
he DL POLY p og am [126] and he NVT E ans ensemble wi h he same many-body
Su on-Chen po en ial as in Sec. 3.3 o desc ibe he po en ial ene gy o he sys em.
Randomly mixed Au-P NP seg ega e o Au
shell
P
co e
s uc u es e en a compa ably
modes empe a u es and sho simula ion imes. As ou aim was o e ain he homogenous

44 Chap e 3 — The bime allic e ec in Au-P and Au-Pd nanoalloys
mixing pa e n o he unca ed oc ahed a all simula ions we e ca ied ou a 300 K. This
lies well below he mel ing poin o mos o hese sys ems
6
, meaning ha he MSD a e aged
o e he whole simula ion ime is app oxima ely ze o. Howe e , a sho e imescales o
1000 s a di usi e mo ion o Au and P a oms akes place. The ime a e age in Eq. 3.8 was
he e o e compu ed o subsequen ime windows o 1000 s. Fo each Au-P mixing a io
h ee simula ions we e ca ied ou o minimize s a is ical unce ain ies. No e ha e en
hough his me hod yields only an app oxima ion o he di usion o clus e a oms, i can be
used o compa e he sho - ime a omic mobili y o nanoalloys wi h a ying mixing a ios.
0.02
0.04
0.06
0.08
0.10
0.12 38 a oms
201 a oms
586 a oms
0.02
0.04
0.06
0.08
0.10
0 20 40 60 80 100
Au con en [%]
60 a oms
100 a oms
MSD [ ]
Figu e 3.22: Top: MSD om MD simula ions
o unca ed oc ahed al clus e s ha a e solid
solu ions o Au and P wi h 38, 201 and 586
a oms. Bo om: MSDs o 60-a om and 100-
a om co e-shell pa icles.
Fo NP in he size egime ha we a e con-
ce ned wi h he high su ace- o- olume a io
can ha e signi ican impac on he a e age
MSD o he NP. A oms a lowly coo dina ed po-
si ions, e.g., a kinks o edges can show MSDs
ha a e conside ably la ge han hose o high-
ly coo dina ed olume a oms o a oms in a
su ace plane. Fo i egula NP like he 60-
a om and he 100-a om NP his e ec is mo e
p onounced han i is o he egula unca ed
oc ahed a wi h hei magic a om numbe s o
38, 210 and 586. To ob ain compa able MSD
alues i is he e o e necessa y o keep he ge-
ome ies o NP wi h he same numbe o a oms
bu di e en Au-P a ios as close as possible.
Fo he i egula 60-a om and 100-a om clus-
e s his makes a ull geome y op imiza ion
p io o MD simula ions necessa y. Ne e he-
less, he MSDs o hese NP show la ge s a is-
ical a ia ions as compa ed o he MSDs o
he unca ed oc ahed a. Fo his eason we
wan o s ess ha we a e no conce ned wi h
e alua ing he exac alue o he MSD in ou
NP. In con as , we wan o s udy he end
ha he MSD shows wi h inc easing Au con en .
The esul ing MSDs a e depic ed in Fig. 3.22: he unca ed oc ahed a a he op and
he 60-a om and 100-a om co e-shell pa icles a he bo om. I can clea ly be seen ha
he composi ion-dependen end is he same o all clus e s: The MSD inc eases wi h
inc easing Au-con en . This is again independen o pa icula geome ic con igu a ions o
mixing pa e ns. Thus, al hough being o e y di e en na u e, he MD s udy con i ms
he conclusions d awn om he su ace di usion ba ie calcula ions: s uc u al lexibili y
inc eases wi h an inc easing amoun o Au.
6
The mel ing poin o he 60-a om clus e s lies below 300 K. The e o e in his case MD simula ions we e
ca ied ou a a empe a u e o 200 K.
3.4. The in e play be ween luxionali y and elec onic s uc u e 45
3.4.4 Combining elec onic s uc u e and luxionali y
0.0
0.2
0.4
0.6
0.8
1.0
0 20 40 60 80 100
MSDxDOS a FL [a b. uni s]
Au con en [%]
38 a oms
60 a oms
Figu e 3.23: P oduc o a polynomial leas
squa es i o he DOS a he Fe mi le el
(FL) and MSD o 38-a om and 60-a om
Au-P clus e s as a unc ion o Au con en .
Quan i ies a e scaled so ha o 0 and
100% Au con en he cu es in e sec he
y-axis a 0 and ha e a maximum alue o
1.
We can now pu oge he all he indings. The
DOS o Au-P NP de elops p ope ies ha one
na u ally associa es wi h being a o able o ca al-
ysis wi h inc easing P con en , whe eas he s uc-
u al lexibili y inc eases wi h inc easing Au con en .
The e o e, o each eac ion he e can be an ideal
a io o Au and P ha yields o e all op imal p op-
e ies. This is isualized in Fig. 3.23. I shows
he olcano-like plo ha one ob ains by mul iply-
ing a polynomial leas squa es i o he DOS a
he Fe mi le el and he MSD. This has he e been
done o he 38-a om and 60-a om clus e s, as o
hese sys ems we could access bo h quan i ies (see
Fig. 3.24).
An ideal Au-P mixing a io eme ges as a con-
sequence o he in e play be ween s uc u al lux-
ionali y p o ided by Au and a a o able elec onic
s uc u e con ibu ed by P . O cou se wha his ideal mixing a io is will sensi i ely depend
on he eac ion, expe imen al condi ions, as well as on he exac s uc u e and mixing
pa e n o he ca alys s. Ye , he poin ha Fig. 3.23 emphasizes is ha syne gis ic e ec s
Figu e 3.24
: Le : MSD
and linea i o MSD o 38-
a om (black iangles) and
60-a om ( ed iangles) clus-
e s. Righ : DOS a he
Fe mi le el o 38-a om and
60-a om clus e s. Fo con-
s uc ing he ” olcano” plo
he da a was i ed wi h a
cubic polynomial.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 20 40 60 80 100
MSD [Å2]
Au con en [%]
38 a oms
60 a oms
DOS a FL/elec on
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100
Au con en [%]
38 a oms
60 a oms
in Au-P NP a e expec ed on a he gene al g ounds and ega dless o he speci ic chemical
eac ion and en i onmen . Addi ionally, Fig. 3.23 illus a es ano he poin . We do no
expec ” he whole o be g ea e han he sum o i s pa ”. The syne gis ic o a he bime al-
lic e ec in Au-P nanoalloys eme ges as a consequence o adding up ca alysis- a o able
undamen al physical p ope ies o Au and P . The e ec o he combined p ope ies migh
be ampli ied by he high su ace o olume a io in NP, he p esence o s eps and kinks ha
ac as ac i e si es in ca alysis [144] and he elonga ed a e age bond leng hs esul ing om
he mal expansion (see Sec. 3.3) o NP-ma ix in e ac ions (see Appendix A). Di e en o
wha he buzzwo d ”syne gy” sugges s, Au-P nanoalloys migh no possess special ca aly ic
p ope ies ha go beyond a combina ion o he p ope ies o pu e Au and P NP.
4
Magne ic- o-nonmagne ic ansi ion
in Mn-doped Si-clus e s
4.1 Dilu e magne ic semiconduc o s
Semiconduc o s doped wi h ew impu i ies ha ca y a magne ic momen a e called dilu e
magne ic semiconduc o s. Du ing he las decades hey ha e been subjec o in ense s udy,
a e i had been obse ed ha he in oduc ion o a small ac ion o magne ic impu i ies
would lea e he a o able anspo and op ical p ope ies o he semiconduc o s unchanged,
a he same ime being accompanied by la ge magne ic momen s and many in e es ing
magne ic o de phenomena. To name only one example, i has been shown by Ohno e
al., ha (Ga,Mn)As exhibi s e omagne ic o de up o empe a u es as high as 110 K
[147]. La e heo e ical wo k p o ided a model o he o igin o his e omagne ic o de ing
and p edic ed ma e ials wi h Cu ie empe a u es e en exceeding oom empe a u e. E en
hough i is belie ed oday ha dilu e magne ic semiconduc o s wi h such high Cu ie
empe a u es may no be ealizable, he ield ne e heless bea s plen y o undamen al
ques ions, many o which a e s ill unanswe ed.
The seemingly simples o hese ques ions is how a single magne ic impu i y in e ac s
wi h he semiconduc ing hos , i.e., whe he he impu i y’s magne ic momen is quenched o
su i es. Pionee ing s udies ha e been conduc ed by Ludwig and Woodbu y in he 1960s
using elec on-pa amagne ic esonance spec oscopy o in es iga e magne ic p ope ies o
Si doped wi h a ange o 3
d
ansi ion me al impu i ies a subs i u ional and in e s i ial
posi ions [148]. Fu he mo e, Ludwig and Woodbu y p o ided a simple and desc ip i e
model o p edic quenching o su i al o he magne ic momen o he ansi ion me al
impu i y.
54 Chap e 4 — Magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s
MnSi7
+MnSi8
+MnSi9
+MnSi10
+
MnSi11
+MnSi12
+MnSi13
+MnSi14
+
Figu e 4.5: Ene ge ically mos a o able s uc u es
o MnSi
+
n
(
n
= 7
−
14) as p edic ed by PBE0. Con-
a y o expe imen MnSi+
11 is exohed ally doped.
Fo he simula ed annealing simula-
ions di e en s a ing s uc u es we e hea-
ed o empe a u es be ween 3500 and
4500 K and p opaga ed a his empe a-
u e o 3 ps. Subsequen ly, he empe a-
u e o he sys em was educed by a ac o
o 0.9 e e y 0.2 ps un il i ell below 300 K.
A his poin he s uc u e usually was
apped in a s i local minimum. I is
he e o e o g ea impo ance o s a sim-
ula ions om a la ge numbe o di e en
geome ies o scan as much o he po en-
ial ene gy su ace as possible. The lowes
ene gy isome s om hese simula ions we e hen locally elaxed using a quasi-New on me hod
and la ge TZVPP basis se s un il he o al ene gy changed by less han 10
−8
Ha ee and
he o ces ac ing upon he ionic co es we e smalle han 0.001 a.u.. The modi ied big bang
app oach consis ed o andomly gene a ing di e en se s o s a ing coo dina es wi h bond
leng hs comp essed by abou 10% o he equilib ium bond leng h and p opaga ing hese
coo dina es a a ixed empe a u e o 300 K o a sho ime span o 1.5 ps. Again, lowes
ene gy geome ies we e locally elaxed as desc ibed be o e.
Figu e 4.6: S uc u e
o he ene ge ically
lowes lying endohe-
d ally doped MnSi
+
11
as p edic ed by he
PBE0 xc unc ional.
The ene ge ically lowes lying s uc u es ha PBE0 p edic s a e
shown in Fig. 4.5. Consis en wi h expe imen clus e s wi h
n
= 7
−
10
a e exohed ally and clus e s wi h
n
= 12
−
14 a e endohed ally doped.
Simila ly, in pe ec ag eemen wi h he XMCD spec a o Fig. 4.4
clus e s wi h
n
= 7
−
10 exhibi a la ge magne ic momen o 4
µB
, while
he magne ic momen o hose wi h
n
= 12
−
14 is comple ely quenched.
MnSi
+
11
is, con a y o he expe imen ally p edic ed exohed al- o-
endohed al ansi ion, exohed ally doped. Fu he mo e, he calcula ed
s uc u e ca ies a magne ic momen o 2
µB
in con adic ion o he
anishing XMCD signal o MnSi
+
11
in Fig. 4.4. The ene ge ically
lowes lying endohed al s uc u e, al hough 1.1 eV highe in ene gy
han he PBE0 g ound s a e, (shown in Fig.4.6) would howe e ag ee
wi h expe imen .
As he expe imen ally obse ed s uc u es a e expec ed o be he
g ound s a e s uc u es, a close look a he heo e ical esul s e eals ha he ailu e o
PBE0 o
MnSi+
11
can indeed be explained in e ms o he e ec o sel -in e ac ion on he
eigen alue spec um o bo h isome s. To cla i y he si ua ion we calcula ed he o bi al-
SIE, Eq.
(2.14)
, as in oduced in Sec. 2.2. To de e mine
eiσ
a local de elope s e sion
o he p og am package PARSEC [59] was used o calcula e he elec onic s uc u e o
MnSi
+
n
(
n
= 7
−
14). We employed T oullie -Ma ins pseudopo en ials in Kleinman-Bylande
o m cons uc ed wi hin he PBE GGA [24] wi h a non-linea co e co ec ion as discussed
in Sec. 2.4. The pseudopo en ials we e based on he elec onic con igu a ion 4
s1.75
4
p0.25
3
d5
wi h s/p/d cu -o adii o 1.884/2.573/1.980 a.u. o Mn and 3
s2
3
p2
wi h s/p cu -o adii o

4.3. A DFT-s udy o he magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s 55
2.493/2.390 a.u. o Si. I was es ed ha he in luence o he used pseudopo en ials on he
eigen alue spec um was negligible by compa ing hem wi h ou all-elec on TURBOMOLE
calcula ions. A g id spacing o 0.3 a.u. was used.
eiσ
was e alua ed using he PBE GGA
xc unc ional. Following Pe dew and Zunge and neglec ing he di e ence be ween sel -
in e ac ion co ec ed and unco ec ed o bi als, he sel -in e ac ion co ec ed eigen alues can
be es ima ed as
εiσ ≈εapp ox
iσ −eiσ,(4.9)
whe e
εapp ox
iσ
esul s om a sel -consis en calcula ion using
app ox
xc
, which is PBE in ou
case [21]. We can now compa e hese app oxima ely sel -in e ac ion co ec ed eigen alues
wi h hose ha PBE0 yields. The smalle he di e ence ∆
εiσ
=
εiσ −εPBE0
iσ
, he mo e
eliable he PBE0 eigen alues εPBE0
iσ a e.
Figu e 4.7
: Eigen alue spec um
(ba s), o al DOS (do ed line), and
Mn-p ojec ed local DOS (solid line) o
endohed al
MnSi+
11
( op) and he exo-
hed al PBE0 g ound s a e (bo om).
∆
εi
is a measu e o how much he
PBE0 eigen alues a e a ec ed by he
SIE.
−200
0
200
−200
0
200
MnSi11
+
−3
−2
−1
0
1
−3
−2
−1
0
1
−7−6−5−4−3−2−1 0 1
DOS DOS
Fig. 4.7 shows he occupied eigen alue spec um in e p e ed as a DOS and he espec i e
∆
εi
o bo h MnSi
+
11
isome s, he endohed ally doped a he op and he exohed ally doped
PBE0 g ound s a e a he bo om. While o he endohed ally doped isome ∆
εi≈
0 o
all uppe o bi als, he si ua ion is conside ably di e en o he exohed ally doped isome .
He e, he PBE0 eigen alues a e s ongly a ec ed by he SIE. This is no only ue o he
o bi als 4-5 eV below he Fe mi le el, ha can be associa ed wi h he Mn dopan
5
, bu also
o highe lying s a es ha pa icipa e in bonding. All in all, Fig. 4.7 illus a es ha he
ene ge ic o de ing o MnSi+
11 isome s as p edic ed by PBE0 is un eliable.
In a second s ep we used a comple ely di e en app oach o u he elucida e he
si ua ion. Using he RSH xc unc ional
ω
PBE [43] (see Sec. 2.2) as implemen ed in he
QChem p og am package [174], we checked he ene ge ic o de ing o he exohed al and he
endohed al MnSi
+
11
isome s as a unc ion o he ange-sepa a ion pa ame e
ω
. Fo alues o
ω
= 0
.
2
−
0
.
4 a.u. he
ω
PBE unc ional p edic s he ene ge ic o de ing ha is in ag eemen
wi h expe imen . This inding highligh s he delica e balance o exchange and co ela ion
e ec s ha de e mines he ene ge ic o de ing in MnSi+
11.
I will explain in he ollowing, why he SIE, al hough also plaguing he o he exohed al
sys ems, only becomes decisi e o he ene ge ic o de ing in case o MnSi
+
11
. To his end
5
This can be done by p ojec ing he KS eigen alues on o a omic o bi als ia a Mulliken popula ion
analysis as explained in Sec.3.4.1.
56 Chap e 4 — Magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s
Fig. 4.8 shows he o al DOS, he DOS p ojec ed on o he Mn-
d
-o bi als and ∆
εi
o MnSi
+
7
( op) and MnSi
+
14
(bo om). These wo sys ems a e exempla y o he exohed al and he
endohed al size egime, espec i ely. Addi ionally, isosu ace plo s o he o bi als wi h he
la ges Mn-3dcha ac e and o he HOMO a e shown.
−200
0
200
−2
0
−400
0
400
−2
0
−7−6−5−4−3−2−1 0 1
MnSi7
+
MnSi14
+
DOS DOS
Figu e 4.8
: Eigen alue spec um
(ba s), o al (do ed line), and local
Mn 3
d
-p ojec ed (solid line) DOS wi h
isosu ace plo s (a
±
0.04 a.u.) o he
Mn 3
d
o bi als and he highes occu-
pied o bi al o MnSi
+
7
and MnSi
+
14
.
Posi i e (nega i e) alues ep esen
he spin-up (spin-down) channel. The
d
-like o bi als a e localized on he Mn
a om in MnSi
+
7
, whe eas hey a e delo-
calized in MnSi
+
14
. Also shown is ∆
εiσ
,
he e ec o he SIE on he PBE0
eigen alues.
Fig. 4.8 illus a es se e al poin s. Fi s , o he endohed al size egime, as ep esen ed by
MnSi
+
14
, PBE0 ai h ully p edic s he elec onic s uc u e, while in he exohed al size egime
his is no he case o all ele an s a es. Howe e , he eigen alues mos se e ely a ec ed
by he SIE (4-5 eV below he Fe mi le el) a e ene ge ically well sepa a ed om he Si-s a es.
I is o be expec ed ha he shi o hese o bi als in a ully sel -in e ac ion co ec ed
calcula ion would ha dly inc ease he hyb idiza ion be ween he Mn- and he Si-s a es and
he e o e he elec onic and magne ic p ope ies o hese clus e s a e expec ed o be only
sligh ly a ec ed. Fu he mo e, he ela i e shi be ween delocalized and localized o bi als
ha esul s om he SIE is less c i ical when s uc u es wi h localized and delocalized
o bi als a e ene ge ically well sepa a ed [52]. He e, his is he case o all s uc u es excep
MnSi
+
11
. The la e is he only clus e o which he global geome y op imiza ion esul ed in
bo h exohed al and endohed al isome s close in ene gy. Fo MnSi
+
n
(
n
= 7
−
10) exohed al
isome s a e consis en ly lowe in ene gy han endohed al ones.
We checked, howe e , ha he ene ge ic o de ing o exohed ally and endohed ally doped
isome s emains he same o clus e sizes a he s uc u al ansi ion, i.e., o MnSi
+
10
and
o MnSi
+
12
. To his end we calcula ed he o al ene gy o he g ound s a e geome y as
p edic ed by PBE0 and he ene ge ically lowes lying endohed al (exohed al) isome o
MnSi
+
10
(MnSi
+
12
) using
ω
PBE as be o e wi h a ange sepa a ion pa ame e o
ω
=0.2 a.u.
as his
ω
leads o he co ec ene ge ic o de ing o MnSi
+
11
. Tab. 4.1 shows he ene ge ic
di e ence be ween exohed ally and endohed ally doped isome s calcula ed wi h PBE0 and
ω
PBE ene gies o MnSi
+
n
(n=10-12) and independen ly suppo s he iew ha he SIE
only a ec s MnSi
+
11
in such a way as o change he ene ge ic o de ing o exohed ally and
endohed ally doped isome s. Fo MnSi
+
10
and MnSi
+
12
he ene ge ic o de ing as well as he
4.3. A DFT-s udy o he magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s 57
Table 4.1
: To al ene gies di e ences o MnSi
+
n
(n=10-12) exohed al and endohed al isome s
∆
E
=
Eexo −Eendo
calcula ed using PBE0 and
ω
PBE wi h a ange sepa a ion pa ame e o
ω
= 0
.
2 a.u. Posi i e numbe s mean ha he
endohed al isome is ene ge ically mo e a o able.
sys em ∆EωPBE in eV ∆EPBE0 in eV
MnSi+
10 -0.67 -1.09
MnSi+
11 1.67 -1.13
MnSi+
12 2.05 1.05
ela i e ene gy di e ence be ween he exohed al and he endohed al isome oughly s ay
he same o PBE0 and
ω
PBE. Consequen ly, only MnSi
+
11
needs special conside a ion and
he endohed al s uc u e shown in Fig. 4.6 can in ag eemen wi h expe imen conside ed o
be he g ound s a e s uc u e o MnSi+
11.
The second poin ha Fig. 4.8 emphasizes is ha he change in local elec onic s uc u e
o he Mn dopan ha was obse ed in he x- ay abso p ion spec a (Fig. 4.4) is e lec ed
in he occupied eigen alue spec um and also by he shape o he KS o bi als.
−200
0
200
400
−7−6−5−4−3−2−1 0 1
DOS [a b. uni s]
Figu e 4.9: Eigen alue spec um (ba s) and DOS o
a omic Mn
+
wi h 4 unpai ed elec ons. No e ha he
g ound s a e o Mn+has a spin momen o 6 µB.
Fo
MnSi+
7
, he occupied s a es o
Mn 3
d
cha ac e a e mos ly isola ed
a
≈
4
−
5 eV below he Fe mi le el
and a e igh ly localized a he Mn
dopan , i.e., hey la gely p ese e a
(pe u bed) a omic cha ac e and only
weakly in e ac wi h Si s a es, as can
be seen om he DOS and he isosu -
ace plo s. No e also he simila i y
be ween he eigen alue spec um o
a omic Mn
+
wi h 4
µB
as shown in
Fig. 4.9 wi h he Mn-3
d
-PDOS o MnSi
+
7
. Because o his weak in e ac ion, he localized
o bi als o Mn 3
d
cha ac e a e quali a i ely e y simila o all exohed al
MnSi+
n
clus e s
and lead o he nea ly iden ical x- ay abso p ion spec a in Fig. 4.4.
This no ion o , a leas pa ly, a omic Mn 3
d
s a es is los in he endohed al size egime,
ep esen ed by
MnSi+
14
in Fig. 4.8. He e, o bi als wi h pa ial Mn 3
d
cha ac e a e s ongly
hyb idized wi h Si s a es and a e shi ed o
≈
0
.
5
−
2 eV below he Fe mi le el, i.e., hey
pa icipa e s ongly in bonding and a e delocalized o e he Si ame. Consequen ly, he Mn
3
d
de i ed PDOS sensi i ely depends on he s uc u e o he Si cage, which is e lec ed in he
a ia ion o he x- ay abso p ion spec a o endohed al
MnSi+
n
o di e en
n
(
n
= 11
−
14)
in Fig. 4.4. The s ong
spd
hyb idiza ion wi h he pa icipa ion o all Mn alence o bi als
explains he comple e quenching o he magne ic momen om 4
µB
in exohed ally o 0
µB
in endohed ally doped clus e s, which is again in acco dance wi h he expe imen al XMCD
spec a.
Thi dly, Fig. 4.8 is exempla y o he well-known connec ion be ween he SIE and he
o bi al localiza ion [51]. The igh ly localized, nea ly a omic 3
d
-o bi als o MnSi
+
7
a e mo e
s ongly a ec ed by he SIE han he a he delocalized o bi als o MnSi
+
14
, despi e he
pa ial Mn-3
d
-cha ac e o he la e . Fo a ho ough discussion o o bi al localiza ion and
sel -in e ac ion, he eade is e e ed o Re . [51].
58 Chap e 4 — Magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s
The s uc u al change a he exohed al- o-endohed al ansi ion o
MnSi+
n
can be
quan i ied by he coo dina ion numbe
Nc
o Mn, i.e., he numbe o Si a oms in he i s
coo dina ion sphe e as exempli ied o
MnSi+
8
in he inse o Fig. 4.11. In exohed al clus e s,
Mn adop s a minimal coo dina ion numbe o
Nc
= 2
−
4, while in endohed al clus e s
Nc
is
maximized o 11−14, i.e., all Si a oms a e wi hin he i s coo dina ion sphe e o Mn.
2.35
Figu e 4.10: Lowes endohed al
isome o MnSi
+
10
. The Mn-Si
bond leng h is comp essed o
only 2.35 ˚
A in his clus e .
The a e age Mn-Si bond leng h
a
elucida es why encap-
sula ion o he Mn dopan becomes ene ge ically a o able
only o
n≥
11: In he g ound s a e s uc u es, he Mn-Si
nea es neighbo dis ance expands om
a
= 2
.
43
−
2
.
58
˚
A
in exohed al o
a
= 2
.
53
−
2
.
67
˚
A in endohed al clus e s.
In con as , i would be comp essed o
a
= 2
.
35
˚
A in he
ene ge ically mos a o able endohed al isome o
MnSi+
10
(as illus a ed in Fig 4.10). E en hough Mn a o s high
coo dina ion in Si [175], his s ain, which becomes e en
mo e p onounced in smalle clus e s, p ecludes endohed al
g ound s a es o n≤10.
The ab up change in coo dina ion a he s uc u al
ansi ion is in e ela ed wi h he quenching o he magne ic
momen as illus a ed in Fig. 4.11: He e, he calcula ed magne ic momen s o
MnSi+
n
a e
plo ed e sus he weigh ed coo dina ion numbe
d0Nc/a
, which akes in o accoun bo h
he numbe o Si nea es neighbo s
Nc
as well as hei a e age dis ance
a
o he Mn a om,
no malized o he nea es neighbo dis ance
d0
in bulk Si. Low-coo dina ed exohed al
clus e s wi h
d0Nc/a
= 1
.
9
−
3
.
7 (
Nc
= 2
−
4) ca y a magne ic momen o 4
µB
, which is
quenched o 0
µB
in high-coo dina ed species wi h
d0Nc/a
= 10
.
2
−
12
.
3 (
Nc
= 11
−
14).
This ela ion o magne ic momen and weigh ed coo dina ion also holds o highe -ene gy
isome s ha a e included in Fig. 4.11 and ma k he ansi ion om magne ic o nonmagne ic
impu i ies a ound d0Nc/a ≈4.
# o bonds
MnSi8
+
2 3 4 5
121086420
magne
ic momen
0
1
2
3
4
5
6
14
Mn-Si dis ance 6
0
1
2
3
weigh ed coo dina ion numbe d0Nc/a
Figu e 4.11
: Magne ic momen e -
sus weigh ed coo dina ion
d0Nc/a
o g ound s a e (open ci cles) and
highe ene gy (solid ci cles) isome s
o
MnSi+
n
(
n
= 7
−
14), isola ed neu-
al Mn impu i ies in bulk ([151], solid
squa es) and amo phous Si ([154],
open iangles), and in a Si nanoc ys-
al ([156], solid diamond). Inse :
bond leng h dis ibu ion o
MnSi+
8
wi h i s coo dina ion sphe e (do ed
line).
Fig. 4.11 shows ha his obse a ion can be gene alized o ex ended sys ems, i.e., o a
neu al Mn impu i y a a subs i u ional si e in c ys alline Si [151] o in hyd ogen-passi a ed
4.3. A DFT-s udy o he magne ic- o-nonmagne ic ansi ion in Mn-doped Si-clus e s 59
Si nanoc ys als [156]. I also applies o e y low concen a ions o Mn in amo phous Si, o
which a possible ela ion be ween magne ic momen and coo dina ion has been poin ed
ou [154]. Ye , al hough
Nc
is he leading e m, i does no accoun o he dependence o
he local magne ic momen on he nea es -neighbo dis ance [151] ha becomes impo an
a ound
Nc
= 4 and is included in
d0Nc/a
. As can be seen in Fig. 4.11, Mn-doped bulk Si is
jus a he ansi ion om high-spin o low-spin s a es and he e o e eac s e y sensi i ely
o changes in
d0Nc/a
. This migh explain he la ge sca e in expe imen al esul s on
Mn-doped Si and indica es ha high-spin s a es could be s abilized by an app op ia e
expansion o he la ice pa ame e , e.g., in ul a- hin ilms o passi a ed nanoc ys als.
In summa y, he magne ic momen o Mn-doped Si has been in es iga ed o e a wide
ange o s uc u al pa ame e s, including ex eme coo dina ion numbe s om 2 - 14. The
s udy o singly doped, size-selec ed
MnSi+
n
clus e s a oids impu i y-band o ma ion o
in e ac ion be ween impu i ies ha migh be p esen in expe imen s on bulk samples, bu
also in calcula ions wi h pe iodic bounda y condi ions. Thus he obse ed quenching o
he magne ic momen is no a esul o impu i y band o ma ion bu o he elec onic
in e ac ion wi h he Si hos . While he SIE s ongly a ec s igh ly localized o bi als wi h
Mn-3
d
cha ac e and is hus pe sis en in exohed ally doped clus e s in which he dopan
only weakly in e ac s wi h he Si hos , i only pe u bs he ene ge ic o de ing o exohed al
and endohed al isome s o MnSi
+
11
. Finally, we ound an uni e sal co ela ion o he
magne ic momen and he weigh ed coo dina ion numbe . Bulk Si doped wi h Mn lies a
he ansi ion om high o low magne ic momen s and he e o e is pa icula ly sensi i e o
he nea es neighbo bond leng hs o he Mn dopan .

5
Summa y and ou look
5.1 Summa y
In he p esen hesis s uc u al and elec onic p ope ies o Au-P , Au-Pd nanoalloys and
Mn-doped Si clus e s we e s udied using non-empi ical DFT and MD simula ions employing
empi ical Su on-Chen po en ials. Au-P and Au-Pd nanoalloys show a bime allic e ec , i.e.,
inc eased ac i i y and selec i i y in many di e en ca aly ic eac ions. This wo k con ibu es
o he long-s anding deba e be ween heo y and expe imen on he mixing pa e n o Au-P
nanoalloys. We we e able o show ha a p ominen cha ac e iza ion echnique based on a
combina ion o XRD and Vega d’s law elies on ques ionable assump ions. Au
shell
P
co e
and homogeneously mixed NP in he expe imen ally ele an size ange o
≈
4 nm a e
indis inguishable in a ypical XRD expe imen . Fu he mo e, i was shown ha Vega d’s
law is alid o bo h ypes o mixing pa e ns. Theo y consis en ly p edic s co e-shell
s uc u es as ene ge ically mos a o able, bu homogeneously mixed Au-P nanoalloys a e
obse ed in expe imen using elemen -speci ic cha ac e iza ion echniques. Ou indings
show ha he o ma ion o mixing pa e ns o he han he co e-shell one mus be linked o
e ec s such as in e ac ions wi h he suppo ma e ial o he syn hesis p ocedu e.
The s udy o he elec onic s uc u e o Au-P and Au-P nanoalloys showed ha he
DOS a he Fe mi le el depends on he P and Pd con en o he NP, espec i ely. The
DOS a he Fe mi le el is ela ed o he binding ene gy be ween he ca alys and possible
adso ba es and i inc eases wi h inc easing P (Pd) con en . Addi ionally, he spa ial
dis ibu ion o he HOMO is connec ed o he posi ion o he P (Pd) a oms. Empi ical MD
simula ions we e used o ex ac he MSD o he a oms in an Au-P NP. The MSD is ela ed
o he a omic mobili y o s uc u al lexibili y o he NP. The la e can be bene icial in ha
i allows he ca alys o s uc u ally adjus o eac an s, o m elemen -speci ic binding si es
62 Chap e 5 — Summa y and ou look
and egene a e a e a eac ion has aken place. I was shown ha he MSD inc eases wi h
inc easing Au con en . This esul could be suppo ed by modeling he NP as su ace slabs
and s udying he di usion o a single Au o P ada om on hese su aces. The ac i a ion
ba ie o ada om di usion, he simples ype o su ace econs uc ion, was shown o
dec ease wi h inc easing Au con en .
A combina ion o he undamen al p ope ies DOS a he Fe mi le el and a omic mobili y
migh explain why a bime allic e ec is obse ed o Au-P nanoalloys unde e y a ying
expe imen al condi ions. A speci ic Au-P a io could amoun o an op imal in e ac ion
be ween ca alys and eac an s media ed by an op imal DOS a he Fe mi le el and an
op imal amoun o s uc u al lexibili y.
In he second pa o his hesis he magne ic p ope ies o Mn-doped Si clus e s we e
s udied. These sys ems can be seen as well-de ined models o a semiconduc ing hos ha
in e ac s wi h a single magne ic impu i y. A global geome y op imiza ion was ca ied ou
o iden i y he g ound s a e s uc u es o MnSi
+
n
(n=7-14). In ag eemen wi h expe imen ,
i could be shown ha a s uc u al ansi ion om exohed al o endohed al doping om
MnSi
+
10
o MnSi
+
11
is accompanied by comple e quenching o he magne ic momen . The
size o he magne ic momen is co ela ed wi h he coo dina ion numbe o he Mn dopan
weigh ed wi h i s a e age nea es neighbo dis ance. This ela ion holds also o Mn in
amo phous and c ys alline Si and sugges s ways o s abilize he magne ic momen o a Mn
impu i y by app op ia e la ice expansion.
Sys ems o which he in e ac ion be ween s ongly localized and delocalized o bi als
plays a majo ole pose se ious di icul ies o exis ing app oxima ions o DFT because o he
well-known sel -in e ac ion p oblem. By e alua ing i s o bi al-SIE we ound ha MnSi
+
11
su e s pa icula ly se e ely om sel -in e ac ion. The one-pa ame e hyb id xc unc ional
PBE0 which co ec ly p edic ed s uc u es and magne ic momen s o all o he clus e s
he e o e yields a w ong, exohed ally doped g ound s a e s uc u e in his case. By using
a RSH unc ional we saw ha he co ec ene ge ic o de ing o he endohed al and he
exohed al isome is ob ained o ce ain alues o he ange sepa a ion pa ame e . Toge he
wi h he o bi al-SIE his inding highligh s how delica ely exchange and co ela ion e ec s
de e mine he ene ge ic o de ing in MnSi+
11.
5.2 An ou look o Ni-Pd nanoalloys
The sea ch o bime allic ca alys s ha pe o m e icien ly in la ge-scale ca alysis is equen ly
guided by he simple p inciple o ind he combina ion o ma e ials ha yields he highes
u no e a es and is as cheap as possible. Ni-Pd nanoalloys a e in his sense op imal.
Addi ionally, hey cons i u e a sys em co e ing a a ie y o en icing undamen al ques ions.
Fi s ly, small Ni and Pd clus e s a e known o exhibi high magne ic momen s [11, 140]. The
size- and composi ion-dependen magne ic momen o Ni-Pd nanoalloys is he e o e expec ed
o exhibi in e es ing ea u es. Howe e , Chap. 4.3 showed ha he co ec desc ip ion o
5.2. An ou look o Ni-Pd nanoalloys 63
Table 5.1
: Adso p ion ene gies (in eV) o Pd-
and Ni-ada oms on pu e and doped Pd- and Ni
su aces o he s a (ini) and he end ( in) po-
si ion o each NEB calcula ion. The di usion
ba ie (in meV) is de ined as he ene ge ic di e -
ence be ween he ini al posi ion and he saddle
poin o he minimum ene gy pa h.
sys em Eads ini Eads in Eba ie
Pd/Pd 2.70 2.70 70
Pd/Pd+Ni 2.72 2.69 76
Ni/Pd 3.48 3.38 296
Pd/Ni 3.14 3.14 65
Ni/Ni+Pd 3.63 3.69 380
Ni/Ni 3.63 3.63 80
he geome ical and elec onic s uc u e e en o allegedly simple magne ic ansi ion me al
compounds is a huge challenge o heo y. DFT s udies o small Ni-Pd clus e s ha e up o
now only been ca ied ou using s anda d semilocal xc unc ionals [176, 177] and global
geome y op imiza ions a e a e [178] o hese sys ems. A emp s o cons uc a eliable
pseudopo en ial o Ni ha could be used in conjunc ion wi h o bi al-dependen unc ionals
ha e so a p o ed challenging as well [179].
ini
fin
ini
fin
(a) (b)
Figu e 5.1: Se up o Pd/Ni ada om di usion on
Ni/Pd su ace (a) wi hou and (b) wi h a single
Pd/Ni a om in he uppe su ace laye . The di usion
s ep akes place om one hcp hollow o ano he hcp
hollow si e.
Secondly, a bime allic e ec in ca aly-
sis has ecen ly been obse ed o Ni-Pd
nanoalloys immobilized in so-called me-
al-o ganic amewo ks [180] as well as in
o he eac ions [78]. A close lying ques ion
is he e o e whe he he gene al concep s
ha apply o Au-P nanoalloys, a e also
sui ed o explain he special p ope ies o
Ni-Pd pa icles. This would again equi e
a ai h ul desc ip ion o hei elec onic
s uc u e, a leas close o he Fe mi le el.
Fu he mo e, he a omic mobili y o luxionali y o Ni-Pd sys ems has o be es ed. Ini ial
s eps in o his di ec ion ha e been aken ollowing a simila line o a gumen as desc ibed
in Sec. 3.4.3. Pu e and doped Ni- and Pd-su aces ha e been modeled by 4x4x4-laye slabs
wi h equilib ium la ice pa ame e s o 3.520
˚
A o Ni and 3.939
˚
A o Pd. A su ace di usion
s ep be ween wo equi alen hcp hollow si es as depic ed in Fig. 5.1 has been conside ed.
CI-NEB calcula ions we e ca ied ou in o de o de e mine he ac i a ion ene gy o
his di usion s ep (see Sec. 2.5). Fu he mo e, he adso p ion ene gies o he ada om a he
ini al and he inal posi ion ha e been de e mined using Eq.
(3.7)
. The esul ing ba ie s
and adso p ion ene gies a e lis ed in Tab. 5.1. No e ha bo h he adso p ion ene gies and
he ba ie s a e conside ably smalle han o Au-P su aces (c . Tab. 3.3). This inding is
in line wi h he ecen obse a ion ha la ge Ni-Pd clus e s (wi h diame e s o
≈
4 nm)
p e e ably o m solid solu ions and ha hei su ace is co uga ed due o he la ge la ice
misma ch o Ni and Pd [180]. The s ong endency o seg ega ion o he wo componen s
ound in Au-P NP hus seems no o be p esen in Ni-Pd NP. Fu he mo e, no speci ic
end o he di usion ba ie s can be seen in Tab. 5.1. Excep ions o he o e all small
ba ie s o be ween 65 and 80 meV a e ound o he di usion o a Ni ada om on Pd wi h
a ba ie o almos 300 meV and di usion o a Ni ada om on a Ni su ace doped wi h a
70 Appendix A — Tempe a u e and suppo e ec s
Figu e A.4: DOS a he Fe mi le el wi h inc easing la ice pa ame e o bulk Au (le ) and P
( igh ). Di e en in eg a ion h esholds a e shown, ha demons a e ha he Au bulk DOS inc eases
mo e apidly, as soon as he 5d-de i ed DOS is aken in o accoun .
Au P
3.90 3.95 4.00 4.05 4.10 4.15 4.20
la ice pa ame e [Å]
up o -1 eV
up o -2 eV
0
1
2
3
4
5
4.00 4.05 4.10 4.15 4.20
DOS a Fe mi le el [a b. uni s]
up o -1 eV
up o -2 eV
up o -3 eV
subs i u ion o one Au a om in, e.g., Au
38
by a P a om (upon which he mean in e a omic
dis ance e en dec eases, as shown in Sec. 3.3), leads o a ela i e inc ease o he DOS a
he Fe mi le el o nea ly 100%, while he posi ion o he Fe mi le el emains app oxima ely
cons an . The e ec o he mal expansion on he elec onic s uc u e o Au-P NP is
he e o e negligibly small as compa ed o he inc ease ha is obse ed o alloying Au
clus e s wi h P a oms.
A.2 In luence o he nanopa icle suppo
The p ac ical use ulness o ca aly ic NP is o en dic a ed by how success ully hey can be
s abilized agains coagula ion, by hei handling and hei e-usabili y. S abiliza ion by
end g oups ha s ongly in e ac wi h he NP’s su ace can se e ely al e and e en limi
he ca aly ic ac i i y. Recen ly, i has been shown ha highly ca aly ically ac i e Au-P
nanoalloys wi h a diame e o
≈
3-4 nm can be syn hesized and immobilized in so-called
sphe ical polyelec oly e b ushes (SPBs) [80]. SPBs consis o a solid polys y ene co e
on o which long ca ionic polyelec oly e chains a e densely g a ed as ske ched in Fig. A.5.
The polyelec oly e is 2-amino-e hyl me hac yla e (AEMH) which is posi i ely cha ged in
aqueous solu ion. Cl
−
anions ep esen he coun e ions which a e mos ly con ined o he
su ace laye o he SPB, ha is indica ed in ligh g ay in Fig. A.5. The Cl
−
coun e ions can
be eplaced by me al ions like [AuCl
4
]
−
and [P Cl
6
]
−2
. These a e hen educed o elemen al
Au and P using NaBH
2
. Du ing he p ocess o Au-P nanoalloy o ma ion he su ace
laye conside ably dec eases om abou 70 nm o only 20 nm. This can be a ibu ed o he
nanoalloys ca ying a nega i e su ace cha ge and he e o e s ongly in e ac ing wi h he
ca ionic polyelec oly e chains. Howe e , his in e ac ion seems o be weak enough no o
obs uc he ca aly ic ac i i y o he Au-P nanoalloys [80].

A.2. In luence o he nanopa icle suppo 71
Figu e A.5
: Au-P nanoalloys
can be syn hesized wi hin he
dense polyelec oly e laye o a
sphe ical polyelec oly e b ush.
C
H
CH3
O
CH2
NH3
C
C
H
O
CH2
n
+
polys y ene
70nm
Cl-
Cl-
Cl-
Cl-
Cl-
polys y ene
20nm
[AuCl4]-
[P Cl6]2-
NaBH4
+
C
H
CH3
O
CH2
NH3
C
C
H
O
CH2
n
+
C
H
CH3
O
CH2
NH3
C
C
H
O
CH2
n
+
C
H
CH3
O
CH2
NH3
C
C
H
O
CH2
n
+
C
H
CH3
O
CH2
NH3
C
C
H
O
CH2
n
+
polyelec oly e
laye wi h NP
In his sec ion, I wan o p esen i s esul s on how he in e ac ion be ween he NP
and he SPB suppo a ec s he undamen al s uc u al and elec onic p ope ies o he
Au-P nanoalloys ha ha e been es ablished in he main pa o his hesis. As he simples
possible model se up we assume ha he me al NP in e ac wi h monome ic AEMH uni s
and ha he combined sys em consis ing o NP and AEMH uni s is neu al. The polys y ene
co e is assumed o be ine and will no be conside ed he e. Fu he mo e, we dis ega d he
aqueous solu ion in which he eac ion akes place, as we wan o concen a e on he e ec
o he NP-AEMH in e ac ion.
pu e Au andom co e-shell
Figu e A.6: Two AEMH monome uni s a e placed
close o he su ace o an Au
20
, a andomly mixed
Au10P 10 and a co e-shell Au10P 10 clus e .
Ou i s model se up is shown in Fig.
A.6. Two AEMH monome uni s a e plac-
ed close o he su ace o an Au
20
, a an-
domly mixed Au
10
P
10
and a co e-shell
like Au
10
P
10
clus e
1
. The dynamical
e olu ion o hese sys ems is simula ed us-
ing cons an empe a u e MD simula ions
ia a Nos´e-Hoo e he mos a o 300 K
empe a u e.
In he o iginal o mula ion o Nos´e,
a canonical ensemble is achie ed by aug-
men ing he classical Hamil onian by a ime scale a iable
s
, i s conjuga e momen um
ps
and a pa ame e Q
HNos´e =
M
X
i=1
p2
i
2mis2+U(q1, ..., qM) + ps
2Q+ (N + 1)kBTln s. (A.4)
The ime scale a iable
s
luc ua es which amoun s o a coupling o a hea ba h o
empe a u e T.
N
is he numbe o deg ees o eedom. I can be shown ha he
mic ocanonical dis ibu ion in he augmen ed se o a iables is equi alen o a canonical
dis ibu ion o he a iables
{q1, ..., qM}
,
{p0
1, ..., p0
M}
, whe e
p0
i
=
pi/s
[182]. As i is
incon enien o wo k wi h luc ua ing ime in e als in p ac ical simula ions, one o en
uses he o mula ion o Hoo e , in which
ps/Q
is eplaced by a he modynamic ic ion
1
Simila o Sec. 3.2, he label ”co e-shell” indica es ha all P a oms a e as highly coo dina ed and all
Au a oms a e as lowly coo dina ed as possible.
72 Appendix A — Tempe a u e and suppo e ec s
coe icien η, which can be exp essed ia a phenomenological elaxa ion ime τ[183]
η=ps
N kBTτ2,(A.5)
which is he e chosen ou imes as la ge as he simula ion ime s ep ∆ = 80 a.u. b= 1.9 s.
All sys ems we e p opaga ed o abou 16 ps. The elec onic s uc u e in each imes ep
was calcula ed using he PBE GGA and a SVP basis se augmen ed as implemen ed in he
TURBOMOLE p og am package [184]. As an-de -Waals o ces a e expec ed o play a ole
in he in e ac ion be ween he Au-P nanoalloys and he AEMH molecules, he empi ical
dispe sion co ec ion o G imme was employed [185], which adds a e m
Edisp =−s6
M−1
X
i=1
M
X
j=i+1
Cij
6
R6
ij
damp(Rij) (A.6)
o he o al ene gy o he sys em. He e,
s6
is a global scaling pa ame e , which depends on
he xc unc ional employed,
Cij
6
a e empi ical dispe sion coe icien s o a om pai
i
and
j
,
Rij
=
|Ri−Rj|
,
damp
is a damping unc ion ha a oids singula i ies a small in e a omic
dis ances
Rij
and
M
deno es he numbe o a oms. To di e en ia e be ween he e ec s o
empe a u e and hose o he AEMH monome uni s, a second se o MD simula ions o
jus he ba e sys ems wi hou AEMH molecules was ca ied ou .
andom
pu e Au co e-shell
Figu e A.7: S uc u e snapsho aken a he
end o each simula ion, showing ha conside -
able s uc u al changes ha e se e ely dis o ed
he e ahed al geome y o all h ee sys ems.
Fig. A.7 p o ides a isual imp ession o he
i s impo an esul o hese simula ions. I
shows an exempla y s uc u e snapsho aken
a he end o he simula ion. The geome y
o all h ee sys ems is conside ably di e en
om he e ahed al s uc u e we s a ed wi h.
Tha his is no only an e ec o empe a u e
can be seen by compa ison wi h he s uc u es
o he ba e Au
20
and Au
10
P
10
sys ems ha
o e all e ain hei e ahed al shape. The
s uc u e o he ba e sys em is e en s able
up o empe a u es o 600 K, as men ioned in
Sec. 3.2 and Re . [94]. In ac , du ing he whole
simula ion s ong s uc u al changes ake place in he combined NP-AEMH sys em, while
in he ba e sys ems mainly ib a ions o he a oms abou hei equilib ium posi ions can
be seen.
To quan i y hese e ec s we calcula ed he a e age nea es neighbo bond leng h o
he NP wi h and wi hou AEMH monome s o e e y imes ep. Fig. A.8 shows he nea es
neighbo bond leng h o Au
20
(le ), andomly mixed Au
10
P
10
(middle) and co e-shell
Au
10
P
10
( igh ). The nea es neighbo bond leng h was de ined as he a e age dis ance
o e e y a om o i s ou nea es neighbo s. No e ha he elaxed co e-shell Au
10
P
10
was aken as he ini ial geome y o all NP. Fo Au
20
all P a oms in his NP we e hen
eplaced by Au a oms. Fo he andomly mixed clus e , he P a oms we e edis ibu ed
o e he clus e as depic ed in Fig. A.6. This means, ha one has o compa e he nea es
A.2. In luence o he nanopa icle suppo 73
Figu e A.8: A e age nea es neighbo bond leng h o e e y ime s ep o he simula ion o he Au
20
(le ), he Au
10
P
10
andomly mixed (middle) and he Au
10
P
10
co e-shell sys em wi h ( op) and
wi hou (bo om) AEMH monome s. The yellow line, a mo ing window a e age, is a guide o he
eye.
2.75
2.80
2.85
2.90
2.95
0 2000 4000 6000 8000 10000 12000 14000 16000
nea es neighbo dis ance [Å]
Au20
2.75
2.80
2.85
2.90
2.95
0 2000 4000 6000 8000 10000 12000 14000 16000
Au20
wi h AEMH
wi hou AEMH
simula ion ime [ s]
2.70
2.75
2.80
2.85
2.90
0 2000 4000 6000 8000 10000 12000 14000 16000
andom
2.70
2.75
2.80
2.85
2.90
0 2000 4000 6000 8000 10000 12000 14000 16000
andom
2.70
2.75
2.80
2.85
2.90
0 2000 4000 6000 8000 10000 12000 14000 16000
co e-shell
2.70
2.75
2.80
2.85
2.90
0 2000 4000 6000 8000 10000 12000 14000 16000
co e-shell
neighbo bond leng h o he NP-AEMH sys em wi h he equilib ium bond leng h o he
ba e NP, a e all ansien p ocesses ha e decayed. On a e age, he nea es neighbo
bond leng h inc eases om 2.84
˚
A o 2.85
˚
A in Au
20
, om 2.78
˚
A o 2.79
˚
A in he andomly
mixed Au
10
P
10
clus e and om 2.78
˚
A o 2.80
˚
A in he co e-shell Au
10
P
10
clus e . Mo e
signi ican han his sligh inc ease o he a e age bond leng h by less han 1% is ha he
nea es neighbo bond leng h luc ua es much mo e s ongly in he NP-AEMH sys ems
han in he ba e clus e s. This is consis en wi h he la ge s uc u al changes in he o me .
Addi ionally, we coun ed he numbe o Au-Au, Au-P and P -P bonds o he wo
Au
10
P
10
sys ems in each simula ion s ep. A bond is he e de ined as e e y in e a omic
dis ance
≤
2.9
˚
A. Fo he ba e NP hese numbe s a e cons an du ing he whole simula ion.
Fo he combined NP-AEMH sys ems one has o dis inguish wo ime domains, simila ly as
o he nea es neighbo bond leng h. The ansien ime domain om 0 o
≈
6000 s and
he s eady s a e un il he end o he simula ion. O cou se, ansien e ec s a e also p esen
o he ba e clus e s, bu hey do no a ec he numbe o Au-Au, Au-P and P -P bonds
he e. Tab. A.1 shows he a e age s eady s a e numbe o bonds and he espec i e s anda d
de ia ions o Au
10
P
10
wi h and wi hou AEMH monome s. Again, we compa e he a e age
numbe o bonds o he combined NP-AEMH sys em wi h he numbe o bonds o he ba e
NP. Fo bo h Au
10
P
10
+AEMH sys ems he numbe o Au-Au bonds dec eases as compa ed
o hei ba e coun e pa s. Fo he andomly mixed clus e also he numbe o Au-P bonds
dec eases, while he numbe o P -P bonds inc eases. Fo he co e-shell clus e he numbe
o Au-P bonds sligh ly inc eases and he numbe o P -P bonds dec eases. I wan o s ess
ha he o e all numbe o Au-Au, Au-P and P -P bonds is oo small o allow conclusi e
74 Appendix A — Tempe a u e and suppo e ec s
wi hou AEMH andom co e-shell
Au-Au 4 ±1 8 ±1
Au-P 22 ±2 13 ±2
P -P 12 ±1 19 ±1
wi h AEMH andom co e-shell
Au-Au 2 ±1 5 ±2
Au-P 20 ±2 14 ±2
P -P 14 ±1 16 ±1
Table A.1
: Numbe o Au-Au, Au-P and P -
P bonds
≤
2.9
˚
A o andomly mixed and co e-
shell clus e s wi hou and wi h wo AEMH
monome s. The a e ages o he ba e sys em
is aken o e he comple e simula ion ime.
Fo he combined sys em he a e age was
compu ed om 6000 o 16 000 s.
s a emen s he e. A i s cau ious in e p e a ion o hese esul s, howe e , indica es ha he
co e-shell clus e pa ly looses i s clea P -co e/Au-shell cha ac e is ics, while he andomly
mixed clus e unde goes s uc u al changes making i mo e co e-shell like. In o he wo ds, in
he combined NP-AEMH sys em he di e en ia ion be ween andomly mixed and co e-shell
clus e s is no meaning ul anymo e. Fi s ly, because on a e age clus e s will exhibi an
in e media e mixing pa e n in be ween co e-shell and a andom dis ibu ion o Au and
P . Secondly, a ealis ic expe imen al condi ions, i.e., a ini e empe a u e and embedded
in a suppo ing ma ix, Au-P nanoalloys canno be desc ibed in a s a ic, monos uc u e
ashion anymo e [146]. Indeed, in ou case a 300 K in e ac ion wi h he AEMH monome s
seems o be he dominan ac o ha induces s uc u al luxionali y.
Figu e A.9: To al ene gy o andomly mixed and co e-shell Au
10
P
10
in he MD simula ion o he
combined NP-AEMH sys em and he ba e NP sys em.
−93394
−93392
−93390
−93388
−93386
−93384
−93382
−93380
0 2000 4000 6000 8000 10000 12000 14000 16000
o al ene gy [eV]
simula ion ime [ s]
andom
co e-shell
−69464
−69462
−69460
−69458
−69456
−69454
−69452
−69450
0 2000 4000 6000 8000 10000 12000 14000 16000
simula ion ime [ s]
andom
co e-shell
wi h AEMH wi hou AEMH
These conclusions a e u he suppo ed by conside ing he o al ene gy o he wo
Au
10
P
10
sys ems wi h and wi hou AEMH suppo as depic ed in Fig. A.9. Fo he ba e
sys em he o al ene gy o he co e-shell clus e is consis en ly lowe han ha o he
andomly mixed pa icles. This esul is no su p ising conside ing ha s uc u e and
mixing pa e n in hese simula ions emain la gely undis u bed. The si ua ion is comple ely
di e en o he combined NP-AEMH sys em. He e he co e-shell clus e -AEMH sys em
is ene ge ically mo e a o able a he beginning o he simula ion. F om
≈
6000 s on he
o al ene gies o he wo sys ems a e nea ly iden ical.
Finally, we will ake a close look a he elec onic s uc u e o ou model sys em. To
A.2. In luence o he nanopa icle suppo 75
his end, we ook 11 s uc u e snapsho s o each sys em, being 194 s apa om each
o he (
b=
100 MD s eps) s a ing a 13 545 s. The elec onic s uc u e o hese sys ems was
calcula ed using a TZVPP basis se . No s uc u al elaxa ion was ca ied ou , as we a e
in e es ed in he elec onic s uc u e o each pa icula snapsho he e. Fo each s uc u e
snapsho we calcula ed he o al DOS and he me al DOS o he combined NP-AEMH
sys em (in he ollowing called me al-PDOS), which is ob ained by p ojec ing he o al
DOS on o he Au and P a oms.
Fig. A.10 shows he o al DOS o he ba e Au
20
and Au
10
P
10
sys ems and he espec i e
me al-PDOS o he combined NP-AEMH sys ems. The depic ed DOS’s ep esen he
a i hme ic mean o he DOS’s o each o he 11 s uc u e snapsho s o each sys em. The
me al-PDOS o he combined sys em is in e es ing, because we assume ha possible
eac an s in a ca aly ic p ocess a e adso bed o he NP and eac a i s su ace. Thus,
ollowing he conside a ions o Sec. 3.4.1, he in e ac ion s eng h be ween he ca alys s
and he adso ba es is go e ned by he me al-PDOS a he Fe mi le el.
Figu e A.10: To al DOS o ba e NP (black) and DOS p ojec ed on o he me al a oms o he combined
NP-AEMH sys em (yellow) a e aged o e 11 s uc u e snapsho s each, as explained in he ex .
0
500
1000
1500
2000
2500
3000
−10 −8−6−4−2 0
densi y o s a es
NP +AEMH PDOS
ba e NP DOS
−10 −8−6−4−2 0−10 −8−6−4−2 0
pu e Au andom co e-shell
The le panel o Fig. A.10 again demons a es he special elec onic s uc u e o he
ba e Au
20
e ahed on [68]. I ’s DOS exhibi s disc e e ea u es and is high close o he
Fe mi le el as compa ed o o he Au clus e s (see Sec. 3.4.1). In con as , he DOS o
he ba e Au
10
P
10
clus e s, is mo e con inuous and band-like. No e ha con a y o he
isual imp ession he DOS a he Fe mi le el o Au
10
P
10
is signi ican ly highe han ha
o Au
20
in acco dance wi h he esul s o Sec. 3.4.1. No iceably, Fig. A.10 shows ha he
me al-PDOS a he Fe mi le el is conside ably educed as compa ed o he ba e NP case.
This is mos p onounced o Au
20
. He e, he me al-PDOS is mo e con inuous han ha o
he ba e NP. Mo e impo an ly, he me al-PDOS a he Fe mi le el is educed by 60% as
compa ed o he o al DOS o he ba e NP. The same e ec , hough less dis inc , is seen o
Au
10
P
10
. The me al-PDOS a he Fe mi le el is educed by 16% o he andomly mixed
and by 30% o he co e-shell clus e . The la ge de ia ions be ween he DOS educ ion
o he wo Au
10
P
10
sys ems can be asc ibed o he o e all small numbe o s uc u al
snapsho s o which he DOS was e alua ed. A educ ion o he DOS a he Fe mi le el
is expec ed o lead o weake in e ac ions wi h possible adso ba es. Whe he i esul s in
an inc eased o dec eased ca aly ic ac i i y, howe e , depends on he speci ic eac ion one
is in e es ed in. Qui e gene ally he esul s o his sec ion indica e ha he in e ac ion o

76 Appendix A — Tempe a u e and suppo e ec s
ou 20-a om Au and Au-P NP wi h AEMH monome uni s leads o a ma ked inc ease
o he luxionali y o he clus e s on he one hand. On he o he hand he DOS a he
Fe mi le el dec eases in he combined NP-AEMH sys em. In e ms o he olcano pic u e
in oduced in Sec. 3.4.4, his migh co espond o a shi o he olcano peak as compa ed
o he ba e NP case. Ou indings suppo he no ion ha liquid-phase ca alysis canno be
modeled using he same concep s ha ha e success ully been applied o gas-phase ca alysis
on su aces [131]. Unde ealis ic expe imen al condi ions he desc ip ion o suppo ed
Au-P nanoalloys as s a ic en i ies being go e ned by hei ( acuum and ze o- empe a u e)
g ound s a e p ope ies is likely o be lawed.
Ye , e en hough he esul s p esen ed in his sec ion allow aluable i s insigh s in o he
in e ac ion be ween suppo molecules and Au-P NP u he simula ions ha e o be ca ied
ou o achie e conclusi e esul s and o judge he signi icance o he indings p esen ed
abo e. Fi s , simula ions ha e o be done o la ge NP, e.g., 40-a om Au-P nanoalloys,
possibly wi h a less ”special” geome y han he e ahed on, which has only su ace and
no olume a oms and is he e o e expec ed o be pa icula ly eac i e. Second, i has o be
cla i ied how signi ican he ype o NP suppo in e ms o he epo ed e ec s is. Typical
suppo s ha could be modeled wi h easonable compu a ional e o a e, e.g., ca bon [87]
o silica [79] suppo s.
B
Op ical p ope ies o Au-P
nanoalloys
The use o inely dispe sed Au pa icles in uby glass and he colo ul s ained-glass windows
o Eu opean’s medie al ca hed als shows ha hei special op ical p ope ies ha e been
known o cen u ies. The i s scien i ic examina ion o he subjec is a ibu ed o Michael
Fa aday, who s udied he in e ac ion o ligh wi h colloidal Au pa icles, as well as hin
Au ilms and lea es as ea ly as 1857 [186]. Today i is well unde s ood ha he beau i ul
colo o suspensions o colloidal Au is a esul o collec i e exci a ions o he conduc ion
elec ons ha domina e he abso p ion spec um, accumula ing in a so called Mie esonance
o su ace plasma esonance
1
. The posi ion o he Mie esonance depends on he size o
he Au colloids, bu he op ical ma e ial unc ions ha desc ibe he linea esponse o
he clus e s o elec omagne ic wa es, a e la gely size-independen and simila o he bulk
alues. Wi h hese op ical ma e ial unc ions one can de e mine he op ical esponse o
( a he la ge) NP using classical elec odynamics and he so called Mie heo y [188].
Fo NP smalle han
≈
10 nm, ha a e s ill oo la ge o assess hem wi h quan um
chemical me hods such as ime-dependen DFT, he si ua ion is mo e di icul . The op ical
esponse unc ions become size dependen and can de ia e subs an ially om he bulk. A
comp ehensi e accoun on op ical p ope ies o me al clus e s is gi en in Re . [187] and
pe inen e e ences he ein. He e, he ocus will be on sphe ical clus e s o 10 nm diame e
(
R
= 5 nm) in e ac ing wi h isible ligh o wa eleng h
λ
, i.e.,
Rλ
. The op ical esponse
o clus e s in his size ange can be de e mined by i ue o Mie heo y. Fo
Rλ
(quasi-s a ic case) phase e a da ion e ec s and highe mul ipole o de s can be neglec ed
and he abso p ion c oss sec ion in he dipola limi is
σ(ω) = 4πω
c√εm=[α(ω)],(B.1)
1
The e m su ace plasma esonance e e s o he su ace pola iza ion being he main es o a i e o ce in
clus e s. This su ace pola iza ion is due o cha ges wi hin he elec onic sc eening leng h [187].
78 Appendix B — Op ical p ope ies o Au-P nanoalloys
whe e
=
[
α
(
ω
)] is he imagina y pa o he pola izabili y o he clus e , which o a
homogeneous sphe e is
αhomogeneous(ω) = ε−εm
ε+ 2εm
εmR3.(B.2)
−10
−5
0
5
10 ε1
ε2
−100
−50
0
50
100
0 1 2 3 4 5
dielec ic unc ion
ene gy [eV]
ε1
ε2
dielec ic unc ion
Gold
Pla inum
Figu e B.1: Real and imagina y pa o
he dielec ic unc ion o bulk Au and P ,
aken om Re . [189] and [190].
In Eq.
(B.1)
and
(B.2)
,
ε
is he (complex and
ω
-dependen ) dielec ic unc ion o he clus e . We
will he e assume ha
ε
is simila o i s bulk alue.
The alidi y o his assump ion will be discussed
below. The eal and imagina y pa o he dielec ic
unc ion
ε
=
ε1
+
iε2
desc ibe pola iza ion and
ene gy dissipa ion o ma e , espec i ely, and a e
ela ed by he amous K ame s-K onig ela ions.
Fig. B.1 shows
ε1
and
ε2
o bulk Au and P as
abula ed in Re . [189] and [190]. Fu he mo e,
Eq.(B.1) and B.2 con ain he ela i e pe mi i i y
εm
o he ma ix in which he pa icle is embedded.
Fo all ollowing calcula ions
εm
= 2
.
7 was used,
which co esponds o he ela i e pe mi i i y o
polys y ene, one o he majo ing edien s o he
polyelec oly e ma ices used o Au-P nanoalloys
s abiliza ion in Re . [80]. Finally,
c
is he acuum
speed o ligh .
Fig. B.2 depic s he op ical abso p ion spec a
o a pu e Au and a pu e P NP o 10 nm diame e .
The Mie esonance o he Au NP can clea ly be
seen a a ound 2.25 eV. The P NP exhibi s no Mie
esonance in he isible ene gy ange.
0
200
400
600
800
1000
1200
1400
1600
1800
0 1 2 3 4 5
abso p ion c oss sec ion [nm2]
ene gy [eV]
pu e Au
pu e P
Figu e B.2
: Op ical abso p ion spec-
um calcula ed using Mie heo y in
he dipola limi o sphe ical me al
sphe es o 10 nm diame e . Con a y
o P , Au NP show a p onounced Mie
esonance.
79
A his poin he ques ion a ises how he op ical esponse o an Au-P nanoalloy will
e ol e as a unc ion o he Au/P a io and how he mixing pa e n o Au and P in luences
he op ical abso p ion spec um o he NP. The op ical p ope ies o Au-P NP ha e
been s udied expe imen ally [191, 192] and o co e-shell clus e s also heo e ically using
Mie- heo y as will be explained in he ollowing [192]. Ou app oach ollows a s udy o
Ni-Ag clus e s by Gaud y e al. [193].
Mie heo y can be ex ended o he sca e ing o an elec omagne ic wa e by wo
concen ic sphe es [194]. In he dipola limi one hen ob ains o he pola izabili y
αco e-shell(ω) = (εshell −εm)(εco e + 2εshell) + (εco e −εshell)(εm+ 2εshell)
(εshell + 2εm)(εco e + 2εshell)+2 (εshell −εm)(εco e −εshell)εmR3,(B.3)
whe e
εco e
and
εshell
a e he dielec ic unc ions o he co e and he shell, espec i ely. He e,
=
Rc/R
and
Rc
is he adius o he co e, ha one can es ima e using he Au-P a io
(1 −x)/x and he a omic adii o Au and P o a AushellP co e clus e
Vco e =4
3πR3
c(B.4)
Vshell =4
3π(R3−R3
c).(B.5)
Assuming he clus e o consis o MAu Au and MP P a oms
MAu =Vshell
VAu
(B.6)
MP =Vco e
VP
,(B.7)
whe e VAu,P =4
3π 3
Au,P is he olume occupied by a single Au o P a om, one ob ains
MAu
MP
=1−x
x= 3
P
3
Au
R3−R3
c
R3
c
.(B.8)
Wi h his, he co e adius is de e mined o be app oxima ely
Rc=R3
sx 3
P
(1 −x) 3
Au +x 3
P
.(B.9)
Fo
εco e
and
εshell
we ake he bulk dielec ic unc ions o P and Au. This migh no
be jus i ied, no ably o he shell egion and only small pe cen ages o Au. Howe e , o
he case o Ni-Ag NP (R=1–2.5 nm) his app oxima ion ep oduced he expe imen ally
obse ed Mie esonance and i s blueshi wi h inc easing Ni-con en quali a i ely well [193].
Fo a Au-P solid solu ion, he op ical abso p ion can be de e mined using Eq.
(B.1)
and (B.2) wi h an a e aged dielec ic unc ion [187]
ε=εP x0Au1−x0(ω) = x0εP (ω) + (1 −x0)εAu(ω),(B.10)
86 Appendix C — Su ace slab calcula ions wi h VASP
The selec i e dynamics lag allows o de e mine which a omic posi ions a e supposed o
be kep ixed du ing a geome y op imiza ion o a ansi ion s a e sea ch using he NEB
me hod (see Sec. 2.5). Fixing, e.g., he bo om ew laye s o he su ace slab a he bulk
equilib ium la ice cons an can educe compu a ional cos conside ably and simul aneously
imp o e he con e gence pe o mance. This, howe e , has o be es ed ca e ully, as will be
explained in he ollowing sec ion. Simila ly, he numbe o a oms pe su ace laye depends
on he speci ics o he p oblem one is in e es ed in. In he p esen wo k 4x4 a oms pe laye
we e necessa y o a oid in e ac ions be ween ada oms in adjacen uni cells.
C.3 Slab calcula ions
P io o any slab calcula ion one has o de e mine he numbe o k-poin s ha yield accu a e
esul s a easonable compu a ional cos . In he di ec ion no mal o he su ace one k-poin
is usually su icien
1
. In he wo o he di ec ions one can s a wi h he bulk alues and hen
es con e gence o he ee ene gy when dec easing he alue along hese wo di ec ions. Fo
he 4x4x4 a oms su ace slabs a 5x5x1 k-poin mesh was used h oughou all calcula ions.
620
625
630
635
640
645
650
655
660
2 3 4 5 6 7 8 9
su ace ene gy/a om [meV]
numbe o laye s
un elaxed
elaxed
Figu e C.3: Su ace ene gy pe a om o a 2x2 a oms
pe laye P (111) slab as a unc ion o he numbe
o laye s.
One hen has o de e mine how many
laye s o bulk a e necessa y o ge con-
e ged esul s o he su ace ene gy
σ=1
2(Eslab −MEbulk),(C.3)
whe e
Eslab
is he ee ene gy o he slab,
Ebulk
is he ee ene gy pe a om o he
bulk sys em and
M
is he numbe o a oms
used o cons uc ion o he su ace slab.
The ac o 1
/
2 a ises as a consequence
o he su ace slab ha ing wo su aces.
Fig. C.3 depic s
σ
pe a om as a unc ion
o he numbe o laye s (using 4 a oms
pe laye ) o a P (111) su ace slab. As
16 a oms pe laye we e used o he inal calcula ions, a minimum numbe o 4 laye s is
chosen. No e, ha e en his seemingly small se up yields uni cells con aining 64 a oms
which in he case o a pu e P slab, using he PAW me hod o desc ibe he elec on-ion
in e ac ion (see Sec. 2.4), co esponds o a o al o 640 elec ons. The compu a ional cos
can be educed by ixing he bo om wo laye s a he equilib ium la ice pa ame e o he
bulk using VASP’s selec i e dynamics lag. I was es ed ha eac ion ba ie s change only
insigni ican ly as compa ed o a ull elaxa ion o he slab.
1
Using mo e han one k-poin in his di ec ion only imp o es he desc ip ion o he in e ac ion be ween
adjacen uni cells ha has o be minimized anyway by choosing an adequa e amoun o acuum space in
be ween neighbo ing slabs.

C.3. Slab calcula ions 87
-164.5175
-164.5170
-164.5165
-164.5160
-164.5155
-164.5150
5 10 15 20 25 30 35
ene gy [eV]
acuum heigh [Å]
ee
Figu e C.4: F ee ene gy o a 2x2x7 P (111) su ace
slab as a unc ion o he acuum be ween adjacen
uni cells.
Finally, he con e gence wi h espec o
he acuum heigh in be ween neighbo ing
slabs has o be es ed. Fig. C.4 shows he
ee ene gy o a 2x2x7 laye P (111) slab as
a unc ion o acuum heigh . Fo he inal
calcula ions a acuum heigh o 20
˚
A was
chosen.
The ini ial and inal con igu a ion be-
ween which he NEB algo i hm is supposed
o ind a ansi ion s a e, ha e o be elaxed
p io o se ing up he NEB calcula ion. The
ini ial guess o he elas ic band can be a
linea in e pola ion be ween s a and end
con igu a ion. I one is in e es ed in he en-
e gy o he saddle poin i is ecommended
o use he CI-NEB oge he wi h a mini-
mum amoun o elas ic band images. Fo he simple di usion s ep conside ed in case o
he Au-P su aces one single image was su icien o de e mine he eac ion ba ie . Using
h ee ins ead o one image did no change he heigh o he ba ie signi ican ly. Howe e ,
i a u h ul map o he MEP is equi ed, mo e images migh be necessa y depending on
he pa icula s o he sys em one is in e es ed in. A ypical inpu ile used o he NEB
calcula ions p esen ed in Sec. 3.4 is
SYSTEM = P /P (111) #inse sys em name
ENCUT = 450 #plane wa e cu o
ISTART = 0 #s a calcula ion om sc a ch
ISPIN = 2 #allow spin pola ized solu ion
PREC = accu a e #con ols se e al p ecision pa ame e s
# elax
NSW = 100 #maximum o 100 ionic s eps
IBRION = 2 #conjuga e g adien algo i hm
EDIFFG = -0.02 # elax ole ance
SPRING = -5 # u ns on NEB
IMAGES = 1 #numbe o images
LCLIMB = .TRUE. # u n on CI-NEB
IALGO=48 #algo i hm o elec onic elaxa ion
LREAL=au o #p ojec ion ope a o s e alua ed in eal space
LCHARG=.TRUE. #w i e elec onic densi y
LWAVE=.TRUE. #w i e wa e unc ions
# hese can be u ned o i memo y is an issue
Lis o abb e ia ions
AEMH 2-amino-e hyl-me hac yla e
Au Gold
(CI)-NEB (Climbing-image)-Nudged Elas ic Band
DFT Densi y Func ional Theo y
GGA Gene alized g adien app oxima ion
(G)KS (Gene alized) Kohn-Sham
HOMO Highes occupied (gene alized) Kohn-Sham o bi al
LDA Local densi y app oxima ion
LUMO Lowes unoccupied (gene alized) Kohn-Sham o bi al
MEP Minimum ene gy pa h
Mn Manganese
MD Molecula dynamics
Ni Nickel
NP Nanopa icle(s)
OEP Op imized e ec i e po en ial
PAW P ojec o augmen ed wa es
PBE xc unc ional o Pe dew, Bu ke and E nze ho
Pd Palladium
P Pla inum
RSH Range-sepa a ed hyb id
SIC Sel -in e ac ion co ec ion
SIE Sel -in e ac ion e o
Si Silicon
SVP Spli alence basis se
TZVPP T iple-ζbasis se
VASP Vienna-Ab-ini io-Simula ion Package
XAS X- ay abso p ion spec oscopy
xc exchange-co ela ion
XMCD X- ay magne ic ci cula dich oism
XRD X- ay di ac ion
Lis o Publica ions
1.
V. Zamudio-Baye ,
L. Leppe
, K. Hi sch, A. Langenbe g, J. Ri mann, M. Kossick,
R. Rich e , A. Te asaki, T. M¨olle , B. . Issendo , S. K¨ummel, and J. T. Lau.
Coo dina ion-d i en magne ic- o-nonmagne ic ansi ion in manganese-doped silicon
clus e s. Phys. Re . B, 88, 115425 (2013).
2. L. Leppe
, R. Q. Albuque que, A. S. Fos e , and S. K¨ummel. The in e play o
elec onic s uc u e and a omic mobili y in nanoalloys o Au and P . J. Phys. Chem.
C117, 17268 (2013).
3. L. Leppe
, R. Q. Albuque que, and S. K¨ummel. Gold-pla inum alloys and Vega d’s
law on he nanoscale. Phys. Re . B, 86, 241403(R) (2012).
4.
J. Kaise ,
L. Leppe
, H. Welz, F. Polze , S. Wunde , N. Wande ka, M. Alb ech ,
T. Lunkenbein, J. B eu, S. K¨ummel, Y. Lu, and M. Ballau . Ca aly ic ac i i y o
nanoalloys om gold and palladium. Phys. Chem. Chem. Phys. 14, 6487 (2012).
5. L. Leppe
, S. K¨ummel. The Elec onic S uc u e o Gold-Pla inum Nanopa icles:
Collec ing Clues o Why They A e Special. J. Phys. Chem. C 115, 6694 (2011).

Re e ences
[1] R. Pool, “Clus e s: S ange Mo sels o Ma e ”, Science 248, 1186 (1990).
[2]
H. H¨akkinen, “A omic and elec onic s uc u e o gold clus e s: unde s anding lakes,
cages and supe a oms om simple concep s.”, Chem. Soc. Re . 37, 1847 (2008).
[3]
J. A. Alonso, “Elec onic and a omic s uc u e, and magne ism o ansi ion-me al
clus e s.”, Chem. Re . 100, 637 (2000).
[4]
M. Ha u a, “Size- and suppo -dependency in he ca alysis o gold”, Ca al. Today
36, 153 (1997).
[5]
M. Ha u a, T. Kobayashi, H. Sano, and N. Yamada, “No el Gold Ca alys s o he
oxida ion o ca bon monoxide a a empe a u e a below 0
◦
C”, Chem. Le ., 405
(1987).
[6]
P. Pyykk¨o, “Theo e ical chemis y o gold.”, Ang. Chem. (In . Ed.)
43
, 4412 (2004).
[7]
A. Sanchez, S. Abbe , U. Heiz, W.-D. Schneide , H. H¨akkinen, R. N. Ba ne , and
U. Landman, “When gold is no noble: nanoscale gold ca alys s”, J. Phys. Chem. A
103, 9573 (1999).
[8]
A. A. He zing, C. J. Kiely, A. F. Ca ley, P. Landon, and G. J. Hu chings, “Iden i i-
ca ion o ac i e gold nanoclus e s on i on oxide suppo s o CO oxida ion.”, Science
321, 1331 (2008).
[9]
M. J. Walsh, K. Yoshida, A. Kuwaba a, M. L. Pay, P. L. Gai, and E. D. Boyes,
“On he s uc u al o igin o he ca aly ic p ope ies o inhe en ly s ained ul asmall
decahed al gold nanopa icles.”, Nano Le . 12, 2027 (2012).
[10]
A. S. K. Hashmi, “Gold-ca alyzed o ganic eac ions.”, Chem. Re .
107
, 3180 (2007).
[11]
I. M. Billas, A Chˆa elain, and W. A. de Hee , “Magne ism om he a om o he
bulk in i on, cobal , and nickel clus e s.”, Science 265, 1682 (1994).
[12]
I. M. L. Billas, A. Chˆa elain, and W. A. de Hee , “Magne ism o Fe , Co and Ni
clus e s in molecula beams”, J. Magn. Magn. Ma e . 168, 64–84 (1997).
[13]
M. Niemeye , K. Hi sch, V. Zamudio-Baye , A. Langenbe g, M. Vogel, M. Kossick,
C. Eb ech , K. Egashi a, A. Te asaki, T. M¨olle , B. . Issendo , and J. Lau, “Spin
coupling and o bi al angula momen um quenching in ee i on clus e s”, Phys. Re .
Le . 108, 057201 (2012).
94 Re e ences
[14]
W. Kohn, “Nobel Lec u e: Elec onic s uc u e o ma e - wa e unc ions and densi y
unc ionals”, Re . Mod. Phys. 71, 1253 (1999).
[15]
P. Hohenbe g and W. Kohn, “Inhomogeneous elec on gas”, Phys. Re .
136
, B864
(1964).
[16]
W. Kohn and L. J. Sham, “Sel -consis en equa ions including exchange and co ela-
ion e ec s”, Phys. Re . 385, A1133 (1965).
[17]
E. Engel and R. M. D eizle , Densi y Func ional Theo y - An Ad anced Cou se
(Sp inge , Be lin, Heidelbe g, 2011).
[18]
S. K¨ummel and L. K onik, “O bi al-dependen densi y unc ionals: Theo y and
applica ions”, Re . Mod. Phys. 80, 3 (2008).
[19]
D. M. Cepe ley and B. J. Alde , “G ound s a e o he elec on gas by a s ochas ic
me hod”, Phys. Re . Le . 45, 566 (1980).
[20]
S. H. Vosko, L. Wilk, and M. Nusai , “Accu a e spin-dependen elec on liquid
co ela ion ene gies o local spin densi y calcula ions: a c i ical analysis”, Can. J.
Phys. 58, 1200 (1980).
[21]
J. P. Pe dew and A. Zunge , “Sel -in e ac ion co ec ion o densi y unc ional ap-
p oxima ions o many-elec on sys ems”, Phys. Re . B 23, 5048 (1981).
[22]
J. P. Pe dew and Y. Wang, “Accu a e and simple analy ic ep esen a ion o he
elec on-gas co ela ion ene gy”, Phys. Re . B 45, 13244 (1992).
[23]
O. Gunna sson and B. I. Lundq is , “Exchange and co ela ion in a oms, molecules,
and solids by he spin-densi y- unc ional o malism”, Phys. Re . B
13
, 4274 (1976).
[24]
J. P. Pe dew, K. Bu ke, and M. E nze ho , “Gene alized G adien App oxima ion
made simple.”, Phys. Re . Le . 77, 3865 (1996).
[25]
A. D. Becke, “Densi y- unc ional exchange-ene gy app oxima ion wi h co ec asymp-
o ic beha io ”, Phys. Re A 38, 3098 (1988).
[26]
C. Lee, W. Yang, and R. Pa , “De elopmen o he Colle-Sal e i co ela ion-ene gy
o mula in o a unc ional o he elec on densi y”, Phys. Re . B 37, 785 (1988).
[27]
L. H. Thomas, “The calcula ion o a omic ields”, P oc. Camb idge Philos. Soc.
23
,
542 (1927).
[28]
E. Fe mi, “Eine s a is ische Me hode zu Bes immung einige Eigenscha en des
A oms und ih e Anwendung au die Theo ie des pe iodischen Sys ems de Elemen e”,
Z. Phys. 48, 73 (1928).
[29]
J. P. Pe dew, “O bi al unc ional o exchange and co ela ion: sel -in e ac ion
co ec ion o he local densi y app oxima ion”, Chem. Phys. Le . 64, 127 (1979).
[30]
J. B. K iege , Y. Li, and G. J. Ia a e, “Cons uc ion and applica ion o an accu a e
local spin-pola ized Kohn-Sham po en ial wi h in ege discon inui y: Exchange-only
heo y”, Phys. Re . A 45, 101 (1992).
[31]
T. K¨o zd¨o e , S. K¨ummel, and M. Mund , “Sel -in e ac ion co ec ion and he
op imized e ec i e po en ial.”, J. Chem. Phys. 129, 014110 (2008).
Re e ences 95
[32]
T. K¨o zd¨o e , S. K¨ummel, N. Ma om, and L. K onik, “When o us pho oelec on
spec a om Kohn-Sham eigen alues: The case o o ganic semiconduc o s”, Phys.
Re . B 79, 201205 (2009).
[33]
T. K¨o zd¨o e , S. K¨ummel, N. Ma om, and L. K onik, “E a um: When o us pho-
oelec on spec a om Kohn-Sham eigen alues: The case o o ganic semiconduc o s”,
Phys. Re . B 82, 129903 (2010).
[34]
M. Johansson, A. Lech ken, D. Schooss, M. Kappes, and F. Fu che, “2D-3D ansi ion
o gold clus e anions esol ed”, Phys. Re . A 77, 053202 (2008).
[35]
J. Tao, J. Pe dew, V. S a o e o , and G. Scuse ia, “Climbing he densi y unc ional
ladde : nonempi ical me a-gene alized g adien gpp oxima ion designed o molecules
and solids”, Phys. Re . Le . 91, 146401 (2003).
[36]
A. D. Becke, “A new mixing o Ha ee-Fock and local densi y- unc ional heo ies”,
J. Chem. Phys. 98, 1372 (1993).
[37]
M. Le y, “Elec on densi ies in sea ch o Hamil onians”, Phys. Re . A
26
, 1200
(1982).
[38]
J. P. Pe dew, M. E nze ho , and K. Bu ke, “Ra ionale o mixing exac exchange
wi h densi y unc ional app oxima ions”, J. Chem. Phys. 105, 9982 (1996).
[39]
C. Adamo and V. Ba one, “Towa d eliable densi y unc ional me hods wi hou
adjus able pa ame e s: The PBE0 model”, J. Chem. Phys. 110, 6158 (1999).
[40]
A. D. Becke, “Densi y- unc ional he mochemis y. IV. A new dynamical co ela ion
unc ional and implica ions o exac -exchange mixing”, J. Chem. Phys.
104
, 1040
(1996).
[41]
P. J. S ephens, F. J. De lin, C. F. Chabalowski, and M. J. F isch, “Ab Ini io
Calcula ion o Vib a ional Abso p ion and Ci cula Dich oism Spec a Using Densi y
Func ional Fo ce Fields”, J. Phys. Chem. 98, 11623 (1994).
[42]
M. Roh danz and J. He be , “Simul aneous benchma king o g ound- and exci ed-
s a e p ope ies wi h long- ange-co ec ed densi y unc ional heo y.”, J. Chem. Phys.
129, 034107 (2008).
[43]
T. M. Hende son, B. G. Janesko, and G. E. Scuse ia, “Gene alized g adien app ox-
ima ion model exchange holes o ange-sepa a ed hyb ids.”, J. Chem. Phys.
128
,
194105 (2008).
[44]
L. K onik, T. S ein, S. Re aely-Ab amson, and R. Bae , “Exci a ion Gaps o Fini e-
Sized Sys ems om Op imally Tuned Range-Sepa a ed Hyb id Func ionals”, J. Chem.
Theo y Comp. 8, 1515 (2012).
[45]
A. Seidl, A. G¨o ling, P. Vogl, J. A. Majewski, and M. Le y, “Gene alized Kohn-Sham
schemes and he band-gap p oblem.”, Phys. Re . B 53, 3764 (1996).
[46]
A. G¨o ling, “Densi y- unc ional heo y o exci ed s a es”, Phys. Re . A
54
, 3912
(1996).
102 Re e ences
[142]
F. Pi away, L. O. Paz-Bo bon, R. L. Johns on, H. A slan, R. Fe ando, C. Mo e ,
G. Ba ca o, and A. Fo unelli, “Theo e ical S udies o Palladium-Gold Nanoclus e s:
Pd-Au Clus e s wi h up o 50 A oms”, J. Phys. Chem. C 113, 9141 (2009).
[143]
H. H¨akkinen, S. Abbe , A. Sanchez, U. Heiz, and U. Landman, “S uc u al, elec onic,
and impu i y-doping e ec s in nanoscale chemis y: suppo ed gold nanoclus e s.”,
Ang. Chem. In . Ed. 42, 1297 (2003).
[144]
R. Gaspa i, C. Pignedoli, R. Fasel, M. T eie , and D. Passe one, “A omis ic insigh
in o he adso p ion si e selec i i y o s epped Au(111) su aces”, Phys. Re . B
82
,
041408 (2010).
[145]
S. Wunde , Y. Lu, M. Alb ech , and M. Ballau , “Ca aly ic ac i i y o ace ed gold
nanopa icles s udied by a model eac ion: e idence o subs a e-induced su ace
es uc u ing”, ACS Ca al. 1, 908 (2011).
[146]
E. C. Be e , L. M. Ghi inghelli, and M. Sche le , “F ee gold clus e s: beyond he
s a ic, monos uc u e desc ip ion”, Fa aday Discuss. 152, 153 (2011).
[147]
H. Ohno, A. Shen, F. Ma suku a, A. Oiwa, A. Endo, S. Ka sumo o, and Y. Iye,
“(Ga,Mn)As: A new dilu ed magne ic semiconduc o based on GaAs”, Appl. Phys.
Le . 69, 363 (1996).
[148]
G. W. Ludwig and H. H. Woodbu y, “Elec on Spin Resonance in Semiconduc o s”,
Solid S a e Phys.
13
, edi ed by H. Eh en eich, F. Sei z, and D. Tu nbull, 223 (1962).
[149]
F. Beele , O. K. Ande sen, and M. Sche le , “Elec onic and magne ic s uc u e o
3d- ansi ion-me al poin de ec s in silicon calcula ed om i s p inciples”, Phys.
Re . B 41, 1603 (1990).
[150]
H. Wu, P. K a ze , and M. Sche le , “Densi y-Func ional Theo y s udy o hal -
me allic he e os uc u es: in e s i ial Mn in Si”, Phys. Re . Le .
98
, 117202 (2007).
[151]
Z. Zhang, B. Pa oens, K. Chang, and F. Pee e s, “Fi s -p inciples s udy o ansi ion
me al impu i ies in Si”, Phys. Re . B 77, 1–8 (2008).
[152]
M. Shaughnessy, C. Y. Fong, R. Snow, K. Liu, J. E. Pask, and L. H. Yang, “O igin
o la ge momen s in MnxSi1−xa small x”, Appl. Phys. Le . 95, 022515 (2009).
[153]
F. K¨uwen, R. Lei smann, and F. Bechs ed , “Mn and Fe doping o bulk Si: Concen-
a ion in luence on elec onic and magne ic p ope ies”, Phys. Re . B
80
, 045203
(2009).
[154]
L. Zeng, J. Cao, E. Helg en, J. Ka el, E. A enholz, L. Ouyang, D. Smi h, R. Wu, and
F. Hellman, “Dis inc local elec onic s uc u e and magne ism o Mn in amo phous
Si and Ge”, Phys. Re . B 82, 165202 (2010).
[155]
X. Huang, A. Makmal, J. Chelikowsky, and L. K onik, “Size-dependen spin onic
p ope ies o dilu e magne ic semiconduc o nanoc ys als”, Phys. Re . Le .
94
,
236801 (2005).
[156]
R. Lei smann, C. Panse, F. K¨uwen, and F. Bechs ed , “Ab ini io cha ac e iza ion o
ansi ion-me al-doped Si nanoc ys als”, Phys. Re . B 80, 104412 (2009).

Re e ences 103
[157]
X. Chen, X. Pi, and D. Yang, “Silicon nanoc ys als doped wi h subs i u ional o
in e s i ial manganese”, Appl. Phys. Le . 99, 193108 (2011).
[158]
S. Khanna, B. Rao, and P. Jena, “Magic numbe s in me allo-ino ganic clus e s:
Ch omium encapsula ed in Silicon cages”, Phys. Re . Le . 89, 016803 (2002).
[159]
W. Zheng, J. M. Nilles, D. Radisic, and K. H. Bowen, “Pho oelec on spec oscopy
o ch omium-doped silicon clus e anions.”, J. Chem. Phys. 122, 071101 (2005).
[160]
L.-J. Guo, G.-F. Zhao, Y.-Z. Gu, X. Liu, and Z. Zeng, “Densi y- unc ional in es iga-
ion o me al-silicon cage clus e s MSi
n
(M=Sc, Ti, V, C , Mn, Fe, Co, Ni, Cu, Zn;
n=8-16)”, Phys. Re . B 77, 195417 (2008).
[161]
V. T. Ngan, E. Janssens, P. Claes, J. T. Lyon, A. Fielicke, M. T. Nguyen, and
P. Lie ens, “High magne ic momen s in Manganese-doped Silicon clus e s.”, Chem.
Eu . J. 18, 15788 (2012).
[162]
D. Palagin and K. Reu e , “E alua ion o endohed al doping o hyd ogena ed Si
ulle enes as a ou e o magne ic Si building blocks”, Phys. Re . B
86
, 045416 (2012).
[163]
F. Male and P. Go i-Gio gi, “S ong co ela ion in Kohn-Sham Densi y Func ional
Theo y”, Phys. Re . Le . 109, 246402 (2012).
[164]
O. V. G i senko, P. R. T. Schippe , and E. J. Bae ends, “Exchange and co ela ion
ene gy in densi y unc ional heo y: Compa ison o accu a e densi y unc ional
heo y quan i ies wi h adi ional Ha ee-Fock based ones and gene alized g adien
app oxima ions o he molecules Li2, N2, F2”, J. Chem. Phys. 107, 5007 (1997).
[165]
P. Mo i-S´anchez, A. J. Cohen, and W. Yang, “Many-elec on sel -in e ac ion e o in
app oxima e densi y unc ionals.”, J. Chem. Phys. 125, 201102 (2006).
[166]
J. P. Pe dew, R. G. Pa , M. Le y, and J. L. Balduz, “Densi y Func ional Theo y
o ac ional pa icle numbe : De i a i e Discon inui ies o he Ene gy”, Phys. Re .
Le . 4, 1691 (1982).
[167]
J.-D. Chai and P.-T. Chen, “Res o a ion o he de i a i e discon inui y in Kohn-Sham
Densi y Func ional Theo y: an e icien scheme o ene gy gap co ec ion”, Phys.
Re . Le . 110, 033002 (2013).
[168]
A. J. Cohen, P. Mo i-S´anchez, and W. Yang, “Challenges o Densi y Func ional
Theo y”, Chem. Re . 112, 289 (2012).
[169] K. Hi sch, P i a e communica ion, 2013.
[170]
K. Hi sch, J. T. Lau, P. Kla , A. Langenbe g, J. P obs , J. Ri mann, M. Vogel,
V. Zamudio-Baye , T. M¨olle , and B. on Issendo , “X- ay spec oscopy on size-
selec ed clus e s in an ion ap: om he molecula limi o bulk p ope ies”, J. Phys.
B42, 154029 (2009).
[171] Ph.D. hesis o V. Zamudio-Baye a Technische Uni e si ¨a Be lin.
[172]
B. T. Thole, P. Ca a, F. Se e, and G. an de Laan, “X-Ray Ci cula Dich oism as
a p obe o o bi al magne iza ion”, Phys. Re . Le . 68, 1943 (1992).
104 Re e ences
[173]
P. Ca a, B. T. Thole, A. Massimo, X. X. Wang, and M. Al a elli, “X-Ray Ci cula
Dich oism and local magne ic ields”, Phys. Re . Le . 70, 694 (1993).
[174]
Y. Shao, L. F. Molna , Y. Jung, J. Kussmann, C. Ochsen eld, S. T. B own, A. T. B.
Gilbe , and e al., “Ad ances in me hods and algo i hms in a mode n quan um
chemis y p og am package”, Phys. Chem. Chem. Phys. 8, 3172 (2006).
[175]
H. Wu, M. Ho amani, P. K a ze , and M. Sche le , “Fi s -P inciples s udy o
e omagne ism in epi axial Si-Mn hin ilms on Si(001)”, Phys. Re . Le .
92
,
237202 (2004).
[176]
Q. Wang, Q. Sun, J. Z. Yu, Y. Hashi, and Y. Kawazoe, “Fi s -p inciples s udies
on magne ism o Ni clus e s coa ed and alloyed wi h Pd”, Phys. Le . A
267
, 394
(2000).
[177]
A. Chu ia and M. Tokuyama, “O bi al in e ac ion and local s abili y o Ni subs i u ed
Pd nanoalloys”, Chem. Phys. Le . 515, 96 (2011).
[178]
V. Fo s e , “S uk u und Eigenscha en on Nickel-Palladium Clus e n”, Bachelo
hesis (Uni e si y o Bay eu h, 2012).
[179]
T. Ascheb ock, “Kons uk ionsp inzip und Tes on i s -p inciples Pseudopo en-
ialen”, Bachelo hesis (Uni e si y o Bay eu h, 2012).
[180]
J. He mannsd¨o e , M. F ied ich, N. Miyajima, R. Q. Albuque que, S. K¨ummel,
and R. Kempe, “Ni/Pd@MIL-101: Syne ge ische Ka alyse mi ka i ¨a enkon o men
Ni/Pd-Nanopa ikeln”, Ang. Chem. 124, 11640 (2012).
[181]
P.-P. Fang, A. Ju and, Z.-Q. Tian, and C. Ama o e, “Au-Pd co e-shell nanopa icles
ca alyze Suzuki-Miyau a eac ions in wa e h ough Pd leaching”, Ang. Chem. In .
Ed. 123, 12184 (2011).
[182]
S. Nos´e, “A uni ied o mula ion o he cons an empe a u e molecula dynamics
me hods”, J. Chem. Phys. 81, 511 (1984).
[183]
W. G. Hoo e , “Canonical dynamics: Equilib ium phase-space dis ibu ions”, Phys.
Re . A 31, 1695 (1985).
[184] Tu bomole, V6.4.2 (2012).
[185]
S. G imme, “Accu a e desc ip ion o an de Waals complexes by densi y unc ional
heo y including empi ical co ec ions”, J. Comp. Chem. 25, 1463 (2004).
[186]
M. Fa aday, “The Bake ian Lec u e: Expe imen al ela ions o Gold (and o he
me als) o ligh ”, Phil. T ans. R. Soc. Lond. 147, 145 (1857).
[187]
U. K eibig and M. Vollme , Op ical P ope ies o Me al Clus e s, edi ed by P. Toennies
(Sp inge -Ve lag, Be lin, Heidelbe g, 1995).
[188]
G. Mie, “Bei ¨age zu Op ik ¨ube Medien, speziell kolloidale Me alll¨osungen”,
Ann. Phys. 25 (1908).
[189]
E. D. Palik, Handbook o Op ical Cons an s o Solids (Academic P ess, New Yo k,
1985).
Re e ences 105
[190]
J. H. Wea e , “Op ical p ope ies o Rh, Pd, I , and P ”, Phys. Re . B
11
, 1416
(1975).
[191] A. Henglein, “P epa a ion and op ical abso p ion spec a o Auco eP shell and
P
co e
Au
shell
colloidal nanopa icles in aqueous solu ion”, J. Phys. Chem. B
104
,
2201 (2000).
[192]
L. M. Liz-Ma zan and A. P. Philipse, “S able hyd osols o me allic and bime allic
nanopa icles immobilized on imogoli e ibe s”, J. Phys. Chem. 99, 15120 (1995).
[193]
M. Gaud y, E. Co ancin, M. Pella in, J. Le m´e, L. A naud, J. Hun zinge , J. Vialle,
M. B oye , J. Rousse , M. T eilleux, and P. M´elinon, “Size and composi ion depen-
dence in he op ical p ope ies o mixed ( ansi ion me al/noble me al) embedded
clus e s”, Phys. Re . B 67, 155409 (2003).
[194]
A. L. Aden and M. Ke ke , “Sca e ing o elec omagne ic wa es om wo concen ic
sphe es”, J. Appl. Phys. 22, 1242 (1951).
Acknowledgmen
I hank he ollowing people o hei help and suppo wi h his hesis:
S ephan K¨
ummel
. I ha e i on good au ho i y, ha
≈
8.23 ou o 10 o my sen-
ences du ing an a e age week in he las couple o yea s s a ed wi h ”S ephan says ha ...”.
I hank him o he mos inspi ing quan um mechanics lec u e o all ime (in my second
yea o unde g adua e s udy), o con incing me o s ay jus a li le bi longe in Bay eu h
(in my hi d and i h yea ) and o all he ad ice, discussions and pa ience du ing he las
yea s ha we e o ines imable alue o me.
Rod igo Albuque que
, who has been inc edibly pa ien in pe o ming ye ano he
molecula dynamics un. I hank him o inspi ing discussions abou he bime allic e ec in
Au-P nanoalloys, aluable insigh in o molecula dynamics simula ions and his indes uc ible
en husiasm o ou p ojec .
Adam Fos e
, o always lending a hand when i came o Nudged Elas ic Band
calcula ions. I enjoyed his and his g oup’s hospi ali y in Tampe e, Finland, o six win e ly
weeks and lea ned a lo abou VASP, ansi ion s a e sea ch and (no so) Finnish bee .
Tobias Lau
and
Vicen e Zamudio-Baye
, o coun less physics discussions, he mos
amusing science gossip, a desk in Tobias’ o ice whene e I a eled o Be lin, o mo e
suppo han I e e expec ed o ecei e and o le ing me con ince hem ha DFT can
ac ually be a lo o un.
And eas Ka olewski
has been my bes iend o he las 8 yea s and he bes o ice
is-`a- is one could wish o . F om physics o poli ics and especially ”beyond”; he e is li le
ha And eas does no know abou . He always imp essed me wi h his g ea cu iosi y and
s amina. Besides, he’s jus p e y cool.
Ma hias Dau h
,
Tobias Schmid
and all he o he membe s and alumni o he
K¨
ummel g oup
. I hank you o making hese las yea s mos exci ing and ins uc i e
bu i s and o emos o making hem an aw ul lo o un. Fu he mo e, I hank And eas,
Ma hias and Tobias o hei ho ough p oo - eading o pa s o his hesis.
Ma kus Hil
,
Be nha d Winkle
and
Monika Bi kelbach
o echnical and ad-
minis a i e suppo whene e i was needed.
My amily, bu especially
Ka ena
and
J¨
o g
, he second physicis in he amily, who
a oused an ea ly in e es o physics in me.
Kons an in Hi sch
, o pa ien p oo - eading o his hesis and o many help ul
commen s, ad ice and discussion. Mos o all, I wan o hank him o p o ing an easy and
a di icul hing o me, ha changed my li e in coun less ways: 1. Only a physicis can be a
physicis . 2. All can be well.
Fo inancial and in ellec ual suppo I am g a e ul o he
SFB 840
o he DFG, he
Wilhelm und Else He aeus S i ung
and he
Eli e S udy P og amme Mac o-
molecula Science.

E kl¨a ung
Hie mi e kl¨a e ich, dass ich die o liegende A bei selbs s ¨andig e ass und keine ande en
als die angegebenen Quellen und Hil smi el e wende habe. Die A bei wu de wede
in gleiche noch in ¨ahnliche Fo m bei ande en P ü ungsbehö den zu E langung eines
akademischen G ades o geleg .
Ich e kl¨a e, dass ich keine Hil e on gewe blichen P omo ionsbe a e n bzw. - e mi le n
ode ¨ahnlichen Diens leis e n in Ansp uch genommen habe und auch nich beabsich ige
diese zuk¨un ig in Ansp uch zu nehmen.
Wei e hin e kl¨a e ich, dass ich bishe keinen ande wei igen P omo ions e such un e nommen
habe.
Bay eu h, den 29. Mai 2013 Linn Leppe