S e ic Hind ance o NH3Di usion on P (111) by Co-Adso bed
O‑A oms
Dmi iy Bo odin,*Oihana Galpa so o, Igo Rahino , Jan Finge hu , Michael Schwa ze , S e an Hö andl,
Daniel J. Aue bach, Alexande Kand a senka, Di k Schwa ze , Theo anis N. Ki sopoulos,*
and Alec M. Wod ke*
Ci e This: J. Am. Chem. Soc. 2022, 144, 21791−21799
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sı Suppo ing In o ma ion
ABSTRACT: A de ailed eloci y- esol ed kine ics s udy o NH3
he mal deso p ion a es om p(2 ×2) O/P (111) is p esen ed.
We ind a la ge educ ion in he NH3deso p ion a e due o
adso p ion o O-a oms on P (111). A physical model desc ibing
he in e ac ions be ween adso bed NH3and O-a oms explains
hese obse a ions. By i ing he model o he de i ed deso p ion
a e cons an s, we ind an NH3s abiliza ion on p(2 ×2)
O/P (111) o 0.147−0.014
+0.023 eV compa ed o P (111) and a o a ional
ba ie o 0.084−0.022
+0.049 eV, which is no p esen on P (111). The
model also quan i a i ely p edic s he s e ic hind ance o NH3
di usion on P (111) due o co-adso bed O-a oms. The de i ed
di usion ba ie o NH3on p(2 ×2) O/P (111) is 1.10−0.13
+0.22 eV,
which is 0.39−0.14
+0.22 eV highe han ha on p is ine P (111). We ind
ha Pe dew Bu ke E nze ho (PBE) and e ised Pe dew Bu ke E nze ho (RPBE) exchange−co ela ion unc ionals a e unable o
ep oduce he expe imen ally obse ed NH3−O adso ba e−adso ba e in e ac ions and NH3binding ene gies a P (111) and p(2 ×
2) O/P (111), which indica es he impo ance o dispe sion in e ac ions o bo h sys ems.
1. INTRODUCTION
The s udy o enzymes has p o ided us many o he
p o o ypical concep s o ca alysis, including he idea ha a
ca alys lowe s he ba ie o eac ion and he eby accele a es
he app oach o chemical equilib ium. Enzymes a e able o
bind eagen s o he ac i e si e di ec ing hem in o an
ene ge ically s abilized s uc u e ha esembles he eac ion’s
ansi ion s a e.
1−3
This ca aly ic mechanism is he esul o
millions o yea s o e olu ion ha p oduced s e ic e ec s,
o iginally desc ibed by a “lock and key” model.
3
These s e ic
e ec s success ully accele a e eac ions a he mode a e
empe a u es o li ing beings. By con as , eac ions on man-
made indus ial ca alys s using me al su aces o en de ia e
s ongly om his elegan pic u e. Indus ial ca alys s ypically
ope a e a ele a ed empe a u es enhancing he in luence o
deso p ion. Fu he mo e, he e a e no lock-and-key p ope ies
ha b ing he eac an s o he ac i e si e. Ins ead, su ace
di usion accomplishes his unc ion; hus, a eac an ’s abili y o
di use on he ca alys su ace o he ac i e si e while
compe ing agains he mal deso p ion may de e mine he
ca alys ’s ac i i y. This poin s ou he impo ance o accu a e
de e mina ion o he mal di usion coe icien s and deso p ion
a e cons an s unde ealis ic eac ion condi ions on ca aly ic
su aces.
The high co e ages p oduced unde indus ial high-p essu e
condi ions o en lead o complex s eady-s a e su ace s uc u es
in ol ing in e ac ions be ween di e en adso ba es.
5−8
As a
esul , he po en ial ene gy landscape o di usion o one
eac an may depend s ongly on he p esence (o absence) o
he o he .
9,10
De e mining his ene gy landscape and how i
depends on su ace s uc u e and adso ba e concen a ion
ep esen s a ascina ing p oblem in physical chemis y o g ea
ele ance o unde s anding ca aly ic beha io . Un o una ely,
disen angling he di usional in luences on ca aly ic ac i i y
om he con en ional ba ie - educing e ec s can be qui e
challenging, since hese no mally occu in pa allel. This is he
eason why o many impo an ca aly ic eac ions, li le is
known abou he impac o co-adso ba e in e ac ions on
eac an and ansi ion s a e ene gies and en opies. The
si ua ion is no made easie by he ac ha s a e-o - he-a
elec onic s uc u e heo y�densi y unc ional heo y (DFT)
a he le el o gene alized g adien app oxima ion (GGA)�is
Recei ed: Oc obe 2, 2022
Published: No embe 18, 2022
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unable o desc ibe an de Waals ( dW) in e ac ions ha a e
hough o be c ucially impo an o a co ec desc ip ion o
adso ba e−adso ba e in e ac ions.
11−14
Accu a ely measu ing he kine ic compe i ion o di usion
and deso p ion unde indus ially ele an high- empe a u e
condi ions has ecen ly become possible wi h he in oduc ion
o he eloci y- esol ed kine ics (VRK) me hod.
15,16
This
me hod p o ides highly accu a e deso p ion a e cons an s ha
can be modeled by s a is ical a e heo ies o yield adso ba e
binding ene gies and en opies. Recen wo k showed ha NH3
di usion on P (111) is ema kably slow, due o an
unexpec edly high di usion ba ie o 0.71 ±0.04 eV
cons i u ing ∼65% o he NH3binding ene gy o P .
17
This
called in o ques ion he wisdom o a gene ally applied
assump ion in he modeling o indus ial ca alysis ha di usion
is no a a e-de e mining p ocess.
9,18,19
Wi hin he con ex o
NH3oxida ion on P , we hypo hesized ha NH3di usion
could be u he in luenced by co-adso bed oxygen a oms on
P (111), which will be also p esen a he ca alys unde
indus ial ammonia oxida ion condi ions.
17
He e, we p esen a de ailed VRK s udy o NH3deso p ion
and di usion on p(2 ×2) O/P (111). We obse e ha when
compa ed o P (111) a he same empe a u e, he he mal
deso p ion a e is subs an ially educed. In ag eemen wi h
p e ious wo k, we ind no e idence o NH3decomposi ion o
oxida ion on P (111), which means ha he obse ed
di e ences in deso p ion a es a e a ibu ed o non eac i e
in e ac ions be ween NH3and O. The empe a u e depend-
ence o he deso p ion a e cons an s shows ha NH3binds
mo e s ongly o P (111) in he p esence o co-adso bed O-
a oms and ha he adso bed NH3en opy is subs an ially
educed. Using a nonco alen addi i e in e ac ion model (NC-
AIM) desc ibing a ac i e and epulsi e o ces ac ing be ween
NH3and O on P (111), we could ep oduce he obse ed
he mal deso p ion a es quan i a i ely o e a b oad empe -
a u e ange. In his way, he NC-AIM explains he s e ic
in e ac ions be ween adso bed O-a oms and NH3molecules.
Speci ically, NH3exhibi s a ba ie o 0.084−0.022
+0.049 eV o
o a ion abou i s N−P bond (no ba ie on P (111)), an
inc eased di usion ba ie o 1.10−0.14
+0.22 (0.71 ±0.04 eV on
P (111)), and an inc eased binding ene gy 1.28−0.02
+0.03 eV (1.13
±0.02 on P (111)). These esul s p o ide c i ical benchma ks
o i s -p inciples calcula ions o non eac i e in e ac ions
be ween NH3and O on P (111). Compa ing hese quan i ies
o DFT p edic ions e eals ha dispe sion co ec ions a e
c ucial o ob aining a chemically accu a e desc ip ion o he
ene ge ic landscape. These indings se a s ong basis o a
comp ehensi e kine ic modeling s udy o ammonia oxida ion
o he Os wald p ocess.
2. RESULTS
The me hods used in his wo k a e desc ibed in de ail in
Sec ion 5.1. B ie ly, he su ace is dosed wi h a sho molecula
beam pulse o NH3seeded in He (1%, 5 ×10−4ML/pulse)
and he lux o he mally deso bing molecules is ob ained using
spa ial ion imaging. The deso p ion lux s esidence ime is
hen eco ded a a a ie y o empe a u es be ween 473 and
573 K. The p(2 ×2) O/P (111) su ace is p epa ed by dosing
O2 om a molecula beam wi h a lux o 1.5 ±0.5 ML/s o 30
min a 573 K. To ensu e ha O-a oms do no deso b om o
di use ou o he dosing egion o he NH3beam, he O2
dosing is con inued du ing he ansien NH3deso p ion
expe imen s. These condi ions ha e been shown p e iously o
ensu e he o ma ion o he p(2 ×2) O/P (111)
s uc u e.
20−22
We also conduc ed DFT calcula ions o NH3
deso p ion and di usion pa hways on P (111) and p(2 ×2)
O/P (111) using he Pe dew Bu ke E nze ho (PBE) and
e ised Pe dew Bu ke E nze ho (RPBE) unc ionals wi h and
wi hou he inclusion o D3 co ec ion
23
o dispe sion
o ces�see Sec ion 5.2.
Figu e 1a compa es ypical kine ic aces o ammonia
deso bing om p(2 ×2) O/P (111) and p is ine P (111).
17
The kine ic aces exhibi wo componen s� empe a u e-
independen di ec sca e ing (DS) and empe a u e-depend-
Figu e 1. (a) Kine ic aces o NH3deso bing om p(2 ×2) O/P (111) ( ed ci cles: expe imen ; ed line: i o eq 1) and om p is ine P (111)
(black c osses: expe imen ; black lines: i o eq 1) a ou su ace empe a u es. The empo al esolu ion o he expe imen is ∼40 μs. All kine ic
aces a e ob ained a cons an lase powe and beam lux allowing compa ison o deso p ion yields di ec ly�see he ex . (b) A henius plo o
expe imen al NH3deso p ion a e cons an s: om p(2 ×2) O/P (111) and p is ine P (111) as ob ained om da a in panel (a). The dashed lines
a e he co esponding A henius i s o he expe imen al a e cons an s. The inse s show he pa ame e dis ibu ions (black: P (111); ed: p(2 ×2)
O/P (111)) o he ac i a ion ene gy Ea(uppe igh ) and he decadic loga i hm o he p e ac o A(lowe le ).
Jou nal o he Ame ican Chemical Socie y pubs.acs.o g/JACS A icle
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J. Am. Chem. Soc. 2022, 144, 21791−21799
21792
en apping deso p ion (TD). The DS componen peaks a
ze o esidence ime and becomes mo e e iden wi h dec easing
su ace empe a u e. This is because he TD componen
becomes empo ally dilu ed due o an inc eased a e age
esidence ime on he su ace. The TD componen is an
exponen ial decay in bo h sys ems, and he VRK measu e-
men s show ha NH3deso p ion is 3−6 imes slowe on p(2 ×
2) O/P (111), compa ed o he oxygen- ee P (111).
Ammonia decomposi ion and oxida ion p oduc s (e.g., NO,
N2, H2, N2O, and H2O) a e absen in ou expe imen s bo h o
p is ine and oxygen-co e ed P (111). Fu he mo e, we obse e
no a ia ion in he ammonia deso p ion a e o e a long
exposu e ime, indica ing ha buildup o decomposi ion
p oduc s on he su ace does no ake place. We conclude
ha he di e ences in NH3deso p ion a es o he wo
su aces a e exclusi ely due o adso ba e−adso ba e in e -
ac ions a P (111) e aces.
The kine ic aces o ammonia deso p ion we e i by he
ollowing exp ession:
= × + × a b k( ) DS( ) TD( , ).
d
(1)
He e, he empe a u e-independen DS componen ollows
he empo al p o ile o he molecula beam, wi h he pa ame e
adesc ibing i s ampli ude. The su ace empe a u e-depend-
en , TD componen is cha ac e ized by he ampli ude band
deso p ion a e cons an kdeme ging om he mally deso bing
NH3molecules ha ha e been adso bed and he malized a he
su ace. We also ob ain he NH3deso p ion yield� eloci y
and ime in eg a ed TD con ibu ion (∝b/kd om eq 1). We
ind ha be ween 473 and 573 K he deso p ion yield om he
oxygen-co e ed su ace amoun s o 93 ±15% o he p is ine
P (111), indica ing ha NH3’s s icking coe icien is almos
una ec ed by he p esence o he p(2 ×2) O-a om o e laye .
This conclusion is u he suppo ed by he indis inguishable,
sub he mal speed dis ibu ions o deso bing NH3molecules
om p(2 ×2) O/P and clean P (111). F om he p inciple o
de ailed balance, his indica es ha he ini ial s icking
p obabili y has he same ansla ional ene gy dependence in
bo h cases�see e 17�and is no a ec ed by adso bed O-
a oms. In e es ingly, hese esul s a e consis en wi h he
obse a ions o King and co-wo ke s o NH3s icking a O-
co e ed P (100).
24
By i ing he A henius exp ession o he de i ed deso p ion
a e cons an s (Figu e 1b), we ind ha O-a om adso p ion o
he P (111) su ace al e s he p e ac o and he ac i a ion
ene gy, Aand Ea, o deso p ion om clean P (111)�Ea=
1.08 ±0.02 eV and A= 1014.8 ±0.2 s−1�compa ed o oxygen-
co e ed P (111)�Ea= 1.21 ±0.02 eV and A= 1015.3 ±0.2 s−1.
The highe ac i a ion ene gy o NH3deso p ion om p(2 ×2)
O/P (111) indica es ha i binds mo e s ongly o he su ace
due o he p esence o co-adso bed O-a oms. The highe
p e ac o indica es ha he O-a om o e laye educes he
en opy o he NH3adso ba e. I is impo an o ealize ha
ac i a ion ene gies o deso p ion a e equal o adso p ion
en halpies, which a e s ic ly empe a u e-dependen quan i-
ies. By modeling he deso p ion p e ac o , which p o ides he
adso ba e en opy, i becomes s aigh o wa d o con e he
adso p ion en halpy o a binding ene gy, which can be di ec ly
used o e alua e he accu acy o elec onic s uc u e me hods.
Su p isingly, DFT calcula ions employing PBE and RPBE
unc ionals we e no able o ep oduce he O-induced
di e ence in ac i a ion ene gies obse ed in he expe imen .
This mo i a ed us o implemen a semiempi ical co-adso ba e
in e ac ion po en ial om which he s abiliza ion ene gy and
he adso ba e en opy o NH3could be de e mined.
The main idea behind ou app oach o he co-adso ba e
in e ac ion po en ial is o desc ibe he change in he NH3−
P (111) ene gy landscape induced by he p(2 ×2) O-a om
o e laye assuming ha oxygen co e age does no al e he
co alen NH3−P bond om wha i is on clean P (111). This
means ha he changes o he NH3binding ene gy a he
su ace eme ge ully om a ac ion and epulsion by O-a oms.
The co alen NH3−P (111) ene gies ha e been de e mined
wi h DFT calcula ions o di usion pa hways using he PBE
unc ional. We jus i y he use o PBE, o e any o he
unc ional, because i p o ided almos exac ag eemen wi h
expe imen ally de i ed di usion ba ie s,
17
which a e c ucial
o a good desc ip ion o he adso ba e en opy. To a oid
e o s in oduced by he DFT-PBE-de i ed NH3/P (111)
binding ene gy, we use ins ead he expe imen ally de i ed
alue
17
in he ollowing a e cons an modeling. We assumed
ha nonco alen in e ac ions be ween NH3and O can be
ea ed addi i ely. The in e ac ion o NH3wi h adso bed O-
a oms is desc ibed by a semiempi ical pai -po en ial which
includes elec os a ic, dispe si e, and epulsi e con ibu ions.
We e e o his nonco alen ene gy con ibu ion as he NC-
AIM.
The NC-AIM is explained in de ail in Suppo ing
In o ma ion (SI) Sec ion S1; he e, we p o ide only a b ie
desc ip ion. In Figu e 2, he unde lying adso ba e s uc u es
and key coo dina es o he NC-AIM a e shown. In he NC-
AIM, he elec os a ic con ibu ions o he NH3−O
in e ac ions a e desc ibed by Coulomb in e ac ions be ween
poin cha ges, placed a he posi ions o each a om o he
adso ba es as well as hei induced image cha ge posi ions
wi hin he me al�see also Figu e S1. The e ec i e a omic
cha ges a e pa ame ized using he dipole momen o gas-phase
NH3 oge he wi h wo k unc ion measu emen s o NH3
4
and
O
25
co e ed P (111). The dispe sion o ces be ween wo
a oms a e es ima ed om London heo y
26
using a omic
ioniza ion po en ials and pola izabili y olumes o gas-phase
species. To accoun o Pauli epulsion be ween wo a oms a
Figu e 2. S uc u al model employed o cha ac e ize NH3in e ac ion
ene gies a O-a om-co e ed P (111) using DFT calcula ions and he
NC-AIM. The ligh g een shaded egion is he elemen a y cell o he
p(2 ×2) O-a om o e laye in which he NH3*con igu a ions a e
sampled o de e mine he adso ba e pa i ion unc ion.
Jou nal o he Ame ican Chemical Socie y pubs.acs.o g/JACS A icle
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J. Am. Chem. Soc. 2022, 144, 21791−21799
21793
sho dis ances, we included he −12 e m, as used in he
Lenna d-Jones po en ial. The pa ame e s o he epulsion e m
we e es ima ed using an de Waals adii o gas-phase a oms.
27
The NC-AIM model desc ibes he obse ed dec ease o
NH3adso ba e en opy on oxygen-co e ed P (111) as a esul
o o a ional and ansla ional hind ance
13
o he molecule due
o in e ac ions wi h O-a oms. No e ha his is consis en wi h
elec on-s imula ed H+ion angula dis ibu ions (H+-ESIAD),
da a o Ne ze and Madey ha p o ide di ec e idence o
NH3 o a ional hind ance on O-co e ed Ni(111).
28
The e o e,
o accu a e ea men o co-adso ba e in e ac ions in he NC-
AIM, we accoun ed o NH3in-plane displacemen (x,y) and
i s o a ion a ound he C3-axis (φ)�see Figu e 2.
Based on he comp ehensi e di usional po en ial ene gy
landscape o NH3on P (111) cons uc ed om DFT, we used
he NC-AIM o o mula e he he mal deso p ion a e cons an
o NH3 om p(2 ×2) O/P (111).
29
He e, he deso p ion a e
cons an is o mula ed as a p oduc o he adso p ion a e
cons an and he equilib ium cons an be ween adso bed and
gas phases�see also e 30. Fo NH3deso p ion om p(2 ×
2) O/P (111), i is gi en by
=×*···
×*··· *
i
k
j
j
j
j
j
y
{
z
z
z
z
z
k T S k T
m
Q Q
Q
E
k T
( ) 2
exp .
p
p
d
O/P 0B
NH
(2 2)O () NH
(2 2)O NH
0
B
3
3
(g)
3
(2)
He e, ⟨S0⟩and E0a e he NH3 he mal s icking coe icien
and he binding ene gy a he su ace, espec i ely. As e isks
deno e adso ba es. The quo ien o pa i ion unc ions Qis
c ucial o accu a e desc ip ion o he p e ac o and includes
con ibu ions om he gas-phase molecule (QNHd
3
(g)), he p(2 ×
2) O-a om o e laye in he absence o ammonia
(Qp(2 ×2)O*···()), and he p(2 ×2) O-a om o e laye wi h
adso bed ammonia (Qp(2 ×2)O*···NHd
3
*).
In gene al, modeling deso p ion a e cons an s has in he
pas igno ed he adso ba e-induced changes o he su ace
phonon spec um.
13,31
We also employ his assump ion o
model ou expe imen , as he in luence o NH3adso p ion, he
phonon spec um o P (111) is expec ed o be small, due o
he la ge mass di e ence be ween P and NH3which esul s in
good sepa abili y be ween NH3’s deg ees o eedom (which
we ake in o accoun ) and P ib a ions (which cancel ou in
eq 2). Fu he mo e, phonons a e collec i e p ope ies, which
will emain una ec ed by he low co e ages o NH3(≤5×
10−4ML) p esen in ou expe imen . No e ha changes o he
densi y o s a es associa ed wi h he O-a om o e laye a e
aken in o accoun �O-a oms in close coo dina ion o NH3
exhibi al e ed ib a ional equencies
32
�see he SI, Sec ion
S2 o de ails.
The analysis is simpli ied by modeling o he a io o NH3
he mal deso p ion a e cons an s om p(2 ×2) O/P (111)
and p is ine P (111). The simpli ica ion a ises as some ac o s
appea ing in eq 2, o example, s icking coe icien s, cancel ou
when he a io is aken. The a io o he mal a e cons an s is
gi en by eq 3.
=×*··· *···
×*··· *
i
k
j
j
j
j
j
y
{
z
z
z
z
z
k
k
Q Q
Q
E
k T
exp
p
p
d
O/P
d
P
(2 2)O () NH ()
(2 2)O NH
c
B
3
3
(3)
He e, ΔEcis he complexa ion ene gy which ep esen s he
ene ge ic s abiliza ion o NH3induced by co-adso bed O
a oms. O cou se, his a e cons an a io equi es knowledge o
he pa i ion unc ion o NH3*on clean P (111), deno ed as
QNHd
3
*···(). When compu ing he pa i ion unc ions, all O*
deg ees o eedom a e app oxima ed as ha monic oscilla o s,
which is jus i ied by he es ic ed O*di usion inside he p(2
×2) s uc u e. The equi ed ha monic equencies o NH3*,
O*, and he (NH3−O)*complex on P (111) a e adop ed
om he DFT calcula ions o O e mans e al.
32
wi h scaling
co ec ions employed o be e ep oduce expe imen ally
a ailable ib a ional spec a o NH3*and O*on
P (111)
33−35
�see he SI, Sec ion S2 o de ails. The NH3*
ansla ional pa i ion unc ion on p(2 ×2) O/P (111) is
de e mined using NH3−P (111) in e ac ion ene gies om
Figu e 3. (a) Ra e cons an a io om VRK expe imen s compa ed wi h modeling esul s o he NC-AIM wi h wo se s o pa ame e s. The oo
mean squa e de ia ion ( msd) is shown o each model. The blue do ed line is he p edic ion o he NC-AIM based on es ima ed in e ac ion
pa ame e s. Op imizing he pa ame e s o he bes i o he expe imen p oduces he ed dashed line. Panels (b,c) show A henius pa ame e s o
he mal deso p ion a e cons an s o NH3deso p ion om O/P . Accu a e kd
O/P alues we e ob ained om he op imized NC-AIM a e cons an
a io (eq 3) mul iplied by p e iously de e mined and highly accu a e alues o kd
P .
17
(b) Expe imen ally de i ed A henius ac i a ion ene gy
dis ibu ion (black) compa ed o he NC-AIM p edic ions. (c) Analogous plo o (b) o he decadic loga i hm o he A henius p e ac o . No e
ha he NC-AIM a e cons an s do no pe ec ly obey an A henius law; hence, wo e ical lines a e indica ed o each pa ame iza ion, o indica e
he de ia ion om A henius beha io o e his empe a u e ange.
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DFT calcula ions
17
and he NC-AIM wi h he C3-axis o a ion
coupled o he in-plane displacemen coo dina es�see SI
Sec ion S2.
The a e cons an a io model (eq 3) is compa ed o
expe imen al esul s in Figu e 3a. E en when using he NC-
AIM p edic ion based on c udely es ima ed pa ame e s (blue
do ed line in Figu e 3a), he ag eemen wi h he expe imen is
good. Since he es ima ion o dispe si e and epulsi e
in e ac ions was highly simpli ied, we op imized he associa ed
in e ac ion pa ame e s o be e i he expe imen al a e
cons an a ios ( ed dashed line in Figu e 3a). He e, we scaled
he dispe sion coe icien and he epulsion coe icien o he
H−O and N−O in e ac ions (see Sec ion S1.2 in he SI); he
pa ame e s ela ed o he elec os a ic con ibu ions o he
in e ac ions we e held cons an , as hey ely on p e ious
expe imen s ha de e mined he adso ba e in luence on he
su ace wo k unc ion.
25,36
The op imized NC-AIM pa ame e s
yield excellen ag eemen wi h he a e cons an a ios and
ep oduce he empe a u e dependence o he measu ed
deso p ion a es�see Figu e 3b,c.
3. DISCUSSION
The excellen ag eemen wi h he expe imen clea ly shows
ha he op imized NC-AIM yields bo h an accu a e adso ba e
en opy and binding ene gy o NH3on p(2 ×2) O/P (111).
Looking deepe in o he implica ions o his success, we ind
ha he NC-AIM yields a complexa ion ene gy ΔEco
147 meV and a o a ional ba ie o 84 meV. Tha is, he
eclipsed con igu a ion o NH3*, whe e he H a oms o he
molecule a e o ien ed owa d he h ee nea es O*neighbo s,
is s abilized by 84 meV in compa ison o he s agge ed
con igu a ion. Bo h he complexa ion ene gy and he o a ional
ba ie a e domina ed by he dispe sion o ces in he NC-AIM;
when dispe sion o ces a e neglec ed, bo h ΔEcand he
o a ional ba ie a e educed in magni ude by ∼80%. The
impo ance o dispe sion o ces sugges ed by he NC-AIM
mo i a ed us o ca y ou DFT calcula ions o desc ibe he
NH3−O in e ac ions in his sys em, wi h and wi hou
dispe sion co ec ions. To ob ain esul s compa able o he
low co e ages ound in ou expe imen s, we used a (4 ×4)
uni cell. The esul s o ou calcula ions a e p esen ed in Table
1.
DFT-GGA esul s ha neglec dispe sion in e ac ions, i.e.,
PBE and RPBE unc ionals, gi e complexa ion ene gies ΔEco
only 22 and 43 meV, espec i ely; his is inconsis en wi h he
expe imen , ΔEc= 147−14
+23 meV. These alues a e howe e
ema kably close o he elec os a ic con ibu ion o he NH3
s abiliza ion ob ained om he NC-AIM�22 meV. Analogous
DFT-GGA calcula ions using he D3 an de Waals
co ec ion
23
o PBE and RPBE unc ionals ga e ΔEc=−265
and 146 meV, espec i ely. Resul s o PBE-D3 a e e en in
quali a i e disag eemen wi h he expe imen . This inding is
consis en wi h p e ious wo k, which ound ha PBE-D3 has
poo pe o mance when i comes o he desc ip ion o
nonco alen in e ac ions a me al su aces.
37
RPBE-D3 esul s
compa e well wi h he expe imen , suppo ing he conclusions
om he NC-AIM ha dispe sion o ces a e c i ical o
desc ibing he NH3−O in e ac ions o NH3adso bed on
p(2 ×2) O/P (111).
I is also in e es ing o compa e he pe o mance o he
chosen exchange−co ela ion unc ionals o he desc ip ion o
simila sys ems. Ammonia on Cu(100) is a a e example o an
expe imen al binding ene gy o his molecule on a ansi ion
me al su ace, de e mined wi h chemical accu acy.
38
He e, he
adso p ion en halpy (0.61 ±0.02 eV) was epo ed a ∼230 K,
a empe a u e ha is low enough ha he binding ene gy is
likely o be wi hin ∼0.02 eV o his alue. Calcula ions wi h
PBE and RPBE bo h unde -bind NH3 o Cu by 0.18 and
0.40 eV, espec i ely.
39
The unde -binding e o s a e qui e
simila o NH3/P (111)�0.16 eV o PBE and 0.51 eV o
RBPE shown in Table 1. These compa isons sugges u he
ha he VRK-de i ed binding ene gies o NH3on P a e
wi hin chemical accu acy. Finally, we poin ou ha RPBE-D3
calcula ions o NH3/Cu(100) ga e a binding ene gy wi hin 1
kcal/mol o he expe imen .
40
Ou calcula ions show ha NH3
binding o bo h P (111) and p(2 ×2) O/P (111) is also
p edic ed accu a ely wi h his unc ional.
The success o he NC-AIM encou aged us ge a deepe look
a he di usional po en ial ene gy su ace o NH3on O-
co e ed P (111). In Figu e 4, he ene gies o he NH3
Table 1. Summa y o he Ene ge ic Pa ame e s and Recommended Tempe a u e-Dependen Ra e Cons an s o Deso p ion
and Hopping om/on P (111) and p(2 ×2) O/P (111) De i ed in This Wo k
a
ene gies/eV expe imen PBE
c
PBE-D3
c
RPBE
c
RPBE-D3
c
binding ene gy E0
P (111) 1.13 ±0.02
17
0.973
17
1.641 0.637 1.162
di usion ba ie Wx
P (111) 0.71 ±0.04
17
0.70
17
1.110
binding ene gy E0
p(2 ×2) O/P (111) 1.28−0.02
+0.03 0.995 1.376 0.680 1.308
complexa ion ene gy
b
ΔEc0.147−0.014
+0.023 0.022 −0.265 0.043 0.146
di usion ba ie Wx
p(2 ×2) O/P (111) 1.10−0.13
+0.22 0.947 0.969
hinde ed o a ion ba ie Wφ
p(2 ×2) O/P (111) 0.084−0.022
+0.049 0.045 0.058
ecommended a e cons an s
d
A/s−1n E/eV
deso p ion
17
kd
P (111) 5.492 ×1016 2.852 1.217
hopping
17
kh
P (111) 1.191 ×1014 0.872 0.750
di usion
e
DP (111) 0.137 cm20.872 0.750
deso p ion kd
p(2 ×2) O/P (111) 2.766 ×1017 3.157 1.351
hopping
kh
p(2 ×2) O/P (111) 4.979 ×1014 −0.476 1.146
di usion
e
Dp(2 ×2) O/P (111) 0.764 cm2−0.476 1.146
a
De ails on he unce ain y es ima ion can be ound in Sec ion S1.3 o he SI. The a e and di usion cons an s a e epo ed as pa ame e s o he
ex ended A henius equa ion: k(T) = A×(298 K/T)nexp(−E/kBT). No e ha he empe a u e-dependen A henius p e ac o is A(T) = A×(298
K/T)n.
b
E0
p(2 ×2) O/P (111) −E0
P (111).
c
Calcula ed ene gies do no include ze o-poin ene gy co ec ion.
d
De ia ion due o app oxima ed o m is ≤1%
be ween 298 and 1300 K.
e
De ails on he con e sion o he hopping o di usion coe icien a e p o ided in he SI, Sec ion S3.1.
Es ima ed om
he ansi ion-s a e heo y using he NC-AIM ba ie and RPBE-D3 equencies�see he SI, Sec ion S3.2.
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molecule a e shown o a ious in-plane posi ions on clean
P (111)�panel (a)�and o he same posi ions on p(2 ×2)
O/P (111)�panel (b). F om he NC-AIM, we deduced a
s ong epulsion be ween N and O (see also Figu e S2 in SI
Sec ion S1.2). This epulsion s ems om he ac ha O is
coo dina ed o h ee P a oms, when bound a he cc hollow
si es o P (111);
41
his educes he p opensi y o hose h ee P
a oms o o m P −N bonds wi h NH3. The whi e ci cles in
Figu e 4b show hese N−O epulsi e egions. This e ec i ely
means ha a single O*blocks h ee ou o ou on- op binding
si es ha would ha e been a ailable o NH3on P (111). O
cou se, his lowe s he con igu a ional en opy o NH3
compa ed o he P (111) su ace.
The elimina ion o binding si es goes hand in hand wi h a
s ong s e ic hind ance o si e- o-si e hopping pa hways,
p e iously a ailable o NH3*on clean P (111). The same
N−O epulsi e egions, indica ed by he whi e ci cles in Figu e
4b, p e en he molecules om passing o e he nea es b idge
si e, a pa hway p e e ed on clean P (111) (black dashed a ow
in Figu e 4a). This o ces hopping o occu h ough highly
coo dina ed si es, whe e NH3*binding o he su ace is
subs an ially weakened. A hopping pa hway on p(2 ×2) O/
P (111) ends o in ol e a op- cc-b i-hcp-b i- cc- op sequence
(see black dashed a ows in Figu e 4b). T a eling along his
pa h a e ses a ba ie o ∼1.1 eV, which is almos 0.4 eV
highe han he di usion ba ie ound o NH3on clean
P (111).
17
Despi e an unde es ima ed binding ene gy, PBE p edic s
di usion ba ie s in good ag eemen wi h he expe imen �see
Table 1. This inding is easonable since epulsi e in e ac ions
be ween NH3and O domina e he inc eased di usion ba ie
on p(2 ×2) O/P (111), which can be well cap u ed e en
wi hou inclusion o dispe sion o ces. In e es ingly, RPBE-D3
yields no only he co ec binding ene gies o NH3*a
P (111) and p(2 ×2) O/P (111) bu also p edic s he
di usion pa hway and di usion ba ie s o O/P (111) o
0.97 eV, in good ag eemen wi h he alue de i ed om he
expe imen , using he NC-AIM. Howe e , he di usion ba ie
on clean P (111) is subs an ially o e es ima ed compa ed o
he expe imen , indica ing ha sub le e o compensa ion is
in ol ed in many appa en ly accu a e DFT esul s.
We close he discussion wi h a wo d o cau ion abou he
NC-AIM model. While we ind ha he op imized NC-AIM
pa ame e s ag ee qui e well wi h he ange o epo ed N−O
and H−O in e ac ion pa ame e s known om he li e a u e
(see Table S1 and Sec ion S1.3 in he SI), we do no claim o
p o ide he bes dispe sion coe icien s o uni e sally
applicable in e ac ion pa ame e s. In ac , he exac alues o
he in e ac ion pa ame e s a e qui e unce ain om ou i and
su e om la ge co ela ion e o s be ween he a ac i e and
epulsi e coe icien s. None heless, he de i ed ene ge ic
pa ame e s�binding ene gy, o a ional ba ie , and di usion
ba ie �a e much less a ec ed by hese unce ain ies�see
Table 1. This is because he a e cons an a ios a e much mo e
closely ela ed o ene gy di e ences, which p o i om e o
cancela ion be ween a ac i e and epulsi e e ms o he
in e ac ion po en ial.
4. CONCLUSIONS
In his wo k, we ha e epo ed ansien deso p ion a es o
ammonia om p(2 ×2) O/P (111) be ween 473 and 573 K.
We ound ha he adso p ion o O-a oms on P (111) educes
he NH3deso p ion a e. The absence o NH3 eac ions
o e ed us he oppo uni y o exclusi ely cha ac e ize he
non eac i e in e ac ion be ween O*and NH3*. The he mal
deso p ion a es clea ly indica ed an ene ge ic s abiliza ion o
NH3*and a educed adso ba e en opy on p(2 ×2) O/
P (111) compa ed o P (111). We de eloped an NC-AIM o
a ac i e and epulsi e in e ac ions be ween NH3*and O*
which ga e an accu a e i o he expe imen al esul s. The NC-
AIM allowed he de e mina ion o aluable benchma k da a
epo ed in Table 1, bu mos impo an ly, he solid basis o
he NC-AIM allowed us o quan i y he s e ic hind ance o O-
a oms on he di usion o NH3. Compa ed o clean P (111)
which al eady exhibi s a la ge di usion ba ie , he NH3
di usion ba ie is inc eased u he by 0.39−0.14
+0.22 eV on p(2
×2) O/P (111). Addi ionally, om he NC-AIM, we ind ha
a ac i e in e ac ions be ween NH3and O-a oms a e
domina ed by dispe sion o ces, a esul which we could
con i m wi h DFT calcula ions. Speci ically, he RPBE-D3
unc ional appea s o be he bes choice o he non eac i e
desc ip ion o NH3−O in e ac ion on P (111). I de ini ely
should be conside ed o mic okine ic modeling NH3oxida ion
Figu e 4. (a) Po en ial ene gy su ace (PES) o NH3on clean P (111) de i ed om DFT calcula ions om e 17. The p e e ed di usion pa hway
is indica ed by he black dashed a ow and p oceed as op-b i- op. The di usion ba ie is 0.71 ±0.04 eV. (b) PES o NH3on p(2 ×2) O/P (111)
esul ing om he sum o DFT ene gies (see panel (a)) and he NC-AIM wi h op imized pa ame e s. The la ge ed ci cles indica e he posi ion o
he oxygen a oms wi h whi e ci cles indica ing egions a ound each O a om wi h s ong O−NH3 epulsion. The di usion (indica ed by he black
dashed a ows) ollows he op(1)- cc(2)-b i(3)-hcp(4)-b i(3)- cc(2)- op(1) pa hway wi h a ba ie o 1.10−0.13
+0.22 eV. The ene gies o ele an binding
si es a e indica ed in he colo ba . The ene gies in each panel a e se ela i ely o he minimum ene gy o he co esponding PES, and he binding
ene gies a e indica ed in he colo ba as E0.
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21796
on P , equi ed o he desc ip ion o he Os wald p ocess. The
indings epo ed he e p o ide a solid ounda ion o a de ailed
kine ics s udy o NH3oxida ion on s epped P su aces.
5. METHODS
5.1. Expe imen al Sec ion. The expe imen al appa a us has been
desc ibed ea lie in de ail.
15,16,42
A supe sonic molecula beam o NH3
(∼1% NH3in He, 6 ba backing p essu e) was gene a ed wi h a piezo-
elec ically d i en pulsed al e a 25 Hz. The beam passed h ough
wo di e en ially pumped s ages and en e ed he su ace-sca e ing
chambe , held a a base p essu e o 2 ×10−10 mba , impinging he
P (111) su ace (MaTeck GmbH) a an incidence angle o 30° om
he su ace no mal. The empo al du a ion o he pulsed beam had a
ull wid h a hal maximum o ∼40 μs. The mean kine ic ene gy o
NH3in he beam was ∼0.35 eV. The su ace was p epa ed by
spu e ing wi h A +(3 keV) o 10 min and subsequen annealing a
1300 K o 20 min. The cleanliness o he sample was e i ied wi h
Auge elec on spec oscopy. The s ep densi y o he P (111) c ys al
is es ima ed, based on i s cu -angle accu acy, o be 0.1−0.2%. The
deso bing NH3is de ec ed, 20 mm om he su ace, using
non esonan mul ipho on ioniza ion accomplished wi h a Ti:Sapphi e
lase (35 s, 0.3 W a 1 kHz). A pulsed homogeneous elec ic ield,
o med be ween wo pa allel la meshes ( epelle and ex ac o ),
p ojec s he ions on o a pulsed MCP de ec o . The mass- o-cha ge
a io o he ions is selec ed by delaying he MCP pulse wi h espec o
he pulsed ield ex ac ion. The ion image is ob ained om he
phospho sc een a he back o he MCP de ec o using a CCD
came a.
P io o he expe imen s, O2is dosed (1.5 ±0.5 ML/s) om a
second molecula beam (500 Hz), a no mal incidence, o 30 min a
he P (111) su ace a 573 K. This condi ion is su icien o es ablish
he p(2 ×2) s uc u e o oxygen a oms wi h 0.25 ML a P (111). The
O2beam was con inuously ope a ed du ing deso p ion expe imen s o
p e en any O-co e age dilu ion as a consequence o O-a om
di usion o ecombina i e deso p ion. These condi ions we e ound
ea lie o ensu e a s able p(2 ×2) s uc u e.
20−22
Due o he absence
o NH3 eac ion and due o he small NH3co e ages pe molecula
beam pulse (∼5×10−4ML), we assume ha he p(2 ×2) s uc u e
o O-a oms on P (111) is no pe u bed du ing he expe imen s.
The kine ic aces�de ined as he lux o NH3depa ing om he
su ace s esidence ime�ha e been ob ained acco ding o he
p ocedu e, documen ed in de ail in ou p e ious wo k.
15,16
B ie ly, he
densi y ion images a e co ec ed o he he mal backg ound,
sepa a ed om he signal by i s eloci y, and ion images a e
con e ed o lux. The posi ions o he image a e ans o med o
eloci ies wi h he ion’s ime-o - ligh om he lase ocus o he
de ec o . The lux images a each beam-lase delay a e in eg a ed o
eloci ies be ween 500 and 1000 m/s, close o he su ace no mal. By
using his eloci y ange, we supp ess DS con ibu ions in he kine ic
aces. The beam-lase delay ime-axis is co ec ed by NH3’s ime o
ligh om he su ace o he lase ocus in o de o ex ac i s
esidence ime a he su ace.
5.2. DFT Calcula ions. NH3in e ac ions wi h P (111) and p(2 ×
2)O/P (111) su aces ha e been modeled using he Vienna ab ini io
simula ion package.
43−47
Pe iodic DFT calcula ions we e pe o med
a he le el o GGA using he PBE
48
and he RPBE
49
exchange−
co ela ion unc ionals. In addi ion, he sys ems ha e been
cha ac e ized using hese unc ionals and including he D3 dispe sion
co ec ion (PBE-D3 and RPBE-D3) om G imme and cowo ke s.
23
The co e−elec on in e ac ion is app oxima ed by he p ojec o
augmen ed wa e po en ials.
50,51
A cu o ene gy o a plane-wa e basis
o 400 eV is applied in he case o he clean P (111) su ace, whe eas
o p(2 ×2)O/P (111), i is se o 765.5 eV. Bo h he P (111) and
he p(2 ×2)O/P (111) su aces a e modeled by a (4 ×4) uni cell
and 4-laye slab, and he wo lowes P laye s a e kep ixed. A 24 Å
acuum egion was added o he slab o a oid in e ac ion be ween
pe iodic images in he z-di ec ion. The B illouin zone was sampled
wi h an 8 ×8×1 and 3 ×3×1Γ-cen e ed g id o special k-poin s
o he P (111) and he p(2 ×2)O/P (111) su aces, espec i ely.
To p edic adso p ion ene gies, he wo opmos su ace laye s, he
NH3molecule, and O a oms, whene e p esen , we e allowed o elax
un il o ces we e lowe han 0.02 eV/Å. The eac ion pa hs and
ansi ion s a es o di usion and deso p ion we e iden i ied by he
climbing image a ian o he nudged elas ic band me hod.
52
The
calcula ion was conside ed con e ged when o ces we e <0.05 eV/Å.
■ASSOCIATED CONTENT
*
sı Suppo ing In o ma ion
The Suppo ing In o ma ion is a ailable ee o cha ge a
h ps://pubs.acs.o g/doi/10.1021/jacs.2c10458.
Fo malism and cons uc ion o NC-AIM, pa ame iza-
ion o poin cha ges, pa ame iza ion o dispe si e and
epulsi e con ibu ions, unce ain y es ima ion o NC-
AIM-de i ed ene gies, de ails on he modeling o a e
cons an a ios, modeling o hopping a e cons an s wi h
ha monic TST, and ela ionship be ween hopping and
di usion coe icien s (PDF)
■AUTHOR INFORMATION
Co esponding Au ho s
Dmi iy Bo odin −Ins i u e o Physical Chemis y, Geo g-
Augus Uni e si y o Goe ingen, Goe ingen 37077,
Ge many; Depa men o Dynamics a Su aces, Max Planck
Ins i u e o Mul idisciplina y Sciences, Goe ingen 37077,
Ge many; o cid.o g/0000-0002-2195-0721;
Email: [email p o ec ed]
Theo anis N. Ki sopoulos −Ins i u e o Physical Chemis y,
Geo g-Augus Uni e si y o Goe ingen, Goe ingen 37077,
Ge many; Depa men o Dynamics a Su aces, Max Planck
Ins i u e o Mul idisciplina y Sciences, Goe ingen 37077,
Ge many; Depa men o Chemis y, Uni e si y o C e e,
He aklion 71500, G eece; Ins i u e o Elec onic S uc u e
and Lase −FORTH, He aklion 70013, G eece;
o cid.o g/0000-0001-6228-1002;
Email: [email p o ec ed]
Alec M. Wod ke −Ins i u e o Physical Chemis y and
In e na ional Cen e o Ad anced S udies o Ene gy
Con e sion, Geo g-Augus Uni e si y o Goe ingen,
Goe ingen 37077, Ge many; Depa men o Dynamics a
Su aces, Max Planck Ins i u e o Mul idisciplina y Sciences,
Goe ingen 37077, Ge many; o cid.o g/0000-0002-
6509-2183; Email: [email p o ec ed]
Au ho s
Oihana Galpa so o −Donos ia In e na ional Physics Cen e
(DIPC), Donos ia-San Sebas ián 20018, Spain; Kimika
Fakul a ea, Euskal He iko Unibe si a ea UPV/EHU,
Donos ia-San Sebas ián 20018, Spain; o cid.o g/0000-
0003-4964-1696
Igo Rahino −Depa men o Na u al Sciences, The Open
Uni e si y o Is ael, Raanana 4353701, Is ael
Jan Finge hu −Ins i u e o Physical Chemis y, Geo g-
Augus Uni e si y o Goe ingen, Goe ingen 37077, Ge many
Michael Schwa ze −Ins i u e o Physical Chemis y, Geo g-
Augus Uni e si y o Goe ingen, Goe ingen 37077, Ge many
S e an Hö andl −Ins i u e o Physical Chemis y, Geo g-
Augus Uni e si y o Goe ingen, Goe ingen 37077, Ge many
Daniel J. Aue bach −Depa men o Dynamics a Su aces,
Max Planck Ins i u e o Mul idisciplina y Sciences,
Goe ingen 37077, Ge many
Alexande Kand a senka −Depa men o Dynamics a
Su aces, Max Planck Ins i u e o Mul idisciplina y Sciences,
Jou nal o he Ame ican Chemical Socie y pubs.acs.o g/JACS A icle
h ps://doi.o g/10.1021/jacs.2c10458
J. Am. Chem. Soc. 2022, 144, 21791−21799
21797
Goe ingen 37077, Ge many; o cid.o g/0000-0003-
2132-1957
Di k Schwa ze −Depa men o Dynamics a Su aces, Max
Planck Ins i u e o Mul idisciplina y Sciences, Goe ingen
37077, Ge many; o cid.o g/0000-0003-3838-2211
Comple e con ac in o ma ion is a ailable a :
h ps://pubs.acs.o g/10.1021/jacs.2c10458
Funding
Open access unded by Max Planck Socie y.
No es
The au ho s decla e no compe ing inancial in e es .
■ACKNOWLEDGMENTS
D.B., J.F., A.K., and T.N.K. acknowledge suppo om he
Eu opean Resea ch Council (ERC) unde he Eu opean
Union’s Ho izon 2020 esea ch and inno a ion p og am
(g an ag eemen no. [833404]). O.G. acknowledges inancial
suppo by he Spanish Minis e io de Ciencia e Inno ación
[G an no. PID2019-107396GB-I00/AEI/10.13039/
501100011033]. I.R. g a e ully acknowledges he suppo by
Is ael Science Founda ion, ISF (g an No. 2187/19), and by
he Open Uni e si y o Is ael Resea ch Au ho i y (g an No.
31044). M.S. hanks he BENCh g adua e school, unded by
he DFG (389479699/GRK2455).
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