Ci a ion: Ba ena-Espés, D.; Bone a,
S.; Polo, V.; Muná iz, J. Explo ing he
Po en ial Ene gy Su ace o P 6
Sub-Nano Clus e s Deposi ed o e
G aphene. In . J. Mol. Sci. 2023,24,
870. h ps://doi.o g/10.3390/
ijms24010870
Academic Edi o :
Abde azzak Douhal
Recei ed: 29 No embe 2022
Re ised: 22 Decembe 2022
Accep ed: 30 Decembe 2022
Published: 3 Janua y 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
In e na ional Jou nal o
Molecula Sciences
A icle
Explo ing he Po en ial Ene gy Su ace o P 6Sub-Nano
Clus e s Deposi ed o e G aphene
Daniel Ba ena-Espés1, Se gio Bone a 2,3 , Vic o Polo 3,4,* and Julen Muná iz 1
1Depa amen o de Química Física y Analí ica, Uni e sidad de O iedo, 33006 O iedo, Spain
2
Depa amen o de Bioquímica y Biología Molecula y Celula , Facul ad de Ciencias, Uni e sidad de Za agoza,
50009 Za agoza, Spain
3Ins i u o de Biocompu aciónyFísica de Sis emas Complejos (BIFI), Uni e sidad de Za agoza,
50009 Za agoza, Spain
4Depa amen o de Química Física, Uni e sidad de Za agoza, 50009 Za agoza, Spain
*Co espondence: ipolo@uniza .es
Abs ac :
Ca aly ic sys ems based on sub-nanoclus e s deposi ed o e di e en suppo s a e p omis-
ing o e y ele an chemical ans o ma ions such as many elec oca aly ic p ocesses as he ORR.
These sys ems ha e been demons a ed o be e y luxional, as hey a e able o change shape and
in e con e be ween each o he ei he alone o in he p esence o adso ba es. In addi ion, an accu a e
ep esen a ion o hei ca aly ic ac i i y equi es he conside a ion o ensemble e ec s and no a
single s uc u e alone. In his sense, a eliable heo e ical me hodology should assu e an accu a e and
ex ensi e explo a ion o he po en ial ene gy su ace o include all he ele an s uc u es and wi h
co ec ela i e ene gies. In his con ex , we applied DFT in conjunc ion wi h global op imiza ion
echniques o ob ain and analyze he cha ac e is ics o he many local minima o P
6
sub-nanoclus e s
o e a ca bon-based suppo (g aphene)—a sys em wi h elec oca aly ic ele ance. We also analyzed
he magne ism and he cha ge ans e be ween he clus e s and he suppo and paid special a -
en ion o he dependence o dispe sion e ec s on he ensemble cha ac e is ics. We ound ha he
ensembles compu ed wi h and wi hou dispe sion co ec ions a e quali a i ely simila , especially
o he lowes -in-ene gy clus e s, which we a ibu e o a (mainly) co alen binding o he su ace.
Howe e , he e a e some signi ican a ia ions in he ela i e s abili y o some clus e s, which would
signi ican ly a ec hei popula ion in he ensemble composi ion.
Keywo ds:
sub-nano clus e s; global op imiza ion; ca alysis; DFT; dispe sion in e ac ions; ensem-
ble e ec s
1. In oduc ion
In he las yea s, suppo ed noble me al sub-nanoclus e s (SNC) ha e p o en o be
p omising he e ogeneous ca alys s due o hei high su ace a ea, which allows o educe
he amoun o ca alys loading, and hei abili y o ac i a e ine chemical bonds [
1
–
3
].
Hence, a wide ange o ca aly ic p ocesses in ol ing SNC ha e been epo ed in he
li e a u e [
4
,
5
]. Fo example, P SNC a e being in es iga ed as ca alys s o echnologically
impo an p ocesses, such as he oxygen educ ion eac ion (ORR) [
6
–
9
]. This way, a
de ailed heo e ical unde s anding o he s uc u e and p ope ies o hese P -based SNC is
equi ed.
Realis ic in es iga ions on he elec onic s uc u e o P SNC should conside i s lux-
ional beha io [
10
,
11
] as ensemble e ec s a e o he u mos impo ance in SNC-ca alyzed
p ocesses, and he ca aly ically mos ac i e species is likely o be a s uc u e di e en om
he global minimum (GM) [
12
]. In addi ion, he suppo plays an impo an ole in he
sys em ac i i y, as me al–me al and me al–suppo in e ac ions lead o complex po en ial
ene gy su aces (PES). In his ega d, we no e ha he e a e some epo s on he in e ac ion
be ween P -clus e s and ca bon-based suppo s ha e eal ha he clus e size plays an
In . J. Mol. Sci. 2023,24, 870. h ps://doi.o g/10.3390/ijms24010870 h ps://www.mdpi.com/jou nal/ijms
In . J. Mol. Sci. 2023,24, 870 2 o 12
impo an ole on he na u e o he in e ac ion [
13
–
17
]. Fo example, based on ene gy
decomposi ion analysis and changes in he elec on densi y upon adso p ion o P SNC on
a g aphene model, i was ound ha smalle clus e s a e p one o bond co alen ly, while in
la ge s uc u es, an de Waals in e ac ions a e p edominan [
16
]. Mo eo e , some au ho s
ha e epo ed ha he e is a cha ge ans e om he me allic clus e o he suppo [
18
–
20
].
Besides, he P –C in e ac ion is signi ican ly a ec ed by he suppo cu a u e o he ca bon
suppo , which was used by Yang e al. o s eng hen adso p ion o me hanol on o P
7
SNC [15].
The e o e, a ho ough and accu a e sampling o he PES is equi ed o ai h ully model
a ealis ic ensemble. In his con ex , we pe o med a de ailed analysis o P
6
SNC suppo ed
on g aphene by using densi y unc ional heo y (DFT) combined wi h global op imiza ion
(GO) echniques. Mo eo e , special a en ion was paid o analyzing dispe sion e ec s on he
clus e ensemble composi ion, which was made by compa ison be ween esul s pe o med
wi h and wi hou dispe sion co ec ions. We chose a ca aly ically ele an sys em, as P
6
clus e s deposi ed o e ca bon-based suppo s ha e p o en o be ac i e in such impo an
p ocesses as ORR [
20
] and hyd ogen elec o-oxida ion [
21
]. This sys em has been p e iously
s udied by o he au ho s: Nakajima and co-wo ke s s udied P
6
clus e s deposi ed o e
g aphene by p e-op imizing he clus e s in he gas phase and hen deposi ing hem in
he su ace [
20
]; a simila s a egy (combined wi h molecula dynamics simula ions) was
applied by Da Sil a e al., bu hey ound a di e en geome y o he GM [
22
]. In addi ion,
o he bes o ou knowledge, comple e GO in which clus e s a e di ec ly gene a ed o e
he su ace, which is equi ed o modelling he PES o high- luxional SNC [
11
], has no
been pe o med ye . No e ha , as p e iously in oduced, SNC exhibi a ema kable abili y
o change shapes and e-adap hei s uc u e in he p esence o adso ba es and/o a
suppo [
23
], and hus, o an accu a e explo a ion o he PES, i is manda o y o gene a e
(hund eds o ) he ini ial s uc u es di ec ly o e he suppo o a oid (o a leas mi iga e)
incomple e sampling e ec s de i ed om deposi ing p e iously op imized SNC on i .
We no e ha while a de ailed knowledge on he low-lying ene gy s uc u es o in e -
aces deco a ed wi h P
6
SNC is equi ed o an accu a e ep esen a ion and unde s anding
o he sys em, modelling elec oca aly ic sys ems is a e y di icul ask. As a consequence,
a a ie y o no el compu a ional me hodologies has been p oposed in he las yea s [
24
–
30
],
and o he di e en e ec s a e also expec ed o in luence he ensemble composi ion, such as
he applied po en ial [
31
,
32
] o he expe imen al condi ions (such as pH) [
33
,
34
], whose
in es iga ion is ou o he scope o his con ibu ion.
2. Resul s and Discussion
We i s pe o med a GO o P
6
sub-nano clus e s deposi ed o e a g aphene laye by
means o PBE exchange-co ela ion unc ional, including a D3BJ scheme o accoun ing
o dispe sion in e ac ions [
35
,
36
]. Du ing geome y op imiza ions, we allowed a ee
elaxa ion o he magne ic s uc u e o he sys em, which was u he e ined by means o
single-poin calcula ions by using he e ahed on me hod wi h Blöchl co ec ions (see Com-
pu a ional De ails sec ion). The main mo i a ion o such p ocedu e was ob aining mo e
accu a e ela i e ene gies, which will a ec he ensemble composi ion as well as magne ic
s a es. In his ega d, some epo s ha e pu o wa d he ele ance o magne ic in e ac ions
wi hin he ca alys s (and be ween he ca alys s and eac an s) in hei ac i i y [37–43].
The e we e 123 s uc u es wi hin a ela i e ene gy cu o o 1.0 eV, ou o which he
15 mos s able sys ems a e p o ided in Figu e 1( he coo dina es o he 50 mos s able
s uc u es a e p o ided in he Supplemen a y Ma e ials). The a ious s uc u es a e named
as P
6
-#, whe e # co esponds o he o de o he s uc u e in inc easing ene gy ela i e o
he GM (P 6-I).
In . J. Mol. Sci. 2023,24, 870 3 o 12
In .J.Mol.Sci.2023,24,xFORPEERREVIEW3o 12
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Figu e1.F on alandschema ic op iews o  he i eenlowes ‐in‐ene gylocalminimum o 
P
6
/g apheneop imizedwi hdispe sion‐co ec edDFT.ΔEco esponds o heene gydi e ence
wi h espec  o heGM; he o almagne icmomen o  hesys em(pe uni cell)isp o idedinBoh 
magne ons.Theg eendo sco espond o heP a omsa  he op,while heblackc ossesco espond
o hea omsa  hebo om.
Figu e 1.
F on al and schema ic op iews o he i een lowes -in-ene gy local minimum o
P
6
/g aphene op imized wi h dispe sion-co ec ed DFT.
∆
E co esponds o he ene gy di e ence
wi h espec o he GM; he o al magne ic momen o he sys em (pe uni cell) is p o ided in Boh
magne ons. The g een do s co espond o he P a oms a he op, while he black c osses co espond
o he a oms a he bo om.
In . J. Mol. Sci. 2023,24, 870 4 o 12
As shown in Figu e 1, he GM co esponds o a double-squa e-shaped s uc u e ha
in e ac s wi h he g aphene suppo by means o a b idge coo dina ion o C–C bonds (i.e.,
P a oms lie in he cen e o he bond). Such kind o P –C in e ac ion has been epo ed
o be he mos a o able one o he in e ac ion be ween P a oms and g aphene-like
su aces [
18
,
22
,
32
,
44
], which ag ees wi h ou obse a ions. On he con a y, o he bes o
ou knowledge, he GM shape had no been p e iously p oposed by o he au ho s bu has
been epo ed as a low-lying s uc u e o he gas-phase sys em, wi h an ene gy di e ence
om he GM ha anges be ween 0.034 eV [
22
] and ~0.3 eV [
45
]. Nakajima e al. ob ained
a GM in which P in e ac s wi h he suppo by means o wo P a oms, o ming a squa e
P
4
-co e ha was comple ed by wo b idge P a oms ha o med a iangula -like geome y
wi h wo di e en P –P bonds al hough hey hen ma ched he ca aly ically ele an ac i e
species o a di e en s uc u e by means o spec oscopy measu emen s (see e . [
20
]).
The GM ob ained by Da Sil a and co-wo ke s is ela ed o he o me one [
22
], bu he
s uc u e exhibi s a mo e plana cha ac e , being close o a iangle-like geome y ha has
been epo ed as he GM o gas-phase P
6
clus e s by se e al au ho s by means o pu e
unc ionals [
20
,
45
–
48
]. Howe e , we did no ind any s uc u e di ec ly de i ed om he
a o emen ioned iangula gas-phase clus e in he se o low ene gy s uc u es, wi h he
pa ial excep ion o P
6
-V (and ela ed s uc u es such as P
6
-VI, P
6
-VIII, and P
6
-IX), which
esembles a dis o ed P
6
- iangle, in which he cen al P o a hypo he ical h ee-a om base
is displaced upwa ds, and he apical P a om bulges. In o de o ule ou ha he di e ence
is due o an incomple e PES sampling, we sea ched o simila s uc u es o ha epo ed
by he a o emen ioned au ho s in he whole se o local minima we ob ained (a o al o 244
s uc u es). We ound ela i e ene gies o 0.88 eV and 1.60 eV o wo s uc u es ha a e
e y ela ed o he GM as p oposed by da Sil a [
22
], as hey co espond o P
6
- iangles
ha in e ac wi h he su ace by wo o he h ee P a oms ha o m he iangle base. No e
ha he ene gy di e ence be ween hem is due o a di e en pa e n o in e ac ion wi h he
suppo and s uc u al dis o ions in he P
6
co e. The geome ies o hese s uc u es, which
a e iden i ied as P 6-min da Sil a and P 6-min’ da Sil a, a e p o ided in he Supplemen a y
Ma e ials (Table S2). We also ound a ela i e ene gy o 1.04 eV o he ollowing s uc u e
in ene gy o de ing (o a closely ela ed s uc u e) epo ed by he same au ho s (iden i ied
as P 6-min2 da Sil a in Table S2), which co esponds o a P
6
- iangle ha in e ac s wi h he
suppo by means o h ee P a oms. Mo eo e , we ob ained a s uc u e ha co esponds o
a la P
6
- aingle ha in e ac s wi h he suppo by means o an de Waals in e ac ions
a a dis ance o he su ace o abou 3.1 Å. Such s uc u e p esen s a ela i e ene gy o
1.15 eV, wi h i s geome y p o ided in Table S2 (P 6-min6 da Sil a). When compa ing ou
local minima wi h hose epo ed by Nakajima and co-wo ke s, we ound ha hei GM
is closely ela ed o a s uc u e ha , in ou se , has a ela i e ene gy o 0.87 eV (Table
S2, P 6-min Nakajima) [
20
]. They also p oposed a low-ene gy s uc u e wi h iangula ,
p isma ic shape o which we ob ained a ela i e ene gy o 0.92 eV (Table S2, P 6-s 7
Nakajima) and he a o emen ioned an de Waals s uc u e al hough wi h a ela i e ene gy
signi ican ly highe han da Sil a: 0.433 eV s. 0.0668 eV, espec i ely, while in ou case,
i was 1.15 eV, and he s uc u e is no exac ly he same, as i is pa ially displaced wi h
espec o he suppo . O e all, hese di e ences pu o wa d he ex eme sensi i i y o
hese sys ems o he compu a ional app oach, including bo h DFT calcula ions and PES
sampling p ocedu e.
I we u n back o ou ensemble (Figu e 1), we can see ha he ou mos s able
s uc u es, P
6
-I o P
6
-IV, wi h a maximum ene gy di e ence be ween hem o 0.14 eV,
exhibi a closely ela ed shape. Bo h P
6
-I and P
6
-II show a plana double-squa e shape,
which only di e s on he in e ac ion mode wi h he g aphene shee (see op iew o
Figu e 1). Namely, while P
6
-I binds o C–C bonds o he suppo in a zig-zag manne , P
6
-II
binds o pa allel C–C bonds, wi h he ene gy di e ence be ween bo h s uc u es being only
0.02 eV. The geome ical s uc u e o P
6
-III and P
6
-IV consis s o wo P
4
squa es ha a e
joined by a P –P bond, ha ing a shape ha esembles a hinge, and as o he p e ious
couple o s uc u es, he main di e ence be ween bo h minima (which ansla es in o an
In . J. Mol. Sci. 2023,24, 870 5 o 12
ene gy di e ence o only 0.03 eV) is due o he di e en o ien a ion wi h espec o he
suppo ( op iew o Figu e 1). The ollowing local minima by ela i e ene gy o de ing a e
P
6
-V, (
∆
E = 0.17 eV). This sys em exhibi s a signi ican ly di e en shape, whose geome y
(which has al eady been in oduced) migh be desc ibed as a co e o 5 P a oms o ming wo
iangles ha a e joined oge he by means o a cen al a om—which has been epo ed by
some o us as a ele an local minimum o P
5
/g aphi e [
32
]—and an addi ional P a om
on he op ha o ms an angle ha b eaks he plana i y o he sys em. As o he p e ious
SNC, P
6
-V in e ac s wi h C–C bonds in a b idge ashion, while in his case, i is bonded o
he suppo by wo P a oms (ins ead o h ee). No e ha his s uc u e is in ima ely ela ed
o P
6
-VI, P
6
-VIII, and P
6
-IX, which p esen essen ially he same geome ical s uc u e bu
show a di e en in e ac ion pa e n wi h he suppo (see Figu e 1, op iew). This change
in he in e ac ion mode ansla es in o signi ican ene gy di e ences in he ela i e ene gy,
which is, o example, 0.2 eV highe o P 6-VIII han o P 6-V.
We do no commen in de ail he geome ical s uc u es o all he o he local minima
shown in Figu e 1, bu we can see ha all o hem in e ac wi h he C–C bonds o he suppo
in he b idge posi ions and by wo o h ee P a oms, which ag ees wi h epo s om
o he au ho s [
22
], and ha he e a e some o he s uc u es whose main di e ence is he
in e ac ion pa e n wi h he suppo (i.e., P
6
-VII, P
6
-X, and P
6
-XI). To ou unde s anding,
his esul pu s o wa d he ele an ole o he suppo in SNC s abili y and hus he
impo ance o an exhaus i e sampling o he su ace.
Fu he mo e, he mos s able s uc u es a e associa ed o highly plana geome ies,
which is in line wi h p e ious obse a ions ha mo e la s uc u es a e a o ed by pu e
unc ionals (such as PBE), while hyb id ones a o mo e globula geome ies [45,49].
Wi h espec o magne ic s a es, mos o he clus e s ha e magne ic momen s close
o 2.0
µB
. Namely, his is he case o he nine mos s able s uc u es (P
6
-I o P
6
-IX), in
line wi h p e ious epo s o bo h gas-phase and g aphene-suppo ed P
6
clus e s [
22
,
45
].
Mo eo e , mos o he s uc u es epo ed he ein ha e di e en magne ic s a es, which
a e e y close in ene gy, which is also consis en wi h p e ious spin-s a e analysis o P
6
sys ems [45,50].
In his ega d, u ning back o he GM, we ound ha i s g ound s a e co esponds
o a iple s a e wi h wo unpai ed elec ons o e all and a o al magne ic momen o 1.9
µB
. Howe e , he e is a non-magne ic s a e ha is only 0.09 eV highe in ene gy, which we
e e o as P
6
-I’ (see Figu e 2), and would in ol e ha bo h s uc u es may be accessible
e en a low empe a u es (i we do no conside limi a ions o o bidden spin c osso e
e ec s). No e ha while P
6
-I co esponds o a magne ic s uc u e wi h e omagne ic
coupling be ween all he indi idual magne ic momen s o he a ious P a oms, P
6
-I’
exhibi s an an i e omagne ic s a e, in which he P a oms di ec ly bonded o he suppo
show nega i e indi idual magne ic momen s, while hose ha a e only bonded o o he
P a oms ha e posi i e magne ic momen s. While he absolu e alues o he magne ism
o a oms bonded o g aphene ha e simila magni udes (abou 0.1
µB
), hose o P a oms
ha a e no bonded o C di e om 0.49–0.58
µB
in P
6
-I o 0.09–0.13
µB
in P
6
-I’. The
magni ude o he indi idual magne ic momen s is in he same ange as ha epo ed by
Kuma and Kawazoe o gas-phase P
n
clus e s [
48
]. We no e ha a u he discussion o
magne ic s a es is ou o he scope o his con ibu ion, bu o e all, hese esul s suppo
he impo ance o an adequa e conside a ion o he magne ic s a e o he me al a om, as i
is likely o a ec he ca alysis [38,51].

In . J. Mol. Sci. 2023,24, 870 6 o 12
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Figu e2.Spindensi y, o alandindi iduala omicmagne icmomen s,andene gydi e en  o  he
wolow‐lyingspins a eso P
6
‐I.No e ha αspindensi yisshowninligh blueandβspindensi y
inligh pink(iso alue=0.03au).
We henanalyzed hedi ec iono cha ge ans e encewhen heclus e binds o he
suppo .Fo  ha ,wecalcula edBade cha ges,wi h he esul s o  heGMshowninFig‐
u e3(seeFigu eS1 o  hecha geso selec edlocalminimawi hsigni ican lydi e en 
geome icals uc u e).Wecansee ha  heP a oms ha a edi ec lybonded o heg a‐
phenesuppo ha eposi i echa ges:0.31au o  hecen alP a omand0.10au o P 
a omsa  heendso  heclus e ,and his esul holds o all heanalyzedlocalminima
(Figu eS1).Wi h espec  o heo he  h eeP a oms, he opcen aloneexhibi sa iny
posi i echa ge(0.02au),while hosea  heco ne sa enega i elycha ged(−0.17au).Ou 
esul sindica e ha  hecha ge ans e  akesplace om heclus e —whichwouldha e
ane ec i echa geo 0.19au(ob ainedbysummingup heindi idualcha geso  hesix
P a oms)— o hesuppo .This esul ag eeswi h epo s omo he au ho s[18–20,22].

Figu e3.Bade cha gesin(inau) o  ele an a omso  heGM(P
6
‐I).Posi i echa gesa edepic ed
in.
Figu e 2.
Spin densi y, o al and indi idual a omic magne ic momen s, and ene gy di e en o he
wo low-lying spin s a es o P
6
-I. No e ha
α
spin densi y is shown in ligh blue and
β
spin densi y
in ligh pink (iso alue = 0.03 au).
We hen analyzed he di ec ion o cha ge ans e ence when he clus e binds o he
suppo . Fo ha , we calcula ed Bade cha ges, wi h he esul s o he GM shown in
Figu e 3(see Figu e S1 o he cha ges o selec ed local minima wi h signi ican ly di e en
geome ical s uc u e). We can see ha he P a oms ha a e di ec ly bonded o he g aphene
suppo ha e posi i e cha ges: 0.31 au o he cen al P a om and 0.10 au o P a oms a
he ends o he clus e , and his esul holds o all he analyzed local minima (Figu e S1).
Wi h espec o he o he h ee P a oms, he op cen al one exhibi s a iny posi i e cha ge
(0.02 au), while hose a he co ne s a e nega i ely cha ged (
−
0.17 au). Ou esul s indica e
ha he cha ge ans e akes place om he clus e —which would ha e an e ec i e cha ge
o 0.19 au (ob ained by summing up he indi idual cha ges o he six P a oms)— o he
suppo . This esul ag ees wi h epo s om o he au ho s [18–20,22].
In .J.Mol.Sci.2023,24,xFORPEERREVIEW6o 12
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Figu e2.Spindensi y, o alandindi iduala omicmagne icmomen s,andene gydi e en  o  he
wolow‐lyingspins a eso P
6
‐I.No e ha αspindensi yisshowninligh blueandβspindensi y
inligh pink(iso alue=0.03au).
We henanalyzed hedi ec iono cha ge ans e encewhen heclus e binds o he
suppo .Fo  ha ,wecalcula edBade cha ges,wi h he esul s o  heGMshowninFig‐
u e3(seeFigu eS1 o  hecha geso selec edlocalminimawi hsigni ican lydi e en 
geome icals uc u e).Wecansee ha  heP a oms ha a edi ec lybonded o heg a‐
phenesuppo ha eposi i echa ges:0.31au o  hecen alP a omand0.10au o P 
a omsa  heendso  heclus e ,and his esul holds o all heanalyzedlocalminima
(Figu eS1).Wi h espec  o heo he  h eeP a oms, he opcen aloneexhibi sa iny
posi i echa ge(0.02au),while hosea  heco ne sa enega i elycha ged(−0.17au).Ou 
esul sindica e ha  hecha ge ans e  akesplace om heclus e —whichwouldha e
ane ec i echa geo 0.19au(ob ainedbysummingup heindi idualcha geso  hesix
P a oms)— o hesuppo .This esul ag eeswi h epo s omo he au ho s[18–20,22].

Figu e3.Bade cha gesin(inau) o  ele an a omso  heGM(P
6
‐I).Posi i echa gesa edepic ed
in.
Figu e 3.
Bade cha ges in (in au) o ele an a oms o he GM (P
6
-I). Posi i e cha ges a e depic ed
in.
Finally, we s udied he e ec o dispe sion co ec ions in he ela i e ene gy and
geome y o he clus e s. Fo ha , we pe o med he GO calcula ions wi hou including
dispe sion co ec ions. To di e en ia e hese s uc u es om he dispe sion co ec ion-
In . J. Mol. Sci. 2023,24, 870 7 o 12
op imized ones, we e e o hem as P
6
(no-D)-#, whe e # indica es he s uc u e posi ion
in he ela i e ene gy o de ing. The 10 mos s able s uc u es a e shown in Figu e 4, in
which we also include he equi alen dispe sion-co ec ed s uc u e (in pa en heses), and in
Table 1, in which we also include he ene gy alues o he analogous dispe sion-co ec ed
s uc u e. A i s glance, we can see ha he geome ies o he s uc u es ob ained wi h
and wi hou dispe sion co ec ions a e e y simila . Howe e , he e a e some signi ican
changes in ela i e s abili y ha lead o a ia ions in he ela i e o de . Fo example,
he e is a swi ch in o de be ween P
6
(no-D)-IV and P
6
(no-D)-V, which we e P
6
-V and
P
6
-IV in he dispe sion-co ec ed ensemble (see Figu e 4), al hough such change only
in ol es a mino ela i e ene gy di e ence o up o 0.03 eV (see Table 1). The e is also an
o de ansposi ion in P
6
(no-D)-IX ( o me P
6
-VII), which swi ches om posi ion 7 o 9.
Con a y o he p e ious case, his s uc u e is signi ican ly mo e s able (0.18 eV) in he
dispe sion-co ec ed scheme al hough bo h geome ies a e e y simila . Ano he ele an
posi ion change co esponds o P
6
(no-D)-X, which was P
6
-XV in he dispe sion-co ec ed
scheme, and in his case, he ela i e ene gy wi hin he ensemble is 0.07 eV lowe in he
non-dispe sion co ec ed se o s uc u es.
In .J.Mol.Sci.2023,24,xFORPEERREVIEW7o 12
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Finally,wes udied hee ec o dispe sionco ec ionsin he ela i eene gyandge‐
ome yo  heclus e s.Fo  ha ,wepe o med heGOcalcula ionswi hou includingdis‐
pe sionco ec ions.Todi e en ia e heses uc u es om hedispe sionco ec ion‐op i‐
mizedones,we e e  o hemasP
6
(no‐D)‐#,whe e#indica es hes uc u eposi ionin
he ela i eene gyo de ing.The10mos s ables uc u esa eshowninFigu e4,inwhich
wealsoinclude heequi alen dispe sion‐co ec eds uc u e(inpa en heses),andinTa‐
ble1,inwhichwealsoinclude heene gy alues o  heanalogousdispe sion‐co ec ed
s uc u e.A  i s glance,wecansee ha  hegeome ieso  hes uc u esob ainedwi h
andwi hou dispe sionco ec ionsa e e ysimila .Howe e , he ea esomesigni ican 
changesin ela i es abili y ha lead o a ia ionsin he ela i eo de .Fo example, he e
isaswi chino de be weenP
6
(no‐D)‐IVandP
6
(no‐D)‐V,whichwe eP
6
‐VandP
6
‐IV
in hedispe sion‐co ec edensemble(seeFigu e4),al houghsuchchangeonlyin ol es
amino  ela i eene gydi e enceo up o0.03eV(seeTable1).The eisalsoano de 
ansposi ioninP
6
(no‐D)‐IX( o me P
6
‐VII),whichswi ches omposi ion7 o9.Con‐
a y o hep e iouscase, hiss uc u eissigni ican lymo es able(0.18eV)in hedis‐
pe sion‐co ec edschemeal houghbo hgeome iesa e e ysimila .Ano he  ele an 
posi ionchangeco esponds oP
6
(no‐D)‐X,whichwasP
6
‐XVin hedispe sion‐co ec ed
scheme,andin hiscase, he ela i eene gywi hin heensembleis0.07eVlowe in he
non‐dispe sionco ec edse o s uc u es.

Figu e4.F on al iew o  he enlowes ‐in‐ene gylocalminimum o P
6
/g apheneop imizedwi h‐
ou dispe sionco ec ions.ΔEco esponds o heene gydi e encewi h espec  o heGM; he o al
magne icmomen o  hesys em(pe uni cell)isp o idedinBoh magne ons.
Ino de  o a ionalize hisobse a ion,we ecu ed o hedispe sionene gy e m
ob ained omD3BJscheme(E
disp
inTable1).Wesee ha mos  aluesa e ela i elysimila ,
abou −7.92eV.Howe e , o P
6
‐VI,Ii is−8.115eV,whichexplains hesigni ican des a‐
biliza ionwhenexcludingsuchco ec ion.Theopposi e endisalsoobse ed,as, o 
example,s uc u esP
6
(no‐D)‐VII,VIII,andX(P
6
‐VIII,IX,andXVin hedispe sion‐co ‐
ec edse , espec i ely)a ecompa a i elys abilized(by0.05–0.07eV,seeTable1)in he
non‐dispe sionensemble,whichco ela eswi h helowe weigh o dispe sionco ec ion
(−7.87eVona e age).
Figu e 4.
F on al iew o he en lowes -in-ene gy local minimum o P
6
/g aphene op imized
wi hou dispe sion co ec ions.
∆
E co esponds o he ene gy di e ence wi h espec o he GM; he
o al magne ic momen o he sys em (pe uni cell) is p o ided in Boh magne ons.
In o de o a ionalize his obse a ion, we ecu ed o he dispe sion ene gy e m
ob ained om D3BJ scheme (E
disp
in Table 1). We see ha mos alues a e ela i ely
simila , abou
−
7.92 eV. Howe e , o P
6
-VI,I i is
−
8.115 eV, which explains he signi ican
des abiliza ion when excluding such co ec ion. The opposi e end is also obse ed, as,
o example, s uc u es P
6
(no-D)-VII, VIII, and X (P
6
-VIII, IX, and XV in he dispe sion-
co ec ed se , espec i ely) a e compa a i ely s abilized (by 0.05–0.07 eV, see Table 1) in he
non-dispe sion ensemble, which co ela es wi h he lowe weigh o dispe sion co ec ion
(−7.87 eV on a e age).
In . J. Mol. Sci. 2023,24, 870 8 o 12
Table 1.
Co espondence o he 10 mos s able s uc u es ob ained om he ensemble wi hou
dispe sion (P
6
(no-D)-#) wi h hose ob ained wi h dispe sion co ec ions (P
6
-#’). All ene gy alues
a e p o ided in eV.
P 6(no-D)-# P 6-#’ ∆E(P 6(no-D)-#) ∆E(P 6-#’) ∆(∆E) Edisp
I I 0.00 0.00 0.00 −7.920
II II 0.03 0.02 0.01 −7.930
III III 0.12 0.11 0.01 −7.928
IV V 0.14 0.17 −0.03 −7.884
V IV 0.15 0.14 0.01 −7.936
VI VI 0.21 0.23 −0.02 −7.900
VII VIII 0.32 0.37 −0.05 −7.877
VIII IX 0.38 0.43 −0.05 −7.872
IX VII 0.52 0.34 0.18 −8.115
X XV 0.53 0.60 −0.07 −7.858
No e ha
∆
(
∆
E) co esponds o he di e ence be ween he ela i e ene gy o equi alen s uc u es ob ained
wi hou dispe sion and wi h dispe sion:
∆
(
∆
E) =
∆
E(P
6
(no-D)-#)—
∆
E(P
6
-#’). Thus, a posi i e alue indica es
ha he s uc u e is compa a i ely mos s able when compu ed wi h dispe sion co ec ions, and a nega i e alue
indica es ha he s uc u e is compa a i ely less s able wi hou including dispe sion. E
disp
is he dispe sion
ene gy e m ob ained om D3BJ scheme.
Al hough o e all ou indings ag ee wi h hose epo ed in e . [
22
], in which he
au ho s obse ed ha dispe sion co ec ion e ec s ba ely a ec he clus e s uc u e, we
ound ha , o some cases, dispe sion co ec ions a e impo an in p o iding co ec ela i e
ene gies (and hus clus e popula ions), as some s uc u es a e signi ican ly mo e a ec ed
han o he s, and his e ec migh be ele an in he ca aly ic ac i i y.
As p e iously in oduced, he in e ac ion o small clus e s wi h ca bon-based su aces
has p e iously been a ibu ed o p edominan co alen in e ac ions wi h he suppo [
16
].
In quali a i e e ms, his esul co ela es wi h ou indings, as he mos s able s uc u es
ob ained by means o dispe sion and non-dispe sion-co ec ed p ocedu es show e y
simila geome ies, and we did no ind any low-lying s uc u e bonded o he suppo
in he cha ac e is ic pa allel manne ha would esul om p edominan an de Waals
in e ac ions.
3. Compu a ional De ails
Spin-pola ized densi y unc ional heo y (DFT) calcula ions we e pe o med by means
o he Vienna Ab ini io Simula ion Package (VASP), Ve sion 5.4.4 [
52
–
54
]. We applied he
PBE exchange-co ela ion unc ional [
55
] in conjunc ion wi h he p ojec o augmen ed
wa e (PAW) me hod [
56
,
57
] o ep esen in e ac ions be ween co e and alence elec ons.
Clus e s we e di ec ly gene a ed and op imized o e a p(6
×
6) g aphene su ace (aand
bla ice pa ame e s o 14.777 Å) wi h a acuum o 18 Å (be ween g aphene laye s) o
a oid in e ac ions be ween pa allel images. Fo geome y op imiza ions, we conside ed a
Gaussian smea ing (wid h 0.1 eV) and a cu o o 400 eV o plane wa es. Fo he elec onic
minimiza ion algo i hm, we selec ed he “ALGO = Fas ” op ion, which selec s a mix u e
o he Da idson and RMM-DIIS algo i hms, while o geome y elaxa ion, we selec ed
“IBRION = 2”, which applies a conjuga e-g adien algo i hm. The con e gence c i e ia o
ene gy calcula ions was se o 10
−6
eV (“EDIFF = 1e-06”), as he c i e ia o he geome y
op imiza ion we e a di e ence lowe han 10
−5
eV be ween wo consecu i e s eps ( he
de aul VASP alue, which is EDIFF
×
10). We also conside ed a eal-space e alua ion
o p ojec o ope a o s (“LREAL = Au o”). We u he pe o med single-poin ene gy
calcula ions o e ine he p e ious esul s by using he e ahed on me hod wi h Blöchl
co ec ions, a cu o o 500 eV and a blocked Da idson algo i hm o op imizing he o bi als
(“ALGO = No mal”). The B illouin zone was in eg a ed by a 1
×
1
×
1 K-poin mesh o
geome y op imiza ions, which was inc eased o 5
×
5
×
1 in single-poin calcula ions.
Dispe sion in e ac ions we e accoun ed o by means o D3BJ scheme de eloped by G imme
and co-wo ke s [
35
,
36
]. In a i s s ep, we conside ed 250 and 200 ini ial s uc u es o GO
op imiza ion wi hou and wi h dispe sion co ec ions, espec i ely. In o de o minimize
In . J. Mol. Sci. 2023,24, 870 9 o 12
PES incomple e sampling, we also e-op imized he 20 mos s able s uc u es o each se
wi h he se ings o he o he . Then, we added 100 addi ional s uc u es o make su e ha
he PES was p ope ly sampled. S uc u es we e gene a ed and il e ed ho ough PGOPT
p og am sui e de eloped in Alexand o a’s g oup, which uses a bond leng h dis ibu ion
algo i hm (BLDA) [58,59].
4. Conclusions
The po en ial ene gy su ace o P
6
sub-nano clus e s deposi ed o e a g aphene laye
was explo ed using DFT me hodology and global op imiza ion echniques. The global
minimum ene gies co espond o s uc u es ea u ing a plana double-squa e shape o
P
6
a oms in e ac ing wi h he g aphene suppo by b idge coo dina ion o h ee P a oms
o C–C bonds (P
6
-I o IV). We also ound o he low-lying s uc u es wi h ela i ely high
plana i y as well as some o he s wi h mo e p isma ic cha ac e . In addi ion, al hough P
a oms always in e ac wi h he C–C bond by means o a b idge coo dina ion, we obse ed
some di e en pa e ns o in e ac ion wi h he suppo due o se e al in e ac ion modes
wi h he g aphene suppo (in ol ing di e en combina ions o C–C bonds). The e o e,
an ex ensi e sampling in global op imiza ion echniques is equi ed o accu a ely sample
he PES o g aphene-suppo ed P
6
SNC. Analysis o magne ic p ope ies shows ha he
global minimum (GM) s uc u e ea u es a iple s a e wi h wo unpai ed elec ons and
a o al magne ic momen o 1.9
µB
. Inspec ion o a omic cha ges o he GM e eals a
ans e o elec on densi y om he clus e o he suppo o 0.19 au. Finally, he e ec o
dispe sion in e ac ions in oduced by D3BJ co ec ions was analyzed by compa ison o
global op imiza ion pe o med wi hou dispe sion in e ac ions. Al hough he geome ies
a e no e y a ec ed (which we associa e o p edominan co alen bonding wi h he
suppo ), and he na u e o he GM does no change, and he dispe sion co ec ions a ec
s uc u es in a di e en manne . While he ela i e ene gy does no change much in gene al,
i does o some s uc u es, which would dis o ensemble popula ion and pu s o wa d
he impo ance o including dispe sion co ec ions in he calcula ions.
Supplemen a y Ma e ials:
The ollowing suppo ing in o ma ion can be downloaded a : h ps:
//www.mdpi.com/a icle/10.3390/ijms24010870/s1.
Au ho Con ibu ions:
Concep ualiza ion, D.B.-E. and J.M.; me hodology, D.B.-E. and S.B.; so wa e,
S.B.; alida ion, o mal analysis, da a cu a ion, D.B.-E. and J.M.; w i ing—o iginal d a p epa a ion,
V.P. and J.M.; w i ing— e iew and edi ing, D.B.-E., V.P. and J.M.; supe ision, V.P. and J.M.; unding
acquisi ion, V.P. and J.M. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This esea ch was unded by Spanish “Minis e io de Ciencia e Inno ación” (MICINN),
g an numbe s PID2021-122763NB-I00 and PID2021-126212OB-I00, and “Fundación pa a el Fomen o
en As u ias de la In es igación Cien í ica Aplicada y Tecnológica (FICyT)”, g an numbe IDI-2021-
000054. S.B. was unded by a p edoc o al con ac om “Gobie no de A agón” (Spain).
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Acknowledgmen s:
Resou ces om he supe compu e “Memen o” and he echnical expe ise and
assis ance p o ided by he “Ins i u o de Biocompu aciónyFísica de Sis emas Complejos” (BIFI) a e
g a e ully acknowledged.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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