Decons uc ing he O igins o In e acial Ca alysis: Why Elec ic Fields a e
Insepa able om Sol a ion
Solana Di Pino,1Deba shi Bane jee,1, 2 Ma a Mon i,1Gonzalo Díaz Mi ón,1Giuseppe
Cassone,3and Ali Hassanali1, a)
1)In e na ional Cen e o Theo e ical Physics (ICTP), S ada Cos ie a 11, 34151 T ies e,
I aly
2)Scuola In e nazionale Supe io e di S udi A anza i (SISSA), Via Bonomea 265,
34136 T ies e, I aly
3)Ins i u e o Chemical-Physical P ocesses, Na ional I alian
Resea ch Council (CNR-IPCF), V.le F. S agno d’Alcon es 37,
98158 Messina (I aly)
In he las decade, he e has been a su ge o expe imen s showing ha ce ain chemical
eac ions unde go an eno mous boos when aken om bulk aqueous condi ions o mi-
c od ople en i onmen s. The mic oscopic basis o his phenomenon emains elusi e and
con inues o be widely deba ed. One o he key d i ing o ces in oked a e he speci ic
p ope ies o he ai -wa e in e ace including he p esence o la ge elec ic ields and dis-
inc sol a ion a he su ace. He e, using a combina ion o classical molecula dynamics
simula ions, he chemical physics o sol a ion, and unsupe ised lea ning app oaches, we
place hese assump ions unde close sc u iny. Using phenol as a model sys em, we demon-
s a e ha he elec ic ield a he su ace o wa e is no anomalous o unique compa ed
o bulk wa e condi ions. Fu he mo e, he elec ic ield luc ua ions de-co ela e on a
imescale o ∼10 ps implying ha hei ole in ac i a ing much slowe chemical eac ions
emains inconclusi e. We deploy a ecen ly de eloped unsupe ised lea ning app oach,
dubbed in o ma ion balance, which de ec s in an agnos ic ashion he ela ionship be ween
he elec ic ield and sol a ion collec i e a iables. I u ns ou ha he elec ic ield on
he hyd oxyl g oup o he phenol is mos ly de e mined by phenol hyd a ion including he
p oximi y and o ien a ion o nea by wa e molecules. We cau ion ha he g owing a en-
ion o he ole ha elec ic ields ha e ga ne ed in enhancing chemical eac i i y a he
ai -wa e in e ace, may no e lec hei ac ual impo ance.
a)Elec onic mail: [email p o ec ed]
1
a Xi :2506.23988 2 [physics.chem-ph] 24 Oc 2025
I. INTRODUCTION
The s uc u al, dynamical and dielec ic p ope ies o aqueous in e aces ha e been implica ed
o a wide ange o p oblems anging om a mosphe ic chemis y1,2 o he o igins o li e3,4. O e
he las decade o so he e ha e been a lu y o s udies sugges ing ha chemical eac ions can be
signi ican ly accele a ed nea wa e in e aces compa ed o when hey occu in he bulk4. Sha p-
less and co-wo ke s coined he e m ‘on-wa e ’ ca alysis obse ing ha some o ganic chemis y
eac ions d ama ically speeded up when conduc ed in wa e suspensions compa ed o o ganic sol-
en s as well as in nea condi ions5. The consis en expe imen al obse a ion is ha mo ing om
bulk wa e o mic od ople condi ions, leads o he accele a ion o ce ain chemical eac ions6–11.
This enhancemen is hough o occu a he bounda y be ween wa e and ai whe e he chemical
eac an s may expe ience di e en unde lying physical d i ing o ces. The molecula o igins ha
lead o he enhanced ca alysis emains a opic o li ely deba e in he li e a u e.
The e ha e been se e al ac o s ha a e cu en ly being examined in he communi y o a ional-
ize he o igins o he enhanced chemical eac i i y including he p esence o la ge elec ic ields
and hei luc ua ions ( anging be ween 109−1010 V/m)12–17, in e acial sol a ion and aniso opy
o chemical eac an s induced by he ai -wa e bounda y18–20, cu a u e o he in e ace21, he
su ace ac i i y o p o ons o hyd oxide ions17,22,23 and inally, geome ic con inemen e ec s9,24.
A pa icula eac ion ha has caugh signi ican a en ion is he one leading o he o ma ion o
hyd ogen-pe oxide (H2O2) in mic od ople s obse ed by he Za e g oup25. O e he pas ew
yea s, he Mish a g oup has shown h ough a se ies o ca e ul and sys ema ic s udies ha he high
yields o H2O2o iginally obse ed by he Za e g oup a ise no om he p esence o in insic ields
a he in e ace, bu a he om impu i ies such as ozone o dissol ed oxygen26–29. The impo ance
o dissol ed oxygen as a sou ce o bo h H2O2and hyd oxyl adicals has also ecen ly been poin ed
ou by o he s udies30. On he o he hand, he Head-Go don g oup using molecula simula ions,
ha e implica ed la ge elec ic ields and pa ial sol a ion as playing a key ole in he c ea ion o
hyd oxyl adicals a he ai -wa e in e ace31.
The po en ial ole o in e acial elec ic ields is pa ly oo ed on he e idence ha s ong ex e -
nal s a ic elec ic ields a e some imes capable o p oducing ca aly ic e ec s. In ac , expe imen-
al e idence has shown ha elec os a ic po en ial g adien s can selec i ely enhance and ca alyze
Diels-Alde eac ions32 and o he indus ially signi ican ans o ma ions33. Complemen a y in-
sigh s in o he e ec s o s ong elec ic ields ha e come om quan um chemical compu a ions on
2
isola ed molecules34–36 and om ex ensi e simula ions on condensed-phase sys ems37,38. These
s ong ex e nal a i icial ields on he o de o ∼109−1010 V/m align in magni ude wi h he local
elec ic ields na u ally occu ing in condensed ma e 39–42 and a e he e o e hough o in oduce
ca aly ic ac i i y. A ecen s udy by Xie and cowo ke s showed using ab ini io molecula dynam-
ics simula ions coupled wi h ee ene gy calcula ions, ha he ba ie o a ce ain Diels-Alde
eac ion was ac ually sligh ly highe a he ai -wa e in e ace and ha he in insic ields and hei
luc ua ions did no help speed up he eac ion43. In he same sense, Bonn’s g oup has ca ied ou
su ace sensi i e expe imen s ha ques ion he s eng h o elec ic ields and he ime scale o hei
luc ua ions44.
The a e o a chemical eac ion is ypically de e mined by he slowes deg ee o eedom ha
shapes he lowes ee ene gy pa h going om he eac an o he p oduc 45. Fo a chemical p ocess
ha occu s in solu ion, sol a ion can play an impo an ole in, e.g., s abilizing he ansi ion-s a e
o acili a ing cha ge- ans e e en s such as p o on o elec on ans e 46–48. I is known ha
he luc ua ions o molecula dipoles in liquid wa e can p oduce ields la ge han 1010 V/m49,
whe eas in aqueous solu ions50–53 and in p esence o sol a ed ions54,55 local ield in ensi ies ex-
ceeding ∼3×1010 V/m ha e been epo ed. Besides, elec ic ield s eng hs on he o de o 109
V/m ha e been sugges ed o pe sis a he ai -wa e in e ace15,18,56. I hese elec ic ields play
a cen al ole in chemical eac ions, he imescales associa ed wi h hei luc ua ions mus also
be aken in o conside a ion. In addi ion, since elec ic ields a e ul ima ely oo ed in cha ge den-
si y dis ibu ions a ising om he wa e molecules o ien ed a he in e ace, can hey eally be
de-coupled om sol a ion?
In his wo k, we ackle he ques ion o he in e play be ween elec ic ields and sol a ion us-
ing phenol as a es case. Elec ic ields a in e aces and how hey modula e su ace po en ials
has been a e y ac i e a ea o heo e ical in es iga ion using bo h classical and i s p inciples
app oaches57,58. Ou choice o using phenol is oo ed in he ac ha he phenolic chemical g oup
is abundan ly ound in o ganic ma e and plays a c ucial ole in he c ea ion o ae osols59. Fu -
he mo e, due o i s complex acid-base chemis y, i can also unde go a ious ypes o chemical
eac ions59. Taha a and co-wo ke s ecen ly demons a ed ha he pho odissocia ion o phenol oc-
cu s se e al o de s o magni ude as e han in he bulk60. The p ecise o igins o his e ec emain
unknown, al hough i is e y likely uned by speci ic de ails o how he g ound and exci ed-s a e
po en ial ene gy su aces e ol e di e en ly o phenol in he bulk and a he in e ace, as ecen ly
shown by Mo i a61. Ou goal he e is o use his sys em as a simple model o in es iga e how elec-
3
ic ields on he hyd oxyl moie y o he phenol change mo ing om bulk o in e acial en i on-
men s and o examine he connec ion be ween sol a ion and elec ic ields. We wan o accomplish
his using an agnos ic, unsupe ised lea ning app oach based on he In o ma ion Imbalance (II)
in oduced by Laio and collabo a o s62. This me hod allows us o di ec ly commen on which se
o collec i e a iables a e mo e in o ma i e in a gi en sys em.
Using classical molecula dynamics simula ions o phenol in di e en en i onmen al condi-
ions, we show ha he elec ic ields along he hyd oxyl g oup o he phenol a e no di e en in
bulk o in e acial condi ions. In ac , in ou cu en models, he elec ic ield on a wa e molecule
in he bulk is ac ually sligh ly la ge han ha o he phenol a he in e ace. Fo bo h he si ua ions
whe e he phenol is in he bulk and a he in e ace, we obse e la ge luc ua ions in he elec ic
ield. Howe e , he imescales associa ed wi h hese luc ua ions a e a he as , anging be ween
∼1−10 ps. This sugges s o us a leas , ha i elec ic ield luc ua ions a e o play a ole in
speeding up chemis y, he eac ion mus occu on a simila imescale and i s eac ion axis mus
be p ope ly aligned wi h he ield di ec ion wi hin his ime- ame. In ac , i is well-known ha ,
o ex e nally applied s a ic elec ic ields, bo h he magni ude and he o ien a ion de e mine he
a e o a chemical eac ion owa d ei he ca alysis o inhibi ion36,63. By examining he sol a ion
s uc u e o wa e a ound he phenol using he II es , we demons a e ha he elec ic ield on he
phenol is essen ially desc ibed by he p oximi y and o ien a ion o he nea by sol en molecules.
These indings e y closely mi o hose o Ruiz-López and co-wo ke s who, using QM/MM sim-
ula ions, examined he coupling be ween he ield on a hyd oxyl ion and sol en eo ganiza ion14.
The pape is o ganized as ollows. We begin in Sec ion II by a e iew o he Me hods employed
in ou wo k. Subsequen ly, we mo e o he Resul s s a ing in Sec ion IIIA wi h he analysis o
he s a ic p ope ies o he elec ic ield on he phenol in he di e en sys ems s udied. In Sec ion
IIIB and Sec ion IIIC we examine he coupling be ween he elec ic ield and sol a ion and inally
we conclude in Sec ion IV wi h ou pe spec i es.
II. METHODS
A. Molecula Dynamics Simula ions
We ca ied ou classical molecula dynamics simula ions o h ee sys ems: bulk wa e wi h a
single phenol molecule in i (bulk), a wa e slab wi h a phenol molecule a he ai /wa e in e ace
4
(1 PHX) and a wa e slab wi h 25 phenol molecules a each ai /wa e in e ace o he slab, wi h a
o al o 50 phenol molecules in he whole sys em (25 PHX). We chose his concen a ion o phenol
molecules which esul s in a su ace excess o phenol o app oxima ely 0.7 molecules pe nm2
co esponding o he lowe concen a ion limi employed in he expe imen al wo k by Taha a on
he pho odissocia ion o phenol a he ai /wa e in e ace60. Snapsho s o he 3 simula ed sys ems
a e p esen ed in Figu e1. This sys em also se es as a good limi ing case o p obing he e ec o
agg ega ion/clus e s a he ai -wa e in e ace on he elec ic ields.
Figu e 1. Snapsho s o he h ee sys ems s udied in his wo k: a) phenol in he bulk, b) one phenol molecule
a he ai /wa e in e ace (1PHX) and c) 25 phenol molecules a bo h in e aces o a wa e slab (25PHX).
The a ious sys ems we e p epa ed as ollows. The bulk sys em consis ed o 66054 wa e
molecules and one phenol molecule (bulk), wi h a simula ion box o 128 Å x 12 Å x 12 Å (ob ained
a e NPT equilib a ion, see below). Fo he slab sys ems, we used a p e iously equilib a ed wa e
box con aining 3636 wa e molecules wi h dimensions o 60 Å x 60 Å x 140 Å, as epo ed in
Re .64. To his slab, ei he one (1PHX) o 25 (25PHX) phenol molecules we e added o each side
o he in e ace.
Following sys em p epa a ion, simula ions we e ca ied ou in mul iple s ages. Fo he bulk
sys em, we i s pe o med ene gy minimiza ion, ollowed by a 50 ns equilib a ion in he NPT
ensemble a 1 a m and 300 K o s abilize he densi y. A 100 ns p oduc ion un was hen pe o med
in he NVT ensemble. Fo he slab sys ems, ene gy minimiza ion was conduc ed a e he phenol
molecules we e added, ollowed by a 100 ns p oduc ion simula ion in he NVT ensemble.
All simula ions we e conduc ed using a Lange in he mos a se o 300 K wi h a damping
cons an (γ) o 2.0 ps−1and a ime s ep o 2 s. Pe iodic bounda y condi ions we e used in all
5
di ec ions o all sys ems, o he in e ace sys ems he z-axis (no mal o he in e ace) was la ge
enough o ensu e no in e ac ions be ween pe iodic bounda ies in ha di ec ion. The OPC wa e
model65,66 was employed since i has been shown o accu a ely p edic he su ace ension o wa e .
Speci ically, a oom empe a u e OPC yields a su ace ension o 75 mN/m in excellen ag eemen
wi h he expe imen ally measu ed 70 mN/m67. Pa ame e s o phenol we e gene a ed using he
LEaP p o ocol wi hin he AMBER package. Long- ange elec os a ic in e ac ions we e ea ed
using he Pa icle Mesh Ewald (PME) me hod wi h a cu o o 1 Å. Simula ions we e pe o med
using he AMBER68 and GROMACS69–75 so wa e package. The la e was used since i allows
o mo e con enien pos p ocessing ools o ex ac he su ace ension in o de o alida e he
models o he in e acial sys ems which due o he low concen a ion (su ace access) a e basically
he same as o he OPC nea ai -wa e in e ace.
In his wo k, we calcula ed he elec ic ield a he middle o he O-H bond o he phenol
molecule. This was de e mined conside ing only he elec ic ield p oduced by all he wa e
molecules in he box o he sys em consis ing o only one phenol. In he case o he sys em
o 50 phenol molecules, he con ibu ion o all he phenol molecules was also ac o ed in addi-
ion o he wa e con ibu ion, excluding he sel con ibu ion. The elec ic ield was calcula ed
acco ding o Equa ion 1, as done in p e ious s udies76,77, using he a omic poin cha ges gi en by
he OPC o ce ield, used o desc ibe he wa e molecules. Since he GAFF o ce ields used o
desc ibe he in e ac ion in hese sys ems don’ include pola iza ion and cha ge ans e e ec s we
alida ed his me hodology using he QM/MM app oach ha is desc ibed in he SI ex .
¯
E=1
4πε0
N
∑
i=1
qi
|
i|2ˆ
i(1)
In his equa ion
iis he dis ance o he cha ge o he midpoin o he O-H bond and N is he
o al numbe o wa e molecules in he sys em. The ield ob ained a he cen e o he O-H bond
can be subsequen ly p ojec ed along he O-H bond di ec ion yielding a h ee componen ec o ,
acco ding o equa ion 2, used o he ensuing analysis ha will be desc ibed in mo e de ail la e .
p o jE
E
E= (E
E
E·ˆ
)ˆ
(2)
6
B. In o ma ion Imbalance (II)
In ecen yea s machine lea ning has become an in eg al pa o bo h conduc ing and unde -
s anding molecula simula ions78. I is a he well app ecia ed ha mos molecula sys ems need
o be desc ibed in e ms o luc ua ions occu ing in high dimensional ee ene gy landscapes79.
The e is hus a lo o e o being placed in o de eloping me hods ha help quan i y, p obe, and
in e p e he complexi y ha is inhe en in molecula sys ems. In his pa icula wo k, we explo e
he ela ionship be ween elec ic ields and he sol a ion o phenol. Speci ically, we e-cas his
p oblem wi hin he language o a s a is ical es known as he in o ma ion imbalance62 (II), which
seeks o quan i y he ela ionship be ween di e en dis ance measu es applied o he same da a.
Wi hin he con ex o ou wo k he e, we ask whe he he elec ic ield on he phenol can be a io-
nalised solely, o a leas mos ly, by sol a ion coo dina es. We begin by i s b ie ly e iewing he
II heo y.
II is a measu e o compa e he in o ma ion con en be ween wo dis ance measu es dAand dB,
de ined o e a gi en da a se . Wi hin ou con ex dBwould be he dis ances in he elec ic ield
ec o while dAwill be he dis ances wi h espec o sol a ion deg ees o eedom. Then, dis ances
dBcan be de ined be ween poin s iand j(which a e wo di e en alues o he elec ic ield ec o
componen s a wo imes in ou ajec o y) as: di j
B=||Ei
x−Ej
x||+||Ei
y−Ej
y||+||Ei
z−Ej
z||, whe e
||.|| deno es he Euclidean no m. Dis ances in dAa e de ined simila ly using a se o sol a ion
coo dina es ha we will de ine below in he ex .
Gi en hese dis ances, one e e s o i j
A he dis ance ank o poin jwi h espec o poin i
acco ding o dA. Simila ly, i j
Bis he dis ance ank o iwi h espec o jacco ding o dis ance dB.
In his way, one can say ha dAis in o ma i e wi h espec o dBi poin s close acco ding o dA
a e also close acco ding o dB. I is possible o say ha dAis in o ma i e wi h espec o dBwhen
poin s i j ha a e close neighbo s acco ding o dA emain close also acco ding o dB.
The II om dA o dBis de ined as:
∆(dA→dB):=2
N⟨ B| A≤k⟩=2
N2k∑
i,j: i j
A≤k
i j
B,(3)
whe e Nis he o al numbe o poin s in he da a se and kis he numbe o nea es neighbo
poin s ha a e conside ed. Eq.3 gi es us he II, ep esen ed as ∆(dA→dB), as a numbe be ween
0 and 1. ∆(dA→dB) = 0 occu s when all poin s ha a e nea es neighbo s acco ding o dA emain
7
nea es neighbo s in dB, whe eas ∆(dA→dB) = 1 occu s when he nea es neighbo s acco ding
o dAa e andomly dis ibu ed in dB. The o me case is when dAis maximally in o ma i e wi h
espec o dB, and he la e is when i is minimally in o ma i e.
Recen ly, an ex ension o he II has been p oposed80, whe e each ea u e ha makes up a gi en
dis ance measu e is scaled by a weigh , and hen hese weigh s a e op imized h ough g adien
descen . This o malism allows us o combine he e ogeneous ea u es, which migh ha e e y di -
e en uni s o measu emen , in a s aigh o wa d manne , wi hou needing o wo y abou scaling
he da a app op ia ely. This is e e ed o as he Di e en iable In o ma ion Imbalance (DII) and i
allows us o de e mine he mos in o ma i e subse o coo dina es o ea u es o de ine a dis ance
me ic wi hin a gi en da a se . The DII is de ined as:
DII(dA(w
w
w)→dB):=2
N2
N
∑
i,j=1
ci j(λ,dA(w
w
w)) i j
B(4)
whe e,
ci j(λ,dA(w
w
w)) :=e−di j
A(w
w
w)/λ
∑m=ie−dim
A(w
w
w)/λ(5)
He e, w
w
wa e a ia ional pa ame e s o be op imized ia g adien descen in o de o assign
di e en weigh s o di e en ea u es in dis ance dA, and he pa ame e λis chosen acco ding o he
a e age and minimum nea es neighbo dis ances. In his way, i is possible o bo h au oma ically
iden i y he mos ele an ea u es in dis ance dA ha a e maximally p edic i e wi h espec o
dis ance dB, as well as he espec i e a ios in which hey should be combined. In he limi λ→
0, he DII (Eq. 4) is equi alen o and can be iewed as a con inuous e sion o he s anda d
In o ma ion Imbalance (Eq. 3).
In his wo k, we p ima ily applied he DII o de e mine he in o ma ion con en o a se o
sol a ion- ela ed ea u es on he elec ic ield ec o along he O-H bond o he phenol molecule.
To pe o m a ea u e sea ch and o a oid he p oblem o combina o ial explosion ha would na -
u ally a ise i one we e o es e e y possible ea u e subse , we use he o wa d g eedy sea ch
algo i hm in oduced in Re . 62 coupled wi h he DII app oach ha is implemen ed in he Py hon
package DADApy81.
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III. RESULTS
A. Phenol Elec ic Field: S a ics and Dynamics
As indica ed ea lie , one o he main goals o his s udy is o in es iga e wi h classical empi ical
po en ials, how he elec ic ield on he phenol moie y is uned and a ec ed by en i onmen al
ac o s. To his end, we begin by i s compa ing how he elec ic ield on an O-H bond in liquid
wa e compa es o ha o he hyd oxyl g oup o he phenol. Figu e 2a) illus a es he dis ibu ion
o he elec ic ield on he cen e o he O-H o a wa e molecule in he bulk. We obse e ha he
a e age ield is (1.7±0.4)×1010 V/m consis en wi h p e ious s udies examining elec ic ields
in bo h bulk wa e using di e en wa e models76,82–84, as well as in wa e a ound amino acids77.
Figu e 2. a) P obabili y densi y dis ibu ion o he magni ude o he elec ic ield a he midpoin o he O-H
bond o andomly selec ed wa e molecules (do ed cu e) and o phenol molecules in all he h ee sys ems
s udied in his wo k (solid lines). b) Magni ude o he elec ic ield gene a ed by he wa e molecules a he
midpoin o he O-H bond o he phenol molecules o he h ee sys ems s udied as a unc ion o he dis ance
o his bond. As expec ed he decay goes as 1/ 2.
Mo ing o he elec ic ield on he phenol, we compa ed he beha io o he ields and he
co esponding luc ua ions along he hyd oxyl g oup o a single phenol in he bulk, a he in e ace
and a si ua ion consis ing o 25 phenol molecules a he su ace which co esponds o a su ace
access o 0.7 molecules/nm2consis en wi h hose p obed in p e ious expe imen s by Taha a and
co-wo ke s. Cu iously, we obse e ha he elec ic ield dis ibu ions a e essen ially he same - he
9
Figu e 6. S uc u al a iables used as ea u e se o he in o ma ion imbalance algo i hm. The same ea u es
we e aken o he 20 nea es wa e molecules o he phenol (conside ed as he OPHX Owa e dis ance).
Figu e 7. a. In o ma ion imbalance be ween he |p o j ¯
E|and a se o s uc u al ea u es o phenol molecules
in he 3 analyzed sys em. b. The same in o ma ion imbalance bu o a subs e o high and low luc ua ions
o he |p o j ¯
E| o he 1PHX sys em. c. II analysis o wa e molecules in he bulk and a he in e ace.
Using all he 100 ea u es o he h ee sys ems, we ob ain a II o app oxima ely 0.4 (ho izon al
do ed lines in Figu e 7). In e es ingly, we ind ha we need only 5 sol en ea u es o each his
minimum II o 0.4 as seen in all he h ee cu es o Figu e 7 a. Table I summa izes he bes
combina ion o ea u es selec ed by he DII going om he bes single o quin uple combina ion
o all he h ee sys ems. In e es ingly, he bes ea u es o he phenol in he bulk appea o be
hose associa ed wi h he o ien a ion o he wa e dipoles ela i e o he O-H o he phenol. Fo he
wo o he cases in ol ing he phenol a he in e ace, i appea s as hough he bes ea u es selec ed
a e a iables associa ed wi h he p oximi y o 1NN o 2NN. We no e, howe e , ha in he case o
p edic ing he elec ic ield o he phenol in bulk, he II dec eases qui e ma ginally when going
16
Table I. Fea u es sequen ially selec ed by he II algo i hm in each sys em.
Sys em 1-Bes ea u e 2-Bes ea u es 3-Bes ea u es 4-Bes ea u es 5-Bes ea u es
bulk [µ1,x] [µ1,x,µ1,y] [µ1,x,µ1,y,µ1,z] [µ1,x,µ1,y,µ1,z,µ2,z] [µ1,x,µ1,y,µ1,z,µ2,z,θOOC,1]
1PHX [dOO,2] [dOO,2,µ1,x] [dOO,2,,µ1,x,µ1,y] [dOO,2,µ1,x,µ1,y,µ1,z] [dOO,2,,µ1,x,µ1,y,µ1,z,µ2,x]
25PHX [dOO,1] [dOO,1,µ1,x] [dOO,1,µ1,x,µ1,y] [dOO,1,µ1,x,µ1,y,µ1,z] [dOO,1,µ1,x,µ1,y,µ1,z,µ2,x]
om he bes 4 o he bes 5 ea u es (by abou 0.02, see SI Table S1), and hese 4 ea u es a e
all ela ed o he a o emen ioned o ien a ion o he wa e dipoles. Thus, i is p ima ily he same
sol en ea u es ha play a ole in de e mining he elec ic ield bo h o phenol in he bulk and a
he ai -wa e in e ace.
P e ious wo ks64,80,88–90 ha e shown ha ge ing alues below 0.7 is usually conside ed a
obus sign o ha ing a iables ha a e e y in o ma i e on he a ge space. While i is possible
o ge an “ideal” II alue close o 0.0 in model sys ems, which is he limi ing case when ou a ge
space is ully desc ibed by ou selec ed ea u es, in eal-wo ld da a se s, his is e y unlikely.
The p esence o noise in he da a, along wi h hidden a iables ha may be e desc ibe he a ge
space bu we e no conside ed, leads o a de ia ion om he condi ion o pe ec ly in o ma i e
ea u es. Tha being said, howe e , as we see in Figu e 7, he II educes om a alue close o 1.0
(which ep esen s he limi ing case wi h unin o ma i e ea u es), o 0.4 as we add mo e meaning ul
a iables. This allows us o de e mine he sol a ion coo dina es ha bes p edic he elec ic ield
ec o .
One o he a gumen s ha has been loa ed in he li e a u e ega ding he ole o elec ic ields
on chemical eac i i y a ai -wa e in e aces is ha i is hei luc ua ions ha need o be aken in o
accoun and ha his could be a key d i e in ca alysis10,16. To assess he ole o hese luc ua ions,
we epea he DII analysis ocusing on he da a-space whe e he |p o j ¯
E|a ises exclusi ely om he
ails o he dis ibu ion. We ocused speci ically on he egime ha was g ea e han app oxima ely
±1.5σo he dis ibu ion, in o he wo ds, elec ic ields less han 6×109and g ea e han 1.6×
1010 V/m. F om his cons ained da ase we epea ed ou analysis looking o he bes se o
ea u es ha leads o an op imal p edic ion o he elec ic ield which is shown in Figu e 7 b) ( he
alues o he II co esponding o his plo can be ound in Table S2). In e es ingly, we obse e
ha using he high- ield egion o he da a ( ields g ea e han 1.6×1010 V/m), he II pla eaus
a a sligh ly lowe alue when using he en i e 100 ea u es compa ed o wha is obse ed in he
17
le panel o Figu e 7. We hus included wo mo e ea u es in o he analysis, which ex ends he
se o wa e molecules conside ed beyond he 4 h NN up o he 11 h NN ( he comple e se o
bes ea u es can be ound in Table S3). Looking a he co ela ion be ween he |p o j ¯
E|and he
dis ance o he 4 nea es wa e molecules in Fig. S8 (uppe panel) in he SI, i becomes clea ha
alues o he elec ic ield om he ails o he dis ibu ion yields s onge co ela ions wi h he
nea es neighbo wa e dis ances. This in u n leads o a lowe alue o he II. On he o he hand,
o he lowe luc ua ions pa o he dis ibu ion ( ields less han 6×109) he II based on sol a ion
coo dina es, is much highe and he co ela ion o he |p o j ¯
E|wi h he 4 nea es wa e molecules
is less p onounced (see bo om panel o Fig. S8 in he SI). The in ui ion behind his is ha when
he phenol begins o de ach om he su ace, i is less sol en exposed and he e o e will na u ally
expe ience weake ields.
As a inal compa ison, we pe o med he same II analysis o he elec ic ields ac ing a he
midpoin o he OH bond in wa e molecules loca ed in he bulk and a he in e ace. To his
end, we calcula ed he Gibbs di iding su ace (GDS) in he 1PHX sys em and, o each ame,
selec ed one andom molecule wi hin GDS ±2 Å and one andom molecule in he bulk egion.
Fo bo h cases, we e alua ed he elec ic ield a he midpoin o one OH bond. We hen epea ed
he analysis ca ied ou o phenol: p ojec ion o he ield on o he OH bond, calcula ion o he
co ela ion o he ield wi h espec o OO dis ances (Fig. S10), and co ela ion wi h he dipole
componen s (Fig. S11 and S12) o he ou nea es neighbo s using he II analysis shown in
Fig. 7c. Fo he II analysis we employed analogous desc ip o s as in he phenol case, wi h he
only modi ica ion being he eplacemen o he angle de ini ion om θOOC o θOOH , whe e H
co esponds o he hyd ogen a om o he a ge molecule no used as he e e ence poin o he
ield calcula ion (see Fig. S9). As shown in igu e 7, he II alues a e la ge han hose ob ained
o phenol. This di e ence can be a ibu ed o he ac ha he desc ip o s selec ed o he wa e
analysis—chosen o mi o hose used o phenol—do no ully cap u e he unde lying physical
phenomena in wa e . To alida e his, we plo ed he elec ic ield magni ude agains he dis ance
o he ou nea es oxygen a oms (analogous o Fig. 4), as well as he elec ic ield componen s
agains he co esponding dipole momen componen s o he ou nea es wa e molecules (Figs.
9–12, SI). These esul s show ha , in he bulk, he co ela ions wi h dis ance emain s ong up o
he ou nea es neighbo s, whe eas a he in e ace hey weaken al eady a he ou h neighbo ,
simila ly o he case o phenol. Rega ding co ela ions wi h espec o he dipole momen , in he
bulk only he i s neighbo shows a signi ican co ela ion, which hen decays apidly, while a
18
he in e ace co ela ions pe sis up o he hi d neighbo be o e ading. Al oge he , hese indings
indica e ha he molecula o igin o he elec ic ields ac ing on phenol and on wa e molecules is
go e ned by di e en ea u es in each case. This sugges s ha , beyond he mac oscopic 1/ 2decay
o he ield wi h dis ance, speci ic sol a ion cha ac e is ics mus be conside ed when analyzing he
e ec o elec ic ields on a gi en sys em.
IV. DISCUSSION AND CONCLUSIONS
Mo ing wa e om bulk o mic od ople condi ions has been shown o signi ican ly accele a e
a b oad class o chemical eac ions. The mic oscopic o igins o his e ec is hough o be induced
by anomalous p ope ies o he ai -wa e in e ace. Howe e , he exac o igins o his enhanced
eac i i y emain ho ly deba ed and whe he hey ac ually a ise om in insic e ec s due o wa e
a he su ace, emains unde se ious sc u iny. Among he a ious leading a gumen s ha ha e
been pu o wa d, he p esence o la ge elec ic ields and pa icula sol a ion e ec s wi hin he
in e acial egion ha e been sugges ed o be key playe s in he unde lying sou ce o accele a ed
eac ions.
I one conside s a chemical eac ion in ol ing he b eaking o a co alen bond, he no ion is ha
he elec ic ield expe ienced along he pu a i e eac ion coo dina e may ac in a di e en manne
bo h in e ms o i s magni ude and di ec ion a he su ace o wa e compa ed o he bulk. A he
same ime, o some eac ions, pa ial sol a ion a he in e ace could s abilize o des abilize in
di e en ways, he eac an s, ansi ion-s a es o p oduc s. Since he elec ic ields mus o igina e
o a la ge ex en om he cha ge densi y induced by he sol en o mo e gene ally en i onmen ,
he wo ac o s a e inex icably in e wined.
In his compu a ional wo k, we ake a s ep owa d unde s anding he ela ionships be ween
elec ic ield luc ua ions and sol a ion using phenol as a model sys em. Using classical molecula
dynamics simula ions o an empi ical po en ial o phenol in he bulk, a he in e ace and unde
mo e concen a ed condi ions ha p obe clus e /agg ega e en i onmen s, we show ha he mag-
ni ude and luc ua ions o he elec ic ields along he hyd oxyl g oup o he phenol show e y
simila cha ac e is ics. Al hough ou models p esen la ge ield luc ua ions up o ∼2×1010 V/m,
he imescales associa ed wi h his a e a he as occu ing wi hin ∼10 ps. In he language o slow
collec i e a iables ha de e mine ac i a ion ba ie s, hese imescales seem a he sho li ed and
may no be ele an o being he slow deg ee o eedom needed o ac i a e he eac ion.
19
To quan i y he ela ionship be ween he elec ic ield expe ienced by phenol and he sol a ion
en i onmen , we deploy an in o ma ion heo e ical es ha measu es how well he elec ic ield
can be p edic ed om sol a ion coo dina es including p oximi y and o ien a ion o wa e o he
hyd oxyl moie y o he phenol. Pe haps unsu p isingly, elec ic ields and sol a ion canno be
ea ed as independen physical e ec s. The elec ic ield on he phenol is de e mined by he
su ounding wa e molecules and his e ec is simply a gene al ea u e ound bo h in phenol in
bulk solu ion as well as a he ai -wa e in e ace. These ole o sol a ion is e en mo e p onounced
o elec ic ield luc ua ions c ea ing la ge alues om he mean.
While he cu en wo k has ocused on a model sys em, phenol, o s udy he beha io and e-
la ionships be ween elec ic ields and sol a ion, we specula e ha hese obse a ions a e a he
gene ic and apply o mos chemical sys ems especially hose ha consis o a leas one pola
moie y. We hus posi ha he no ion o he impo ance o elec ic ields in enhancing chemical
eac ions has pe haps been o e -sensa ionalized in he communi y, a ci cums ance possibly oo ed
on he e idence ha s ong ex e nally applied elec ic ields a e capable o p o oundly modi ying
eac ion ne wo ks and ee ene gy landscapes. In he case o hyd ogen-pe oxide o example, he
Mish a g oup has shown expe imen ally ha i s appa en enhanced yields in mic od ople s may
no be ela ed o i occu ing a he ai wa e in e ace27. Al hough his ma e emains con o-
e sial in he li e a u e o he a ea. Whe he his ex ends o o he eac ions, howe e , emains
an open ques ion. A he same ime, i is also wo h no ing ha su ace po en ials o in e aces
ex ac ed om classical empi ical models a e di e en compa ed o hose ea ed wi h ab ini io
me hods57,58,91. I would be in e es ing in he u u e o use he in o ma ion heo e ic echniques o
examine he ela ionships be ween he elec ic ields and sol a ion a ising om models explici ly
including elec onic deg ees o eedom and pola iza ion.
In summa y, he cu en in es iga ion no only highligh s he inex icable connec ion be ween
he no ion o chemical en i onmen and local elec ic ields, bu also poin s ou he deep di e ence
exis ing be ween ex e nally applied (s a ic and homogeneous) elec ic ields – which migh p o-
duce ca aly ic e ec s – and he spon aneous ields a ising om o ganized ma e which luc ua e
in magni ude and o ien a ion. The physical and chemical impac o in insic e sus ex e nally ap-
plied elec ic ields on chemical eac ions a e hus dis inc and any compa isons should be ea ed
wi h cau ion. I may also be he case, ha he key playe in ol ed in enhancing ca alysis unde
he ac ion o la ge ex e nal ields a e ac ually sol a ion coo dina es. This would be an in e es ing
opic o explo e in u u e s udies.
20
V. SUPPLEMENTARY MATERIAL
The Supplemen a y Ma e ial includes da a on he bes ea u es selec ed by he in o ma ion im-
balance p ocedu e and he II alues. Addi ionally, i has supplemen a y igu es showing he un-
ning coo dina ion numbe o he O a om o he phenol and he O a oms o he wa e molecules and
he angle be ween he O-H bond o he phenol and he elec ic ield. I also includes supplemen a y
igu es showing densi y dis ibu ions be ween each ca esian componen o he p ojec ed elec ic
ield and he co esponding componen o he dipole ec o o he ou nea es wa e molecules o
each sys em.
ACKNOWLEDGMENTS
DB, MM, GDM, and AH hank he Eu opean Commission o unding on he ERC G an
HyBOP 101043272. SDP, DB, MM, GDM, and AH also acknowledge Ma eNos um5 (p ojec
EHPC-EXT-2023E01-029) o compu a ional esou ces.
DATA AVAILABILITY STATEMENT
The da a ha suppo he indings o his s udy a e a ailable om he co esponding au ho
upon easonable eques .
21
S1. METHODS: VALIDATION OF CLASSICAL FORCE FIELDS
In o de o alida e he desc ip ion o classical o ce ields ha do no include pola iza ion
and cha ge ans e e ec s we conduc ed QM/MM calcula ions o he single phenol molecule
a he in e ace using he AMBER/ORCA combined scheme92. We un QM/MM dynamics a
he DFT le el o heo y, using he CAM-B3LYP unc ional oge he wi h he 6-31G* basis se .
To do his, we ook 50 ames om he classical ajec o y and un 1 ps o QM/MM dynamics,
including only he phenol molecule in he QM egion. We hen un a single poin calcula ion
on he las ame o hese QM/MM dynamics, ob aining he dipole ec o and magni ude o he
phenol om DFT he elec onic densi y. We also calcula ed hese quan i ies on he same s uc u es
using he classical cha ges aken om he GAFF o ce ield. The magni ude o he dipole momen
acco ding o he DFT calcula ions is o 2.23±0.05 D whe eas using he classical cha ges we ge
a alue o 1.85±0.02 D, gi ing a 20% unde es ima ion o he classical model wi h espec o he
DFT calcula ion. We also calcula ed he cosine dis ance o he dipole momen ec o calcula ed
wi h DFT and wi h he classical cha ges ob aning a alue o 0.91 ±0.01, his indica es ha he
di ec ion o he dipole momen is well ep oduced by he classical model. Based on hese esul s
we conclude ha o he po poise o s udying he magni ude and he molecula o igins o he
elec ic ield a a he middle poin o he OH bond o he phenol molecule he classical model
desc ibes well enough he sys em.
S2. PHENOL ELECTRIC FIELD: STATICS AND DYNAMICS
22
Figu e S1. Running coo dina ion numbe o he O a om o he phenol and he O a oms o he wa e
molecules.
Figu e S2. Angle be ween he OH bond o he phenol and he elec ic ield. I can be seen ha he OH bond
is mos ly aligned wi h he elec ic ield.
23
Figu e S3. Dis ibu ion o o ien a ions o he phenol OH bond wi h espec o he z-axis, he no mal axis
o he in e ace, o he 1PHX and 25PHX sys ems. The mos p obable o ien a ion o he OH bond is
pe pendicula o he z-axis, being pa allel o he in e ace.
24
S3. SOLVATION AND ELECTRIC FIELDS
Figu e S4. Densi y dis ibu ions showing he co ela ion be ween each ca esian componen o he p ojec ed
elec ic ield (p o jEi) and each componen o he dipole ec o o he i s nea es wa e molecule (µi o
1NN) in he 1PHX sys em. Co ela ion is only obse ed o he co esponding componen s o p o jE and
µ.
25
Figu e S10. Co ela ion be ween OPHX Owdis ance and he |p o j ¯
E| o wa e molecules in he bulk (a) and
a he in e ace (b).
Figu e S11. Densi y dis ibu ions showing he co ela ion be ween each ca esian componen o he p o-
jec ed elec ic ield (p o jEi) and he co esponding componen o he dipole ec o o he i s ou nea es
wa e molecules (µi) o wa e molecules in he bulk.
32
Figu e S12. Densi y dis ibu ions showing he co ela ion be ween each ca esian componen o he p o-
jec ed elec ic ield (p o jEi) and he co esponding componen o he dipole ec o o he i s ou nea es
wa e molecules (µi) o wa e molecules a he in e ace.
33
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