On he halide hyd a ion s udy: De elopmen o i s -p inciples halide
ion-wa e in e ac ion po en ial based on a pola izable model
Regla Ayala, Jose
´M. Ma ı
´nez, Ra ael R. Pappala do,
and En ique Sa
´nchez Ma cosa)
Depa amen o de Quı
´mica Fı
´sica, Uni e sidad de Se illa 41012, Se illa, Spain
共Recei ed 27 May 2003; accep ed 13 Augus 2003兲
The de elopmen o i s -p inciples halide-wa e in e ac ion po en ials o luo ide and iodide anions
is p esen ed. The model adop ed is he mobile cha ge densi ies in ha monic oscilla o ha allows o
a lexible and pola izable cha ac e o he in e ac ing pa icles. The se o poin s o he quan um
mechanical po en ial ene gy su aces a e calcula ed up o he MP2 le el. The nonaddi i e
many-body con ibu ions we e included explici ly a he h ee-body e ms. S uc u al and ene ge ic
p ope ies o he 关X(H2O)n兴⫺clus e s (n⫽1–6) a e s udied wi h he new in e ac ion po en ials
de eloped. Halide aqueous solu ions a e also s udied by means o Mon e Ca lo simula ions. The
ag eemen be ween expe imen al and ou p edic ed es ima ions shows he good beha io o he
p oposed po en ials. The de eloped po en ials a e able o p ope ly desc ibe bo h he mic osol a ion
o clus e s in gas phase and hei hyd a ion in aqueous solu ions. The di e en na u e o he
in e ac ions among F⫺,B
⫺,I
⫺and wa e appea s in he se o s udied p ope ies, hus gi ing a
g adual change in he beha io along he g oup. © 2003 Ame ican Ins i u e o Physics.
关DOI: 10.1063/1.1615764兴
I. INTRODUCTION
The s uc u e and eac i i y o sol a ed molecules and
singly cha ged ions ha e been ex ensi ely in es iga ed by
bo h expe imen and heo y.1–9 Expe imen al de e mina ion
o a de ailed mic oscopic s uc u e o sol a ion shells a ound
ions is gene ally di icul , he e o e, compu e simula ions
could be o help p o iding c ucial insigh in o he s uc u e
and dynamics o hese sol a ion shells. Compu e simula-
ions ha e eme ged as a powe ul ool o in es iga ing he
mic oscopic p ope ies o liquids and liquid solu ions.10,11
The eliabili y o he esul s de i ed om nume ical simula-
ions depends c i ically on he po en ial model desc ibing he
in e ac ions among he pa icles de ining he sys em. Thus,
he de elopmen o in e ac ion po en ials is cu en ly a opic
o inc easing impo ance in bo h undamen al and applied
esea ch.12,13 Mos o hese s udies ha e been ocused on
ca ion hyd a ion, due o i s impo an ole in many chemical
and biochemical p ocesses.4Anion hyd a ion has been less
s udied, al hough i s ole e en as coun e ions is needed o
ul ill he pic u e o sol a ion. Halide anions a e among he
mos common anions p esen in na u e, and consequen ly
halide anion-wa e a e among he mos ex ensi ely s udied
sys ems.1
The pu pose o his wo k is o p o ide insigh in o he
halide hyd a ion aking in o accoun he di e ences and simi-
la i ies ha appea as a unc ion o he ion size, i s pola izing
and pola izable cha ac e and he s eng h o he halide-wa e
in e ac ion. In o de o add ess some key poin s abou halide
hyd a ion, such as he way ha wa e -wa e s uc u e is
modi ied by he halide p esence, we ha e de eloped i s -
p inciples halide ion-wa e in e ac ion po en ials using he
mobile cha ge densi ies in ha monic oscilla o model
共MCDHO兲de eloped by O ega-Blake e al.14 This po en ial
includes he pola izable and lexible cha ac e o he in e ac -
ing pa icles. S ess has been pu in he compa ison be ween
p ope ies o he sol en in he i s sol a ion shell and hose
o he bulk. The chlo ide anion has been emo ed om his
s udy due o he g ea deal o wo k ha has been ca ied ou
on his anion and because o i s simila i y wi h he b omide
ion. Recen ly, we ha e epo ed he de elopmen o a i s -
p inciples b omide-wa e in e ac ion po en ial based on he
MCDHO model,15 concluding ha a po en ial buil on he
basis o BSSE-co ec ion o wo-body in e ac ions, inclusion
o h ee-body con ibu ions and pola izable cha ac e o he
pa icles in combina ion wi h a MCDHO wa e -wa e po en-
ial is use ul in s udying 关B (H2O)n兴⫺clus e s in gas phase,
as well as simula ion o hese clus e s a 298 K and b omide
aqueous solu ions. The no inclusion o BSSE co ec ion in
he pai wise in e ac ions implied an o e es ima ion o bo h
sol a ion en halpy and he numbe o wa e molecules su -
ounding he b omide anion in i s icini y. An examina ion o
he di e en con ibu ions o he b omide ion-wa e
in e ac ions16 showed ha h ee-body in e ac ions a e mainly
esponsible o he non-pai wise addi i e cha ac e o he in-
e ac ions. Wha ’s mo e, i has been demons a ed ha he
inclusion o h ee-body e ec s is impo an o a mo e accu-
a e desc ip ion o he sol a ion s uc u e.17,18 Fou -body
con ibu ions we e by a less signi ican and hey implied a
conside ably la ge compu a ional e o . A alida ion o he
me hodology used is also shown in a ecen ly XAS 共x- ay
abso p ion spec oscopy兲s udy19 o he b omide hyd a ion in
a兲Au ho o whom co espondence should be add essed. Elec onic mail:
[email p o ec ed]
JOURNAL OF CHEMICAL PHYSICS VOLUME 119, NUMBER 18 8 NOVEMBER 2003
95380021-9606/2003/119(18)/9538/11/$20.00 © 2003 Ame ican Ins i u e o Physics
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which expe imen al spec a a e ai ly well ep oduced. In
his wo k, we p esen an ex ension o his me hodology o
he luo ide and iodide anions.
The s uc u e o halide hyd a es has long been a subjec
o con o e sy,20–26 ega ding he in e nal o su ace a ange-
men o he halide ion in he clus e . I is well es ablished ha
he s uc u e o wa e molecules in he icini y o an ion is
he esul o a comp omise be ween ion-wa e in e ac ions
and he coope a i e o ces binding he sol en . When anions
a e sol a ed by wa e molecules, he ionic hyd ogen bonding
dis up s o a gi en ex en he ne wo k o he sol en mol-
ecules depending on he pa icula ion. In his sense, he
luo ide ion ac s dis up ing he amewo k o wa e s uc u e
in i s close icini y, whe eas iodide does no induce his
pe u ba ion. This is one o he easons why luo ide hyd a-
ion s uc u e is di e en om ha o he o he halides.
Fluo ide hyd a ion has been s udied in g ea de ail in
li e a u e. In his way, quan um-mechanical27–37 and
QM/MM25,38 calcula ions, as well as classical39–44 and ab
ini io simula ions,45 ha e been ca ied ou . Ne e heless, po-
la izable luo ide ion-wa e in e ac ion po en ials jus based
on i s -p inciples ha e no been de eloped ye . In a pa allel
way, he iodide hyd a ion has been s udied by bo h
quan um23,28,36,46–50 and s a is ical51–55 me hods. Again, o
ou bes knowledge, he e is no ab ini io iodide ion-wa e
in e ac ion po en ial. In his wo k, we de elop i s -p inciples
halide ion-wa e in e ac ion po en ials and explo e he unda-
men al easons o he di e ences in halide hyd a ion.
The emainde o he a icle is o ganized as ollows: Sec-
ion II ou lines he compu a ional me hod. The de elopmen
o he luo ide- and iodide-wa e in e ac ion po en ials and
hei alida ion, as well as a compa ison o he mic ohyd a-
ion and hyd a ion along he g oup, is ca ied ou in Sec. III;
inally, he concluding ema ks a e p esen ed in Sec. IV.
II. METHODOLOGY
This sec ion is spli up in o wo pa s: in he i s one he
de elopmen o he luo ide- and iodide-wa e in e ac ion po-
en ials is explained and, in he second pa , he p ocedu es
o ca y ou minimiza ions o 关X(H2O)n兴⫺(X⬅F,I) clus e s
and Mon e Ca lo 共MC兲simula ions condi ions a e p esen ed.
A. De elopmen o luo ide- and iodide-wa e
in e ac ion po en ials
1. Ou line o he MCDHO model
The de elopmen o luo ide- and iodide-wa e in e ac-
ion po en ials has been pe o med adop ing a MCDHO- ype
model. This shell-model includes in amolecula lexibili y
and pola izable cha ac e in he desc ip ion o he species
ha o m he sys em o simula e. The wa e molecule is de-
sc ibed by h ee posi i e cha ges loca ed in he expe imen al
gas-phase geome y o he molecule, ZOand ZHbeing he
alue o he posi i e cha ges o he oxygen and hyd ogen
a oms, espec i ely. A nega i e mobile cha ge, qO⫽⫺ZO
⫺2ZH, a ached o he oxygen a om by an ha monic oscil-
la o is used o model he pola izabili y 共see Fig. 1兲. The
in amolecula lexibili y o wa e molecules is included by
means o a Mo se po en ial o he O–H bonds and a ou h
deg ee polynomial o he HOH angle, combined bo h wi h
he elec os a ic in e ac ion among he cha ges, excep he
in e ac ion be ween ZOand qOcha ges. In he case o he
halide anions, he monoa omic ion is desc ibed by a posi i e
cha ge, ZX⫺, and a nega i e mobile cha ge, qX⫺, wi h a o al
alue, qX⫺⫽⫺ZX⫺⫺1, a ached o i 共see Fig. 1兲. The in a-
a omic ene gy is de ined by UX⫺⫽1
2k 2, whe e is he dis-
ance be ween he co e and i s associa ed mobile cha ge.
Wa e -wa e and b omide ion-wa e MCDHO- ype in e -
ac ion po en ials ha e al eady been published in Re s. 14 and
15, espec i ely. The luo ide- and iodide-wa e in e ac ion
po en ials ha e been buil by means o i ing a se o 14
pa ame e s o each one on he basis o he ollowing in e -
molecula e ms:
共1兲a classical 12-6-1 po en ial be ween he nega i e mo-
bile cha ges qOand qX⫺, being he dis ance be ween hem,
and Aand B he Lenna d-Jones pa ame e s,
U共qO,qX⫺兲⫽
冉
AX–O
冊
12
⫺
冉
BX–O
冊
6
⫹qOqX⫺
;共1兲
共2兲an elec os a ic in e ac ion be ween qOand ZX⫺, ⬘
being he dis ance be ween he qOand he nucleus o halide
ion,
U共qO,ZX⫺兲⫽qOZX⫺
⬘
冋
1⫺
冉
⬘
␭O
⬘⫹1
冊
exp
冉
⫺2 ⬘
␭O
⬘
冊
册
,共2兲
whe e ␭O
⬘co esponds o he in e molecula sc eening and i
is esponsible o he densi y cha ac e o he mobile cha ge;
共3兲an elec os a ic in e ac ion be ween qX⫺and each
o he cha ges on he nuclei o he wa e molecule Zi(i
⬅O,H):
U共Zi,qX⫺兲⫽ZiqX⫺
i
冋
1⫺
冉
i
␭X⫺
⬘⫹1
冊
exp
冉
⫺2 i
␭X⫺
⬘
冊
册
,
共3兲
whe e iis he dis ance be ween qX⫺and Zi, and he ␭X⫺
⬘
no a ion has been main ained o in e molecula in e ac ions;
and
共4兲an in e ac ion po en ial be ween he halide nucleus
and each o he nuclei o he wa e molecule, which includes
he elec os a ic epulsion o hei espec i e poin -cha ges,
and has wo addi ional e ms:
FIG. 1. Schema ic ep esen a ion o MCDHO model. Posi i e cha ges ZO,
ZHand ZX⫺a e placed a he nuclei posi ions 共bold sphe e兲, and he mobile
cha ges qOand qB ⫺a e a ached o he oxygen a om and he b omide a om
by a ha monic oscilla o po en ial 共whi e sphe e兲.
9539J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Halide ion-wa e in e ac ion
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U共Zi,ZX⫺兲⫽CX⫺i
Ri
sX⫺i⫺DX⫺i
Ri
pX⫺i⫹ZiZX⫺
Ri,共4兲
whe e CX–O,CX–H,DX–O,DX–H,sX–O,sX–H,pX–O,
pX–H, a e adjus able pa ame e s, and Riis he dis ance om
he halide nucleus o he i- h nucleus o he wa e molecule.
2. Explo a ion o he luo ide- and iodide-wa e
po en ial ene gy su aces
The i s s ep o de elop a i s -p inciples in e ac ion po-
en ial is ca ying ou he explo a ion o he po en ial ene gy
su aces 共PES兲o he sys em. Dime s, 关X(H2O)兴⫺, and i-
me s, 关X(H2O)2兴⫺, we e conside ed in he case o he
luo ide- and iodide-wa e sys ems. Wa e molecules we e
desc ibed by he aug-cc-pVTZ basis se in he dime s,56–58
whe eas he aug-cc-pVDZ57–59 basis se was used o he
ime s. The use o he aug-cc-pVTZ and aug-cc-pVDZ basis
se is easonable60–62 o he s udy o clus e s wi h mo e han
one wa e molecule which e ain an impo an deg ee o hy-
d ogen bonding. The luo ide ion was desc ibed wi h he
aug-cc-pVTZ basis se ,56,57 in bo h dime s and ime s. An
e ec i e co e pseudopo en ial 共ECP兲was used o desc ibe
he co e elec ons in he desc ip ion o he iodide ion,
namely, he SDB-ECP,63 while he aug-cc-pVTZ basis se s
augmen ed wi h pola iza ion unc ions64 we e used o he
alence elec ons. P e ious s udies33,65,66 ha e emphasized
he need o aking in o accoun basis se s con aining di use
unc ions when hyd ogen bond plays a ole in he bonding.
The in e ac ion ene gy o he dime s we e ob ained wi h
Mølle –Plesse second-o de pe u ba ion heo y 共MP2兲,
whe eas he nonaddi i i ies o h ee-body e ms whe e com-
pu ed a he SCF le el. The basis se supe posi ion e o
共BSSE兲was co ec ed by he coun e poise me hod67 in he
case o he dime s. The choice o his compu a ional s a egy
was guided by ou ea lie wo k on he b omide hyd a ion,15
in which he desc ip ion o pai wise in e ac ions a he MP2
le el BSSE-co ec ed and he inclusion o h ee-body e ms
a he SCF le el we e sui able o de elop an app op ia e
i s -p inciples b omide ion-wa e in e ac ion po en ial.
Wha ’s mo e, he co esponding b omide ion-wa e in e ac-
ion po en ial, labeled as POT–2 in ou p e ious wo k,15 was
able o adequa ely ep oduce ou -body e ms e en hough
hey we e no included in i s de elopmen .
The e we e 526 dime s and 123 ime s conside ed in he
de elopmen o he luo ide-wa e in e ac ion po en ial,
which will be named he ea e POT–F. Dime s we e ob-
ained by scanning he F–O dis ance 共 om 1.5 o 6.0 Å兲, he
⬔FHO angle 共 om 180° o 50°) and he ⬔FHOH dihed al
angle 共 om 0° o 270°). Nine y- i e o he dime s consid-
e ed p esen ed a wa e molecule geome y di e en om he
expe imen al gas-phase one 共 he e e ence geome y used in
he MCDHO wa e model兲, i.e., he s uc u e o wa e mol-
ecules we e op imized in hose poin s. Wi h ega d o he
nonaddi i i ies, he geome ies o he wa e molecules we e
no cons ained o he expe imen al one. The geome ies o
he ime s we e aken du ing he op imiza ion p ocedu e o
关F(H2O)n兴⫺clus e s (n⫽2–6). To es i inclusion o he
h ee-body con ibu ions is able o accoun o he ep oduc-
ion o he ou -body ones, 103 e ame s, 关F(H2O)3兴⫺, we e
conside ed. The compu a ional le el o he e ame s was he
same as ha used o he ime s.
The iodide-wa e in e ac ion po en ial, labeled as
POT–I, was de eloped aking in o conside a ion 545 dime s
and 67 ime s. Again, dime s s uc u es we e ob ained by
scanning he I–O dis ance 共 om 2.0 o 6.5 Å兲, he ⬔IHO
angle 共 om 180° o 50°) and he ⬔IHOH dihed al angle
共 om 0° o 270°). All he wa e molecules in he dime s bu
one, ha co esponding o he 关I(H2O)兴⫺global minimum,
we e igid dime s, in he sense ha he expe imen al gas-
phase geome y was kep ixed. This app oxima ion is sup-
po ed by he small change be ween he op imized isola ed
wa e molecule geome y a he le el o compu a ion used
and he wa e molecule geome y a he global minimum o
关I(H2O)兴⫺. The geome ies o he ime s we e selec ed in a
simila way o he luo ide case.
All he calcula ions we e ca ied ou wi h he GAUSS-
IAN 98 p og am package.68
3. Fi ing p ocedu e
The in e ac ion ene gy de i ed om he PESs o he
luo ide- and iodide-wa e clus e s we e i ed o Eqs. 共1兲–共4兲
by means o a leas -squa e i ing. Table I shows he se o
pa ame e s o POT–F and POT–I and he goodness o he
i . Valida ion o he po en ials has been ca ied ou by com-
pa ing he esul s o clus e s minimiza ions and MC simula-
ions wi h he a ailable expe imen al and heo e ical da a.
B. Minimiza ions p ocedu e and Mon e Ca lo
simula ions condi ions
Nume ical minimiza ions o he halide clus e s and MC
Me opolis simula ions o he halide ion in wa e we e ca -
ied ou using he MCHANG p og am de eloped by Cue na-
aca g oup.69
TABLE I. POT–F and POT–I pa ame e s in a. u. The s anda d de ia ions
␴
a e in kcal/mol and show he deg ee o con idence o he i . The pa ame e s
ZO,qOand ␭O
⬘used in Eqs. 共1兲–共4兲we e ob ained in he de elopmen o he
MCDHO wa e model 共Re . 14兲and ha e a alue o 2.6, ⫺3.9, and
0.555 050 09, espec i ely.
Pa ame e s POT–F POT–I
ZX0.78 12.017
qX⫺1.78 ⫺13.017
k0.483 062 09 4.499 825 6
AX–O 2.670 081 7 ⫺3.832 845
BX–O 1.891 122 18 ⫺2.650 078
␭X⫺
⬘0.606 084 10 0.667 162 62
CX–O 357.9775 277.961 27
sX–O 5.387 649 6 5.565 085 0
DX–O ⫺257.792 46 ⫺156.019 07
pX–O 5.168 734 1 4.963 832 9
CX–H 19.124 510 34.117 550
sX–H 7.742 733 4 7.859 578 8
DX–H 38.481 319 17.218 706
pX–H 9.106 964 7 10.649 260
S anda d de ia ions
␴
F⫺0.8920
I⫺0.2288
9540 J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Ayala
e al.
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Nume ical minimiza ions o 关X(H2O)n兴⫺(X⬅F,I and
n⫽1–6) clus e s we e pe o med a 0 K. These clus e s
we e minimized in acuum, wi h no pe iodic bounda y con-
di ions. Kim e al.27,28,36 among o he s,15,16,25,32,38,45,70,71
show he g ea numbe o possible minima ha a e accessible
in halide ion-wa e PESs. The in e play be ween ion-wa e
and wa e -wa e in e ac ions esul s in he exis ence o mo e
han one s uc u e exhibi ing di e en hyd ogen bonding ne -
wo k and simila ene gies. To ensu e adequa e sampling o
he mul idimensional PESs, minimiza ions ini ia ed a di e -
en s a ing poin s we e pe o med. On one hand, he
关B (H2O)n兴⫺minima s uc u es ob ained in ou p e ious
wo ks15,16 we e chosen as ini ial guess. On he o he hand,
andom geome ies we e aken as s a ing con igu a ions.
To compa e wi h expe imen al binding en halpies o
关X(H2O)n兴⫺clus e s, ⌬Hbind , MC simula ions in he ca-
nonical ensemble 共NVT兲a 300 K we e pe o med, including
la e on he en halpy co ec ion. To his end, we ha e aken
he app oxima ion o he ideal gas beha io o he o ma ion
eac ion o he ionic clus e , i.e., ⌬(PV)⬃⌬nRT.
MC simula ions 共NVT兲a 298.15 K we e also pe -
o med. Pe iodic bounda y condi ions and a sphe ical cu o
adius o Rcu ⫽L/2, Lbeing he box leng h, we e used. Box
dimensions we e chosen o keep he densi y equal o
0.997 g/cm3 o he di e en sys em sizes conside ed. The
Ewald Summa ion echnique10 including he cha ged sys em
e m72,73 was used o handle long- ange coulombic in e ac-
ions. The ⬃40% o accep ance o he con igu a ions gen-
e a ed was kep du ing he simula ion. De ails o he di e en
simula ion sys ems conside ed a e con ained in Table II.
Long equilib a ion pe iods we e pe o med because he in-
clusion o he pola izabili y and he in amolecula lexibili y
highly inc eases he numbe o deg ees o eedom o he
sys em, compa ed o igid and nonpola izable pa icles.
P e ious o discussing he alida ion o he po en ials,
he capabili y o POT–F o ep oduce ou -body nonaddi i i-
ies will be p esen ed. Figu e 2 illus a es he co ela ion be-
ween ou -body con ibu ions a SCF le el and hose de-
i ed om POT–F, indica ing ha a i s -p inciples halide
ion-wa e in e ac ion po en ial ha includes h ee-body con-
ibu ions is able o ep oduce highe o de e ms.
III. RESULTS AND DISCUSSION
A. Minimiza ions
Nume ical minimiza ions o clus e s uc u es wi hou
cons ain s we e ca ied ou . Some ep esen a i e esul s a e
shown in Fig. 3. I s analysis shows how wa e molecules in
关F(H2O)n兴⫺clus e s in e ac wi h he ion qui e indi idually.
The F⫺–H2O in e ac ion ene gy is s onge han ha o he
es o he halide ions, being esponsible o he dec easing
o he hyd ogen bonds among wa e molecules. Fo n⬎3, he
p esence o wa e molecules in he second hyd a ion shell
becomes impo an . F⫺–H2O in e ac ion ene gy is abou i e
imes mo e s abilizing han he H2O–H2O one, he e o e, in
a i s s ep, i is di icul o unde s and his end. The analy-
sis o he dipole momen o wa e molecules cla i ies he
eason o he p e e ence o wa e molecules in he second
sol a ion shell agains a di ec in e ac ion wi h he luo ide
ion. The alues o he wa e dipole momen
兩
␮
ជ
H2O
兩
and he
F–O dis ance o wa e molecules in some o he clus e s
conside ed a e displayed in Table III. In clus e e, wa e mol-
ecules simul aneously in e ac ing wi h he luo ide ion and
he wa e molecule o he second sol a ion shell p esen a
highe alue o dipole momen module han hose in clus e
d共2.8 D e sus 2.6 D兲, as well as sho e F–O dis ances 共2.6
Å e sus 2.7 Å兲. These wo e ec s a e esponsible o he
g ea s abili y o he clus e e. On one hand, he F⫺–H2O
in e ac ion ene gy inc eases ⬃4.5 kcal/mol o each wa e
molecule in e ac ing wi h a second sol a ion shell sol en
molecule 共1-2 and 2-3兲in clus e ewi h espec o he
F⫺–H2O in e ac ion ene gy in clus e d. The
F⫺–(H2O)2nd shell in e ac ion ene gy is 14.6 kcal/mol smalle
han he a e age o F⫺–H2O1s shell in e ac ion ene gy in
clus e d. On he o he hand, he o al H2O–H2O in e ac ion
ene gy in clus e eis s abilized by 5.1 kcal/mol compa ed o
clus e d. This beha io appea s in he di e en minima
sampled; o example, all he wa e molecules in clus e
FIG. 2. Compa ison o he ab ini io and POT–F ou -body con ibu ions.
Ene gies in kcal/mol.
TABLE II. De ails o he sys ems conside ed in he Mon e Ca lo simula-
ions (M⬅106and G⬅109).
Sys em No. o
ions No. o wa e
molecules L 共Å兲
No. o
equilib a ion
s eps No. o un
s eps
F⫺
A 1 120 15.3668 300 M 1 G
B 1 215 18.6399 500 M 1 G
C 1 511 24.8520 500 M 1 G
B ⫺
A 1 116 15.3406 300 M 800 M
B 1 211 18.6221 500 M 3.5 G
C 1 507 24.8420 500 M 1 G
I⫺
A 1 115 15.4088 300 M 1 G
B 1 210 18.6684 500 M 1 G
C 1 506 24.8680 500 M 1 G
9541J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Halide ion-wa e in e ac ion
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p esen a alue o he dipole momen module in he ange
2.5–2.6 D, while he wo i s -shell wa e molecules ha in-
e ac wi h he hyd ogen a oms o he wa e molecule in he
second sol a ion shell in clus e hha e a la ge dipole mo-
men 共2.7 D兲, as well as a sho e F–O dis ance. Likewise,
he e is an inc easing o he dipole momen module 共3.0 and
2.9 D兲and a sho ening in he ion–wa e dis ances o hose
sol en molecules in e ac ing wi h he second sol a ion shell
in clus e kcompa ing o hose in clus e j共2.5 D兲.I is
ema kable ha dipole momen s o wa e molecules depend
s ongly on hei loca ion in he clus e . The pola iza ion o
i s -shell wa e molecules due o he luo ide ion inc eases
he in e ac ion be ween i s and second shell wa e mol-
ecules o such ex en ha makes compe i i e he loca ion o
wa e molecules in he second shell. This ac has al eady
been discussed by Vaughn e al.45 in a p e ious s udy o
关F(H2O)4兴⫺clus e s.
The ex en o he halide ion-wa e in e ac ion dec eases
as descending in he g oup, going om ⬃⫺26 kcal/mol o
he luo ide ion o ⬃⫺10 kcal/mol o he iodide ion. The
small iodide ion-wa e in e ac ion ene gy leads o a mo e
impo an compe i ion be ween H2O–H2O and I⫺–H2O in-
e ac ions, enhancing he impo ance o H2O–H2O s uc-
u es, especially compa ed o he luo ide ion. A ailable
quan um-mechanical s udies abou 关I(H2O)n兴⫺clus e s
show se e al simila i ies wi h espec o 关B (H2O)n兴⫺
ones.28,32,36 Some ep esen a i es esul s o he 关I(H2O)n兴⫺
(n⫽1–6) minimiza ions a e also displayed in Fig. 3. I is
wo h poin ing ou he g ea impo ance o he H2O–H2O
in e ac ions wi h espec o he es o he halide ions. In his
sense, H2O–H2O in e ac ion is ⫺5.92 kcal/mol in he
关B (H2O)2兴⫺minimum and ⫺8.17 kcal/mol in he
关I(H2O)2兴⫺one 共Fig. 3 B兲. Likewise, H2O–H2O con ibu-
ions o he o al in e ac ion ene gy in 关B (H2O)4兴⫺and
FIG. 3. Op imized minimum ene gy geome ies o
关F(H2O)n兴⫺and 关I(H2O)n兴⫺clus e s (n⫽1–6) ob-
ained wi h POT–F and POT–I, espec i ely. In e ac-
ion ene gies appea be ween squa e b acke s in kcal/
mol. 关F(H2O)n兴⫺and 关I(H2O)n兴⫺clus e s a e labeled
in small le e s and capi al le e s, espec i ely.
关B (H2O)n兴⫺agg ega es a e aken om Re . 15.
9542 J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Ayala
e al.
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关I(H2O)4兴⫺global minima 共Fig. 3 E兲a e ⫺13.4 and
⫺17.6 kcal/mol, espec i ely. This beha io is epea ed
along all minima in es iga ed.
The a angemen o wa e molecules a ound halide ions
e eals impo an di e ences be ween he luo ide and he
b omide and iodide ions. The b omide and iodide ions cause
a small pe u ba ion in he amewo k o wa e molecules
s uc u e, while he luo ide ion is able o dis up ha s uc-
u e. In ac , he pa e ns ha can be iden i ied in pu e wa e
can also be ecognized in he b omide and iodide hyd a es,
he e ec being mo e no iceable in he la e case. The size o
hese wo anions allows ion-wa e in e ac ions wi hou sub-
s an ial inc easing o wa e -wa e dis ance which would de-
s abilize he sys em. F om n⭓2, B ⫺- and I⫺-wa e clus e s
a e mainly supe icials; by being on he su ace he anion
does no al e he hyd ogen bonded ne wo k be ween he
wa e molecules lowe ing he o al ene gy o he clus e .
关F(H2O)n兴⫺clus e s a e cha ac e ized because wa e mol-
ecules o m a chain in which end wa e s in e ac wi h he ion
whe eas he cen al wa e does no 共e.g., e,g,h, in Fig. 3兲.
Con a y, wa e molecules in e ac simul aneously among
hem and wi h halide ion in 关B (H2O)n兴⫺and 关I(H2O)n兴⫺
clus e s 共e.g., D,E,F, in Fig. 3兲.
The analysis o Fig. 3 indica es a g ea e impo ance o
he in e io s uc u es in he case o he luo ide agg ega es
wi h espec o he b omide and iodide ones. Besides, he
ene gy di e ences be ween in e io and su ace clus e s in-
c ease as descending in he g oup 共see o example clus e s k
and l o F⫺ion and Jand K o I⫺ion兲.
P e ious s udies ha e shown25,27,28,36,45,74 ha he gap
be ween su ace and in e io s a es dec eases when ze o poin
ib a ional e ec s and he mal co ec ions a e aken in o
conside a ion. These e ms could e e se he s abili y o de
in he case o he luo ide ion.
The compa ison o he in e ac ion ene gies o he
minima ob ained wi h POT–F and POT–I and hose com-
pu ed om ab ini io calcula ions28,32,36 is shown in Table IV.
The e is a good co ela ion especially when la ge basis se s
a e used a he MP2 le el. I is signi ican o men ion ha no
only a e he alues e y simila o he ab ini io esul s bu
also he s abili y o de de i ed om he de eloped po en ials
holds up. The only disc epancy appea s o n⫽4 in he case
o he luo ide ion; ne e heless, p e ious esul s32,36,38 abou
he ela i e s abili y o hese wo s uc u es 共dand e兲and he
small di e ences be ween hem make his pa icula case less
impo an .
The compa ison o he expe imen al en halpies o bind-
ing o halide ion-(H2O)nclus e s a 300 K, ⌬Hbind , wi h
da a de i ed om POT–F and POT–I is shown in Table V.
Es ima ions gi en by o he in e ac ion po en ials a e also in-
cluded in he able. I is no ewo hy ha classical simula ions
canno be e ec i ely pa ame ized o desc ibe quan um be-
ha io s, such as unneling e ec s. Thus, he expe imen al
TABLE III. Va ia ion o he dipole momen o he wa e molecules in he
关F(H2O)n兴⫺clus e s.
S uc u es F–O dis ance
共Å兲
兩
␮
ជ
H2O
兩
共D兲S uc u es F–O dis ance
共Å兲
兩
␮
ជ
H2O
兩
共D兲
a2.49 3.09 b2.55 2.87
2.55 2.87
2.62 2.61 2.59 2.81
d2.68 2.67 e2.59 2.81
2.68 2.65 2.60 2.61
2.69 2.66 4.02 2.58
2.68 2.51 2.62 2.73
2.72 2.61 2.62 2.73
2.75 2.60 h2.64 2.56
2.76 2.55 2.77 2.57
2.82 2.56 3.73 2.53
2.80 2.53 2.55 3.01
2.80 2.53 2.64 2.55
j2.80 2.53 k2.68 2.89
2.80 2.53 2.80 2.54
2.80 2.53 4.03 2.57
2.80 2.53 4.03 2.58
TABLE IV. Compa ison be ween esul s calcula ed using he in e ac ion po en ials de eloped and ab ini io
me hods. In e ac ion ene gies in kcal/mol.
S uc u eanPOT–Fab ini io S uc u eaPOT–Iab ini io
a1⫺26.4 ⫺26.1⫾0.6,b⫺25.9⫾1.5cA⫺10.5 ⫺10.6⫾0.6c
b2⫺47.6 ⫺47.3⫾1.0,b⫺46.5⫾2.6cB⫺22.6 ⫺22.3⫾1.5c
c3⫺65.3 ⫺64.9⫾1.4,b⫺63.7⫾3.7cC⫺36.6 ⫺35.4⫾2.9c
d4⫺80.5 ⫺79.7⫾1.7,b⫺78.9⫾4.9cD⫺46.0 ⫺44.6⫾3.73c
e4⫺80.6 ⫺78.3⫾5.3cE⫺49.4 ⫺48.0⫾4.3c
5⫺92.7 ⫺90.2dF⫺59.3 ⫺54.59d
g5⫺94.1 ⫺90.6dG⫺61.2 ⫺56.26d
i6⫺105.3 ⫺100.6dI⫺66.1 ⫺60.8d
l6⫺109.2 ⫺106.2dL⫺73.5 ⫺67.7d
m6⫺111.3 ⫺107.4dM⫺73.5 ⫺67.7d
aMinimum s uc u es conside ed a e displayed in Fig. 3.
bIn e ac ion ene gies a MP2/TZ(2d ,pd)⫹⫹ le el, epo ed in Re . 28. In e ac ion ene gy is compu ed as
ollows: ⌬Ee⫽(⌬Ee
N⫹⌬Ee
B)/2⫾BSSE/2, whe e ⌬Ee
Nand ⌬Ee
Ba e he in e ac ion ene gies wi hou and wi h
BSSE co ec ion.
cIn e ac ion ene gies a MP2/6-311⫹⫹G** le el, epo ed in Re . 28. In e ac ion ene gy is compu ed as in he
p e ious no e.
dIn e ac ion ene gies a BLYP/6-311⫹⫹G** le el, epo ed in Re . 36. In e ac ion ene gies included 50% o
BSSE co ec ion.
9543J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Halide ion-wa e in e ac ion
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indings can only be ep oduced easonably. The ag eemen
ound is accep able conside ing ha de ia ions a e smalle
han 5%.
In he case o he luo ide ion, bo h quan um27–36 and
s a is ical25,38–45 calcula ions pos ula e he exis ence o
minima whe e no all he wa e molecules di ec ly in e ac
wi h he halide ion. Ne e heless, Caba cos e al.29 do no
ind e idences o H2O–H2O hyd ogen bonding h ough he
s udy o O–H s e ching egion in he expe imen al ib a-
ional spec a o size-selec ed 关F(H2O)3⫺5兴⫺clus e s a
⬃300 K. Among he expe imen al echniques, ib a ional
spec oscopy is an especially use ul ool since a ib a ional
analysis may con i m o exclude he exis ence o pa icula
s uc u al agmen . I seems hen in e es ing o s udy he
e ec o empe a u e on he s uc u e o 关F(H2O)n兴⫺clus-
e s. The analysis o 200M (M⬅106) con igu a ions o n
⫽3–4 a 300 K showed he p e alence o s uc u es which
do no p esen wa e -wa e hyd ogen bonds agains hose ha
do p esen hem. Howe e , in he case o n⫽5, he pe cen -
age o s uc u es wi h hyd ogen bonds is mo e signi ican . I
may be s essed ha he e is no a igid de ined s uc u e a
his empe a u e, la ge geome y luc ua ions and wa e ex-
changes being a o ed, so ha one should no y o educe
he unde s anding o halide hyd a ion in e ms o local
minima a 0 K.
B. Mon e Ca lo simula ions
In o de o desc ibe he he modynamic and s uc u al
p ope ies o he halide hyd a ion and compa e among hem,
nume ical MC simula ions unde he condi ions p e iously
desc ibed we e pe o med.
A summa y o he he modynamic and s uc u al p ope -
ies de i ed om nume ical MC simula ions con aining he
halide ions is gi en in Table VI.
1. X
–
O and X
–
H RDFs
The F–O and F–H RDFs, as well as hei unning in e-
g a ion numbe s, a e displayed in Fig. 4. The F–O RDF
shows a i s peak cen e ed a 2.7 Å which goes down o 0.16
and in eg a es o 5 oxygen a oms. The i s peak o F–O
RDF is sha pe han in he case o he b omide and iodide
ions. In he same way, F–H RDF p esen s a i s peak cen-
e ed a 1.65 Å and also in eg a es o 5 hyd ogen a oms,
indica ing ha all he wa e molecules o he i s sol a ion
shell o ien one o hei hyd ogen a oms owa d he luo ide
ion. In ou p e ious wo k,15 he in eg a ion numbe s o oxy-
gen and hyd ogen a oms a ound he b omide ion we e 7 and
6, espec i ely, which indica ed an incomple e linea i y o
hyd ogen bonding in he i s hyd a ion shell wi h ega d o
he ion.
The I–O and I–H RDFs and hei unning in eg a ion
numbe s a e also displayed in Fig. 4. The I–O and I–H
RDFs show a i s peak cen e ed a 3.64 and 2.71 Å, espec-
i ely. The i s one in eg a es o ⬃8 oxygen a oms and he
second one o ⬃6 hyd ogen a oms.
The analysis o he se o X–O and X–H RDFs in Fig. 4
shows ha he deple ion beyond he i s peak disappea s as
descending in he g oup. This complica es he quan i ica ion
o he coo dina ion numbe s as a consequence o he inc eas-
ing exchange be ween i s and second sol a ion shells. Ex-
pe imen al e idences show his ac .1Fu he mo e, he
highe he a omic numbe is, he g ea e di e ence appea s
be ween he X–O and X–H coo dina ion numbe s 共see Table
VI兲. This beha io could lie on he o ien a ion o he wa e
molecules a ound he halide ion. Besides, he ela i e impo -
ance o he second and hi d peaks dec eases wi h espec o
FIG. 4. X–O and X–H adial dis ibu ion unc ions and hei unning num-
be s om Mon e Ca lo simula ions.
TABLE V. Compa ison o he expe imen al binding en halpies o he o ma ion eac ion o he ionic clus e a
300 K wi h he es ima ions de i ed om POT–F and POT–I. Ene gies in kcal/mol.
nPOT–F O he po en ials Exp. POT–I O he po en ials Exp.
1⫺24.7 ⫺26.5a⫺23.3c⫺9.5 ⫺10.2,e⫺10.2 ⫺10.2,c⫺10.2d
2⫺44.2 ⫺48.1,a⫺45.5b⫺39.9,c⫺42.5d⫺19.3 ⫺19.8,c⫺20.0 ⫺19.8,c⫺20.0d
3⫺60.2 ⫺66.4,a⫺61.8b⫺53.6,c⫺57.8d⫺30.0 ⫺29.5,c⫺29.6 ⫺29.0,c⫺29.4d
4⫺72.1 ⫺80.2,a⫺73.6b⫺67.1,c⫺71.7d⫺40.6 ⫺39.0,c⫺39.1 ⫺38.2,c⫺38.5d
5⫺83.0 ⫺91.1,a⫺86.2b⫺80.3,c⫺84.0d⫺51.5 ⫺48.1,c⫺48.5c⫺47.2d
6⫺92.8 ⫺101.6,a⫺96.4b⫺94.6c⫺61.4
7⫺102.2 ⫺112.0,a⫺109.1b⫺105.3c
8⫺115.8 ⫺120.7,a⫺118.7b⫺116.5c
9⫺129.9 ⫺134.3,a⫺128.5b⫺127.6c
aRe e ence 40.
bRe e ence 42.
cRe e ence 6.
dRe e ence 79.
eRe e ence 52.
Re e ence 53.
9544 J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Ayala
e al.
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he i s one as descending in he g oup, indica ing a loss o
s uc u e in he second and hi d sol a ion shells.
2. Dis o ion o wa e molecules
The e ec s o he anion p esence on he in amolecula
geome y o he wa e molecules ha e been in es iga ed. S a-
is ically independen samples o 60 M con igu a ions we e
analyzed o sys ems con aining 1 luo ide ion and 215 wa e
molecules, 1 b omide anion and 211 wa e molecules, and 1
iodide ion and 210 wa e molecules. Along he di e en a-
jec o ies he ollowing pa ame e s we e s udied: he ⬔HOH
angle and he O–H dis ance.
The dis o ion o he wa e molecule angle as a unc ion
o he X–O dis ance is shown in Fig. 5共a兲. The dis ibu ion
o his alue in he i s sol a ion shell is displayed in Fig.
5共b兲. The analysis o bo h plo s concludes ha wa e mol-
ecules do no su e impo an angula dis o ions in he i-
cini y o he anion. The halide e ec on he wa e s uc u e is
mo e signi ican on he O–H dis ance 关Fig. 5共c兲兴. This dis-
o ion dec eases when going om F⫺ o I⫺, only being
impo an in he i s hyd a ion shell.
I is wo h s essing ha wa e dis o ion is mo e impo -
an om an ene ge ic poin o iew han om a s uc u al
one. The compa ison be ween he ene ge ic cos o wa e
dis o ion in he 关F(H2O)兴⫺and 关Li(H2O)兴⫹global mini-
mum s uc u e is 5.17 e sus 0.05 kcal/mol. This ac could
be su p ising aking in o accoun ha he ca ion-wa e in e -
ac ion is mo e impo an han he anion-wa e one (⫺36.6
e sus ⫺26.4 kcal/mol).75 Ne e heless, ca ion-wa e in e -
ac ion is mainly an ion-dipole one, whe eas anion-wa e in-
e ac ion is based on a s ong hyd ogen bonding. Thus, wa e
dis o ion in he 关F(H2O)兴⫺clus e implies a nonsymme ic
leng hening o he O–H dis ance which assumes a highe
ene gy cos .
3. O ien a ional pa ame e s
The e ec o he halide on he amewo k o wa e mol-
ecules in i s icini y has also been in es iga ed by means o
he analysis o he il angle,
␾
, o med by he wa e dipole
momen and he X–O ec o , and he ⬔XHO angle,
␥
共Scheme 1兲:
Figu e 6共a兲shows he a ia ion o he
␾
and
␥
angles as
a unc ion o he X–O dis ance. The e is a dec easing o he
␥
angle o he wa e molecules close o he ion as descend-
ing in he g oup. This a ia ion is caused by wo di e en
e ec s. On one hand, he linea i y o he X-wa e hyd ogen
bonding dec eases, as al eady obse ed o he dime s. On
he o he hand, he loss o o ien a ion o wa e molecules in
he i s hyd a ion shell om F⫺ o I⫺causes a dec easing o
he a e age alue o he
␥
angle. The analysis o he dis i-
bu ion o
␾
and
␥
angles in he i s hyd a ion shell 关Figs.
6共b兲and 6共c兲, espec i ely兴indica es an inc easing o he
dispe sion o hese alues om F⫺ o I⫺.
4. Wa e dipole momen
The use o a pola izable model allows he s udy o he
a ia ion o he wa e dipole momen in halide solu ions. The
dis ibu ion o he module o he dipole momen o wa e
molecules,
兩
␮
ជ
H2O
兩
, in he i s hyd a ion shell o he halide
ion and one wa e molecule in pu e wa e is shown in Fig.
7共a兲. The analysis o his plo indica es a dec easing o he
magni ude as descending in he g oup. This dec easing is
pa ly esponsible o he di e en s uc u es o luo ide-
TABLE VI. Summa y o he s uc u al and ene ge ic p ope ies de i ed om Mon e Ca lo simula ions 共
␣
in Å3and ene gies in kcal/mol兲.
Pa ame e s POT–FO he
po en ials Exp . POT–B aO he
po en ials Exp . POT–IO he
po en ials Exp .
␣
F⫺0.97 0.87b4.0 4.85b5.8 7.5b
⌬Hhydc⫺134.5⫾8⫺78.5⫾3⫺74.2⫾4
⌬Hhydd⫺132.0⫾5⫺115⫾4 ⫺124.⫾10g⫺80.8⫾5⫺82.5⫾4⫺75.7⫾6⫺64.4⫾3,h⫺81.2⫾4i⫺71.4⫾10g
⌬Hhyde⫺137.8⫾8⫺81.5⫾4⫺76.2⫾10
gX–O( )
max. i s peak 2.65 2.7 2.62–2.69j3.43 3.37 3.30–3.43 3.64 3.55,h3.60,i3.68k3.55–3.70j
Ncoo X–O
i s shell
5.1 6, 5.7l4–6j7.0 7.5m6–8j8.3 6.5,h7.3,i8.7l6–9j
gX–H( )
max. i s peak 1.7 2.50m2.32 2.71 2.55,g2.70,h2.70l
Ncoo X–H
i s shell
5 5.96 5.7m6
aPOT–B was labeled as POT–3 in Re . 15.
bRe e ence 3.
cAll he p ope ies e e o he sys em labeled in Table II as A.
dAll he p ope ies e e o he sys em labeled in Table II as B.
eAll he p ope ies e e o he sys em labeled in Table II as C.
Re e ence 40.
gRe e ence 2.
hRe e ence 53.
iRe e ence 52.
jRe e ence 1.
kRe e ence 80.
lRe e ence 39.
mRe e ence 76.
9545J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Halide ion-wa e in e ac ion
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wa e clus e s and he b omide and iodide-wa e ones. The
same consequence is ob ained when he a ia ion o
兩
␮
ជ
H2O
兩
wi h he X–O dis ance is conside ed 关Fig. 7共b兲兴.
5. Induced dipole momen and pola izabili y
o halide ion
The induced dipole momen o halides can also be com-
pu ed because o he pola izable cha ac e o he anion in he
model used. A alue ⬃0.2 D is ob ained o he luo ide ion.
The alues o his magni ude o he b omide and iodide ions
a e in he in e als 0.8–0.9 and 1.2–1.5 D, espec i ely. The
inc easing o he
兩
␮
ជ
X⫺
兩
wi h a omic numbe is a consequence
o he pola izable cha ac e o he halide ions. In he case o
b omide ion, Raugei and Klein76 ge simila esul s o he
alue o
兩
␮
ជ
B ind
⫺
兩
in an ab ini io simula ion s udy. On he
o he hand, Tun
˜
on e al.77 ob ain a much smalle dipole mo-
men 共0.21 D兲in a QM/MM s udy o b omide aqueous so-
lu ions. Raugei and Klein76 explain he disc epancy wi h
QM/MM esul s on he basis o he nonpola izable wa e
FIG. 5. S uc u al p ope ies o wa e molecules ob ained om MC simula-
ions wi h POT–F, POT–B and POT–I. 共a兲A e age HOH angle as a unc-
ion o he X–O dis ance. 共b兲Dis ibu ion o he angle in he i s sol a ion
shell is displayed. 共c兲A e age O–H dis ance nea e o he halide ion as a
unc ion o he X–O dis ance.
FIG. 6. O ien a ional pa ame e s o wa e molecules wi h espec o he
halide anion, as de ined in Scheme 1:
␥
is he ⬔XHO angle, and
␾
is he
angle be ween he dipole momen o a wa e molecule and he ec o con-
nec ing he anion and he oxygen a om. 共a兲A e age
␥
and
␾
angles as
unc ions o he X–O dis ance. 共b兲Dis ibu ion o he angle
␾
in he i s
sol a ion shell. 共c兲Dis ibu ion o he angle
␥
in he i s sol a ion shell.
9546 J. Chem. Phys., Vol. 119, No. 18, 8 No embe 2003 Ayala
e al.
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