Solute electronic structure and solvation in chemical reactions in solution

SOLUTE ELECTRONIC IN SOLUTION

JAMES

-I-. HYNES.

STRUCTURE

HYUNG

Department USA

of Chemistry

(Received

.Ju ty IS,

AXD

SOLVATION

J. KIM. JEFFERY

R. MATHIS.

and Biochemistry.

University

IN CHEMICAL

REACTIONS

and J. JUANOS

of Colorado,

Boulder,

i TIMONEDA

CO 80309-02

15.

1992)

ABSTRACT A review efforts,

is given of a recent theoretical

novel aspects

of the theory

time scales

of the solvent

encrgetics.

The

theory

include

electronic

approach

incorporation

poliIriz3tion

is illustrated

to the issue of the title. of norequi!ibrium

and construction

with examples

of electron

Compared

soIvation.

of reaction 2nd proton

to past

attention

paths

to

and free

transfer

and

Ss:I

ionization.

I. INTRODUCTION Whik

there cIearly

classic31.

nuclear

example.

the theory

effects

types

aspects

wili influence above

[3].

0167~7322/93/$05.00

useful

by the solvent. the reaction

stage

microscopic in interpretin,

compu:er

of maturity.

of solvent

State Theory

For

dynamical

value has proven

simulations

0 experimental

of the

io

for a v;ide range

results

\velI [a].

3s

A

for a survey. of prediction

is comparatively

barrier

height.

developed_

on solution

By contrast.

5cicncc Publishers

for, solute electronic

poorly

impact

only the (nonexponential)

Q 1993 - Elscvicr

3 certain

for ;Issessin, 0 the influence

will have a significant

free energy

influence

has reached

of. and capzbi!ity

in solution

to say that our understanding

below its Trunsition

to detailed

may be consulted

reactions

II,21

rate constax

our understJnciing

wiI1 generalIy

reactions

and Hpnes

It has proven

[3.5]

of chemical

their alteration

of Grate

when compared

of reviews However.

of solution

the reaction

successful

of reaction number

aspects

on reducing

k highly

is more IO learn. it seems reasonable

reaction

the dynamical

prefactor

These

structure!

features.

and

rates. since they effects

in the reaction

B.V. Ail rights rcscmcd

referred

rate constant.

to

Quantum

chemical

transfer

electronic

features

or shift in polar sol\cnts. studied.

completely self-consistent special

aspects

One csample

or significantly

for. solute eIectronic

past efforts.

profiles

field methods

to examine

polarization.

The ourline framework.

ii;r!ude

which

The

remaining

electron

transfer

give 3 brief overview

problem

the barrier

soiute electronic

have

often

is

involving

structure

b) explicit

reaction

context

in the

whether

3 self-consistent

to

or Born-

on reaction

energetic

coupling. the issues and the theoreticzi

deal with the kA&hIights of the results

and a fe\v highlights

[!I]. Compared

of the time scale of the

and c) a focus

In Sec. 2. we sketch

ionization

and construct

to be out of equilibrium

incorporation

is rtppropr’-!te;

is 3s follows.

to understand

for the solvent

in part determines

(Sec. 3). Ssl

in solution

there are many studies

in LLchrmicat

I ange of solute etecrronic

seciiczs

interactions.

[6]. in which

of our o\vn efforts

a) allo$rxnce

description

of this review

charge

to the solute.

salvation:

or some intcrmedizte

and paths. OVCTthe entire

systems:

Further.

involving

solute-solvent

structure

by the soIvent.

in so!ution

involved

electronic rrrlnsfers

;_eview of some

i..e.. nonequilibrium

electronic

Oppenheimer

in reactions

important

electron

is eqc,l!ibrrlted structure

the nw* aspects

with the solute. solvent

is activated

[7] and direct ]S ] rextior:

I-icre we i_ sent ;1 brief theories

of the solute

determined

case lvhon the solvent

be especially

where there are strong Coulombic

Actu~~lly. some special long been

should

(Sec. 4). and proton

for differing

(Sec. 5). We only

transfer

in each case, and refer the reader

reaction

to the origina!

papers

for dctzils.

2. THEORY

Consider

A central issue of electronic structure 3s an rsampIe (91 t\\‘o degenerate

symmetric coupling

between

ground

transfer

discussed

). while

the Ss!

ionization Whiie

in tl,_, manner

a moiccular

. with ID=.&. The

ofa delocalized. instead \vi!l

tivor

ba.rriers for acrivated.

adiabatic

interactions

that localized

resonance symmetric

of either

structure.

eleccronica~ly

consequence

cr

electronic

electronically

the Coulombic

191. One important

description

at any point 5 in the solvent,

vibrational

DA-

Although

adiabatic

striking

not

ET reactions

of this competition

prrriicularly

diabstic

is that the

example

of this is

(Sec. 4).

In this description,

‘orientational’

-

will be rlltcrcd by the solvent-a

to date have adopted

approach.

solvent

this way. rhe activation structure

D-A

the formation

lvith ;1 polar and polarizable

solute electronic

and

system

them xvi11fwor

can bc comprehended

efforts

(ET)

i w _\-,, + w,,state Y’s = -@

structure usually

electron

in solution is that of delocalization versus localization. diabetic vrtlence bond states V,,-* 2nd W,,for a

polxitation degrees

o f the solvent

a dielectric the solvent related field

continuum

is desirable [ 101 solvent

is characterized

to the electronic

polsrizability

of the solvent

characterization

bjf an electronic

poL.(x). rt=Izted to the nuclear

of freedom)

(and under

molecules.

e.g..

our

3s II useful

polarization

of the solvent

drier.tation

construction).

first

field F&(x)

molccuks.

and an

(as well as translational their

permanent

dipole

moments. electric

The electric

susceptibilities

Xi- the prcportionality

field for these (bvhen equilibrium

=&

x cl

I)

(lo-

x,, =

;

where E, is the high-frequency StrJrring

from

D-eating ECl(x_) in a quantum v. represented

Here Gno

=

and Gsc

approximations,

or static. dielectric

for the nonequilibrium

fashion

sketched

over two diabatic

below.

valence

free

energy

sollrre.

The fraction f = p(2clcr

constant.

of the system.

and with the solute wave function

bond states. (2)

solute-solvent

system

is found to be 191

(WiHol~)-~(l-~)~d~Ano.sc

described

and the spatial

10d

(1)

.

and EIQis the Io*v-frequency

arc. the free energies

solute.

+ pj-l

Lvith the electronic

in the F3orn-Oppenheimer

in some derail

integrals

where the ratio p involving associated

(CO -z&a)

expression

of the nonequilibrium

GBOSC

and the

P_i(x)

+czwz ,

VJ =c*w1 the free energy

&

mechanical

by the expansion

between

holds)-are

(optical).

;? general

constant

below.

are over

E is the (bare)

the solvent

outside

(BO) and self-consistent electric

of ;i cavity

field

(cavities)

= (r,l +~tr)-* ~~1 . the cIectronic polarization

coupling

arising

(SC) from

encasing

the the

(4)

p betiveen

the diabetic

states and the frequency

is (5)

is related

to the time

electron,

yU = 2r&clc~/p.

up to several

sc~lles of the electronic

eV, depending

As discussed

below.

on the reaction.

polarization

r,l = 2~/w,l

Iro, 2 2 CV for typic4

and of the tran:ferring

soivents.

whiIe p can range

In the SC approsimntion is

cquilibrttsd

to the average

the equilibrated distribution. coupling

PC1 “sees” The

variational

Schriidinger

In general,

equation

soIute field. the fieIds

approximation

BO limit p, f -

is slow enough

optimizstio

iz the: soiute to modest

respect

that

charge

electronic

one in equilibrium

use the BO rlpproximation

n of G with

that PC1

0, it is fast enough

VB components

is the common

some of these formulatio,:s principle

reaction

IS]).

to w yieIdx

the nonlinear

[9]

H (whose

Lvhich depends A convenient

In the opposite

polrlrization

has been the strlncf~\rd one for wczk

when f is finite. the Hamiltonian

the Hamiltonkn

1. the electronic

of the individual

IG]; the former

I 71 (alrhough

The

00. f -

approximation

ET reactions

field studies

_P,,(,!.

latter

p -

cspiicit

depends

through

Form is not needed

upon the so!ute representation

the equilibravd

here). the rransfcrring

Qi.5)

on w. i.e.,

etectron

interacts

in

with

wave function.

of Eq. (6) in the basis Eq. 2 is 191 (7)

c;.;= &(1-&, .

(S)

Here pr is 3 renormaIizec!

coupling.

renormalization.

they can be numerically

although

[9] here. with the same proviso. variables. x

respectively. =

Cl2

-d:

For simplicity.

significant

1111. We Aso ignore

In Eqs. (7) and (8). x and y are the localization

for the solute electronic

y=k1q

Gs and G,\ are the symmetric

\ve do not stress in this review

issues of such exchange

terms

and delocaIiration

:trticture (9)

,

and antisymmetric

combinations

of the free energies

(10)

for the kdividual

VB stwzs, and EA is the magnitude

state bare fMds.

Here

spAa

over the solvent

integra:ion

2nd hereafter,

EA = $ i __ El - E-1 of the difference

the inner product

outside

the cavity.

between

two field variables

of the -CrB also impI&

The nonlinear With

Eq.

(S).

eqtiilibrium

Eq. (7) can be soIved

this

for the coefficients

the nonequilibrium

gives

free

energy

Lvhich ar; functions

(ci).

for any

giver.

of For.

nonequilibrium

or

P_,,,.

In the case of fu!l equilibrium.

where both p..l

and

_P(lr zrc equilibrated

to the solute.

one

has

and the equii!brium

versions

electronic

and free energy

st;ucture

predictions

of SC [7] or direct

limits, but in general e!ectron

191 of Eqs. (7) and (S) ;ITZ found (BO)

there

is equilikium

IS] equilibriuim

salvation.

reaction

they differ from those predictions

They

field metho3~

by the inflcence

These

gi~,e;l&

. thr solute

the

[9] via ;1 multiconfiguration

and Q

are trcattr?. quantum

I _P,,.;; are treated

necessitated

reduce

to the

in the iippropriate

p

of me Per and transferring approach

in lvhich.

[9] rigrtoring

exchange

effects

for

mechanicaIIy.

[9] as cohcrrr,t

by its high charxteristic

self-consistent

states

frequency

The qusntum

j12j.

w,~. wh:ich

dzscriptiori

of cc.1 is

the UV-visible

is ,?pprosimstely

absorption ircquency of the solver-& /IW,~ 2 2 eV {91_ A brief discussion of the sylnmetric situation cf = ct for the symlnetric A-k\. s..% usefal here. The symmetric 2nd anrisymmeuic elec:ronic polr?rizations PY,1 = ilpci.i then

give the

time scales via the fact& f. Eq. (7) NQS derived

-.vhtrc

when

upon substi!Lltic?.

AA- system k

_pci.~j

is 37~.

for simplicity)

(13) where Ep -.’ v 2nd EA are the average 2.

In the SC limit,

polarization limit p.f -

value,

governed

locslizcd

electric

Q

I,

to the SC limit

state.

of the electric

_P,t.! =

fields associ;lted

_P,“land there

_3,1.-, =

by the :lverr,q-e field (and F&) [ 13.143.

in the simp!c

relation

i:: only

011 the other

and each is SPDXL~~CIV equiiibra:ed

This is- refiected

with s:;t!cs 1 2nd

between

one eicctronic hand. in the BO

to the ekctric

fic!cf of

z> 2nd the dif~crencr

in that limit.

i .-cording delocalization.

00 and f -

0. EC1I 1 and &I 2 xe different.

its respective field

p -

and difference

to Eqs. (3) and (&,I. if the solute is losalized. which

is identical

howe v:r. rhc

situatior?

to the 20 depends

description

ctcz -

0, the general

in this

limit.

For

result reduces zny

on the vrtlue of p, Eq. (5). and thus f;

degree for

a

of

given

solvent,

t!x dcpcndcnce

ktwccn

rcxct~r~~ clrtsses. and Lvithiz: L given rc,,:io.l

knT

and though

appropriate range

of the elec:ronic

structure-noncquilibrilr;rr

ET rcxtions.

iclr proton

c!ass.

I13.14].

the SC limit was inappropriately

coupling

t,x.sfers

cotip!in;

neither

iliC

vzry

XX:ifJnS.

p

widely

is

approsimation

cf;ca

c

is mere

lvork which

salvation

over the entire

coupling

in this weak coupling

regime.)

theory

zpplied

the co*Api;ng is O( I eV).

where

initiated

the

I?]. as noted in See. 3. Tne

[ 13-161 is appropriate

and S?+ 1 reactions.

1'3

can

(In our originr?l

19. r5.16I

Iillit

s. which

For ricti-:.::LL CT

~lrc nor large in this limit (9.143;.

tha:l i:. an SC :rcatment

of an clccxonic

1I-la,b!.

For higher situation

the clill;=rcrxx:.

[S.IS.lG]

construCtio!l

is OII the v;lluc

is discussed

lli’ 1o:L’.

3. ELECTRON

TRASSFER

Application gives the xtivation

[9] of the theory skeiched

in Sec. 2 to the symmetric

ET reaction

A- A -

AA-

frc’e cr?ergy 3s

(14)

thrcugh

first order in p. for a polar solvent

ne$ecrcd.

The BC? approximation AG&

Lvhere Q >> 1 and E, i 2, and when exchange

tn rhe ET bxricr

is

=

where the solvent

(151 reorganization

energy

AC& = is associated whose

rznge

Eq. (14) prydictionextra

free

deixalizxi

(16)

\vjth Ellr and j&, is ;r renormzliz~d

only the solvent

orientational

of vaIidity

shows

that

polarization

has onIy recentiy

the barrier

exceeds

which can be ::ignifkant energy

is

cost

t.ransi:;o,;

[9.14] state.

dcctronic

contributes

to the barrier,

come

under

this

vaIue.

for larger ekctronic

associated

with

In an SC rreatmenr

coupling

scrutiny This

[9.i i,14].

in the 90

;t long.standing

[9.14-161. barrier

perspective

However,

enhancement

!imir,

for finite over

equilibrium

[ 14:. this equilibration

.;o!vatIon

p.

the 30

coup:in g 9s shown in Fig. l-reflects

the (partial)

161

XI

of _Pcl elf tt

would be complete

and the

ccst v.r)uIci ~pp:3XiIII:itCly amount cquiribtium

gmp,l,~te ctmpictci>~

absent

The

1

-

exact -~

l

-

since p,t is assumed

activation

numerical

Jr! discussing

inAGrby(l

TS, and would

fast e: ough

to solvatc

for symmetric

electron

- <-.signifyinga

bc larger.

In ;I 80

the individual

treatment.

components

it is of the

and bcloa+).

free energy result

by solving

the transition

;IS “adiabatic”,

Eq. (7):

l

transfer

- 0 the first-order

symmetric

equal

to an equal

linear

order

state

(TS)

charac?

in highiy

perturbation

correctic.1

arising

(xcq = 0, yccl = I ) in character.

mixture

polar resuli

solvents. (Eq. (14):

of Iocalized

states.

The associated

30

= p with p = 0. p a:~! the rtnrisymmerric -c; I-3 -ci. 1

0. the antisymmetric

part is reduced

from

to refer Then

that electron’s

to the BO

the term beyond

mction.

elecuonic

poIarizatIons

by p. In the corresponding A

part P -cl

compared

g electron.

The

TS is

with the wave function

ir. p, Eq. (13) with f there approximated 20

-. it is convenient

i.e., fast Eel and slow transferrin

ir. Eq. (14) is a *adiabatic

delocalized

finite

Y$-)

the RG result Eq. (15).

approximation AGiO

(&-

vf &t Lvith the dc!ocalized

(see Sec. 2

Fig.

10 @acing

=- 1 2

P -P equals -cl. I -cl.2 >

to this adiabaric

result

satisfy.

to

aaiabatic

limit.

C,tEb.

But at

[cf Eq. (13)].

This

I\

=o; pcl,l = P,.I.~) in the SC limit f = 1 (P -Cl but it is onfy p;rrtiaI hew. complctC

If’ ground ::nd excited

A f‘urthcr insight on this is the following. dctincci

and the free cncrgy

L’WI would

zdiabztic

lx higher.

TS BO stdtcs are

by

then the TS W:IVL:function

The qet effxt electron

is to

of p then

of nonadiabatic

can bc expressed

as [9]

mis the two dif-ftrent

rtdkbatic

stat*?s. in anafosy

coupI;ngs

for molecules beyond the Born-Oppenheimer [9]. Note that th e excited st~~te tcm~inolo_ry for 1U$&

systems

state. the electronic

polarizations

:lre not equilibrated

to thr3 conscquenccs

approximation is

to the soIutc clcctron

for nuclcisince in th3f

appiOpriLttc2.

e.g.. thy I30 polxitation

no

s13te I p -Cl $ > aPP ears

in conjunction

.-

>. I I> I ,Pt1.2:.. 1 2)1 _P,I.~). 1 2j 1 &l,1).

I ]>I &.I

There spectroscopy

4.

Ssl

Lvith state

are also of mised

novc:

SOIIX

valence

is also useful

nonreaction

compkxes:

kind of expansion

in other contexts

con:;erluences

in 3 basis set

(ct Sec. 4) [ 171.

of the considerations

the reader is refkred

here for the

to Xf [9] for ;I discussion.

1Oi’c:IzATION

The SsI unimolecular ionization RX in orc*xm; ,U...c chemistry [IS]. It is 3Iso a resction illustrates. then31

This

1 I} 1”).

the vacuum ionization

state that rtllows

valence

bond covalent

is to be expected the ionization

Polanyi.

Ogg and their coworkers

generate

an eiectronically

separations.

The

configurcl:ions;

instead.

simultaneously.

as in the theory

class for which

the solvent

and ionic state energetics

in the gas phase:

:o occur.

This

it is only the soIvent

basic feature

surfke

salvation

one must allow sketched

in vacuum. of this

the electronic in Sec. 2.

it would

state

wouId

reaction

is critical.

classes

As Fig. 2

art rjlpically

such that no

stabilization

of the ionic

was pointed

1191. If one were to electronically

sdiabztic

subsequent

R+ + X- is one of the fundzmenta1

out long ago by Evans.

coupk be purely

the two VB states to covalent

nor produce

couplin 6 and salvation

any effects

at large RX stabIe

ionic

to cperzte

-8@

Fig_ _7 ‘The gas phase vacuum

coalent

for a model

[2fl] via the theory

is taken i.lto account.

W(r,s)

energies

2nd ionic curves.

This process examked

diabrttic

respectively,

of r-BuCl-perhaps

= c,(r,s)\?(,(r)

both

orientational

[20]) covalent on r and

polarization

where it is assumed is the neglect

the most we!l-known structure

. * -~ denote

Sxl

feature

is described

compling

been

that the RX separation

7

by the exy.lnsion

(20)

and ionic valence

bond states. The electronic

eV near the solution

a solvent

the

p.

reactant-has

+ c[ !r.s)WI (r)

these states is strong. p - 0.5 - 0.75 ckpend

and

the elccucnic

in Sec. 2. with tile additionui

sketched

-

for l-BuCI.

while - - - represents

Ttius the solute electronic

over (onhogonalizcd here

and coupling

reaction

transition

s. kvhich gtltlges

coordinate

coupling

bettveen

states. The coefficients

the extent

of the solvent

via rhe definition

for simplicisy

of the covalent

that the cov&%t

state dipole

moment

state has ao dipole moment.

implicit

which is small in comparison

in Eq. (21)

to that of the ionic

state [2Oz.c]. With ionization reaction solvent

this icrmalism,

can be constructed. paths are displayed. is imagined

that wouId

to always

be implied

two dimensional Fig. 3 gives The

an example

first is the equilibrium

be equilibrated.

by considerin,

nonequilibrium

free energy

for t-I3uCl solvrition

at any r, to the solute:

n the equiI~brium

potential

surfaces

for the Ssi

in acetonitrile. path

(ES%.

%/&

of mean

along

= 0. This

force

where which

two the

is the path

12.31 j-the

typical

object

of equilibrium

calcuirltion. and is closzly associated witi] standard. 771. The second path is the solution reaction path equilibrium sotvation transition state theory ILL (SRP). This is the lanerslization to solution. by Lee arrd Hynes [23]. of the familiar intrinsic reaction parh in the sris phase, introduced by Fukui 1241 znii often studied [25]. Fig. 3 shows that near the transition the ESP.

over

to the rapidly

consequence

the barrier changing

the SRP differs

is so rapid that there is not sufficient solute charge

of this is that the transmission

distribution.

considerably

which measures

from

time for the soivcn:

i.c.. for the ESP to be followed.

to One

coefficient

k

K=w

(22) the effect

to its eqr;il;l-rium estimated

mechanical

state, which is the saddle point on the surface.

Passage

equilibrate

statistical

of noaequi!ibrium

so!vation

TST

value

salvation [22].

through

is noticeably

the ratio of the actua1 rate cons?ztnt less than

unit).

For example,

it is

[20bJ that K = 0.65 for r-BuCl in CH>CN.

5.5

r

S

Fig. 3 Free energy

contour

mztp for r-l3uC1 in CH3CN.

in units of 0.1 eV. The free energy r is in A. (ESP).

2

and - - - denote

value for the contour

the soIurion

reac!ion

-

- represent

the equi-free

in the upper center

path (SRP)

energy

lines

of the map is -3.1 eV.

and equilibrium

salvation

path

respectiveiy. The basic characteristics

firmed.

via an application

computer simulation.

simulation

of the reaction

of a vxian:

of a model

K = 0.53. a value

path and ;he deviation

of the formulation.

of the t-BuCl ionization

reproduced

from TST

have been con-

of Ref. 20s. in a Molecular in water 1261. It is noteworthy

[2G] by Grote-Hynes

Theory

Dynamics that in this

i 1.21 and its nonadiabatic

soluation

lirr.it 1211.

In contrast.

the Kramcrs

1 heor?

[?‘?I prediction

is far ~XIGW this:

KKR =

0.02. But perhaps focrltion

no\c‘-1 results

the most

and free cncrgctics.

of the S,yl

It is ..vc!l known

decreases

for r-BuCI

(rend other)

traditional

explanation

of this is due to Hughes

ionic character prcfercntially different ionic

IRS+ I%s-]z while stabilize

r-variation

valence

solvent illustrates

from the Ssl

::tstcs.

The

A simp!ified

the solva:eti

curves.

ionic

location.

character

j29].

and a dctaiIed that

Fig. 4 Hammond

leads

(Acrually

postulate

di;lgrxn.

noted by - - - and - - - wspec*:vcly. With increasing arrow;

solw

’

.i* v. ‘L: r rrflctiorl

.ards

The crossing

state becomes

mar’

The equi!ibrated

.r

Wiiii

growing

Surprisingly.

will ;1 quite

the covalent

end

the curve crossing--which geometries.

also becomes to establish

ionic curves covalent

i.e.,

from the dirlbatir: curve

it). It is the diminishing

TS

the tighter TS Iscation

in’r

for CH3CN curve

and C&;?i

is represen;ed

c as indicated

state _P. This

so!vent pOla.rity.

This is in accord

more reactant-iikc.

directly

k~~ornes iess endothermi the reactam

polzity

decreases with increasing --A is the following [20~11. Fig. 4

solvent stabitizetion;

whiie the equilibrated

state has some

soIvent

between

polarity.

this does not follow TS

The

of AC* for r-EuC1 arises from the

at more reactant-like

[2Oa] is required

LOa less favomble

[ 18.28].

A&

~c:uoIly

solvent

The TS ionic character

analysis

barrier.

(- 13- 1S kcal/mol)

For increasing

postulate

polarity

little, increasing

state

free energy

and Ingold i 181; since the transition

state strtbilization

with the Hammond crossing

solvent

of these strikin g features

to the TS location-occurs fashion.

incrcrlsing

RX has very

coupling

transition

is zz approx:nation

lesx ionic, in ;1 Hammond

with

the transition

that the activation

study IZOrt]: the dccrcasc

explanation

diabatic

expcriment~lly

I2G] concern

state and Iower the activation

of the large electronic

bond

polarity.

the reactant

the transition

picture emerges

separation

ionizations

study

reveals

are

by --.

by the vertical

that the transition

leads to an increased electronic coupling

which increasingly It is interesting

transfers

coupling

suppresses

field designed

number of the features sketched

covalent polar

curve

adiabatic

diagmm

is denoted

solvents

the tmnsition

by -,

Bronsted

by

by -

state is indicated

coupling

while -

l

-

l

-

contribution

and

-

- -

as solvent

experimental

coefficient

avenue

a connecting

perspcctivc.

free energy.

for weakly

, respectively.

The

increases.

stabilization

stabilization

the transition

predictions

displayed

in Fig. 6.

and reaction free en@es

(23) [20a] a mart

Other SN 1 ionizations

reactant-like

TS.

kcal/mol).

features.

Experiment

have been studied as well.

basic features noted above for r-BuCl are repeated txtr;l interesting

state

is [20n] via the

dAG*

a signifies

of

increases.

a=G A smaller

The

and highly

corresponding

of the coupling

polarity

of hydride

site 1301 show a

to the activation

to test these unconventional

the activation

active

ionic curves

and - - -. The magnitude

by an arrow:

for a model

support our theoretical

(i.e. an earlier crossing) and the coupling

decreases

results

for on enzyme

the (equilibrated) l

in r). and it is this increased

barrier (CF. Fig. 5).

of computational

here and may independently

are represented

A possible

exponential

to be appropriate

for electronic

states are denoted

separation

the activation

to note that a number

with a reaction

Fig. 5 Schematic

(approximately

BuCl case is sketched in Fig. 7. However, system in which a larger solvent

In the series r-&Cl,

coupling

coordinate

the solvent

a trend like tlW

t-BuBr and t-&11 the however,

at the TS is sufficiently

for the ionization:

the contrast

barrier is quite low, m 1 kcal/mol.

barrier (- 4.5 kcal/mol)

both these cases. the TS ionic character still decreases

indicate

12Oc]. The r-BuI example,

In this case. the electronic

that there is a barrier in the solvent

should

is calculated

with in-sing

is isopropyl solvent

presents low (= 4 with the fAnother

iodide (2OcJ. In

polarity

and the TS

0.7

0.5

-

a

/

Om3-/ 0.6

0.7

0.8

0.9

@? 1’

Fig. 6 The BrBnsted coefficient

a-transition

$2 state ionic character (ct ) plot.

An almost linear

correlation between the two hold; for a wide solvent polarity range (2.5 S eg 5 80. L, = 2). Since the TS ionic character is found to diminish with increasing solvent polarity in model theoretical study l2l.Q. the solvent polarity dependence of a can serve ZLS tn experimental probe of this novel uspfXt. solvent stabilization decreases. But now the eIectronic coupling r variation is small and is not responsible for the lowering of A@. Instead it is the r variation of the vncuum diabetic energy difference [2Oc&

0

.5

1.0

S

Fig. 7 Free energy profiles in CH3CN along the solvent cordinate s at fixed transition state separation r* for a) t-BuCI and b) t-BuI. For r-BuCI, the coupling is large enough - 18 kcal mol-1) SO that no solvent barrier is present. In the case of r-BuI, however, the coupling is small enough (4 kcal mol-1). to allow for the presence of P solvent barrier.

All the Sgl perturbation

results

method

sort of approach

to :hc numerical

electronic

calculations

to the model po!arizution

were

two-state

contribute

and fourth

would

with those

cbtained

of this’ general

via the perturbation technique

procedure.

it does

unravelling.

e.g.. the source

5. PROTON

in excited

[9,20rt,bJ

will faii.

AH

l

.

l

transfer

an analytical

catalysis

chEractrr While

B -

Jmp!ex

f33].

from the

s:ates

13 1 I agree extremely

weil

method

gcneratc

such

[9.2Oc].

actual

One

electranically disgonalizatior.

a framework

was

key

in

above.

there

has been

some

condition kinetics

studies

complex

change

[33.35].

acid-base

chemistry

approaches

progress

of proton

to produce

will have a

to the proton

on these

transfer.

[32] and

nuclear

nucIear aspects

specializing

to

;i large charge

tha: the electronic

be in equilibrium

to the response

in an ion pair

;;olvation,

structure

and this issue has been

For the most part, however,

[ 1 I]_

separarion

to be large_

by a solvent.

of nonequilibrium

and speciroscopy

smr;ll compared

features

in iZq. (25) indicates

altered

that the soIvent situation

marked

importr?nt

mass. these n:actions

and classical

recent

the most

(25)

can be expected

poiarity

include

among

.

can be markedly

the general

are surely

DUC to the light protonic

in a hydrogen-bonded

: of theoreticzi

for reaction

and

described

for the proton motion,

A----HB+

The pronounced

typically

3s operators

All these

numerical

used to

framework

and biochemistry--exampies

I1 1 I. Here the soI%!ent effects

restrictive

in 3 BO piclure.

On the other hand. since it is a numerical

133d.33 j. our focus here is rather on the electronic

consider

app’ar

in which

state in the BO approximation.

dirtgoncliization

both intro- and inter-molecular.

in enzyme

mechanical

?

states

or the cxzx

of the Ss 1 TS patterns

in chemistry

transfer

2 proton

upon in

basis set constructed

to give the ground

is that it can be easily

system.

not provide

transfers.

cIasscs

motion

chcmicrtf”

system

momentum

P

TRANSFERS

Proton proton

bc involved

states of a solute-solvent

quantum

of the solute-solvent

orthogona!ized)

at finite p and f. The resul:s of the numerical

advantage

rczction

A more “quantum

ei!l-er

in Ref. [9] and commenred

and its conjugate

using 3 (suitably

Eq. (7) via

[3 I I

second

excited

by solving

an~~lysis [9.2Oc].

Hamiltonian

The first 2nd. the third st;ltes here would combine The

produced

is one introduced

of the solvent

191. This may then IX diagonrllited four states

above

or an exact numerical

[9.20a.b!

Sec. 3. Here one returns the quantum

discussed

these studies

with the solute.

the subject

of a

have assumed

the

it is critics1

since this is the relevant nuclear

motion:

to ins:ead

state of affairs

In brief, the time sca.Ie for the light proron time of ;hc solvent

of the

motion

it is then

is

a more

physically

realistic

slow solvent,

description

arrangements

and orbital

salvation

energy

diagram

adjusts

to the (comparatively)

picture would have it.

in quaiitative

tenr.s for the hydrogen-

AH - - - 8. A fairly unconventional Mulliken

there is charge

-4-H bond

transfer

thus

of them,

replace

pm(5) the Fig. significant

=

orbita!

A to 3; however,

valence

of the acid.

H is here

from the conventional

coordinate

is novel.

stabilization

is adopted.

These

valence

[37!, although

Fig. 9 illustrates

picture

bond structures,

the emphasis

the energerics

correspond

Since both states carry 3 dipole s in the defmitiop

$y& - $) 1s!$I @>+ (l-s)

9 shows

The like a of

bond description

by many authors

[ 111, V’s and WI approximateIy

I and

more

or

here on the

of these diabetic

states:

values are [ 11 j p = 1 e:V, 3 quite strong coupling_

orthogonalization.

:he solvent

involving

in solution

coupling

In prac:ice

to an antibondins

(Fis. S), in which

(26)

have been discussed

perspective

symmetric

1361 is sdcptcd

is quite different

pair (N) and ion pair (I) structures

in terms of neutral

electronic

orbital from

proton -this A two-state

picture

+ CIYI

Y = CSYS

Muliiken

transfer

and H can move

a simpIe ?ransfer of an Hi species.

ingredients

charge

from the base nonbonding

is weakened

hydrogen atom than a fully charged

typical

[l l] that the fast proton

rather than vice versa as an equiiibrium

Fig. 8 E!ecrronic bonded

to assume

N electric that ever:

fie!ds

with

in a nonpolar

of the ionic term.

to the states moment

in Fig.

(gs.~~).

5, due to a

it is convenient

to

[cf. Eq. (21)j

(27)

Es ($1 the equivalen: solvent,

coordinate

the electronic

t = sp1 + ( I-s)p_~_

polarization

can lead

to

I 2

7.5

1

r/A Fig. 9

Diabetic

free energy

Fig. 10

Free energy

surface

path is indicated

Fig. there

(Es. Et) 2nd adiabatic

fG) for the same complex

free energy

complex

energies

10 displays

(modeIIed

pi:sse reactant

in a nonpolar

by the dashed

the calculated salvation

and product,

path.

(E) for the isolated

sotvcnt

for the OH - - - N complex

after phenol-amine

is the equilibrium

energy

OH - - N complex. l

and

(y1= G., = 2). both at R = 2.6 A.

af k = 2-7 J%in acetone.

The equilibrium

line. nonequiiibrium

complexes

energy

137~~381) in acetone

The minima

but it is notcorrect

free

on this surface

to think of the reaction

surface solvent. correspond occurring

for an OH - - - N Also

illustrated

to tct along

solution this

p3th.

Since the proton motion. rapid than typ&l fast proton.

solvent

motions.

for fixed nucIear

and the AB separation 3 quantized

protonic proton

equalize

(or nearly).

fluctuat;on

solvent

vibrrrtio,:i:

constants

levels

well.

symmetric

for both neutral

double

reactant

which

in ;I single vibrational

sre also modulated

transfers

well. are relevant reactian

for proton

frequency

5eId perspectives

and ionic product.

I

these levels solvent paths

Tunnelling theoiy

for the rate

but new Lvithin 3 singk line broadening,

rather thr?n

used.

-1310.6

2

L

with (nuclear

A subsequent

in a recent

considerations.

z)

fluctuates.

When

the barrier.

shifts and spectroscopic

sometimes

coordinate

pol;lrizat;on

well in the ion pair well.

I-,elated dynamic

for the

For z = 2~. there is

we11 is gcnera;ed.

my R. are incorporated

[33c,33b].

polarizutio;l

When the so!\ent

is far more

description

fix,-d t “cuts”.

here at z = zb. the protaA can tunnel through

of proton

the equilibrium

(here :he orien:;?tionrll

;?t a fixed R. several

cost. B more

then traps ?he prcron

such 3s these,

coordinates

a nuclear Born-Oppenheimer

level in the reactant

free energy

diabatic)

in the range of 2000-3500 cm-l range,

one can invoke

R. Fig. 1 1 displays vibztional

with an associated

proton

with typical fraluencics

.-_-_-_ 1.2

1

--r .4

1.6

r{A) Fig. 11

Free

compkx

at R = 2.7 4 in acetone

coordina:e

er.ergies

vslues

for the OH - -

l

N

Fig

at the solvrnr

so:vr?tion

2~ = 4.53 D, zb = 8.73 D.

3nd tP = 11. ! D which correspond extrema

in Fig.

IO.

represent

the lowest

The

Free energie*;

along the equiiibrium

path for the 0i-I - -

l

N complex

at

R = 2.6 A i n chIoroform.

to the three

horizontal

vibrational

12

lines

energy

IeveIs

in each well.

Despite path to ilIustrste free energy electronic transfer favor

its severe a number

1imitatior.s of points,

curve and that alculated structure

complex

at various

vis a vis dynamical

in Fig. ! 2. First is ?he striking !abelled

r values.

is polarirable

of the ionic state component

problems.

SAC by so!vating

The latter misses

over the valence

the ESP is a usefui

reference

difference

between

the actual

electronicaI!y

adiabatic

the vacuum

the fundamental

bond states; the solvent

and then solvates

it, leading

feature polarizes

to noticeably

greater

thar the proton the structure solvent

in

stabi-

lizxion.

The cornpetition

footins;

the SAC

clectronica!ly also

S!ICSVS

in clccrron

procedure

;Idiat;ltk hi

betxvcsn the e!cctronic

of

result

transicx

sepr\r;ltes

prior :. an introduction

the

popular

theory.

;~nalog~e

The diabetic

G arise [! I] most

dipole

moment

zione. sites

to provide

antecedents

bond states :X-L’individually

solvated

lie first.

xe understood.

importanti?;

The significant

from stzbitizing

disparities

solration

but present

btxw*crn this GsDc

contributions

from

and the

the transition

in the Iattcr.

REMARKS

have

only

ekcrronic

outlined structure

One direction 1331.

Fig. 12

to give

I_I~I = (N!~II) absent in the former

6. COKCLUDIT:Z

curve crossings

inf!uence.

the

(23)

quan;itics

actual

int‘?lucr:ed

of the solvent

to prcduce

Ir?bel:cd SDC. whose

proct:dure-

N and I valcncc

tr, -ct

;(Gs

=

Lvhere tqcilibrium

We

of a

on the sxr!e

must be trcxed

by alioujin_~ the Toupiing

state in wcuum.

and then arc ctlectror icaily coupled

@‘c

them

couplin, 0 .wd . salvation

here

the tl,eoreticll

aspects

of s z!ution

is the application

importxt

direction

;L more

microscopic

and

reactions.

IO other reaction

of polar VB structures.

Another

issues

classes,

a few

Cir;:rlj such

2nd to other “polar ’ reaction is to incrcrtse

chs;cctr:ization

results

much 3s

IT.OTZ remains

to be

Ss2 [39]. v.ki.e there are

medi;t. such as er,zyme

thr: level of quantum

cf the solvent.

for the solvent-

chemical

Efforts

along

active

description

aI! these

and

lines xc

underway.

ACKNOWLEDGXIENTS We thank supported Teresa

Roberto

by I%.SF Grrtni

Fonseca

Bisnco

and

Brad

No. CHEBS-07S52

w~!s an inspiration

Gcrtner

for useful

and XII-I Grant

fol the completion

discussions.

This

work

was

i ROI

GM31~32.

The

late

described

in Sec. 2.

No.

of the theory

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2 3

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I9

R. A. O&g,. Jr. and M. Polnnyi. Tr;rns I;;lraday SW., 3 I (1935) 604; E. C. Baughan. M. G. Evans ;lnd M. Pol~:lyi. 7’r;lns Almdily SCX.. 37 (1941) 377; A. G. EVUXS. Trans I%~adi~y SW., 42 ( 194B) 719.

2il

21

22 23 24 -25

26 27 28

29

8 32

33

34.

35.

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