93 1 ;_ 55 - NTRS - NASA

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hydrogen atom exchange between three. HF molecules. Andrew. Komornicki ..... ghost basis present as the fragments. The ANO basis was used in all BSSE.

93 Concerted

hydrogen

atom

exchange Andrew

between

three

HF

1 ;_ 55

molecules

,?i/_ ,/21/

Komornicki

Polyatomics Research 1101 San Antonio Rd. Mountain

View,

Institute Suite 420

CA 94043

and David A. Dixon Research and Development Department E.I. du Pont de Nemours and Co. Experimental Station 328 Wilmington DE 1-98ed_ I '_ _ (_ 0 Contribution No. 4558

Central

t

-- _

_ _ _"

t,s1

and Peter R. Taylor ELORET Institute_ Palo Alto, CA 94303

C.J

ABSTRACT We have between

three

various the

investigated

geometries state

exchange

reaction

namely,

and

were

and

analytic

which

include

the

that

the

Thus is very

t Mailing

effects trimer

agreement

is 15 kcal/mol the barrier

all valence

electrons.

derivative

of connected is bound

with

above

We are

corrections

the

trimer,

to hydrogen

and thus

to the

techniques triple

estimates. or only

exchange

we have

The

NASA

Ames

Research

Center,

using

a large

excitations,

SCF in the

level

energetics

level.

Our

to concerted

HF molecules

Field,

natural

were

used,

were

best

separated

three via this

deter-

calculations, procedure, monomers,

hydrogen separated termolecular

CA 94035-1000

func-

of accounting

coupled-cluster

barrier

above

effect

the

of the

coupled-pair

the

to three

and

atomic

treatments

relative

Moffett

located

energetics

low'.

address:

at the

is of Cah symmetry,

correlated

4.7 kcal/mol

between

basis,

to measure

excitations

exchange

of correlation

correlation

at the

The

effects

level,

double able

hydrogen

symmetry.

Several

by 9:51 kcal/mol

previous

which

correlated

single

the

an extended

is of Dah

at the

concerted

on

trimer,

evaluated

methods.

second

Using

which

with

involving

emphasis

reaction.

exchange,

Zero-point

using

particular

the

interaction

coupled-duster

reaction

hydrogen-bonded

then

correlating

mined

excellent

along

for hydrogen

size-extensivity.

indicate

with

stable

configuration

tional, for

points of the

transition

basis

termolecular

HF molecules,

stationary

orbital

the

exchange monomers. process

in

The HF trimer is known to state

for concerted

consider

the

hydrogen

following

adopt

a C3h equilibrium

exchange

three

has

been

_

(HF)3

(HF)3

retain

energies

all three There

of these

been

of the hydrogen

consistent

field (SCF)

a double-zeta

reaction

(R3)

e¢ al.

employed

4-31G

split-valence

and cyclic

and

and

equilibrium clusters,

using

functional In the

points

correlated

calculations

atomic

next

section,

natural

a (10s with

The

SCF

et al.

to

results

large and

coworkers

compared

refine

the

sets.

Our

by a discussion

of our

results

and

the (R2)

the

of the

of

cyclic trimer

investigated

several

averaged

sets

energetics

computational

at

other

HF

coupled-pair

below.

basis

and

5

stability

s has

and

for

Heidrich

that

stabilities

the

to ours

Gaussian

energy

relative

Karpfen

and

self-

kcal/mol

shown

in (HF)3

sets

configuration-interaction

basis

the

recently,

basis

then

37.1

has

segmented

actual

by optimization

_ and

Most

at the

effects.

of the

exchange

are

the

AE(Dah-C3h)=

investigated

C3h and

to be 29.5 kcal/mol

An investigation

have

polarization

data,

obtained

of the

generally

for vibrational

gave

7.

energies

of (R2),

their

geometries

hydrogen

level,

the

with

polarization lp)

2.2 were

basis

stationary

primitive and

the

evaluated

was extended

(TZP)

point

was

basis

of the

set 9. The hydrogen at the

fluorine p set

to locate

the

by performing

methods

are

(HF)3

extensive

coupled-cluster

levels, described

using in the

conclusions.

SCF

level

to [bs 3p 2d]/[3s

PAGE

BLANK

NOT

lqLMED

initially form

optimized [bs 3p ld]/[3s

d set is a two-term

has

a Gaussian

using

analytic

exponent second

2p] for use in MP2 3

PRECEDING

it is convenient

this energy

From

uncorrected

by Karpfen

These

of each

plus

exponent

TZP

but

methods

6p 2d/bs

frequencies

independent,

of the relative

basis.

fragments

plus

orbital

geometry

a triple-zeta

(R2) (R3)

4 calculated

kcal/mol.

concerted

at

followed

not

calculation

Liu

we use

at the

Computational The

and

work

stationary

large

trimer

to isolated

method.

present

sets

of 26.5

split-valence

(ACPF)

(R1)

is, the energy

coworkers

best

while

that

kcal/moi,

Their

stable,

structures

We shall

[D3h].

are

(DZP)

of basis

of the

relative

and

is 14.6

energy(R3) forms

D3h symmetry.

[D3h]

calculations

trimer,

polarization

level.

is more

tetramer

of recent

Gaw

a variety

open

structure

level.

to proceed

an activation

transition

[C3h]

(HF)3

reactions

fluoride

plus

the

of discussion.

a number

D3h forms

using

three

for purposes

have

to display

[Cad-_(HF)3

3HF _ the

4, while

reactions: 3HF

Clearly,

found

structure

at the lp]

SCF

level

contracted

fit to a Slater of 1.0. derivative

calculations:

using from

function

Vibrational methods an additional

a°.

d set

was added

hydrogen

(a two-term

p set

Finally,

in the an f set

MP2

calculations

8p 6d 4f/Ss

gen

even-tempered and

c_(f)

for fluorine the

atomic

molecule

state,

first

method,

second

primitive from

2p

set: van

ld]

the

and from

while

those

an

fluorine

and

2p] basis

atomic

0.35.

was

augmented

initial

SCF

s and

ratio

was

orbital

and

p exponents the

double

on

excitation

the

with

are

a(d)

= 0.16

The

ANOs

hydrogen.

from

a

hydro-

functions

CI (CISD)

were obtained

from

and

polarization

= 0.26

(ANO)

contracted

fi is 2.5 in all cases,

a(d)

for hydrogen

natural

This

13 and

= 0.1 and

a single

original

1.4 and

All of these

used.

Duijeneveldt

a(p)

the

11

was

24 or

ls electron No virtual

size-extensive.

CCSD(T)

18 electrons

spherical

calculation

a calculation

were

and

correlated:

on on the

is neglected

the

were

basis

ANO

were

MOLECULE-SWEDEN performed

using

single

together

with

of connected

were

fluorine

basis

used,

The

suite

of programs

program

_,

compared

ls and

CISD

VCCSD

and

fluorine

calculations

used.

the

and

with

to neglecting

for both

and in the functions

16 --

orbitals

corresponds

CISD

of Ahlrichs

of the effect

SCF

the

CISD+Q.

method

size extensive estimate

former

correlation

method cluster

calculations

the

of the

using

calculations

this is exactly

using

14, denoted

(CPF)

the coupled

in any calculations,

components

performed

functional

correlated

in the latter

deleted

--

performed

excitations

a perturbational

lr In the

while were

was used

was

for higher

Finally,

in which

were

harmonic

coupled-cluster

Results

coupled-pair

the

is included,

orbitals

calculations

was

(CCSD)

correlation

calculations

correction

is nearly

denoted

correlated

Davidson's

used

excitations

excitations

either

the

atoms.

G RADSCF.

aft k, 0 _< k _< n. The

also

15 which

the method

the

fluorine

while

exponents

[5s lip 2d]/[3s

lf/33s

of infinite-order

method

double

triple

set

including

coworkers and

ground

of the

program

on fluorine obtained

the

0.7),

H2.12

The

The

calculations

exponent

Gaussian

lip 2d

taken

were

with

effects,

expansions

= 0.49

functions

with

of correlation

[4s

are

function

studies

6p 4d)

s exponents

MP2

the

elaborate form

two

1.9) on each

utilized

more

by

of these

(exponent

basis 12 of the (13s

replaced

largest

with

For

was

fit to a Slater

2s. only

and

CPF

is, while

19.

Discussion

Geometry Our value

optimized

of 0.917

slightly,

calculated

results

bond

in the distance

bond

/_. In the

increases

0.912/_

SCF

calculated

to 0.910 are

monomer is 1.860

distance

similar and

/_., and

equilibrium the

to those 0.923/_

/_, somewhat

in HF is 0.902

structure

hydrogen-bonded of Gaw

in the shorter

and

4

H-F

co-workers

Cab trimer. than

for

our

Their value,

the

to an experimental trimer,

the

distance 4, who value

which

found for the was

H-F

2° bond

is 1.917

/_. Our

r(H-F)

to be

H-F

determined

hydrogen using

a larger 1.136

basis

set.

Our

It, in excellent

above,

Karpfen

polarization in the

trimer.

although

agreement

s, has

basis

calculated

effect

thus

is larger

bond

the

appears

in the

of 1.139

at the

bond

on the

distance

value

correlation

His optimum

Correlation

the

with

included

set.

H-F

symmetric

_ found

ACPF

by Gaw

level

using

lengths

are 0.919

,_ in the

to have

a rather

small

trimer

than

on the

Dab

trimer

is

et aL As we noted a split-valence

monomer

effect

on

and the

plus 0.932

geometries,

monomer.

Vibrations: For of 172

HF

we calculate

km/mol

using

4138

cm -1 , while

4182

cm-lat

the

frequency

on

decreases

Some

most

have

ACPF

level.

the

HF

bond

The

focused

of the

studies

on the

spectrum

structure,

the

experiments.

of the

observed

others This

are band

twelve

Cab structure

possible

e' bands

trimer

isolation

presumably

due

is found

argon

matrices

spectra

shown

as have The

with may

matrix,

and

that beam

infrared

vibrational

lies at 3712

that

although

Molecular

22'23,

is consistent

cm -a in a neon

experimen-

21 have

24'25.

e' band

forms

"frequency"

species,

structure.

and

to open-chain

at 3706

coworkers

performed

the

vibrational

I.

higher

been

that

of

investigated

also

indicates

in matrix

and

one

bands

infrared correlate

bands

fragments,

that

red

shifted

by 241 cm -1 while

the

monomer. from shifts those

to be very

in the

with

red

monomer

the

the

cm -1.

Only

a C3h symmetry be present

at 3702

in these

cm -1 in an

to trimer,

and

both

coworkers. in our

The

calculations

force

constants.

there

are three

infrared

active

one

of a' and

molecule

bands, fragment

translations in the

degenerate

Karpfen.

computed

HF

modes

although

the

of these

with

is consistent

by

on

Two

separated

correlate

shift

computed

of Gaw large

a" band.

is to "intermolecular"

The

were

trimer

based

in this molecule

active

remaining

than

have

s, a value

computed

of the and

is

calculated

in Table

a C3h symmetry

in neon

is a minimum,

vibrational

of e _ symmetry,

red

trimer

Karpfen

value

matrix. Our

going

with

and

extensively

Klemperer

intensity

experimental

the

are given

been

an infrared

of the

investigations

dimer.

experiments

cm -1,

is elongated

have

with The

dependence

frequencies

consistent

level.

of 4440

bond

included

cm -1

SCF

is a strong

(HF)n

on the

the

a value

trimer

have

of 4455

at

if the

systems

primarily

bands

set

There

calculated

spectroscopy

predissociation

basis

length:

experiments

vibrational

frequency

calculated

of HF is non-polar,

predissociation

argon

et al.

of these

trimer

one

TZP

hydrogen-bonded

tally,

the

the

Gaw

sharply.

The

a harmonic

HF with

other Our

and

trimer.

stretch

the

is red

increase

factors

also

calculated

intensity and

of the

in the other 5

shifted

in the

frequencies degenerate studies.

the

other

while

in the

symmetric

play

degenerate

vibrations,

rotations

The

Of the

the

separated

HF

stretch

is

by 175 cm -1 from

HF

a role, are

bond

distance

of course. somewhat

e' stretch

on

Similar larger

is predicted

The remaining harmonic frequenciesare all below 1000cm-1 and are associatedwith the intermolecular librational motions. The symmetric and degenerate hydrogen bond bends

are

at

predicted

879

to be very

In order by

to our

quency

result

The

bend

value

in the

be intense,

data.

the

constant

with

the

of hydrogens

appears

We assign while

calculated

lowest

the

is 3712

Both

is calculated

is

for the

cm-ldiffering

from

anharmonicity better

of HF fre-

degenerate our

scaled

for this mode.

agreement

is assigned

of these

them

a harmonic

cm -1

large

at 477 cm -1

478 cm -1.

e' band

frequency

at 590 cm -1 to the a" out

band

bend

we scale

predict

3980

to be in much

the band

value

lying

result

thus

and

a remarkably

bands

symmetric

direction

cm -1, stretch

of the

calculations

among

to be 2224i

One

suggesting

experiment, harmonic

calculations stretch

bond

with

of plane

as the

modes weak

when

symmetry

structure

mode,

degenerate

are

to be very

the

predicted

to

compared

to

transitions.

Force state

and

with

experimental

H-F

23, gas phase

hydrogen

of a" symmetry.

frequencies

scaled

symmetric

degenerate

motion

of the

Our

remaining

C3h trimer,

ratio

value.

of 596 cm -1,

while

other

trimer

experimental

experimental

calculated

computed

for the

of the

The

out-of-plane

is the

270 cm -1,

assignment

available

the

cm -1

by almost

The

which

respectively.

as is the

our

computed

of 3919

stretch.

cm -1,

intense

of 0.93,

monomer

531

to compare

a factor

H-F

and

of negative the

half

(4280

the

the

appropriate

dominant

is much

cm-1),

D3h

magnitude

of its value

stretches

trimer

The

with

is about

that

curvature

fluorines.

consistent

degenerate

C3h symmetry

confirm

of the motion

when

lower

and

one

for

involving

(1674

simultaneous

imaginary

compared

is much

the

hydrogens.

than

higher,

exchange

frequency

to the

cm -1)

is a transition

1506

is found The

totally

C3h symmetry the

value

trimer.

found

cm -1 versus

in the

531 cm -x.

Energetic_: Our three

discussion

reactions

of the

R1-R3

energetics

given

of the

in the

Introduction:

3HF

(HF)3

_

only

ultimately

on the

we present CI, stable

as well

the

electronic values

for each

as the

hydrogen

enthalpy

energy

bonded

trimer

we repeat

(HF)3

_

differences.

are Our

reactions

is bound

on

here

for convenience.

(R2) (R3)

important results

by slightly

the

(R1)

[D3h].

Our

6

is based

[D3h]

given

methods.

them

exchange

[C3h]

(HF)3

changes

of the three

coupled-cluster

hydrogen

[C3h]_(HF)3

3HF Although

concerted

are above

most more

chemically,

we will

summarized

in Table

II, where

perturbation

theory,

with

SCF,

accurate

results

than

14 kcal/mol

first

suggest relative

focus

that

the

to the

separated and

fragments,

the

energy

18 kcal/mol. in the

separated

that

of this

with

to about

reaction

by an examination

tion

state.

At equilibrium this

As expected, exothermic.

The

treatments

predict

reactants.

coworkers

SCF

value

that

that Their

were

included

at the

ACCD

kcal/mol)

consideration detail

of basis

effect

stable

ence

complex

to be

ACPF set

previous

results

energy

difference

to be small:

(R2)

work

is

cited

depending

on the

about

from

of these for the

is found

three

7 kcal/mol. H6 system

by replacement

barrier

calculated

between

in the

system

measure

12.4

is slightly

from

some

trimer

A indi-

of three 70 kcal/mol

changes

can

and

to be 0.3e-,

also

the

be

transi-

whereas

level,

with

superposition

at the

the

a rather

each

more

1 kcal/mol

small

while

basis.

these

stable and

to this

basis,

than

roughly Liu

energy,

and some-

correlation

effects

binding

energy

larger We

to be

correlated

of treatment.

a somewhat

changes

of the

1.7 kcal/mol

level

a TZP

obtains

is found

14 kcal/mol

about with

error

while

than

or

contributed

was obtained

monomers

to be about

correlated

Karpfen

three

kcal/mol

more

is found

level 26.

tive

result

the

or approximately this

separation

while

note,

observations,

would of 23.9

be expected. kcal/mol,

the

whereas

single

however,

that

as we discuss

with

inclusion

such

in

7

core. those

are

differ-

reduces

On

the

of the

largely

CI treatment,

CISD,

correction

other

various

insensihere

hand,

to

there

size-extensive

of electrons predicts reduces

this

correlation

be unreasonable

number

+Q

between

energy

excitation

results not

this (MP2)

a large

of the

difference

we find

double

The

and

energy

treatment

so it would

results

simplest

level

and

of an atomic

CISD

the

SCF

correlation

correlated,

treatments; Thus

the

on the

20 kcal/mol.

to be part

between

At

elaborate

of about are

seen

simplest

More

2s electrons

size-extensive

state. the

18 or 24 electrons

differences

dramatically

transition

in a difference

fluorine

significant

the

to 16 kcal/mol.

to whether

regard

and

is most

35 kcal/mol,

difference

treatments

lated

value

of correlation

to be over

energy

are

the

trimer

below. The

the

at

of the

in the

effective

C3h trimer

correlation

we do.

(15.4

of the

of electrons

less than

the

charges

of correlation

what

stable

of hydrogens

on hydrogen

complex

number

found

is found

quantitative

is found

the

effect

the

exchange

reduces

charge

the

3.6 kcal/mol,

to 0.4e-.

formation

of the 7 have

the

the

The

independent

state

Mulliken

increases

variation

into the molecular

approximate of the

and

of most

treatment,

the covalent

atoms

state,

to be only

discuss.

transition

with

An

seen

state

the

is predicted

results

a substantial

as we now

fluorine

7 kcal/mol.

transition

to the

of ionic character

three

(R3)

transition

of correlation

and

introduction

hydrogens

is also

level

HF molecules

the

contrast

employed,

CISD+Q

comparison

the

between

There

treatment the

to reaction

is in marked

introduction.

At

barrier

separation

This

correlation

cates

the

corre-

an energy this

value

to

21.1 be

kcal/mol.

CPF

reduces

an overestimate

sion

of the

(T)

separation

when

hydrogen

exchange

On assumed

initial

for the

deserves

that

transition

for

effects

of nondynamical

the that

larger

enough

to cast

double

excitations.

nondynamical

state

T1.

than

doubt

For the

correlation

a different

we have

three

chemical

value.

computing at the

We can

the

bond

difference

between

these

of the

2.9 kcal/mol

nates

in the

simultaneous

more

to a true bonds

oligomers require

use

such

can

of SCF

we have

now

basis

augmented

bond

lengths

increase

0.8 kcal/mol only two

the

easier

degrees

less for the therefore

relative task

confident

several

that

might

be

large

triples

The

cause.

elongated

to be a little

less

be further

the

large and that

transition

to their

bond

equiby

length

and

to the energy

than

0.7 kcal/mol.

2.1 kcal/mol

only

0.8 kcal/mol

that

in a system

as hydrogen

are

bond-lengthening

almost

Hence

27

contribution

contribution

height,

it is clear

such

At

at equilibrium

found

suggested

indicate

relative

on this

triples

of

to single

would

The

HF bonds.

limited

of the

indicator

effects

which

a simpler)

barrier

norm

It was

treatments

be im-

use of a diagnostic

correlation

state.

would

sources

of error

correlation

exchange

magnified

by a set

of f-type

(less

than

result

we expect

choice

D3h

and

origi-

should where

among would

functions 0.01

SCF

geometry

the

effects for the

of SCF

state on each

/_.), while

at the

the

at the

MP2

of the

fluorine

energy

be even

higher certainly

of the

symmetry

of electron

geometries

correlation state, will not

is the

question

level

using

atoms.

the The

by lessthan

we have

performed

structure

with

its

to be substantially

as discussed be

first

this

is lowered

Although

Dab

The

to address

geometry.

transition

8

calculations.

In order

transition

the

than

in these

treatment.

of the

our

for

might

to be a good

T1 is 0.01,

Nevertheless,

structure

structure

height

and

of the

method.

excitations

to the

of three

of reoptimizing

equilibrium

energy

treatment.

to the MP2

of freedom,

was

effects

slightly

shown

HF moiety,

transition

the

magnitude

significantly

of triple

cumulative

the

TZ2P

effect

effect.

in the

the

been

respects

are

rearrangement,

geometries

barrier

to

inclu-

the

effects)

proposed

be a problem.

in some

in the

examine

reoptimized

not

correction

correlation

on

of (HF)a

geometries

stretching

an appropriate

We

for the

"many-body"

to the

nondynamical

for a single

triples

participate of HF,

the

two

Finally,

is unexpected,

of single-reference

which

contribution

Thus

ascribed

(and bonds

obtained

appears

reduces

(near-degeneracy

has

T1 indicates

should

examine

triples

length

for

of triples

coupled-cluster

D3h geometry

from

contribution

based

T1 diagnostic

effects

this

kcal/mol.

excitations

Lee et al. 27 have

reliability

arises

librium

effect

correlation,

on the

triple

correlation

Recently,

0.02

of 20.9

but

comment. a large

This

1.1 kcal/mol,

result

triples

of a single-reference-based

a value

in fact

state.

denoted

applicability

large

nondynamical

at the

CCSD

of connected

This

such

portant

tl amplitudes,

effects

further

examination,

by another

to the

3 kcal/mol.

to indicate

the

separation

compared

correction

by almost

this

a source

below.

We are

of significant

error. A quantitative superposition

error

transition some

assessment

state.

conceptual

single

molecule

a single

the

ghost

investigations. CCSD thus

the

assign

effects

are

consistent

than

same

bound)

The

that

the

effect

Nevertheless,

polarizability. out

further

is thus what

but ANO

also basis

that

would

is similar height

would,

Enthalpy Our

by

contribute

to that

provide sets

at least,

in the

set used

if anything,

of basis

our

calculations. than

the

that

exaggerated,

since

most

the

of the

transition

1 kcal/mol.

Since

we expect

the

that

the

in these

bonding basis

suggests small.

to hydrogen

bond-

the

bonding

moments

and

requirements too

binding that

in the set

calcula-

sets,

multipole

unlikely

the

is relatively

calculations

it seems

is not

assign

describe

these

on the

co-workers state

basis

contribution correctly

to have

state.

of error

of meeting

However,

and

reasonably

transition

of the

correlation

8 is likely

of Liu

to be

of Karpfen,

greater

of Ref.

trimer

incompleteness

is likely

results

of the

present

We would

suggest

ANO

not only

capable

make

set

complex,

be even

dominant

the

results

and

description

always

would

energy

should

a reasonable

effect

stable

the

TZ2P

at

these

is also a source

in the

BSSE

However,

results

in the

a

with

in all

I-IF moiety.

so we can

BSSE

binding

that

are not

more

complex,

molecules

used

an even

the

both

this

with

structure

space

on the

2s, which

the

underestimated

effects

results,

the

was

with

trimer:

basis

hand,

to the

one-particle

so the basis

augmentation

possible

MP2

other

HF

kcal/mol.

obtain

presents

a counterpoise and

two

for each

polarization

stable

of 1.5 kcal/mol

well understood

and

the

like (HF)a

computing

are grossly

would

plus

of the

0.1

is consistent

Finally,

set extension

it is now

monomer,

that

of the

of basis

ing is electrostatic, in the

from

than

trimer

to ours)

On

the

Nevertheless,

This

split-valence

and

hydrogen-bonded

to BSSE. similar

complex

basis

0.5 kcal/mol

of the

picture.

of the

than

the stable

and

ANO

is less

binding

this

value

BSSE

set

geometry

present

The

for the

basis.

incompleteness

Comparison

the

ANO

with

different

(upper

the

our

qualitatively

tions.

result

to binding:

BSSE

fragments.

basis

by

SCF-optimized sets

of the

systems

to proceed

an underestimate.

is due

an SCF

a larger

basis

greater

on the

lowering

contribution

level

than

of correlation

(assuming

ghost

of 1.5 kcal/mol

rather

energy

less

SCF

is slightly

a BSSE

an overestimate

who

the

the

an estimate

for both

for polyatomic

chosen

using

as the

include

be done

BSSE

have

HF

present

BSSE

the

We

two

must

this should

complex,

with

At

level

of the

stable

basis

energetics

estimating

difl3culties.

for

HF

Ideally,

However,

correction

the

(BSSE).

of our

effect

with-

expensive.

energy the

It

is someremaining

transition

state

on the

barrier

smaller.

Changes calculated

to be corrected

AE

by the

values difference

refer

to the

in zero

bottom

point

of the

vibrational

potential energy,

energy AZPE.

well Our

and

need

correction

is done at the harmonic level using the experimental value for the HF frequency, while the trimer values are derived from our calculated frequenciesscaledby 0.93 as indicated above. The stable trimer contains4.5 kcal/mol more vibrational energy than the separated reactants which reducesits stability to 9.9 kcal/mol. Correcting this value for BSSE will further reduce the stability of the trimer: if the full counterpoisecorrection is applied the result would be as low as 8 kcal/mol. In view of our discussionof basisset incompleteness, it seemsreasonableto assert that the trimer is bound by 94-1kcal/mol. The AZPE correction betweenthe transition state and stable trimer is -3.5 kcal/mol, while it is 1.1 kcal/mol betweenthe transition state and the reactants. Given thesevalues our calculated barrier at 0 K is 4.7 kcal/mol, and the energyseparationbetweenthe stable trimer and the transition state is 14.5kcal/mol. Each of thesevalues may then be further corrected for BSSE, which would raise the computed barrier to 6.2 kcal/mol. These results require further correction for non-zero temperatures. For reaction R2 there are no corrections required to convert AE to AH if we neglect the dependence of the

vibrational

differences and

energy

in the

AH

=

AE

if the

and

For

with

value

= -2).

of -3.9

for the

R3 the

energies

An

to a value

BSSE

R1 and

rotational

+ AnRT

corresponds

2.3 kcal/mol,

temperature.

translational

(AH

at 300 K this

on

and The

kcal/mol

barrier

values

must

for the

difference

correction for the

be corrected

term

for

between

AE

is -6.5RT

correction,

and

or a barrier

of

is used.

Conclusions We tem _4

have

and

investigated

have

shown

kcal/mol.

ionic lent

in the

system,

such the

In addition,

in (HF)a

portant

with

exchange of the

such

at the

increasing

is small, exchange

problem

can

effects CCSD

level,

anticipate

system.

Finally,

activation

since

many

found

alter

barrier

energy

of

presence

of

cova-

once are

the

again

correlated.

barrier

to become

height more

to concerted

from

sys-

in a purely

energetics

effect

contribution

the

electrons

this the

that

on the

significantly

we can expect

a significant

an

to that

when

excitations and

with

correlation errors

in a hydrogen-bonded

demonstrated

relative

of electron

of triple

also

barrier

of size-extensivity

atoms

proceed

we have

the

effects

size of the

we may

of hydrogen

exchange

lowers

The

the

an

this

magnitude

predicted

exchange

bonding

as H6.

demonstrate

that

that

In addressing

character

from

the

im-

hydrogen

tunneling

to the

rate

reaction.

Acknowledgement We providing would

not

would

like

to greatefully

one of us (AK) have

been

with

acknowledge time

on their

the computers,

possible.

10

support

by

without

Cray

Research,

which

much

Inc.

of this

in work

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(1981)

Table Calculated

Mode

w (cm -1 )

harmonic

I vibrational

spectra

I(km/mol)

Description

C3h Structure: a'

4214

0

symmetric

HF

aI

879

0

symmetric

bend

a'

186

0

symmetric

stretch

a"

662

507

out

e_

4280

571

degenerate

HF stretch

531

382

degenerate

angular

e'

157

17

degenerate

stretch

e"

475

0

degenerate

out

2212

0

symmetric

breathing

at

788

0

symmetric

a_

2194i

-

negative

a_'

1449

466

e'

1674

21

degenerate

e'

1506

4154

degenerate

stretch

eI

604

0.3

degenerate

bend

e"

1135

0

degenerate

out

e'

D3h a_

of plane

stretch -libration

torsion

def. - libration

of plane

torsion

Structure:

out

13

HF

str.

curvature

of plane

stretch and

bend

stretch

torsion stretch

plus

bend

+ bend + stretch

of plane

torsion

Table Comparison

Calculation:

SCF, ANO

SCF

ANO

CISD

II

of relative

AE(R1)

CI, and

CPF

energies

AE(R2)

a

AE(R3)

Results:

18 el

-12.4

35.8

23.4

-14.2

23.8

9.6 7.2

ANO ANO

CISD+Q 18 el CPF 18 el

-14.1 -14.1

21.3 20.8

6.7

ANO

CISD

-14.3

23.9

9.6

ANO ANO

CISD+Q 24 el CPF 24 el

-14.2 -14.1

21.1

6.9

20.0

5.9

SCF,

24 el

MP2,

and

CC Results:

TZ2P/SCF

35.1

TZ2P/MP2 ANO SCF

16.7 -12.4

35.8

23.4

ANO/MP2

-14.3

16.1

1.8

-13.9

20.9

7.0

-14.4

18.0

3.6

ANO ANO

CCSD

24 el

CCSD(T) 24 el

a) Relative

energies

are

given

in kcal/mol.

14