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 198ed_ 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 940351000
func
of accounting
coupledcluster
barrier
above
effect
the
of the
coupledpair
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,
Zeropoint
using
particular
the
interaction
coupledduster
reaction
hydrogenbonded
then
correlating
mined
excellent
along
for hydrogen
sizeextensivity.
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 doublezeta
reaction
(R3)
e¢ al.
employed
431G
splitvalence
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
coupledpair
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
configurationinteraction
basis
the
recently,
basis
then
37.1
has
segmented
actual
by optimization
_ and
Most
at the
effects.
of the
exchange
are
the
AE(DahC3h)=
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
coupledcluster
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 twoterm
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 triplezeta
(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
splitvalence
(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 twoterm
p set
Finally,
in the an f set
MP2
calculations
8p 6d 4f/Ss
gen
eventempered 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
sizeextensive.
CCSD(T)
18 electrons
spherical
calculation
a calculation
were
and
correlated:
on on the
is neglected
the
were
basis
ANO
were
MOLECULESWEDEN 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
coupledcluster
Results
coupledpair
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 infiniteorder
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
hydrogenbonded of Gaw
in the shorter
and
4
HF
coworkers
Cab trimer. than
for
our
Their value,
the
to an experimental trimer,
the
distance 4, who value
which
found for the was
HF
2° bond
is 1.917
/_. Our
r(HF)
to be
HF
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.
HF
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 splitvalence
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
cmlat
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 openchain
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 nonpolar,
predissociation
argon
et al.
of these
trimer
one
TZP
hydrogenbonded
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 1000cm1 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
cmldiffering
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
HF
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
outofplane
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
HF
and
of negative the
half
(4280
the
the
appropriate
dominant
is much
cm1),
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
R1R3
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
coupledcluster
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
sizeextensive
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
sizeextensive
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
bondlengthening
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 ftype
(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
"manybody"
to the
nondynamical
for a single
triples
participate of HF,
the
two
Finally,
is unexpected,
of singlereference
which
contribution
Thus
ascribed
(and bonds
obtained
appears
reduces
(neardegeneracy
has
T1 indicates
should
examine
triples
length
for
of triples
coupledcluster
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 singlereferencebased
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
coworkers 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
IIF 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
oneparticle
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
splitvalence
and
hydrogenbonded
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
SCFoptimized 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 941kcal/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 nonzero 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 hydrogenbonded
demonstrated
relative
of electron
of triple
also
barrier
of sizeextensivity
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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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