the equatorial. Cr-C bond distance is very long at the SCF level of treatment compared with the axial distance, whereas in Fe(CO)s the azial Fe-C distance.
NASA-CR-!
92889
Wd'c
:2-
"1'Y/
/ t,/--- 7_ - _,¢--_
The
structure
and
energetics
of Cr(CO)6
and
Cr(CO)5 Leslie
A. Barnes
Eloret
*
Institute
Palo
O
Alto
Caiifornia
94303
_ _
12,
I'M t_
U
tt_
Z
_
0
PW
Z _u'3 WO
Bowen IBM
Research
Almaden
Division
Research
San California
Center
w,O
Jose k),l" v_"t
Lindh
of Theoretical University
L
Chemistry
of Lund
Sweden
_
...._
._
_._ _
_ZLU _L_v
"Mailing
Address:
NASA
Ames
Research
Center,
L.
c_Q
95120-6099
Roland Department
_v f-
Liu
Moffett
Field,
California
94035-1000
_"
mFLk
2
Abstract The
geometric
structure
pair functional
(MCPF),
and
levels
CCSD(T)
nected
triple
are
experimental
data
the structures
shows
of Cr(CO)s than
out limitations
of Cr(CO)s
basis
CO bond
tigation
of 3s3p correlation
the
total
CO binding
the
CCSD(T)
level
discrepancy treatment.
on each C and by the fact that contracted energy
energy
reveals
than
for CO.
total
or about
In particular
effect.
is estimated 86% of the basis,
at the MCPF
An invesbasis
set,
to be 140 kcal/mol
at
than
results.
value.
The
value is prob-
limitations
in the
and an f function This is underscored
set (1042 primitive
the superposition
Calenergy
although
In the largest
d function
a very large primitive
is 22 kcal/mol
study.
value,
and theoretical
quantitative
total of the points
binding
experimental
rather
an additional
to obtain
the total
is well described.
the experimental
larger
An analysis
the experimental
only a small
CCSD
level of treatment
but
for due
binding
at the MCPF, gives a much
MCPF
results
are probably The
methods.
of Cr(C0)s
of Cr(CO)s
to 300 basis functions),
of Cr(CO)s
the best
errors
method
the BSSE,
in the one-particle
even using
gives
basis used here and in a previous
smaller
symmetric with
or CCSD at the
total/y
Comparison
used
CCSD(T)
for con-
of theory.
levels
sets
estimate
opti-
are also determined
sets reduce
between
0 are needed
(CCSD)
is partially
method
(BSSE)
of theory,
coupled-cluster for the
remaining
The
energy
coupled-
of Cr(CO)s
and that
the MCPF
dissociation
constants
geometry
basis
at the modified
a perturbational
CCSD(T)
Cr(CO)s
is still significantly
ably due to limitations
\
one-particle
the first
correlation
the
error
excitation
CCSD(T)
in the one-particle
using larger
remaining
and
either
set superposition
culations
The
levels of theory.
energy
double
the force
that
and
is optimized
(including
and
CCSD
in the
and CCSD(T) basis
of theory
and force constants,
to deficiencies
binding
and
determined.
at the MCPF,
energies
single
excitations),
representation mized
of Cr(CO)6
functions
error for the total binding
level of treatment.
1 The
Introduction calculation
remains great
of accurate
a challenging interest
in many
areas
example,
references
[1, 2, 3] and
is well known
for several
to determine be more
and
for example, From important If this
may
energy
be predicted
energies.
providing
another
useful
Previously, to study
the
providing
systems
the
binding
the
best
energies
are
for Ni(CO)4 respectively,
Fe(CO)s
the
bond
first
dissociation
of 5 kcal/mol bond
experimental For
the
energies
only
bond
could
data
this
be and
than
of Fe(CO)s
were
discussed
in metal
3d configuration
high-spin
coupling
given force
[7], Fe(CO),,,
of treatment
upon
which
as
may
chemically
(see,
when and are
is an
methodology. carbonyl
binding
total
computing
known
binding
individual
vibrational
frequencies
in several
the
(MCPF)
method
n = 1,5
[4] and
time. --
In
82%
cases,
basis
possible
forming
the
in better of the
of the
total
experimental
for Cr(CO)8 error
For
subsequent
only
a lower
energy.
In
bound
contrast,
agreement
with
of error
in the
describing
the
and
loss
the
and
(BSSE).
energies
complex
[4],
the
binding
in accurately
carbonyl
Cr(CO)8
whereas
so that
sources
[6] was used
general,
value
dissociation
generally
on the
in the
energy
if the
set superposition
bond
were
difficulty
double
such
are harder
energies
However,
well determined,
of the
energy
energies
metal
experimental
determine,
last
Cr(CO)6
in terms
and
was to
be expected
and
exchange
energy
the
that
for basis
harder for
at
68% of the
constants
would
the single
functional
correcting
were
for
methods.
level
67% and
(see,
systems
binding
individual
species
energies
dissociation
cases
Recently,
at
without
energies
distances
of the
n = 1,4
to
dissociation
of the theoretical
structure
carbonyl
binding
carbonyl
confidence.
geometrical
Ni(CO),_,
bond
occurring
may be problems
coupled-pair
and
Fe(CO)s,
some
modified
low
metal
then
calibration
too
bond
accurately
saturated
ab initio
individual processes
total
there
synthesis
carbonyl binding
are of
of metals
average
metal
calibration
the
of the
The
a good
then
systems
organometallic
film deposition
systems
therein).
the
with
In addition,
constants)
the
viewpoint,
carbonyl
These
carbonyl
it is the
references
can be computed
(or force
value
[4, 5] and
is not well determined,
binding
individual
the different
since it provides
also
thin
transition
However,
a theoretical
quantity
energies
but
from
therein).
saturated
in understanding
quantity
and
metal
chemistry.
ranging
references
Cr(CO)6,
references
quantum
photophysics
experimentally.
important
for the transition
of chemistry,
chemistry,
Fe(CO)s,
energies
for ab initio
surface
Ni(CO)4,
\
problem
catalysis,
energy
\
binding
the
alone. binding change of the
molecule.
excitation
coupled-cluster
(CCSD)
method
that
includesa perturbational estimatefor connectedtriple excitations (CCSD(T)) [8] has been usedto study Ni(CO)n, n = 1,4, and Ni(C2H4) [9]. This CCSD(T) approach yielded
good
results
for Ni(CO)4 binding were
shown
large
result
In the
previous
theoretical
[12]. recently
a large SCF ground
energy
basis
¢r
level
different
electronic
of a single
carbonyl
one-particle
basis
C4.
symmetry
9 kcal/mol
(square
higher
of Cr(CO)6
They
found
torial
to axial
some
SCF
The
the
The
ground
state
CO angle
calculations
experimental
and these
at the
sets,
studies
found
did not
some
the
the
of Cr(CO)6
level
has
been the
bond
SDCI
calculations
was
and
MCSCF
calculations
photoelectron
binding
energies
used the
MCPF,
CCSD
about energy
at the from
et SCF
Cr(CO)6.
with
[17] has
of Cr(CO)sH2
of
Demuynck
Cr(CO)s,
Pacchioni
state
dissociation
distances
a
[14] on
a 1A1 ground
bond
at
dissociation
bipyramid)
with
the
out
in a small
In addition,
bond
to the
of Hay
[15] on the
(trigonal
at the
correla-
carried
work
in
dissociation
Hall
atom
set,
of electron first
of theory.
of theory
basis
the
the first
calcula-
[t3] relative
to have
recently,
limited
of the
address
SDCI
to be XA1 in C4_ symmetry,
in a study
study
and
experimental
on Cr(CO)s
theoretical
which
Cr(CO)5
92 °. More
out
and
work,
of a rare-gas
of Cr(CO)s
SCF
one-particle
in particular
SCF level
using
CO),
calculations
structure
importance
Sherwood
of around
carried
the
work
work
each
MCPF
by 111 kcal/mol
D3s structure
latteI
interaction basis
et al. [18] have
However,
pyramid).
because
3.5 kcal/mol
(for
electronic
Cr(CO)5
found
errors
set,
[11] and
[13], at the
In the former
lengths
in small the
and
bond
in energy.
studied
of theory
Nilson
Cr(CO)6.
to be 49.8 kcal/mol
al. [16] have level
of Cr(CO)s
at fixed
and
We note
basis
of the
functional
illustrating
sets.
total
remaining
an additional
results
in a large
previous
The
the
exactly.
Davidson
Regarding
energy
for BSSE,
to Ni(CO)4
the
even
of binding
one-particle
yielded
is still unbound
basis
from
in the
almost
However,
is some
states
value.
is applied
and
energy.
in small
experimental
energetics
CO fragments,
there
correction
[10], density
of the
set.
binding
of Cr(CO)s,
qualitative
as X_
Cr(CO)s
and
total
After
[4], we compared
by Kunze
17.5 kcal/mol
set for NiCO
correction
such
out
of treatment
state
basis
analysis
carried
tion for the
to deficiencies
be reproduced
work,
one-particle
level
due
work
A detailed
result.
89% Of the
If this
would
an additional
was
one-particle
energy.
experimental
was
MCPF
the
of Ni(CO)4
binding
tions
with
to be largely
use of a very
to other
giving
compared
energy
in the
in all cases,
an equa-
carried
Cr(CO)4(H2)2,
out and
in a combined
spectrum
of Cr(CO)s.
or geometric
structures
of Cr(CO) or Cr(CO) . In the to study
current
Cr(CO)s
work and
we have
Cr(CO)s
in the
same
basis
as used
and
CCSD(T)
previously
approaches [4] and
in sig-
nificantly larger basissets. The geometric structure of Cr(CO)_ is optimized at the CCSD and CCSD(T) levels of theory and the force constantsfor the totally symmetric representationare determined. The previously published work which gavethe structure and Cr-C totally symmetric force constant of Cr(CO)6 using the MCPF approachis extended to include the C-O totally symmetric force constant and the coupling term. The geometryof Cr(CO)s is partially optimized at the MCPF, CCSD and CCSD(T) levels of theory. The first bond dissociationenergy,that is the energy required for the process
Cr(CO), ---*Cr(CO)s + CO is known
experimentally,
required
for the
as well as the
total
binding
(i)
energy
of Cr(CO)6,
the
energy
process
(2)
Cr(CO) ---*Cr + 6co We have
looked
for BSSE
and
at both the
these
effect
of semi-core
In § 2 we discuss treatments. and
Cr(CO)s
(§ 3.2),
2 The
force
constants
and
3s3p
methods the
in the
including and
for Cr(CO)6
finally
the
results
work,
including
a correction
correlation.
used,
results
current
the
one-particle
discussion,
(§ 3.1), for the
first
then
bond
the
and
giving
the
geometrical
dissociation
n-particle geometrical
structure
energies
for
(§ 3.3).
Methods standard
contracted
Cr basis
a final
is the
basis
by Wachters, set of the
form
[4s 3p] contractions
with except
the
(14s 9p 5d) primitive
to [83 4p 3d] using
recommended
are
the
In § 3 we present
structure
processes
s and
those
done
the
diffuse
d function
(14s
llp
6d)/[8s
6p 4d].
(9s 5p) primitive
contracted
using
scheme
and
of the
p spaces
his contraction
Gaussian
CADPAC
(5211)
basis
2. Two of Hay The
(311)
(see below),
only
diffuse [20] are
standard
Gaussian
and
set of Wachters
respectively. the
pure
p functions, added,
C and
set of van
[19], as
yielding
O basis
Duijneveldt
sets [21],
In all calculations,
spherical
harmonics
are
used. For (13s Orbital
8p 6d)
the
larger
primitive
(ANO)
basis
set
calculations
basis
set
for C and
procedure
[22].
This
on
Cr(OO)s
O, contracted
basis
3
set
is derived
and using from
Cr(OO)s, the the
we
Atomic (13s
use
a
Natural 8p)
set
of
van Duijneveldt [21] supplementedwith polarization functions as prescribedin reference[22] and contractedto [4s 3p id] for usein Cr(CO)6 and Cr(CO)5. For the valencecorrelation calculationson Cr(CO)6 and Cr(CO)5 we haveused two molecular basis setswhich we term "small" and "large". The "small" basis set consists the
of the
same
We use
standard
basis this
used
basis
of treatment. (3f)/[lf] and
previously
set
The
"large"
method,
the
of the
basis
It is well carbonyl
was
MCPF
complexes
between
CO
the
the
valence
only
the
valence
electrons
valence electrons
For the the
"sinai]"
were
the
uncontracted.
The
on the
basis
is,
with
ponent
0.045794
the
with
a
set on
C
set we use
For the CCSD(T) from
basis be
a combination
MCPF
results.
correlated
energies there
is
levels
ANO
this basis
in metal-
[7, 24].
However,
is a significant
overlap
of Cr.
Therefore,
semi-core
3s3p
calculations
or "3s3p
-4- valence"
[25].
inner
contracted However,
we have
also
electrons
and
al.l
as "valence
only"
if
if both
the
3s3p
and
the This
outermost
s, two p and 3d SCF
In addition,
(3f)
primitive
set of the
"large"
tion
optimized
for 3p correlation
and
basis in the
a (4f)/[3f]
referenced Cr
4
atom
set
[26].
binding
The
the of this
of Par-
in a flexible four
contracted [25].
to describe d function
a (lf) contraction
way
d functions
generally
of functions, and
flexibly
energies set
respectively
a diffuse
above
retaining
p and
p functions
and
but
primitive
are
orbitals,
diffuse
more
nature
contracted
from
Cr
the
12p 9d)
d functions
0.051121,
we use
and
was
atomic
on
unbalanced
six s, four
one
two even-tempered
of 0.127803
to the
(20s
set derived
to Cr,
considerably
of Cr.
the
a basis
3p functions
due
5D state with
used
f functions
increased
2s, 3s, 2p, 3p and
exponents
the
used
three
with
we initially
we instead
(1 -4-4)d],
inner
is supplemented
orbital,
was
for the
(2 + 4)p
CO.
error
Therefore,
to [(3 + 6)s
with
of two
set on
superposition
[25], optimized
based
large must
binding
denote
calculations
above,
addition basis
anomalous.
tridge
We
[4s 3p ld]
derived
the
chromium
correlated,
-4- valence
discussed
and
the
were
and
3p electrons
the
CCSD(T)
supplemented
With
point
electrons
accurate
set
the
[13], in Cr(CO)6
of correlating in Cr(CO)6.
3s3p
[4s 3p] segmented basis,
results,
valence
the
for Cr(CO)6.
of Cr(CO)6.
at a single
to compute
and
and
optimization
CCSD(T) all the
functions and
and
are correlated.
set
contracted
metal
for Cr(CO)6.
Davidson
electrons
Wachters
functions
out
above
CCSD
basis
5c_ electrons effect
MCPF,
[23]),
carried
in order
by Kunzeand
investigated
is the
described
202 contracted
reference
that
as discussed the
set
sets
(see
and
known
Duijneveldt
at the
for the geometry
calculation
small
results
basis
function
method
van
[4], containing
269 contracted
only the MCPF
and
to compare
contracted
O, giving
Wachters
This the
with
4p ex-
based
on the
primitive
func-
coefficients
are
taken
from
Cr
atom
the
form
(20s
14p
the
[4s 3p ld]
ANO
which
This
basis
The
exponents
the
the
natural
correlates
consists
of an MCPF
the
3s, 3p,
10d 4f)/[(3
+ 6)s
basis
and
3d and
contraction
calculation
Gaussian
The
(1 + 5)d
to give the
"large
3f]
and
for the
large
and
CCSD(T)
7S state
final
and
3s3p"
functions
coefficients
on the
4s electrons.
(2 + 6)p
set for CO
of 1042 primitive
Cr basis
is of
is combined
basis
with
set for Cr(CO)a.
300 contracted
3s3p
of the
functions.
Cr basis
are
given
in
Appendix. As discussed
lating
above,
56 electrons
of Cr(CO)6, work,
the
MCPF,
in Cr(CO)s
or 74 electrons
and
correlation
computed
method
the
7S state
[27] to compute
(closed
shell)
For
gradient
At
harmonic
frequencies
by fitting
and
0.010
a0 in C-O,
and
then
were used
totally
symmetric
e4b_.
discussion mized
degenerate, found
of the
at the
the
a minimal
with
with level
the
D3h structure basis
with
the
For the
electrons
configuration
CCSD/CCSD(T)
open-sheU
coupled-cluster
with
occupation
geometry
was
under
calculation
force
for
[28], Table
removal
has
e"4e '2 occupation
[29]-[33]).
(see
the
of Cr(CO)s). in the
small
C4u structure
lower
by only
without
symmetry,
geometry
force
was
Cr-C
bond
displacements,
In general,
about
constants
14
for the of the
to be of C4u sym-
CO moiety This
work Both
basis,
by 2.8 kcal/mol, geometry
shown
and
of Hay
optimization).
SCF
with
which
has
[14] for a general
structures were
further
a _A1 state
to Fe(CO)s)
0.8 kcal/mol. at the
without
gives
(analogous
of theory
on CO (and
C-O
analytic
IX, for a definition
been
of a single
a D3h structure
to be lower
and
three
the
ao in the
effects.
and
using
constants).
references
structure
Cr-C
t82g in Oh
of Oh
level
of 0.025
lengths
Cr(CO)s
by the
optimized
constraint
coupling
reference
3d
correlated
displacements
two bond
and
the
independent
(see
is also
electronic
SCF
this many single
1A1 a state
to determine
(see
There
state
in previous
treating
the
in the
At the
performing
Cr(CO)6
occupation
As noted
energy
basis),
matrix-isolated
rearrangement
treatment
binding
the
computed.
coordinates
geometrical
a 3A_ ground
small
points
to determine
from
used
the
of theory
representation
obtained
we use
corre-
correlation
is art SCF
restrictions.
atom
energy
displacements
internal
Cr
only
were
first
Experimentally, metry,
equivalence
the
energy
combined
points
symmetry
level
(using
optimized
when
function
are used,
species.
SCF
techniques
is essential
and
we consider
the
valence
is included.
reference
atomic
for the
methods
correlation
The
of the
the
molecular
Cr(CO)6
symmetry.
and
full symmetry
on
3s3p
method
procedure.
with
calculations
CCSD
66 electrons
when
the use of a size-extensive
in the
the
orbitals
found
were
fully
to be
Previously,
Hay
level of theory, Using
a larger
optialmost [14] with [3s 2p]
CO basis(also without full geometryoptimization) Demuynck et
al. [16] found
C4,
of theory.
structure
dition,
at the
compared was
to be lower
by around
SDCI
the
to the
further
level
and
CCSD(T)
the
C-O
levels
values
and
The
bonds
may
along
the
C4 axis.
distance the
was
SCF
and
that
the
The
Ames
for
MCPF
the
fixed
the
MCPF, SCF
§ 3.1 and with
only
the
insensitive
values
and SCF
§ 3.2 later). axial
bond
equatorial
bond
derived
results
to the
CCSD
of the
the
at a value
correlated
and
for
method
from
for Cr(CO)6.
Cr-C
bond
distance
harmonic
CRAY
frequency
were
evaluated
with
the
calculations
the
closed
the
RISC
on the
the
Y-MP
system.
on
and
of Scuseria
Cr(CO)s The
MOLECULE
The
NASA The
system.
integrals
[35] and using
CCSD/CCSD(T)
SYS-
computers.
were performed
shell
code
and
IBM
calculations
[34] program
are
slightly
and given
different
fitting
the
SESWE-
calculations
open-shell
were
CCSD/CCSD(T)
[27].
Interestingly:
the the
CCSD
MCPF
correction
force
in Table to those
in the current
as exPected
CO,
Center,
CADPAC
using
Cr(CO)6
long,
the triples
facility
NAS
structure
are
(for isolated
and
and
Discussion
too
is much
Research
[38] program
geometric lengths
Almaden
the
and
performed
level
adding
(see
"equatorial",
being
and
at the
[14]
C4,_ structure
a combination
methods
again
at the
fixed
from
In ad-
12 kcal/mol
only the
on an IBM3090/300J
SCF/MCPF
TITAN
for the
and
CCSD(T)
IBM
and
The
grid
MCPF
work
were
and
is relatively
using
use of a finer
s!gnificantly-
and
Cr(CO)6
Facility
system,
were
The
the
by around
for Cr(CO)6
"axial"
performed
calculations
Results
bond
angles
into
level
correlation
deduced
distance
energy
performed
using
The
bond
results
and
were
[36] programs.
calculations
3.1
electron
a value
axial
at the
[37] program
3
the
Cr(CO)s
optimizations
were
performed
The at
CCSD
binding
correlated
WARD DEN
for
Computer
geometry
the
including
correlated
the
computers
Cr(CO)6
current
SCF
angles.
Central
SCF
the
calculations
TEM/6000
in the
be separated
For
the
bond
Therefore,
fixed
optimized,
results
We note
lowered
of theory. were
optimized Cr-C
was
optimized
distances
at the
C4v structure
D3h structure.
(partia_y)
10 kcal/mol
the
, and
approach
has a significant
1.
The
work.
The
is between effect,
basis
previously Cr-C
correlation _elds
of Cr(CO)6
small
published
electron
approach
constants
a shorter CCSD so that
bond and the
using
[4], due to the
distance reduces
results
at the this
distance
distance CCSD(T)
CCSD(T)
SCF
than [39]), method
yields a Cr-C bond distance 41].
As found
significantly
using
the
too long this is largely
reference
[39] in the
The
Cr-C
which changes
distance
of about agreement by
0.02
accounts
almost
Thus
it seems
yield
very
good
that
even
with
isolated
CO
the
entirely
on going
from
which
C-O
C-O
distance
method small the
force
yields
large
to CCSD the
coupling in the
to predict
ao at the
CCSD(T)
CO,
to
the
a very
from
is less than
0.01 ao
improved is 0.05
level,
bond
with
at the
CCSD(T)
in the
C-O
set
decreases
set
[39], which for Cr(CO)6.
for
level
these
in reasonable
distance basis
bond
ao shorter,
for r(Cr-C)
experiment
basis
results.
Applying
a value
large
than
value
Cr(CO)6
would
of treatment,
length
but
on going
how this
large
from
a value well with
and term
Fll
isolated
levels
smaller
smaller will change
at the with
higher
basis
the
for
longer mainly
of 18.11
level
levels
and than
of theory
three
bond due
to
although
the
CCSD(T) value
CCSD(T)
of theory,
all
[4s 3p] basis.
the
MCPF
value
CCSD(T)
2 [28].
for r(C-O)),
2 for the
all levels
aJ/]k
However,
than
experimental
in the large
better,
basis.
so
level
with
(as noted
as found
significantly
[39] in the
is markedly
CO
at
small
consistent
of 18.0 a2//_
small
of treatment,
of 2.44
in the
with
F22, is improved
CCSD(T)
value
in the large
the
consistent
constant,
of reference CO,
basis
are
for F22 is increased
small
CO results
F12 is too
basis,
is too
is significantly
estimate
compares
CCSD(T) value
2, and
force
experimental
experiment
which
Cr-C
in isolated
of the
than
in Table
2.5 a.J//_ 2 at the
Fll,
In the
term
large
is
data.
distances
[39].
we estimate
and
the
the isolated
we may which
CO
basis,
given
MCPF
with
treatment
an Fll
bond
distance
in isolated
The
of around
is Smaller
is larger
and
basis,
The is smaller
with
are
above.
constant,
in Cr(CO)6.
value
basis,
difficult
a value
in the
MCPF
discussed
basis,
constant
improvement the
for Cr(CO)6
large
consistent
force
C-O
C-O
one-particle
change
distance
experimental
significantly
discrepancy
experiment
is to be compared
The
the
basis
in the
the
to the
C-O
[40,
is well described.
level
estimate
The
remaining
MCPF
that
methods,
for the
with
results
In the
and
In isolated
[4s 3p ld]
constants
for r(Cr-C). basis,
data.
the
the error
level gives
2.18
experiment
set effects.
found
of about
compared
we find that
in the small
[4s 3p] basis
the
we may
effect
improvements
the
length
set
than
work,
the isolated
for basis
the
agreement
force
bond
from
that
basis,
ao shorter
distances
to Cr(CO)8
The
0.03
experimental
going
Using
ao longer
previous
when
set at the MCPF
r(C-O)
the
a0 on
set effect.
a basis
ao and
with
level
basis
is about
0.05
in the
correcting
CCSD(T)
3.64
about
after
is mainly
to the
correlated
[4s 3p] segmented
the large
again
is only
approach
a basis
methods
Using
MCPF
at the
However,
for all three
which
in the
method
in
aJ//_ 2 [28]. interestingly MCPF. --
It is
however,
given
the
relatively
experimental
large
value
error
may
bar
on the
be significantly
experimental affected
value
by
and
anharmonic
the
fact
effects,
that
the
the
results
are reasonable. Overall, agreement
with
the
CCSD(T)
3.2
The
The
results
noted
the theoretical experiment method
for the
/C_CrCeq
yields
of Cr(CO)5
are given
Cr(CO)s
[42] (see
results
constants
are
one-particle
than
in good
basis
set,
and
MCPF.
of Cr(CO)5 in Table
is known
93 ° [33], although
Conditions
force
of the
better
structure
matrix-isolated
and
the limitations
consistently
structure
of about
for geometry
within
geometric
above,
certain
results
to have
the Dab structure
also reference
[33]).
3, in the small
basis
set.
C4_ symmetry,
with
has also been
proposed
No gas-phase
structural
As
an angle under
information
is known. We first
look briefly
at the
as found
for Fe(CO)s
--
distance
is very
at the
whereas
in Fe(CO)s
tance
(Luthi
of the
two
long
a pentagonal
the
azial
In
(see
greater
interaction
bonding
tion is ._2 ._2 ._2 _xz _yz t'_x2 are
relation
Hay
d zy_
_y2
favoured
'
with
for the
different
Cr-C
distance.
stronger The
the
axial
Fe-C
equatorial
CO
distance also --
with has
Cr-C
the
Cr
a weaker
than
the
equatorial
d-orbital
CO
when
SCF
atom
and
interaction
group
The
and
z) a
configura-
case the equatorial electron
cor-
be significantly
C-O
bond
of theory
so has
dis-
(along
the
would
level
distance,
occupations
extensive
distance
bond
is predominantly
in this
in Fe(CO)s.
at the
axial
In Fe(CO)5,
However,
Cr-C
the
axial and
structure
with
3A_ state
the
dz_ orbital,
equatorial
the
groups.
equatorial
distances
interaction
giving
groups.
the
of the
equatorial
an empty
longer from
occupation
axial
we expect
as found
a much
is much
is the same
the
compared
be understood
the
only
the
reflect has
may
than
shortened, the
distance
3. This
However,
of treatment
[14], for example),
over
is included,
level
Fe-C
This
in Table
bipyramid.
Cr(CO)s,
d2_'+_z'++._ _2 ._t -u_ dxy, 1
groups
SCF
et al. [43]). species.
D3h structure
the
distances axial
CO
a longer
C-O
bond
so a shorter
C-O
bond
distance. We now level
consider
of theory,
whereas
the
axial
the opposing
the
the
equatorial
distance
"axial"
the
experimental
are
alSO semi-empirical
C4,, structure, Cr-C
is slightly
distance shorter,
CO in Cr(C0)s.
estimate
the
results
is very as may
the
92 ° value
of 93 ° [44] and
in Table
similar
3. At the
to that
be expected
Theangie=2Ca_CrC,_is
of 93 °, and estimates
from
with
in good
of Demuynck
93.5 ° [45] for this
SCF
in Or(CO)s, the
removal
of
agreement
with
et al. [16].
There
angle.
The
angle
/CrC_qOeq are
is very
both
close
Cr(CO)s
to the
level
C-O
For the
should
be suitable
distance
perturbed
of theory
results.
in Cr(CO)6. from
we fix the
the
C-O
CCSD/CCSD(T) for both
be expected,
and
Thus
Cr(CO)_
calculations
of theory,
both
bond
distances
at the
SCF
level
of theory,
based
we use
As noted
C-O
structure.
distances
methods.
the
Given
on the
this fact,
Cr(CO)6
a compromise
previously,
the
angles
at the
correlated
distance
which
are fixed
at the
values. At the
In this Table and
MCPF
case
the
1) and
bond
of configurational
than
distance
a little
the
distance,
mixing
in Cr(CO)6,
Cr(CO)6.
This
axial
may
be
which
optimization
of both
than
the
_
0.032
fully
even
Cr(CO)6
which
value).
additional
is a consequence
orbital
in Cr(CO)s,
poorly
described
in Cr(CO)6
be
optimize
The
level of theory
CCSD may
we did not
[46] from
(see
At the
further,
case
optimized.
in Cr(CO)6
in Cr(CO)6.
diagnostic
is around
are
found
1. (In this
is more
in the
for example,
than
3d4p hybrid
Cr(CO)5
seen
more
at the correlated
of a low-lying so that
distances
contracts
of Table
it at about
distance
bond
less
bond
results fixing
bond
lying
calculations,
contracts
Cr(CO)_
of the axial
Cr-C
distance
of theory,
on the
equatorial
higher
bond
equatorial
levels
based
contraction
level
axial
the
CCSD(T)
expected the
to 180 °, as may
is only slightly
correlated
SCF
close
which at the
the
is much
SCF
level
coupled-cluster
and
around
0.038
in
Or(CO)5. A full CCSD(T)
level in a larger
experimental estimate
data
on the
of the
optimal
results
presented
here,
3.3
Energetics
3.3.1
Basis
set
In the previous energy
extent.
work,
have
However,
BSSE
and (around
BSSE
distances
--
however,
of Cr(CO)s given
this is postponed
by combining footnotes
the
to Table
the paucity
to a later Cr(CO)6
at the
date.
and
of An
Cr(CO)s
7.
error
and
compute
the
work
basis
work
in a basis
the
CCSD/CCSD(T) in Ni(CO)4
in the
in earlier
the recent
error
considered
is given
C-O
desirable
was made
we did not
the
and
of Cr(CO)s,
geometry
although
that
superposition
structure
and
Cr-C
is probably
superposition
of Cr(CO)6,
it was found
basis
the
BSSE
on NiCO
set expansion
of Blomberg
set larger
question
MCPF
methods
8% larger
for
than
with
[47], Ni(CO)2 effects
tended
the
small
detail.
gave
similar
CCSD(T)
basis
results method
indicated here.
et al. for the
compared
binding
WiCO
to cancel
used
Blomberg
the total [7] and
et al. [9] on Ni(CO)4
in some
the
associated
[24],
to a large a large
Therefore found
BSSE
that
we the
correction
to MCPF),
so
that
in the
BSSE,
current
using
5, where sets.
the
work
full counterpoise
we break
Total
clown
energies
For the small
basis,
the
superposition
the
various
binding
is around presented
for all the
results
CO,
with
4 kcal/mol/CO,
Cr
atom.
a total
The computed
essential
of the
is very
large
good,
Davidson
[13], even though
value.
error
is reduced basis
basis.
the
result.
to the
true
basis contains
increase
3s3p
in superposition with
entry
Cr portion and large, (C0)6
the
flexibly
3 kcal/mol
Naively,
one
might
However, account error
and
reasonable
at both has
The
to
sets
are
SCF
result and
higher
than
superposition
is reduced viewed
although
half
by Kunze
to the
when
reduced
MCPF
(4)),
expect
from
the
on a per
CO
much
improved
but
the
this does
In the
MCPF on
correlated
CO
superposition
superposition
10
a smaller
has
increased
then
there
are
ghost
basis
will
work
using
the
basis
a side
has
effect
increased
by around
increase compared
on
at the
the superposition error
basis,
when
nothing
However,
basis
overall
of theory,
to almost level.
error
but
ghost
that
current is an
bound
in a larger
mean
size of the
There
levels
upper
fragment
not
fragment. case.
an
If the
in the
the
is reduced
SCF
true.
increasing
and
be
calculations
usually
set on Cr is to increase --
will
that
deficiencies
is the
basis
error
basis
this
SCF
same
at the
significantly
Thus
BSSE
is not
for the
for a given
the
the
then
will be zero,
(3) and
superposition
the
the
is about
0.01 a.u.
Cr contribution
computed
this
basis.
error
contracted
fragment
the
basis
given
is about
for six CO ligands,
the
(entries
is significantly
of theory.
contribution
correction
which
which
of the
CO
from
error
of 7 kcal/mol
is quite
BSSE.
error
(2),
levels
of Cr(CO)6 the
and
basis
superposition basis
energy
of theory,
is from
for Cr(CO)6.
correction
in the fragment
the
value
to roughly
correction
larger
superposition
MCPF
recent
particle
superposition
no deficiencies
large
one
no functions
computed
and
the
of theory,
contribution large
in
is still large.
correction.
will reduce
the
overall
basis,
a given
level
(2))
level
contribution
Thus
quantities
error
seems
is a very
110 kcal/mol.
basis
Appendix.
(this
small
4 and
and
superposition
result
a comparatively
SCF
the
SCF
in Tables
correlated
dominant
2 kcal/mol/CO,
Thus the
than
the
of the
systems
in the
The
(entry
the total
MCPF
to about
small
For
the
At the
However,
from
lower
At
the
energetic
the
different
is a large
of 28 kcal/mol
reliable
at both
slightly
their
small
basis,
4.
computation
are given
are given
4).
of about
for Cr(CO)6
results
there
times
in Table
energy
basis
small
three
for the
for the
(1) of Table
correction
to compute
The
calculations
with
BSSE
binding
in order In the
that
overall
[48].
of Cr(CO)6
in entry
hold
about
BSSE
error
approach
contributions
energy
as shown
MCPF
method
for various
total
the
we use only the
Cr.
The
SCF
level,
of using
error
a
for the
by nearly 8 kcat/mol,
when comparedwith level
is slightly
though
our
indicate contracted
even
the
basis
first
may
superposition energy
Table
energy
4), being
dissociation Tables
5.6 kcal/mol
difference
estimation
large
and
with
(2)
of Table
energy
in the
MCPF
level These
tion must
basis,
the
(1),
4).
results
be treated
superposition give
counterpoise
results
the
reduction
From basis
these
results
when
about
440
and
the
fragments
total
SCF
binding (1).
(entry
(1) of bond
(entry
(1)
at the
(2) of Table
in
SCF
5 gives
the
(1).
The
equation
MCPF
levels
the
uncertainty
to illustrate
dis-
For the first
from
and
the
CO bond
of 1.7 kcal/mol
derived
the
total
for equation
numbers
entry
superpo-
between
for Cr(CO)e
Cr(CO)s
Alternatively,
the
of theory. in the
method.
only
the
Thus,
computed for the
the
total
in BSSE
results,
is 0.7 kcal/mol
the
BSSE
binding
indirect
level
method.
of Cr(CO)s.
to Cr(CO)n
for the
SCF
the
energy
is similar
BSSE
at the
via
first and
When
(entries
bond
(1)
dissociation
2.3 kcal/mol
at the
of treatment.
fragment
may
the
error
[4s 3p 2d lf]
difference
of CO ligands.
error
serves
(1)),
for the
to that
and
at both
two corrections
5 gives
large
case,
we have
BSSE
number
from
the
via
entry
directly
in this
basis,
(3) in Table
compared
the
between
of BSSE
In the Entry
larger
the
Cr(CO)e
level.
the good
(equation
fragments
a superposition
MCPF
computed
is much
the
giving
at the
error
correction
subtract
results
of theory.
this leads
of Cr(CO)6
similar
to the
very
as the
appropriate
5, we see that
proportional
we
energy
the
These
time.
m indirectly
binding
[13], even
superposition
level,
previously,
SCF
an additional
SCF level
give
of Cr(CO)6
is qualitatively
5, respectively)
superposition
The
of Cr(CO)s
energy,
4 and
level and
(1) in Table
roughly
current
the
correlated
probably
energy
using
at the
as noted
in two ways
or directly
entry
would
value.
m probably
level,
at the
Davidson
their
basis
at the
error
and
than
the increase
at the
total
lower
a larger
However,
dissociation
for the
of Cr(CO)5,
sociation
Cr basis.
by Kunze
O. At the correlated
CO and
be computed
a.u.
significantly
is too large
errors
From
on
our superposition
given
0.05
times
error
bond
Thus
we need
C and three
be used
a larger
For the error
on each
which
(2).
7 kcal/mol
SCF level
superposition
functions
sition
the
by almost
with
in entry
is now almost
at the
should
combined basis
energy
increased
to reduce
results
than
d function
is again
ANO
larger
total
that
the
quite
emphasize
several
with
caution,
and
basis.
Also,
a lower
total
error.
Finally,
different
counterpoise
different
corrections. method
should
points. may
is does
not
give some
within idea
superposition
indication
of computing
Nevertheless,
11
computed
not be a true
energy methods
The
of deficiencies
necessarily the
in
imply
a lower
superposition
error
a particular
of possible
correc-
errors
one
particle
in the
com-
puted
binding
energies.
Only
can give a more
accurate
Cr(CO)s
correlated
at the
3.3.2
The
The
total
total
binding
We give
both
with
without
and
for several CCSD
CO
the
from compared
is about
1.5 kcal/mol
large
effect
was
large
basis
CCSD the
due
Ni(CO)4.
has
MCPF
3s3p
method.
and
the
effect
the total
basis
set
level,
recalling
to the
and
total
binding
energy 3s3p
the
energies
results
energy
are
less than
7.
molecule, energies the
MCPF.
The
36 kcal/mol
contribution
in
per
CO
the
triples
CO is slightly
larger
for
BSSE,
and
total
the
binding
small
total
triples
that
increase
the
set,
although
to the
CCSD
per CO than
CCSD(T)
in the
smaller,
Similarly
basis
smaller
the
is
the
correction
is still
which
for BSSE,
result.
large
of
though
correction basis
energy
basis,
analogous,
in the
seen
of the
for NiCO
method
basis
set
in has
size than
[9].
computed
the total
binding
only the
valence
Cr basis
is 6.1 kcal/mol
correlation,
is only 3.8 kcal/mol,
is increased
by around This
of Cr(CO)6
the
small
but
it is easily
above
6 and
basis,
In Cr(CO)s
after
The
at 41 kcal/mol,
here,
the
per
An
reduced
correlation.
given
small
about
to the
the
MCPF.
a larger
were not included binding
larger than
correlation
including
of theory,
[47]. However,
set, we have
of using
for
total
than
correcting
in BSSE.
NiN2
correlation,
large,
in Ni(CO)4.
compared
reduction
as a function
3s3p basis
of 3s3p
level
10 kcal/mol
as found
difficult
as expected.
MCPF
for BSSE,
smaller
contribution After
sets
CO
the
In the
[9]. Thus
than so the
per
purposes,
(T) is very
basis
in Tables
energy
is slightly
Ni(CO),.
larger,
given
Appendix.
in Ni(CO)4
3 kcal/mol
method,
valence
which
and
[9] and
energy
effect
Thus
which
the
large
correction
binding
The
whereas
effects,
almost
is now even
In the large both
by
is about
in the
excitations
than
at
is reduced
more
energy
significantly,
value
yielded the
smaller
binding
After
given
larger
Cr(CO)s
are
binding
and
this is very
and
For reference
in Cr(CO)6
CCSD(T)
energy
for BSSE.
30 kcal/mol
for NiCO
result
CCSD(T)
binding
the
to the
found
and
and
basis
is reduced
undoubtedly
energy
is reduced
In the Cr(CO)s
binding
31.5 kcal/mol
but
energy
Cr(CO)s
smaller
is about
in Cr(CO)s
binding
and
triple
but
of Cr(CO)6
Cr(CO)6
are
larger
set limitations,
energy
a binding
with
using
for
connected
Cr(CO)6
than
of treatment.
calculations
yields
contribution
level
correction
Cr(CO)6
contribution
of basis
binding
total
of calculations
estimate
energies
the
method
a series
for the
small
[4, 9]. 12
using at the
may and
using
increase
large
to contribute
basis
sets.
MCPF
valence
level,
for BSSE.
the large
at the
around
including the
correction
10 kcal/mol
effect
are expected
after
energy
3s3p
CCSD(T) Relativistic
3-4 kcal/mol
From CCSD(T) about and
the
MCPF
results
in the
140 kcal/mol a small
similar
at the
large
basis
basis
set, at the
gave
an additional CCSD(T)
as the
give very
good
Cr(CO)6
results
of the
was
taken
than
ao gives
this,
we expect
that
The are
results two
harmonic basis
for
recent
37 kcal/mol
not describe
CO
the
a full to the
of
value,
size
to our large
the
use of a very to a smaller
remaining
to the
discrepancy
and
CCSD(T)
the
use
method
total
energy
of a
would
binding
bond
first
CO
experimental
vibrational
which
We note
_ssociation
degrees the
of freedom structure
(_RT
and force
a C-O
basis
set
results would
a total bond
2 kcal/mol
there
and
probably
energy
which which
higher. would
is
is in
Based
yield
is no direct
the
in Cr(CO)8
distance
structure
on
less than
experimental
of Cr(CO)n
energy both
corrected
computed and
and
energy
determinations,
Cr(CO)s
for the large
For example,
ao gives
is
after
geometry
0.03
that
energy larger
of Cr(CO)s.
dissociation bond
basis
energy.
Cr(CO)s
in binding
binding
optimized
small
is less than
of the
energy
frequencies and
by
set the
to
3-4 kcal/mol
but is slightly
of the
binding
similar
increase
to be about
basis
of the
results
total
set result, was not
energy,
energy.
the is seen
optimization
minimum
7) we obtain
large
basis
is inaccurate
binding total
in the
a combination
at 298 K [49, 50]. We have
for Cr(CO)s
rotational
the
(Table
geometry
a full optimization
of the
first
the
a total
additional
determination
from
which
by 0.03
The
with
the
correlation
correction
fimitations,
although
small
The
correction
error
3.3.3
set
set for CO
Again
to the
However,
higher
2 kcal/mol
basis
BSSE
the
and value
of 3s3p
compared
large
that
per CO molecule
Cr(CO)5.
distance
0.5 kcal/mol
the
sets,
experimental
of similar
energy
Recalling
to CCSD(T),
correction.
to a small bond
of binding
of Cr(CO)5
energy
compared
for Cr(CO)6.
a Cr-C
MCPF
than
BSSE
but
only lead
effect
in § 1, for NiCO
this indicates
ANO
basis
a CCSD(T)
of the
in a basis
to one-particle
3s3p
the 86%
As discussed
set,
energy
binding
significantly
calculation
due
from
The
for Cr(CO)6
inclusion
including
for Ni(CO)4
basis
large
we estimate
is around
level of theory.
largest
and
sets,
basis,
3.5 kcal/mol
binding
on going
reduced
basis
This
[4s 3p 2d lf]
total
is lower.
larger
3s3p
large
results.
For the
energy
large
level of theory.
is probably
such
small,
large
of 89% found
in our
for Cr(CO)s
and
correction.
CCSD(T)
energy
basis
in the
value
basis,
in the
small
relativistic
to the
binding
results
for equation constants 13
given
of which
these
at the
a standard
are
correction (1)).
agree
to a D, value
SCF
of these
in Table
level
on
8.
the
value
molecules
of theory
the
of
at 0 K by using in the
[51] for translational
Although
There
SCF
particularly
small and
method
does
well, the
vibrational correction basedon for equation
(2)
the total
computed
CO
18.8 kcal/mol
ment
is fortuitous,
and
isolated
corrections.
using
and
The
Cr-C
frequencies
(in
is 1.4 kcal/mol
stretch
results
giving
is still
between
a net
error
the
frequencies.
This
between
and
SCF level,
whereas
correction
for equation
Cr(CO)_
leading
the C-O
The
and
to in-
stretches
for equation
of only 0.9 kcal/mol. however,
the
agree-
vibrational-excitation
correction
small,
is
[28, 52] and
are too low at the
to a zero-point
example,
for Cr(CO)6
of errors
too high),
For
vibrational-excitation
SCF
the zero-point
remarkably
for Cr(CO)s,
the
is a cancellation
leading
small,
2 kcal/mol
using
good.
and
frequencies
at 298 K (0.5 kcal
Cr(CO)6), too
to zero-point
computed
calculations,
high
similar
when
CO
are
is remarkably
the experimental
there
vibrationa]-excitation
of around
due
because
creased too
frequencies
correction
19.7 kcal/mol [53], and
these
(2) which
combined
since
error
we may
(1) of 1.6 kcal/mol
expect
should
be
reliable. For already
the
first
in good
larger
than
from
constants
dissociation
agreement
MCPF,
We reca_
with
and
were
which
experiment.
the
the
CCSD
superio_to
is not
energy,
interestingly
§ 3.1 that
which
methodl
bond
and
method
is similar
to results
as MC-PF
After
correcting
§ 3.3.1)the energy.
CCSD(T) In the
in the
first
large
bond
of uncertainty
was not
fully
energy
§ 3.3.2). true
The
BSSE
energy
8. However,
the
approach
yields
sets,
so that
cate
that
this
differential
1 kcal/mol.
error
basis
set,
the
is probably
fairly
these
the
the
binding
about
CCSD energies
energy. may
is relatively
small.
effects
uncertainties
14
are
dissociation
are
Cr(CO)5 first
that
and
several
structure
bond
dissocia-
of Cr(CO)5 earlier,
by the figures
Cr(CO)6
increase
There
energy
dissociation
small,
This
see
a 1 kcal/mol
the
small
We note
between
bond
as discussed
as indicated
bond
first
The
reduce
binding
Cr(CO)s.
method
for BSSE).
uncertain,
first
and
indirect
yields
total
be smaller,
similar
Overall,
and force
th.at
total
value.
[9]
for the
which
correction
correlation
!t seems
value
dissociation
a very
3s3p
:Thus
are
8 kcal/mol
distances
of Cr(CO)6
correction
is somewhat
BSSE
bond
(using
good
(after
bond
may
_r-C
previously
approach
(by increasing
correction
binding
a _ery
energy first
set
to the MCPF
CO or the
Ni(CO)2 error
MCPF
in either
by 1-2 kcal/mol
the MCPF
than
yields
optimized
computed
in Table
method
in the
als0 gave
basis
is almost
is superior
description
and
superposition
the
value
small
Cr-COinteractionmoreaccuratelyin these
for
basis
in the
CCSD(T) value
for isolated
balanced
for NiCO
dissociation
sources
tion
a more
found
results
the =MC-PFivalues.
as goocl
Mso yields
The CCSD
ofCr(CO)oand Cr(CO) ,describe systems,
the
in the
test and
and
the
in brackets
large
energy
see
basis,
in both
calculations Cr(CO)s
an estimated
and basis indi-
are less value
of
around
38 kcal/mol
in the
large
basis
experimental
4
for the first set
dissociation
unreasonable
energy
and
for the
is in very
good
CCSD(T)
method
agreement
with
the
value.
Conclusions
The
geometric
structures
MCPF,
at the force
CCSD
constants
experimental for 3s3p
basis
set
The
at the
remaining
energy
tion
on each
by the
fact
tracted
that
even
energy
due
to a cancellation
and
our
best
level
a very the
at the
of Cr(CO)n of basis
basis
large
superposition
MCPF
level
of the
is very
well described
of 38 kcal/mol
experimental
theoretical
(1042
This
primitive
at the
than
an f func-
is underscored functions
binding
con-
energy
the
CCSD(T)
level
of theory,
and
Cr(CO)s,
experimental
first
of
In contrast, for Or(CO)6
the
binding
rather
and
for the total
errors
is within
basis,
the
value.
total
d function
of treatment.
set incompleteness
accounting
in our largest
results.
error
with
140 kcal/mol
an additional
set
and
agreement After
in the one-particle
primitive
structure
error,
and
quantitative
determined
set superposition
86%
experimental
to obtain
the
are in good
to be around
and
were
into account.
or about
the
treatment,
value
and
due to limitations
functions),
estimated
effect,
Cr(CO)s
For Cr(CO)6,
are taken
of theory,
between
using
of theory.
is estimated
O are needed
is 22 kcal/mol
dissociation
5
of Cr(CO)_
and
representation
relativistic
correlation
to 300 basis
Cr(CO)6
set limitations
is probably
C and
levels
basis
discrepancy
in the
of Cr(CO)6
symmetric
CCSD(T)
of Cr(CO)6
limitations
CCSD(T)
a small
energy
energetics
totally
once
correlation,
binding
and
and
for the data
total
error
bond
bars.
Acknowledgements
The
authors
cluster J.
is not
bond
E.
wish
to thank
and
C. W.
code, Rice
for
helpful
Gustavo
Scuseria
Bauschlicher,
discussions.
T.
for prov!ding
L.A.B
J. was
NCC-2-741.
15
Lee,
the
H. Partridge,
supported
by
open-sheU P. R. NASA
coupledTaylor
grant
and
number
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19
H. A. Skinner,
and
D. Todd,
J. Less-
Table 1: Optimized bond lengths for Cr(CO)8, valenceonly (ao)
,(c-o) Small
basis
SCF
3.775
2.142
MCPF
3.692
2.215
CCSD
3.684
2.207
CCSD(T)
3.664
2.227
MCPF
3.666
2.165
Expt _
3.616
2.154
Large
Bond
distances
are from
Jost
basis
et al. [40].
See also
2O
Rees
and
Mitschler
[41].
Table 2: Force constantsfor Cr(CO)6, valenceonly (aJ//_2)=
F11
F=2
F12
MCPF
15.18
2.06
0.31
CCSD
15.70
2.21
0.31
CCSD(T)
14.44
2.24
0.27
MCPF
18.75
2.32
0.23
Expt b
18.11
2.44
0.38
Small
basis
Large
Expt = In the
notation
F22 is for the b Jones
basis
Error
of Jones
totally
+0.16 et al. [28].
symmetric
Cr-C
Fll
+0.02 is for the
stretch
et al. [28].
21
and
+0.13 totally
F12 is the
symmetric coupling
C-O term.
stretch,
Table 3: Cr(CO)s bond distancesand angles,valenceonly (ao and degrees)
_(c_-c)o. ,(c-o)o.
_(c_-c).,
,(c-o).,
LCo.C_C,_ _crc._o,_
SCF
3.734
2.144
3.772
2.146
92.5
179.4
MCPF
3.624
2.215_
3.708
2.215"
92.5 a
179.4"
CCSD
3.567
2.220"
3.670a
2.220a
92.5 _
179.4 a
CCSD(T)
3.554
2.220"
3.670_
2.220"
92.5"
179.4"
3.737
2.153
3.927
2.135
IAI C4_
3A_ D3h SCF " Not
optimized
(see text)
22
Table 4: Basis set superpositionerrors for various Cr(CO)6 fragments (kcal/mol)
SCF
MCPF
(1) Small basis,valenceonly
Cr + (co)6 (ghost) (CO)6+ Cr (ghost)
0.6 8.6
24.5
Sum
9.2
27.6
(ghost)
0.6
2.5
÷ Cr (ghost)
4.7
12.9
5.3
15.4
(2) Large
basis,
Cr + (CO)6 (C0)6
valence
only
Sum
(3) Large
3s3p
Cr ÷ (CO)6
basis,
3.1
valence
(ghost)
only 0.0
0.8
(co)6 + Cr (ghost)
8.0
21.1
Sum
8.0
21.9
(4) Large
3s3p basis,
+ valence
(ghost)
0.0
1.5
÷ Cr (ghost)
8.0
21.1
8.0
22.6
Cr + (CO)6 (C0)6
3s3p
Sum
23
Table 5: Basis set superposition errors for various Cr(CO)5 fragments,valenceonly (kcal/mol)
SCF
MCPF
(1) Small basis
Cr + (co)s (ghost) (CO)s + Cr (ghost)
O.5 7.1
2.8 19.2
Sum
7.6
22.0
(ghost)
1.8
4.4
(ghost)
2.8
6.0
4.6
10.4
(2) Small basis Cr(CO)5 CO
+ CO
+ Cr(CO)s
Sum
(3) Large
basis
Cr + (co)_ (ghost)
0.5
(CO)s
4.!
10.8
4.6
13.1
+ Cr
(ghost)
Sum
24
2.3
Table 6: Total CO binding energiesfor Cr(CO)6 (kcal/mol)
BE
Small
basis,
valence
81.9
13.6
CCSD
103.3
17.2
75.7
12.6
CCSD(T)
139.4
23.2
111.8
18.6
100.0
16.7
84.6
14.1
95.7
16.0
80.4
13.4
136.4
22.7
121.0
20.2
90.7
15.1
19.5
94.5
15.8
27
162
27
basis,
CCSD(T)
Large
valence
a
3s3p
basis,
MCPF
Large
3s3p
18.8
3s3p
÷ valence b
117.1
optimized
basis
experimental
summarized
only b
162 _
not large
valence
basis,
Expt Geometry
only
112.5
MCPF
et al.
only 18.3
CCSD *
tam
(BE-BSSE)/Nco
109.5
MCPF
c The
BE-BSSE
MCPF
Large
b At the
BE/Nco
[54].
(see text),
MCPF
geometry
binding
energy
The
by Pilcher
value
given
r(Cr-C)=3.638
corresponding here
corresponds
et al. [52]
25
ao, r(C-O)=2.177
ao
to Do29s is 153 kcal/mol, to
D,,
derived
using
from
Pit-
the
data
Table 7: Total CO binding energiesfor Cr(CO)s, valenceonly (kcal/mol)
BE
Small
BE-BSSE
(BE-BSSE)/Nco
basis
MCPF
74.8
15.0
52.8
10.6
CCSD
65.1
13.0
43.1
8.6
CCSD(T)
96.7
19.3
74.7
15.0
67.8
13.6
54.7
10.9
Large
basis a
MCPF Geometry
BE/Nco
not
optimized
r(C-O)_=r(C-O),q=2.165
(see text),
r(Cr-C)=_=3.600
ao
26
ao, r(Cr-C)_q--3.680
ao, and
Table 8: First CO binding energyof Cr(CO)6, valenceonly (kcal/mol)
cr(co),
--, cr(co)s + co AE
Small
basis
MCPF
34.8
29.1
(24.3)
CCSD
38.8
32.6
(27.8)
CCSD(T)
42.7
37.1
(32.3)
32.3
30.0
Do298
3t
37
Dr
38.6 _
38.6
Large
basis
MCPF
Experimental
Expt
data
Error
+5_,+2
° Corrected
using
the indirectly
b Corrected
using
the
Correction a Bernstein Lewis
AE-BSSE_(b)
directly
of 1.6 kcal/mol
computed computed
based
_ BSSE
BSSE
on theoretical
et al. [49].
et al. [50].
27
+5,±2 values values results
(see text) (see text) (see text)
m
Appendix For reference
purposes,
position
calculations.
error
calculations, the given
including
wavefunction previously
coefficients
for the
in Table
9 we give the
In Table the
exact
geometries The
[39].
in Table
large
3s3p
energies
10 we give the
is also given. Finally,
total
total
chromium
energies
for various
The
number
of configurations
of the
11 we give atom
28
basis.
for the
total
used. energies
necessary
the
isolated exponents
CO
Cr(CO)s
molecules and
super-
in were
contraction
Table
9: Total
energies
for BSSE
calculations
(a.u.)
SCF (1) SmaLl basis, Cr + (CO)s
valence
only _
(ghost)
Cr
-1043.30325162
-1043.36680779
-1043.30227534
-1043.36188023
-676.09997013
-677.52038240
-676.08622041
-677.48125821
(co)8 + cr (ghost) (co)8 (2) Large
basis,
Cr + (C0)8
valence
only b
(ghost)
Or
-1043.30325705
-1043.39812877
-1043.30227534
-1043.39413050
-676.58083795
-678.61170166
-676.57336447
-678.59116206
(co)8 + Cr (ghost) (co)8 (3) Large
3s3p basis,
Cr ÷ (CO)s
valence
(ghost)
Cr (CO)s
÷ Cr (ghost)
(co)8 (4) Large
3s3p
Cr ÷ (CO)s
basis,
3s3p
(ghost)
Cr
(co)8 + cr (ghost) (co)8
only c
-1043.35596972
-1043.45792578
-1043.35594229
-1043.45664455
-676.59006301
-678.62268211
-676.57728805
-678.58910199
+ valence ¢ -1043.35596972
-1043.79914043
-1043.35594229
-1043.79671781
-676.59006301
-678.62268211
-676.57728805
-678.58910199
a r(Cr-C)=3.684
a.u.,
r(C-0)=2.207
a.u.
b r(Cr-C)=3.696
a.u.,
r(C-0)=2.180
a.u.
c r(Cr-C)=3.666679456
a.u.,
MCPF
r(C-0)=2.164607427
29
a.u.
%
Table
10: Total
energies
and
number
of configurations
r(Cr-C)
Small
basis,
valence
r(C-O)
for Cr(CO)6
E
(a.u.)
#config
only
SCF
3.675000000
2.215000000
-1719.38028800
-
MCPF
3.700000000
2.215000000
-1721.08354571
1550884
CCSD
3.675000000
2.200000000
-1721.06032683
1550884
CCSD(T)
3.675000000
2.230000000
-1721.19228447
Large
valence
basis,
only
SCF
3.638099092
2.177373367
-1719.85243699
MCPF
3.650000000
2.160000000
-1722.21948766
3229861
CCSD
3.638099092
2.177373367
-1722.18375812
3229861
CCSD(T)
3.638099092
2.177373367
-1722.33885385
Large
3s3p
basis,
valence
only
SCF
3.666679456
2.164607427
-1719.92269380
MCPF
3.666679456
2.164607427
-1722.30216532
Large
3s3p
basis,
3s3p
-
4223071
+ vMence
SCF
3.666679456
2.164607427
-1719.92269380
MCPF
3.666679456
2.164607427
-1722.64951637
3O
5321953
Table 11: Large 3s3pbasisexponents andcontraction coefficients
Exponents
Contraction coefficients s functions
3638305.
0.000009
-0.000003
0.000001
0.0
0.0
0.0
0.0
0.0
0.0
544822.5
0.000068
-0.000020
0.000007
0.0
0.0
0.0
0.0
0.0
0.0
123986.8
0.000359
-0.000108
0.000039
0.0
0.0
0.0
0.0
0.0
0.0
35117.88
0.001512
-0.000454
0.000166
0.0
0.0
0.0
0.0
0.0
0.0
11456.10
0.005476
-0.001651
0.000602
0.0
0.0
0.0
0.0
0.0
0.0
4135.206
0.017557
-0.005342
0.001954
0.0
0.0
0.0
0.0
0.0
0.0
1612.295
0.050084
-0.015606
0.005716
0.0
0.0
0.0
0.0
0.0
0.0
668.0686
0.124182
-0.040792
0.015060
0.0
0.0
0.0
0.0
0.0
0.0
290.5773
0.250869
-0.092401
0.034485
0.0
0.0
0.0
0.0
0.0
0.0
131.3286
0.359000
-0.167315
0.064515
0.0
0.0
0.0
0.0
0.0
0.0
60.78704
0.275336
-0.187672
0.075767
27.44308
0.065683
13.08202
-0.001163
0.0
0.0
0.0
0.0
0.0
0.0
0.045233
-0.018997
0.0
0.0
0.0
0.0
0.0
0.0
0.510933
-0.293025
0.0
0.0
0.0
0.0
0.0
0.0
6.244786
0.001961
0.506228
-0.455426
0.0
0.0
0.0
0.0
0.0
0.0
2.753437
0.000000
0.000000
0.000000
1.0
0.0
0.0
0.0
0.0
0.0
1.298441
0.000000
0.000000
0.000000
0.0
1.0
0.0
0.0
0.0
0.0
0.572030
0.000000
0.000000
0.000000
0.0
0.0
1.0
0.0
0.0
0.0
0.125502
0.000000
0.000000
0.000000
0.0
0.0
0.0
1.0
0.0
0.0
0.062470
0.000000
0.000000
0.000000
0.0
0.0
0.0
0.0
1.0
0.0
0.028354
0.000000
0.000000
0.000000
0.0
0.0
0.0
0.0
0.0
1.0
31
Table 11: cont.
Large
3s3p
basis
Exponents
exponents
and
Contraction
contraction
coefficients
coefficients
p functions 6399.333
0.000181
-0.000064
0.000000
0.0
0.0
0.0
0.0
0.0
1515.982
0.001587
-0.000562
0.000000
0.0
0.0
0.0
0.0
0.0
491.9534
0.008813
-0.003146
0.000000
0.0
0.0
0.0
0.0
0.0
187.3677
0.036027
-0.013003
0.000000
0.0
0.0
0.0
0.0
0.0
78.82903
0.111802
-0.041650
0.000000
0.0
0.0
0.0
0.0
0.0
35.40597
0.251912
-0.097437
0.000000
0.0
0.0
0.0
0.0
0.0
16.51195
0.380832
-0.157341
0.000000 0.0 0.0 0.0 0.0 0.0
7.895010
0.310519
-0.115133
0.000000 0.0 0.0 0.0 0.0 0.0
3.713305
0.000000
0.000000
1.000000 0.0 0.0 0.0 0.0 0.0
1.724220
0.000000
0.000000
0.000000
0.772673
0.000000
0.000000
0.000000 0.0 1.0 0.0 0.0 0.0
0.319507
0.000000
0.000000
0.000000 0.0 0.0 1.0 0.0 0.0
0.127803
0.000000
0.000000
0.000000 0.0 0.0 0.0 1.0 0.0
0.051121
0.000000
0.000000
0.000000 0.0 0.0 0.0 0.0 1.0
1.0 0.0 0.0 0.0 0.0
d functions 177.0182
0.000907
0.000000
0.000000 0.0 0.0 0.0
52.85958
0.007660
0.000000
0.000000 0.0 0.0 0.0
20.09064
0.034236
0.000000
0.000000 0.0 0.0 0.0
8.416376
0.104090
0.000000
0.000000 0.0 0.0 0.0
3.759310
0.223015
0.000000
0.000000 0.0 0.0 0.0
1.706759
0.000000
1.000000
0.000000 0.0 0.0 0.0
0.762211
0.000000
0.000000
1.000000 0.0 0.0 0.0-
0.327886
0.000000
0.000000
0.000000
1.0 0.0 0.0
0.129421
0.000000
0.000000
0.000000
0.0 1.0 0.0
0.O45794
0.000000
0.000000
0.000000
0.0 0.0 1.0
/functions 2.7313203 2.0000000
0.486200 -0.024700
1.085700
-2.379100
-0.472000
0.9795143
0.471700
0.175500
0.4194397
0.294700
-0.865300
2.079900 0.661700 -0.832900
32
