Quantum chemical study of the electronic structure of NiCH2 ¿in its ground state and low-lying electronic excited states Se´bastien Villaume, Chantal Daniel,aand Alain Strich Laboratoire
Trang 1Quantum chemical study of the electronic structure of NiCH2 ¿
in its ground state and low-lying electronic excited states
Se´bastien Villaume, Chantal Daniel,a)and Alain Strich
Laboratoire de Chimie Quantique UMR 7551 CNRS, Universite Louis Pasteur, 4 rue Blaise Pascal,
67000 Strasbourg, France
S Ajith Perera and Rodney J Bartlett
Quantum Theory Project, Departments of Chemistry and Physics, University of Florida,
Gainesville, Florida 32611
~Received 30 July 2004; accepted 27 October 2004; published online 10 January 2005!
The electronic structure of NiCH21, representative of transition metal carbene ions, is investigated
by means of several methods of quantum chemistry The relative stabilities of the four low-lying
doublet electronic states (2A1,2A2,2B1, and2B2) are determined at the coupled cluster singles and
doubles level ~CCSD! and triples level @CCSD~T! and CCSDT-3# with both a Hartree–Fock and
density functional theory ~Kohn–Sham! reference The equation-of-motion coupled cluster for
treatment of excited states in singles and doubles approximation ~EOM-CCSD! is used to
characterize the transition energies from the2A1 electronic ground state to the low-lying doublet
excited states The2A2 and2B1 states are nearly degenerate, found to be separated by 940 cm21at
the EOM-CCSD level, in agreement with the CASSCF energy ordering The2B2state is calculated
to be higher in energy by more than 1.0 eV The spin purity of the low-lying doublet and quadruplet
states described by CCSD calculations based on the unrestricted open-shell Hartree–Fock reference
is discussed © 2005 American Institute of Physics @DOI: 10.1063/1.1834897#
I INTRODUCTION
Gas-phase chemistry of ligated transition metal ions has
a rich history extending over at least two decades.1A number
of experimental and theoretical studies were dedicated to the
determination of metal-ligand binding energies which
pro-vides a means of assessing whether a reactive pathway is
energetically favorable A part of the early ion cyclotron
resonance and ion-beam, experiments proposed in the
1970s2,3based on metastable or collision-induced
decompo-sition made possible detailed investigations of
decomposi-tion pathways.4,5 Moreover, the recent use of laser
tech-niques has offered evidence for a variety of dissociative
processes, along with the quantum yield which depends upon
the nature of the metal center.6,7The spectroscopic threshold
determined in these experiments by ion absorption provides
an upper limit to the reaction enthalpy and can be compared
to the thermodynamic bond strengths within the limit of a
high density of electronic excited states near the ground
separated atom limit.8,9
The accuracy of quantum chemical methods describing
molecular structures, spectroscopy, and chemical reactivity
of unsaturated species that are generated in homogeneous or
heterogeneous catalytic processes, such as the C–H or C–C
bonds activation can be critically assessed by having
accu-rate gas-phase experimental data for ligated transition metal
ions MCH21 The first-row group VIII MCH21systems have
been the subject of a number of theoretical studies based
either on ab initio theory or density functional theory ~DFT!.
Molecular structures and reactivity of MCH21 ~M5Fe, Co! have been studied by means of complete active space self-consistent field ~CASSCF! and multireference-single double configuration interaction ~MR-SDCI-CASSCF! approaches,10,11whereas the molecular structures and bond-ing characteristics of MCH21 ~M5Sc to Cu! have been the subject of modified coupled pair functional ~MCPF!, inter-nally contracted average coupled pair functional ~ICACPF!, and coupled cluster singles and doubles level ~CCSD!, and triples level @CCSD~T!# studies.12,13 The series MCH21
~M5Sc to Cu! has been revisited by means of DFT calcula-tions and the structure and bonding properties of NiCH21 reinvestigated within the nonrelativistic and quasirelativistic DFT approaches along the Ni, Pd, Pt triad.14,15Generally, the accurate inclusion of electron correlation was found to be necessary to achieve good agreement between experimental and theoretical bond dissociation energies The local density approximation ~LDA! overestimates the NiCH21 binding en-ergy by as much as 150 kJ/mol ~27 kJ/mol with Becke cor-rection and 60 kJ/mol with Becke–Perdew corcor-rection!15 whereas B3LYP shows excellent agreement.14
In contrast little attention has been devoted to the spec-troscopic properties of transition metal methylidene cations MCH21 In particular these systems are known to be charac-terized by a high density of electronic states within a limited domain of energy, with the occurrence of nearly degenerate states For instance 63 potential energy curves arise from electronic states within 10 000 cm21of the ground separated limit Fe11CH2 that correlate to FeCH21.7The ground state
of this system is described by a pair of nearly degenerate states 4B1 and 4B2 with a 4A2 state lying 8 kJ/mol above a! Electronic mail: daniel@quantix.u-strasbg.fr
122, 044313-1
Trang 2Whereas the electronic ground state of CoCH21 is described
by two nearly degenerate3A1 and3A2 states, the electronic
ground state of NiCH21 has been determined unambiguously
as a single2A1 state An accurate description of the structure
and energetics of the low-lying electronic states should help
to analyze the photofragment spectra and to understand the
photodissociation mechanism
The main goal of the present study is to validate and
calibrate the highly correlated methods of quantum
chemis-try @CCSD, equation-of-motion ~EOM!-CCSD and
~CASSCF!/complete active space perturbation theory second
order ~CASPT2!# to clarify the electronic structure of
NiCH21, an unsaturated intermediate involved in the
meth-ane activation by transition metal cations This is a step
to-ward an accurate description of the spectroscopic properties
of this class of molecules
II COMPUTATIONAL DETAILS
The geometry of the molecule is optimized at the CCSD
and CCSD~T! levels under the C2v symmetry constraint The
optimized geometry is depicted in Fig 1 together with the
MCPF optimized structure.13The CCSD Hartree–Fock ~HF!
@unrestricted open-shell Hartree–Fock ~UHF! based CCSD#
and CCSD-DFT @Kohn–Sham ~KS! based CCSD# transition
energies are calculated for the MCPF structure of NiCH21
~Ni-C51.790 Å, C-H51.09 Å, and /NiCH5124.05°!
whereas the CCSD~T!-DFT and CCSDT-3 transition energies
are obtained for the CCSD~T! ~Ni-C51.776 Å, /NiCH
5123.8°! optimized geometry The excited states geometries
have not been optimized and it is assumed that the C2v
sym-metry is retained when exciting the molecule
The CCSD, EOM-CCSD, and CASSCF calculations are
performed for the 2A1(8a1)2(9a1)2(4b1)2(3b2)2(1a2)2
(10a1)1 electronic ground state corresponding to the
(sNi-C)2(3d x22y2)2(3dp)2(3dp)2(3d xy)2(sNi-C* )1 electronic
configuration and for the 2A2(8a1)2(9a1)2(10a1)2(4b1)2
(3b2)2(1a2)1, 2B1(8a1)2(9a1)2(10a1)2(3b2)2(1a2)2
(4b1)1, and 2B2(8a1)2(9a1)2(10a1)2(4b1)2(1a2)2(3b2)1
states corresponding to the (sNi-C)2(3d x22y2)2(sNi-C* )2
(3dp)2(3dp)2(3d xy)1, (sNi-C)2(3d x22y2)2(sNi-C* )2(3dp)2
(3d xy)2(3dp)1, and (sNi-C)2(3d x22y2)2(sNi-C* )2(3dp)2
(3d xy)2(3dp)1 electronic configurations, respectively In the
2A1electronic ground state thesNi-Corbital (8a1) is a
bond-ing combination of the p(C) orbital with the 3d z2(Ni)
whereas thesNi-C* (10a1) is the antibonding counterpart with
a predominant s p(C) character Thepbonding interaction is
contained in the 3b2 orbital ~Scheme I! The p bond in NiCH21(2A1) is best described as a Ni (3dp) to C( pz) back donation characteristic of Fischer carbene The presence of close lying quadruplet electronic states is assumed to analyze spin contamination effects In particular, the4A1 state corre-sponding to the (8a1)2(9a1)2(10a1)2(4b1)1(3b2)2
(4b2)1(1a2)1 configuration, the 4B1 state corresponding to
the (8a1)2(9a1)2(10a1)1(4b1)2(3b2)2(4b2)1(1a2)1 elec-tronic configuration and the 4A2 corresponding to the
(8a1)2(9a1)2(10a1)1(4b1)1(3b2)2(4b2)1(1a2)2 configura-tion have been calculated The bonding character and the nature of the valence Kohn–Sham orbitals in NiCH21is not dramatically modified when going from the2A1 ground state
to the low-lying doublet and quadruplet states In addition several 4A1 states with formal 4s13d8(Ni) or
s p1(C)3d8(Ni) electronic configurations in NiCH21 have been calculated
Scheme 1
The following sets of atomic natural orbitals
~ANO-Large!16,17basis sets are used for the coupled cluster
and CASSCF calculations: a (21s,15p,10d,6f ) set con-tracted to @ 6s,5p,4d,3f # for the Ni atom, a (14s,9p,4d,3f ) set contracted to @ 4s,3p,2d # for the C atom, and a (8s,4p,3d) set contracted to @ 3s,2p # for the hydrogen A
second set of ANO-Small18 basis sets are used to compute
the CASPT2 transition energies: a (17s,12p,9d,4f ) con-tracted to @ 7s,5p,4d,3f # for the Ni atom, a (10,6p,3d) set contracted to @ 4s,3p,2d # for the C atom, and a (7s,3p) set contracted to @ 2s,1p # for the hydrogen.
Different computational strategies are applied to deter-mine the relative stability of the low-lying doublet electronic
FIG 1 Structure of NiCH21
TABLE I Description of the CASSCF active space.
Character of the occupied orbitals
11a1, 12a1, 13a1, 14a1
2a2
5b1
6b1
4b2
Trang 3states of NiCH21 The single reference coupled cluster
singles and doubles ~CCSD! calculations use both a Hartree–
Fock and a Kohn–Sham DFT19 reference, since it is
ex-pected that the spin-polarized HF wave function will be
qualitatively wrong for transition metal complexes The
tran-sition energies come from the equation-of-motion-CCSD
~EOM-CCSD!20 with the two references ~HF and KS-DFT!
for the ground state CCSD calculations, and with
CASSCF.21,22 Our attempt at performing subsequent
CASPT2 on the top of the CASSCF wave function failed due
to the size of the problem The spin–orbit splitting of the2D
and4F states of Ni1is determined with the moduleRASSIof
MOLCASusing CCSD ~T!-DFT spin-free diagonal energies
Fifteen electrons are correlated in sixteen active orbitals
in the Single State CASSCF ~Table I!
The calculations have been performed with theACES II
~Ref 23! andMOLCAS 5.4~Ref 24! quantum chemistry
pro-gram packages
III RESULTS
A Geometrical structures
The optimized geometries of NiCH21 in its 2A1
elec-tronic ground state obtained at different levels of theory
@MCPF, CCSD, CCSD~T!, DFT# are reported in Table II
~this work and previous references!
The largest CCSD amplitudes near the equilibrium struc-tures of the molecule are within the generally accepted mag-nitudes confirming that this molecule can be adequately treated with single reference correlation methods Further-more, the inclusion of triple excitation by CCSD~T! is ex-pected to reduce the remaining error
The bond distance and angle are underestimated by the DFT approach compared to CCSD~T! and MCPF whereas the MCPF and CCSD~T! geometries are very similar The small DFT Ni-C bond distance ~1.733 Å! has been attributed
to the choice of an @Ar# frozen core for the nickel atom
Inclusion of the metal’s 3s and 3 p electrons in the valence
space leads to a value of 1.763 Å.15 The slightly smaller CCSD~T! bond length and bond angle compared to that of CCSD is consistent with the establish trends of these methods.25 The electronic structure of NiCH21 in its elec-tronic ground and excited states at the MCPF geometry is consistent with previous theoretical studies
B Electronic ground state of NiCH 2 ¿
In contrast to the other first-row transition metal cations such as FeCH21 and CoCH21 whose electronic ground states involve two nearly degenerate states, the nickel methylidene cation NiCH21 had been found to be 2A1 with the open shell electron in the sNi-C* orbital.13 This is confirmed by the energies calculated at the CC level and reported in Table III for the low-lying doublet electronic states (2A1, 2A2, 2B1, and 2B2) and the lowest quadruplet states (4B1, a4A1,b4A1,4A2) of NiCH21 Approximate ‘‘spin multiplicities’’ based on the projected expectation value^Sˆ2& are also reported in Table III for the analysis of spin contami-nation
The2A1electronic configuration with a singly occupied
sNi-C* orbital is stabilized by a decrease of the nickel-carbon antibonding interaction with respect to the other configura-tions (2A2,2B1,2B2) where thesNi-C* orbital is doubly
occu-TABLE II Calculated Ni–C bond distances ~in angstroms! and Ni–C–H
bond angle ~in degrees! at different levels of calculation.
MCPF a
DFT b
~LDA/B/P! CCSD CCSD~T!
R~Ni-C! 1.790 1.733 1.809 1.776
a Reference 13.
b Reference 15.
TABLE III Energies ~21546 in atomic units! of the low-lying doublet and quadruplet electronic states of NiCH 2 1 calculated at the CCSD-HF, CCSD-DFT, CCSD~T!-DFT, and CCSDT-3 levels and projected spin multiplicity.
Electronic state
CCSD-HF
Spin multiplicitya
CCSD-DFTb
Spin multiplicitya
CCSD~T!-DFTc
CCSDT-3
2A1 0.508 55 2.433 ~2.793! 0.500 17
~0.499 95!
2.091 ~2.127! 0.547 19 0.551 71
2A2 0.497 38 2.021 ~2.024! 0.490 17
~0.489 60!
2.040 ~2.050! 0.535 76 0.542 60
2B1 0.493 68 2.036 ~2.039! 0.486 47
~0.485 70!
2.058 ~2.073! 0.531 18 0.537 47
2B2 0.465 82 2.003 ~2.006! 0.459 75
~0.457 58!
2.002 ~2.003! 0.497 21 0.501 36
4B1 0.481 88 4.002 ~4.013! 0.476 07
~0.475 57!
4.000 ~4.003! 0.507 99 0.507 85
a4A1 0.457 71 4.000 ~4.006! 0.451 90 4.000 ~4.003! 0.483 51 0.483 74
b4A1 0.43 555 4.002 ~4.010! 0.430 54
~0.429 12!
4.001 ~4.002! 0.460 64 0.465 92
4A2 0.467 61 4.001 ~4.007! 0.460 47
~0.459 73!
4.000 ~4.002! 0.494 04 0.494 72
a
The projected spin multiplicity before the CCSD treatment is given in parentheses.
b Energies calculated for the CCSD~T!-DFT optimized geometry are given in parentheses.
c Energies calculated for the CCSD~T!-DFT optimized geometry.
Trang 4pied This state is characterized by an unusual large spin
contamination When using the KS determinant as a
refer-ence the spin pure solution of the2A1is restored with values
of ‘‘spin multiplicities’’ of 2.793 ~HF! and 2.127 ~DFT!
be-fore the CC treatment and of 2.433 ~CCSD-HF! and 2.091
~CCSD-DFT! The ensuing CCSD calculations further
im-prove the ‘‘spin multiplicity’’ irrespective of the character of
the reference orbitals ~HF or KS! The spin contamination
does not affect the other doublet states as illustrated by the
reasonable ‘‘spin multiplicities’’ of 2.021, 2.036, and 2.003
obtained at the CCSd-HF level for the 2A2, 2B1, and 2B2
states, respectively
In order to analyze the origin of the spin contamination
in the 2A1 molecular state and to validate our approach the
low-lying quadruplet states have been analyzed and atomic
calculations have been performed on Ni1 in the 2D (3d9)
and4F (3d84s1) states ~Table IV! In contrast to the
molecu-lar system NiCH21 there is no spin contamination at the
atomic level, both states being obtained with nearly pure spin
multiplicities Moreover the agreement between the
experi-mental and calculated atomic spectra is excellent, as
illus-trated by the calculated spin–orbit ~SO! splitting The
rela-tive order of the2D and4F states is well described and does
not depend on the reference ~HF or KS orbitals! in the CCSD
calculation Moreover the agreement is perfect when adding
the triple correction
Two of the molecular quadruplet states (4B1,4A2) fall in
the energy range of the low-lying doublet states However
they belong to the B1 and A2 symmetry point groups and
cannot account for the cause of the large spin contamination
obtained for the2A1 state Among the several4A1 calculated
states only the two lowest a4A1 and b4A1 are reported in
Table III They do not show any spin contamination as
indi-cated by their ‘‘spin multiplicities’’ close to 4.0 regardless
the method is The 4A1 state ~not reported in Table
III! with the following electronic configuration
(8a1)2(9a1)2(10a1)1(4b1)2(3b2)2(1a2)1(2a2)1 has been
found with a large ‘‘spin multiplicity’’ of 4.44 at the HF
level In this state the Ni atom is formally d8, the 10a1
orbital being mainly localized on the carbon atom with a s p z
character This state which does not converge at the CCSD
level is very high in energy at the HF level with respect to
the 2A1 electronic ground state and should not account for
the large spin contamination of this later state The a4A1
state reported in Table III with the following electronic
con-figuration (8a1)2(9a1)2(10a1)1(4b1)2(3b2)1(1a2)2(4b2)1 falls in the range of the low-lying states of NiCH21and could
be responsible for the large spin contamination of the 2A1
Indeed the singly occupied orbitals 3b2and 4b2 correspond
to the bonding and antibonding 3d y z (Ni)/3p y(C) combina-tions, respectively, and are characterized by a large exchange
term Moreover the Ni atom is formally d8in this molecular
state with a 10a1 orbital nearly pure and assigned to the
s p(C).
A careful investigation of the HF, KS, and CASSCF or-bitals and of the 2A1-2A2 energy gap obtained at different levels of calculation ~Scheme II! for NiCH21 points to the dramatic consequence of electronic correlation effects in the description of nearly degenerate states in first row transition metal complexes This analysis will help us to understand the large spin contamination observed in the CCSD ~HF! calcu-lations for the 2A1 electronic ground state Indeed the HF description leads to a 2A1-2A2 energy gap of 125.7 kJ/mol with an over stabilization of the 2A1 state and a spin
multi-plicity of 2.793 The 4s(Ni)/2p z(C) bonding orbital is inter-changed with the sNi-C* orbital @essentially localized on the
Ni atom (3d z2) and antibonding with the p z(C)] by HF theory in order to compensate the failure of the HF method at describing the nondynamical electronic correlation of the
3d(Ni)-like orbital In the 2A1 molecular state the
4s(Ni)/2p z(C) becomes singly occupied whereas the singly
occupied KS and CASSCF 10a1 correspond to thesNi-C* or-bital
Scheme II
TABLE IV Relative energies and spin–orbit splitting ~in cm 21 ! of the low-lying atomic states of Ni 1
Configuration Term
CCSD-HF
CCSD-DFT
CCSD~T!-HF
CCSD~T!-DFT
Atomic spectrum a,b
Experimental splitting
Calculated spin–orbit splitting
3d9 2D 0.0 0.0 0.0 0.0 0.0 ~5/2! 1506.95 1518.20
1506.95~3/2!
3d84s1 4F 8171 8626 10 441 10 260 8393.9 ~9/2! 936.14 997.35
9330.04~7/2!
10 115.66~5/2! 785.62 772.01
10 663.89~3/2! 548.23 550.49
a
Reference 26.
bJ is given in parentheses.
Trang 5In the 2A1 molecular state the HF electronic
configura-tion of Ni1 is formally 3d84s1 in contrast to the 2A1 ~DFT
or CASSCF! which corresponds to a 3d9configuration This
failure of the noncorrelated HF theory which reverses the
two low-lying 2D and 4F states in Ni1 over stabilizing the
4s13d8 electronic configuration is well known but has no
consequence on the CCSD results at the atomic level as
de-picted in Table IV because the doublet and quartet states
have different symmetries In the molecule the2A1 is
prob-ably contaminated by an upper 4A1 state where Ni1 is
for-mally 3d8 It is difficult to conclude from our attempt at
locating such a state Among the several 4A1 states of
NiCH21the best candidate is certainly the a4A1 state When
going from HF to CASSCF or DFT approaches the2A1-2A2
energy gap is reduced to 22.5 kJ/mole ~CASSCF! and 28.72
kJ/mol ~DFT! These values agree with the CCSD-DFT
2A1-2A2 energy gap calculated at 26.25 kJ/mole with a
cor-rect ‘‘spin multiplicity’’ of 2.091 for the2A1
C Low-lying doublet and quadruplet states of NiCH 2 ¿
The relative stability of the low-lying doublet and
qua-druplet states of NiCH21 are reported in Table V The
geo-metrical parameters have not been optimized for these states
The 2A2 and 2B1 states are very close in energy and this
order may be modified by more accurate calculations taking
into account higher excitations in the CC approach or
geo-metrical relaxation effects
The destabilization of the 2A2 and 2B1 states with
re-spect to the2A1state is mainly due to the double occupation
of the sNi-C* antibonding orbital in both states The single
occupation of the 4b1 orbital in the 2B1 state increases the
3dp(Ni)/3p x(C) antibonding character of this orbital which
is nearly a pure 3d xz orbital in the2A2 This could explain
the relative position of the2A2and2B1states The2B2state
is largely destabilized with respect to the 2A1 electronic ground state by more than 100 kJ/mol In this state a strong
bonding interaction between the 3dp and the 3 p y (C) (3b2)
is reduced by the single occupancy leading to an important destabilization of this state with respect to the others The relative stabilities do not depend on the CCSD reference ~HF
or DFT! despite the spin contamination occurring in the CCSD-HF calculation of the 2A1 state Taking into account the triple excitations within a perturbative treatment in-creases the energy gap between the2A1 ground state and the excited states by a few kJ/mol for the doublets and by a few tens of kJ/mol for the quadruplets
The transition energies to the low-lying electronic ex-cited states of NiCH21 calculated by means of CCSD-HF, CCSD-DFT, CCSD~T!-DFT, CCSDT-3, EOM-CCSD-DFT, and CASSCF methods are reported in Table VI
Unfortunately due to the size of our calculations it has not been possible to obtain the ~MS!-CASPT2 transition en-ergies Consequently the CASSCF transition energies are only qualitative due to the lack of dynamical correlation ef-fects The CCSD-HF, CCSD-DFT, CCSDT-3, and CCSD~T!-DFT transition energies are obtained by simple energy dif-ferences The appropriate reference states for CC calculations for different electronic states are generated by controlling the occupation in various irreducible representa-tions Hence, the energy difference calculations of transition energies are feasible only for the lowest states of a given symmetry The orbital relaxation, when going from the elec-tronic ground state to the excited state, is taken into account
in transition energies In contrast, in the EOM-CCSD-DFT calculations most of the correlation effects that are common
to the different electronic states are coherently handled but the orbitals relaxation is ignored The most accurate meth-ods, namely, the CCSD~T!-DFT and EOM-CCSD-DFT give very close transition energies
IV CONCLUSION
The electronic structure of NiCH21, representative of transition metal carbenes ions, has been investigated in de-tails by means of coupled cluster approach based either on Hartree–Fock orbitals or on Kohn–Sham orbitals The 2A1
electronic ground state with an open shell electron in the
sNi-C* orbital is confirmed This electronic configuration is stabilized with respect to the other low-lying doublet states
by a decrease of the nickel-carbon antibonding interaction
TABLE V Relative stability ~in kJ/mol! of the low-lying doublet and
qua-druplet electronic states of NiCH21 calculated at the CCSD-HF, CCSD-DFT,
CCSD~T!-DFT, and CCSDT-3 levels.
Electronic
state CCSD-HF CCSD-DFT CCSD~T!-DFT CCSDT-3
2A2 29.31 26.25 30.00 23.90
2B1 39.02 35.95 42.00 37.63
4B1 69.98 65.55 102.85 115.08
2B2 112.11 106.05 131.14 132.11
4A2 107.42 106.11 139.46 149.53
4A1 191.54 186.42 227.00 225.10
TABLE VI Transition energies in cm 21 ~in electron volts! to the low-lying electronic excited states of NiCH 2 1
calculated by means of various quantum chemical methods.
Transition CCSD-HF
CCSD-DFT
CCSD~T!-DFT
CCSDT-3
EOM-CCSD-DFT
CASSCF ANO-L
2A1 →2A2 2450
~0.304!
2200
~0.272!
2510
~0.311!
1999
~0.240!
2480
~0.307!
1880
~0.233!
2A1 →2B1 3265
~0.405!
3000
~0.373!
3510
~0.436!
3125
~0.391!
3420
~0.424!
3000
~0.372!
2
A1 →2B2 9380
~1.163!
8870
~1.100!
10 970
~1.360!
11 050
~0.381!
11 450
~1.420!
8190
~1.015!
Trang 6When based on HF orbitals the CC calculations indicate
evi-dence of a severe problem of spin contamination in the2A1
electronic ground state which is solved by the use of KS
orbitals as reference This spin contamination illustrated by a
spin multiplicity of 2.798 which is not present in the atomic
calculations performed on Ni1 is due to the artificial single
occupancy of the 4s(Ni)/2p z(C) bonding orbital This
or-bital is brought in the occupied space by the HF approach in
order to compensate the lack of electronic flexibility inherent
to this non-correlated method Consequently the 2A1 is over
stabilized and the2A1-2A2energy gap is overestimated at the
HF level ~125.7 kJ/mol versus 24 –30 kJ/mol in correlated
calculations! The CC calculation restores the correct
ener-getic regardless the reference is ~HF or KS! The relative
stability of the low-lying doublet and quadruplet states of
NiCH21 does not depend dramatically on the CC reference
~HF or KS! Taking into account the triple excitations within
a perturbative treatment increases the energy gap between
the 2A1 state and the low-lying excited states by a few
kJ/mol for the doublets and a few tens of kJ/mol for the
quadruplets The same trends are observed when adding the
triple excitations within the CC scheme ~CCSDT-3! excepted
for the2A1-2A2energy gap which is evaluated at 23.9 kJ/mol
@versus 30.0 kJ/mol at the CCSD~T! level# As far as the
transition energies are concerned the CCSD~T!-DFT and
EOM-CCSD-DFT methods give very close results The
qual-ity and the stabilqual-ity of the EOM-CCSD ~KS! response results
to the problem of nearly degenerate states in transition
met-als containing molecules opens the route to a wide range of
applications The EOM-CCSD method has been recently
ap-plied with success to the low-lying electronic states of NiCO
in a careful analysis of their structure and adiabatic/vertical
transition energies.27The electronic structure of the Co and
Fe carbenes should be investigated in a further study in order
to enhance this conclusion
ACKNOWLEDGMENTS
This work was undertaken as a part of the CNRS/NSF
collaborative Project ~No 17097! and of the NSF grant
~Pro-gram No 03-559! S.V thanks the Ministe`re de l’Education
Nationale, de l’ Enseignement Supe´rieur et de la Recherche
and the Quantum Theory Project The quantum chemical
cal-culations were carried out either at the Quantum Theory
Project ~Gainesville, Florida! or at the IDRIS ~Orsay, France! through a grant of computer time from the Conseil Scienti-fique
1
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