THE JOURNAL OF CHEMICAL PHYSICS 122, 044313 ͑2005͒ Quantum 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, 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 2005͒ The electronic structure of NiCHϩ , 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 ( A , A , B , and B ) are determined at the coupled cluster singles and doubles level ͑CCSD͒ and triples level ͓CCSD͑T͒ and CCSDT-3͔ with both a Hartree–Fock and density functional theory ͑Kohn–Sham͒ reference The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation ͑EOM-CCSD͒ is used to characterize the transition energies from the A electronic ground state to the low-lying doublet excited states The A and B states are nearly degenerate, found to be separated by 940 cmϪ1 at the EOM-CCSD level, in agreement with the CASSCF energy ordering The B state 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: 10.1063/1.1834897͔ I INTRODUCTION Gas-phase chemistry of ligated transition metal ions has a rich history extending over at least two decades.1 A number of experimental and theoretical studies were dedicated to the determination of metal-ligand binding energies which provides 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 1970s2,3 based on metastable or collision-induced decomposition made possible detailed investigations of decomposition pathways.4,5 Moreover, the recent use of laser techniques has offered evidence for a variety of dissociative processes, along with the quantum yield which depends upon the nature of the metal center.6,7 The 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 accurate gas-phase experimental data for ligated transition metal ϩ ions MCHϩ The first-row group VIII MCH2 systems have been the subject of a number of theoretical studies based either on ab initio theory or density functional theory ͑DFT͒ a͒ Electronic mail: daniel@quantix.u-strasbg.fr 0021-9606/2005/122(4)/044313/6/$22.50 Molecular structures and reactivity of MCHϩ ͑MϭFe, Co͒ have been studied by means of complete active space selfconsistent field ͑CASSCF͒ and multireference-single double configuration interaction ͑MR-SDCI-CASSCF͒ approaches,10,11 whereas the molecular structures and bonding characteristics of MCHϩ ͑MϭSc to Cu͒ have been the subject of modified coupled pair functional ͑MCPF͒, internally contracted average coupled pair functional ͑ICACPF͒, and coupled cluster singles and doubles level ͑CCSD͒, and triples level ͓CCSD͑T͔͒ studies.12,13 The series MCHϩ ͑MϭSc to Cu͒ has been revisited by means of DFT calculations and the structure and bonding properties of NiCHϩ reinvestigated within the nonrelativistic and quasirelativistic DFT approaches along the Ni, Pd, Pt triad.14,15 Generally, 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 ͑LDA͒ overestimates the NiCHϩ binding energy by as much as 150 kJ/mol ͑27 kJ/mol with Becke correction and 60 kJ/mol with Becke–Perdew correction͒15 whereas B3LYP shows excellent agreement.14 In contrast little attention has been devoted to the spectroscopic properties of transition metal methylidene cations MCHϩ In particular these systems are known to be characterized 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 cmϪ1 of the ground separated limit Feϩ ϩCH2 that correlate to FeCHϩ The ground state of this system is described by a pair of nearly degenerate states B and B with a A state lying kJ/mol above 122, 044313-1 © 2005 American Institute of Physics Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044313-2 Villaume et al Whereas the electronic ground state of CoCHϩ is described by two nearly degenerate A and A states, the electronic ground state of NiCHϩ has been determined unambiguously as a single A 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 chemistry ͓CCSD, equation-of-motion ͑EOM͒-CCSD and ͑CASSCF͒/complete active space perturbation theory second order ͑CASPT2͔͒ to clarify the electronic structure of NiCHϩ , an unsaturated intermediate involved in the methane activation by transition metal cations This is a step toward 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 CCSD͑T͒ levels under the C2 v symmetry constraint The optimized geometry is depicted in Fig together with the MCPF optimized structure.13 The CCSD Hartree–Fock ͑HF͒ ͓unrestricted open-shell Hartree–Fock ͑UHF͒ based CCSD͔ and CCSD-DFT ͓Kohn–Sham ͑KS͒ based CCSD͔ transition energies are calculated for the MCPF structure of NiCHϩ ͑Ni-Cϭ1.790 Å, C-Hϭ1.09 Å, and ЄNiCHϭ124.05°͒ whereas the CCSD͑T͒-DFT and CCSDT-3 transition energies are obtained for the CCSD͑T͒ ͑Ni-Cϭ1.776 Å, ЄNiCH ϭ123.8°͒ optimized geometry The excited states geometries have not been optimized and it is assumed that the C2 v symmetry is retained when exciting the molecule The CCSD, EOM-CCSD, and CASSCF calculations are performed for the A (8a ) (9a ) (4b ) (3b ) (1a ) (10a ) electronic ground state corresponding to the * ) electronic ( Ni-C) (3d x Ϫy ) (3d ) (3d ) (3d xy ) ( Ni-C 2 configuration and for the A (8a ) (9a ) (10a ) (4b ) 2 (3b ) (1a ) , B (8a ) (9a ) (10a ) (3b ) (1a ) 2 (4b ) , and B (8a ) (9a ) (10a ) (4b ) (1a ) (3b ) * )2 states corresponding to the ( Ni-C) (3d x Ϫy ) ( Ni-C * ) (3d ) (3d ) (3d ) (3d xy ) , ( Ni-C) (3d x Ϫy ) ( Ni-C 2 * ) (3d ) (3d xy ) (3d ) , and ( Ni-C) (3d x Ϫy ) ( Ni-C (3d xy ) (3d ) electronic configurations, respectively In the A electronic ground state the Ni-C orbital (8a ) is a bonding combination of the p(C) orbital with the 3d z (Ni) * (10a ) is the antibonding counterpart with whereas the Ni-C J Chem Phys 122, 044313 (2005) a predominant sp(C) character The bonding interaction is contained in the 3b orbital ͑Scheme I͒ The bond in NiCHϩ ( A ) is best described as a Ni (3d ) to C(p z) back donation characteristic of Fischer carbene The presence of close lying quadruplet electronic states is assumed to analyze spin contamination effects In particular, the A state corresponding to the (8a ) (9a ) (10a ) (4b ) (3b ) 1 (4b ) (1a ) configuration, the B state corresponding to the (8a ) (9a ) (10a ) (4b ) (3b ) (4b ) (1a ) electronic configuration and the A corresponding to the (8a ) (9a ) (10a ) (4b ) (3b ) (4b ) (1a ) configuration have been calculated The bonding character and the nature of the valence Kohn–Sham orbitals in NiCHϩ is not dramatically modified when going from the A ground state to the low-lying doublet and quadruplet states In addition several A states with formal 4s 3d (Ni) or sp (C)3d (Ni) electronic configurations in NiCHϩ have been calculated Scheme The following sets of atomic natural orbitals ͑ANO-Large͒16,17 basis sets are used for the coupled cluster and CASSCF calculations: a (21s,15p,10d,6f ) set contracted 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 ) contracted 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 determine the relative stability of the low-lying doublet electronic TABLE I Description of the CASSCF active space Symmetry Label A1 7a 8a 9a 10a 11a , 12a , 13a , 14a 1a 2a 3b 4b 5b 6b 3b 4b A2 B1 B2 FIG Structure of NiCHϩ Character of the occupied orbitals C-H Ni-C 3d x Ϫy * Ni-C 3d xy C-H 3d 3d Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044313-3 Structure of NiCH2ϩ J Chem Phys 122, 044313 (2005) TABLE II Calculated Ni–C bond distances ͑in angstroms͒ and Ni–C–H bond angle ͑in degrees͒ at different levels of calculation R͑Ni-C͒ ЄNiCH a MCPFa DFTb ͑LDA/B/P͒ CCSD CCSD͑T͒ 1.790 124.05 1.733 121.7 1.809 124.5 1.776 123.8 Reference 13 Reference 15 b states of NiCHϩ The single reference coupled cluster singles and doubles ͑CCSD͒ calculations use both a Hartree– Fock and a Kohn–Sham DFT19 reference, since it is expected that the spin-polarized HF wave function will be qualitatively wrong for transition metal complexes The transition energies come from the equation-of-motion-CCSD ͑EOM-CCSD͒20 with the two references ͑HF and KS-DFT͒ 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 the D and F states of Niϩ is determined with the module RASSI of MOLCAS using CCSD ͑T͒-DFT spin-free diagonal energies Fifteen electrons are correlated in sixteen active orbitals in the Single State CASSCF ͑Table I͒ The calculations have been performed with the ACES II ͑Ref 23͒ and MOLCAS 5.4 ͑Ref 24͒ quantum chemistry program packages III RESULTS A Geometrical structures The optimized geometries of NiCHϩ in its A electronic ground state obtained at different levels of theory ͓MCPF, CCSD, CCSD͑T͒, DFT͔ are reported in Table II ͑this work and previous references͒ The largest CCSD amplitudes near the equilibrium structures of the molecule are within the generally accepted magnitudes confirming that this molecule can be adequately treated with single reference correlation methods Furthermore, the inclusion of triple excitation by CCSD͑T͒ is expected to reduce the remaining error The bond distance and angle are underestimated by the DFT approach compared to CCSD͑T͒ and MCPF whereas the MCPF and CCSD͑T͒ geometries are very similar The small DFT Ni-C bond distance ͑1.733 Å͒ has been attributed to the choice of an ͓Ar͔ frozen core for the nickel atom Inclusion of the metal’s 3s and 3p electrons in the valence space leads to a value of 1.763 Å.15 The slightly smaller CCSD͑T͒ bond length and bond angle compared to that of CCSD is consistent with the establish trends of these methods.25 The electronic structure of NiCHϩ in its electronic ground and excited states at the MCPF geometry is consistent with previous theoretical studies B Electronic ground state of NiCH2¿ In contrast to the other first-row transition metal cations ϩ such as FeCHϩ and CoCH2 whose electronic ground states involve two nearly degenerate states, the nickel methylidene cation NiCHϩ had been found to be A with the open 13 * shell electron in the Ni-C orbital This is confirmed by the energies calculated at the CC level and reported in Table III for the low-lying doublet electronic states ( A , A , B , and B ) and the lowest quadruplet states ( B , a A ,b A , A ) of NiCHϩ Approximate ‘‘spin multiplicities’’ based on the projected expectation value ͗ Sˆ ͘ are also reported in Table III for the analysis of spin contamination The A electronic configuration with a singly occupied * orbital is stabilized by a decrease of the nickel-carbon Ni-C antibonding interaction with respect to the other configura* orbital is doubly occutions ( A , B , B ) where the Ni-C TABLE III Energies ͑Ϫ1546 in atomic units͒ of the low-lying doublet and quadruplet electronic states of NiCHϩ calculated at the CCSD-HF, CCSD-DFT, CCSD͑T͒-DFT, and CCSDT-3 levels and projected spin multiplicity Electronic state CCSDHF Spin multiplicitya CCSDDFTb Spin multiplicitya CCSD͑T͒DFTc CCSDT3 0.500 17 ͑0.499 95͒ 0.490 17 ͑0.489 60͒ 0.486 47 ͑0.485 70͒ 0.459 75 ͑0.457 58͒ 0.476 07 ͑0.475 57͒ 0.451 90 0.430 54 ͑0.429 12͒ 0.460 47 ͑0.459 73͒ 2.091 ͑2.127͒ 0.547 19 0.551 71 2.040 ͑2.050͒ 0.535 76 0.542 60 2.058 ͑2.073͒ 0.531 18 0.537 47 2.002 ͑2.003͒ 0.497 21 0.501 36 4.000 ͑4.003͒ 0.507 99 0.507 85 4.000 ͑4.003͒ 4.001 ͑4.002͒ 0.483 51 0.460 64 0.483 74 0.465 92 4.000 ͑4.002͒ 0.494 04 0.494 72 A1 0.508 55 2.433 ͑2.793͒ A2 0.497 38 2.021 ͑2.024͒ B1 0.493 68 2.036 ͑2.039͒ B2 0.465 82 2.003 ͑2.006͒ B1 0.481 88 4.002 ͑4.013͒ a 4A b 4A 0.457 71 0.43 555 4.000 ͑4.006͒ 4.002 ͑4.010͒ 0.467 61 4.001 ͑4.007͒ A2 a The projected spin multiplicity before the CCSD treatment is given in parentheses Energies calculated for the CCSD͑T͒-DFT optimized geometry are given in parentheses c Energies calculated for the CCSD͑T͒-DFT optimized geometry b Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044313-4 Villaume et al J Chem Phys 122, 044313 (2005) TABLE IV Relative energies and spin–orbit splitting ͑in cmϪ1͒ of the low-lying atomic states of Niϩ CCSD- CCSD- CCSD͑T͒- CCSD͑T͒Configuration Term HF DFT HF DFT 3d 3d 4s D F 0.0 8171 0.0 8626 0.0 10 441 0.0 10 260 Atomic spectruma,b 0.0 ͑5/2͒ 1506.95͑3/2͒ 8393.9 ͑9/2͒ 9330.04͑7/2͒ 10 115.66͑5/2͒ 10 663.89͑3/2͒ Calculated Experimental spin–orbit splitting splitting 1506.95 1518.20 936.14 997.35 785.62 548.23 772.01 550.49 a Reference 26 J is given in parentheses b pied This state is characterized by an unusual large spin contamination When using the KS determinant as a reference the spin pure solution of the A is restored with values of ‘‘spin multiplicities’’ of 2.793 ͑HF͒ and 2.127 ͑DFT͒ before the CC treatment and of 2.433 ͑CCSD-HF͒ and 2.091 ͑CCSD-DFT͒ The ensuing CCSD calculations further improve the ‘‘spin multiplicity’’ irrespective of the character of the reference orbitals ͑HF or KS͒ 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 A , B , and B states, respectively In order to analyze the origin of the spin contamination in the A molecular state and to validate our approach the low-lying quadruplet states have been analyzed and atomic calculations have been performed on Niϩ in the D (3d ) and F (3d 4s ) states ͑Table IV͒ In contrast to the molecular system NiCHϩ there is no spin contamination at the atomic level, both states being obtained with nearly pure spin multiplicities Moreover the agreement between the experimental and calculated atomic spectra is excellent, as illustrated by the calculated spin–orbit ͑SO͒ splitting The relative order of the D and F states is well described and does not depend on the reference ͑HF or KS orbitals͒ in the CCSD calculation Moreover the agreement is perfect when adding the triple correction Two of the molecular quadruplet states ( B , A ) fall in the energy range of the low-lying doublet states However they belong to the B and A symmetry point groups and cannot account for the cause of the large spin contamination obtained for the A state Among the several A calculated states only the two lowest a A and b A are reported in Table III They not show any spin contamination as indicated by their ‘‘spin multiplicities’’ close to 4.0 regardless the method is The A state ͑not reported in Table III͒ with the following electronic configuration (8a ) (9a ) (10a ) (4b ) (3b ) (1a ) (2a ) has been found with a large ‘‘spin multiplicity’’ of 4.44 at the HF level In this state the Ni atom is formally d , the 10a orbital being mainly localized on the carbon atom with a sp 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 A electronic ground state and should not account for the large spin contamination of this later state The a A state reported in Table III with the following electronic con- figuration (8a ) (9a ) (10a ) (4b ) (3b ) (1a ) (4b ) falls in the range of the low-lying states of NiCHϩ and could be responsible for the large spin contamination of the A Indeed the singly occupied orbitals 3b and 4b correspond to the bonding and antibonding 3d yz (Ni)/3p y (C) combinations, respectively, and are characterized by a large exchange term Moreover the Ni atom is formally d in this molecular state with a 10a orbital nearly pure and assigned to the sp(C) A careful investigation of the HF, KS, and CASSCF orbitals and of the A - A energy gap obtained at different levels of calculation ͑Scheme II͒ for NiCHϩ 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 ͑HF͒ calculations for the A electronic ground state Indeed the HF description leads to a A - A energy gap of 125.7 kJ/mol with an over stabilization of the A state and a spin multiplicity of 2.793 The 4s(Ni)/2p z (C) bonding orbital is inter* orbital ͓essentially localized on the changed with the Ni-C Ni atom (3d z ) 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 A molecular state the 4s(Ni)/2p z (C) becomes singly occupied whereas the singly * oroccupied KS and CASSCF 10a correspond to the Ni-C bital Scheme II Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044313-5 Structure of NiCH2ϩ J Chem Phys 122, 044313 (2005) TABLE V Relative stability ͑in kJ/mol͒ of the low-lying doublet and quadruplet electronic states of NiCHϩ calculated at the CCSD-HF, CCSD-DFT, CCSD͑T͒-DFT, and CCSDT-3 levels Electronic state A1 A2 B1 B1 B2 A2 A1 CCSD-HF CCSD-DFT CCSD͑T͒-DFT CCSDT-3 0.0 29.31 39.02 69.98 112.11 107.42 191.54 0.0 26.25 35.95 65.55 106.05 106.11 186.42 0.0 30.00 42.00 102.85 131.14 139.46 227.00 0.0 23.90 37.63 115.08 132.11 149.53 225.10 In the A molecular state the HF electronic configuration of Niϩ is formally 3d 4s in contrast to the A ͑DFT or CASSCF͒ which corresponds to a 3d configuration This failure of the noncorrelated HF theory which reverses the two low-lying D and F states in Niϩ over stabilizing the 4s 3d electronic configuration is well known but has no consequence on the CCSD results at the atomic level as depicted in Table IV because the doublet and quartet states have different symmetries In the molecule the A is probably contaminated by an upper A state where Niϩ is formally 3d It is difficult to conclude from our attempt at locating such a state Among the several A states of NiCHϩ the best candidate is certainly the a A state When going from HF to CASSCF or DFT approaches the A - A energy gap is reduced to 22.5 kJ/mole ͑CASSCF͒ and 28.72 kJ/mol ͑DFT͒ These values agree with the CCSD-DFT A - A energy gap calculated at 26.25 kJ/mole with a correct ‘‘spin multiplicity’’ of 2.091 for the A C Low-lying doublet and quadruplet states of NiCH2¿ The relative stability of the low-lying doublet and quadruplet states of NiCHϩ are reported in Table V The geometrical parameters have not been optimized for these states The A and B 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 geometrical relaxation effects The destabilization of the A and B states with respect to the A state is mainly due to the double occupation * antibonding orbital in both states The single of the Ni-C occupation of the 4b orbital in the B state increases the 3d (Ni)/3p x (C) antibonding character of this orbital which is nearly a pure 3d xz orbital in the A This could explain the relative position of the A and B states The B state is largely destabilized with respect to the A electronic ground state by more than 100 kJ/mol In this state a strong bonding interaction between the 3d and the 3p y (C) (3b ) is reduced by the single occupancy leading to an important destabilization of this state with respect to the others The relative stabilities not depend on the CCSD reference ͑HF or DFT͒ despite the spin contamination occurring in the CCSD-HF calculation of the A state Taking into account the triple excitations within a perturbative treatment increases the energy gap between the A 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 excited states of NiCHϩ calculated by means of CCSD-HF, CCSD-DFT, CCSD͑T͒-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 ͑MS͒-CASPT2 transition energies Consequently the CASSCF transition energies are only qualitative due to the lack of dynamical correlation effects The CCSD-HF, CCSD-DFT, CCSDT-3, and CCSD͑T͒DFT transition energies are obtained by simple energy differences The appropriate reference states for CC calculations for different electronic states are generated by controlling the occupation in various irreducible representations 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 electronic 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 methods, namely, the CCSD͑T͒-DFT and EOM-CCSD-DFT give very close transition energies IV CONCLUSION The electronic structure of NiCHϩ , representative of transition metal carbenes ions, has been investigated in details by means of coupled cluster approach based either on Hartree–Fock orbitals or on Kohn–Sham orbitals The A electronic ground state with an open shell electron in the * orbital is confirmed This electronic configuration is Ni-C stabilized with respect to the other low-lying doublet states by a decrease of the nickel-carbon antibonding interaction TABLE VI Transition energies in cmϪ1 ͑in electron volts͒ to the low-lying electronic excited states of NiCHϩ calculated by means of various quantum chemical methods Transition A → 2A 2 A → 2B A → 2B CCSD-HF CCSDDFT CCSD͑T͒DFT CCSDT3 EOM-CCSDDFT CASSCF ANO-L 2450 ͑0.304͒ 3265 ͑0.405͒ 9380 ͑1.163͒ 2200 ͑0.272͒ 3000 ͑0.373͒ 8870 ͑1.100͒ 2510 ͑0.311͒ 3510 ͑0.436͒ 10 970 ͑1.360͒ 1999 ͑0.240͒ 3125 ͑0.391͒ 11 050 ͑0.381͒ 2480 ͑0.307͒ 3420 ͑0.424͒ 11 450 ͑1.420͒ 1880 ͑0.233͒ 3000 ͑0.372͒ 8190 ͑1.015͒ Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044313-6 Villaume et al When based on HF orbitals the CC calculations indicate evidence of a severe problem of spin contamination in the A 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 Niϩ is due to the artificial single occupancy of the 4s(Ni)/2p z (C) bonding orbital This orbital 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 A is over stabilized and the A - A energy gap is overestimated at the HF level ͑125.7 kJ/mol versus 24 –30 kJ/mol in correlated calculations͒ The CC calculation restores the correct energetic regardless the reference is ͑HF or KS͒ The relative stability of the low-lying doublet and quadruplet states of NiCHϩ does not depend dramatically on the CC reference ͑HF or KS͒ Taking into account the triple excitations within a perturbative treatment increases the energy gap between the A 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-3͒ excepted for the A - A energy gap which is evaluated at 23.9 kJ/mol ͓versus 30.0 kJ/mol at the CCSD͑T͒ level͔ As far as the transition energies are concerned the CCSD͑T͒-DFT and EOM-CCSD-DFT methods give very close results The quality and the stability of the EOM-CCSD ͑KS͒ response results to the problem of nearly degenerate states in transition metals containing molecules opens the route to a wide range of applications The EOM-CCSD method has been recently applied with success to the low-lying electronic states of NiCO in a careful analysis of their structure and adiabatic/vertical transition energies.27 The 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 17097͒ and of the NSF grant ͑Program No 03-559͒ 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 calculations were carried out either at the Quantum Theory J Chem Phys 122, 044313 (2005) Project ͑Gainesville, Florida͒ or at the IDRIS ͑Orsay, France͒ through a grant of computer time from the Conseil Scientifique K Eller and H Schwarz, Chem Rev ͑Washington, D.C.͒ 91, 1121 ͑1991͒ T A Lehman and M M Bursey, Ion Cyclotron Resonance Spectrometry ͑Wiley-Interscience, New York, 1976͒ K P Wanczek, Int J Mass Spectrom Ion Processes 95, ͑1989͒ R G Cooks, J H Beynon, R M Caprioli, and G R Lester, Metastable Ions ͑Elsevier, Amsterdam, 1973͒ K Levsen and H Schwarz, Mass Spectrom Rev 2, 77 ͑1983͒ R L Hettig and B S Freiser, J Am Ceram Soc 108, 2537 ͑1986͒ J Husband, F Aguirre, C J Thompson, C M Laperle, and R B Metz, J Phys Chem A 104, 2020 ͑2000͒ L M Russon, S A Heidecke, M K Birke, J Conceicao, P B Armentrout, and M D Morse, Chem Phys Lett 204, 235 ͑1993͒ L M Russon, S A Heidecke, M K Birke, J Conceicao, M D Morse, and P B Armentrout, J Chem Phys 100, 4747 ͑1994͒ 10 D G Musaev, K Morokuma, N Koga, K A Nguyen, M S Gordon, and T R Cundari, J Phys Chem A 97, 11435 ͑1993͒ 11 D G Musaev, N Koga, and K Morokuma, J Chem Phys 99, 7859 ͑1993͒; D G Musaev and K Morokuma, ibid 101, 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Project ͑University of Florida, Gainesville, Florida, 2002͒ 24 K Andersson, M Barysz, A Bernhardsson et al., MOLCAS VERSION 5.4 ͑Lund University, Sweden, 2002͒ 25 R J Bartlett, in Modern Electronic Structure Theory, Part 1, Coupled Cluster Theory: An Overview of Recent Developments, edited by David Yarkony ͑World Scientific, Singapore, 1995͒ 26 NIST Atomic Spectra Database http://physics.nist.gov/cgi-bin/atData/ levels form 27 L Horny´, A Paul, Y Yamaguchi, and H F Schaefer III, J Chem Phys 121, 1412 ͑2004͒ Downloaded 26 Sep 2005 to 128.227.192.244 Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp ... 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. .. subsequent CASPT2 on the top of the CASSCF wave function failed due to the size of the problem The spin–orbit splitting of the D and F states of Niϩ is determined with the module RASSI of MOLCAS using... 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 A molecular state the