*Ab initio*molecular orbital study of ground and low-lying electronic states of CoCN

^{1,a)}, Rei Okuda

^{2,b)}, Umpei Nagashima

^{2}and Per Jensen

^{3}

### Abstract

The ground and low-lying excited states of CoCN have been studied by *ab initio* multireference single and double excitation configuration interaction (MR-SDCI) calculations with Davidson’s correction and Cowan-Griffin’s relativistic corrections. The electronic ground state of CoCN is and the equilibrium geometry is linear with bond lengths of and , substantially different from the experimentally derived values of and . The first excited state is , separated from the ground state by . Larger dynamical electron correlationenergy for the low-spin state than for the high-spin state makes the state to be the ground state, which is discussed in terms of the differences in natural orbitals. A new spin-orbit interaction scheme between the and states is proposed.

The authors thank P. M. Sheridan and L. M. Ziurys, University of Arizona, for providing their experimental data on CoCN prior to publication. They also thank Kiyoshi Tanaka for enjoyable discussions on the high-spin and low-spin issue and the orbital energies of natural orbitals. This work is partially supported by the research project “Development of Molecular Orbital Calculation System for Large Molecule on Grid,” CREST, JST. Numerical calculations were performed on the AIST supercluster at the National Institute of Advanced Industrial Science and Technology (AIST). The work of one of the authors (P.J.) is supported in part by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.

I. INTRODUCTION

II. CALCULATION METHOD

III. RESULTS AND DISCUSSION

### Key Topics

- Spin orbit interactions
- 12.0
- Chemical bonds
- 11.0
- Electron correlation calculations
- 11.0
- Excitation energies
- 10.0
- Manifolds
- 10.0

## Figures

Potential energy profiles of low-lying electronic states of CoCN plotted as functions of the Co–C distance . The electronic energy is determined at the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] level of theory with fixed at , i.e., of CoCN, and bond angle : (a) Triplet manifold and (b) quintet manifold. The energy zero is at the equilibrium energy of CoCN.

Potential energy profiles of low-lying electronic states of CoCN plotted as functions of the Co–C distance . The electronic energy is determined at the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] level of theory with fixed at , i.e., of CoCN, and bond angle : (a) Triplet manifold and (b) quintet manifold. The energy zero is at the equilibrium energy of CoCN.

Occupation patterns of the dominant electronic configurations (with total weights of approximately 88% and 93%, respectively) for the and states of CoCN, calculated at the SA-CASSCF level of theory. The ordinate represents the relative location of an NO in terms of the diagonal elements of the effective Fock matrix in the NO basis (see Sec. II). The main character of each MCSCF NO is given in parentheses, where , , and denote atomic orbitals of Co, the largest component comes first, and the minor components are shown in smaller fonts. Two highest valence NOs, and , at 0.353 and 1.189 or 0.343 and 1.165 , respectively, are not included since they are located high above the given ordinate scale.

Occupation patterns of the dominant electronic configurations (with total weights of approximately 88% and 93%, respectively) for the and states of CoCN, calculated at the SA-CASSCF level of theory. The ordinate represents the relative location of an NO in terms of the diagonal elements of the effective Fock matrix in the NO basis (see Sec. II). The main character of each MCSCF NO is given in parentheses, where , , and denote atomic orbitals of Co, the largest component comes first, and the minor components are shown in smaller fonts. Two highest valence NOs, and , at 0.353 and 1.189 or 0.343 and 1.165 , respectively, are not included since they are located high above the given ordinate scale.

A model for the large amplitude bending motion for CoCN. is the center of mass of the CN moiety, and the numbers in parentheses are approximate masses, in , of Co and CN.

A model for the large amplitude bending motion for CoCN. is the center of mass of the CN moiety, and the numbers in parentheses are approximate masses, in , of Co and CN.

Spin-orbit interaction, in units of , between and nearby states predicted at the level of MR-SDCI/[ (Co), aug-cc-pVTZ (C, N)] for the equilibrium geometry of the CoCN state. The energy levels for the and states are shifted to those obtained by the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] method. The levels marked by an asterisk will be further perturbed by spin-substates with the same value, not only in the state at , but also in the state at , where energies are for the equilibrium geometry. Thus, the perturbed level at will be pushed further down to by the spin-substate. The predicted values of the for the state and the perturbing state are and , respectively, at the equilibrium geometry.

Spin-orbit interaction, in units of , between and nearby states predicted at the level of MR-SDCI/[ (Co), aug-cc-pVTZ (C, N)] for the equilibrium geometry of the CoCN state. The energy levels for the and states are shifted to those obtained by the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] method. The levels marked by an asterisk will be further perturbed by spin-substates with the same value, not only in the state at , but also in the state at , where energies are for the equilibrium geometry. Thus, the perturbed level at will be pushed further down to by the spin-substate. The predicted values of the for the state and the perturbing state are and , respectively, at the equilibrium geometry.

## Tables

Vertical excitation energies (in ) given relative to the energy of CoCN, calculated at the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] and /[Roos ANO (Co), aug-cc-pVQZ (C, N)] levels of theory.

Vertical excitation energies (in ) given relative to the energy of CoCN, calculated at the /[Roos ANO (Co), aug-cc-pVQZ (C, N)] and /[Roos ANO (Co), aug-cc-pVQZ (C, N)] levels of theory.

Molecular constants for the electronic ground state and for the lowest and states of CoCN.

Molecular constants for the electronic ground state and for the lowest and states of CoCN.

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