Analytical energy gradient of the symmetry-adapted-cluster configuration-interaction general-R method for singlet to septet ground and excited states.

A method of calculating analytical energy gradients of the singlet and triplet excited states, ionized states, electron-attached states, and high-spin states from quartet to septet states by the symmetry-adapted-cluster configuration-interaction general-R method is developed and implemented. This method is a powerful tool in the studies of geometries, dynamics, and properties of the states of molecules in which not only one-electron processes but also two- and multielectron processes are involved. The performance of the present method was confirmed by calculating the geometries and the spectroscopic constants of the diatomic and polyatomic molecules in various electronic states involving the ground state and the one- to three-electron excited states. The accurate descriptions were obtained for the equilibrium geometries, vibrational frequencies, and adiabatic excitation energies, which show the potential usefulness of the present method. The particularly interesting applications were to the C' 1Ag state of acetylene, the A 2Deltau and B 2Sigmau+ states of CNC and the 4B1 and a 4Piu states of N3 radical.

[1]  Hiroshi Nakatsuji,et al.  Description of two- and many-electron processes by the SAC-CI method , 1991 .

[2]  Masahiro Ehara,et al.  Analytical energy gradients of the excited, ionized and electron-attached states calculated by the SAC-CI general-R method , 2001 .

[3]  Carlo Petrongolo,et al.  MRD-CI ground state geometry and vertical spectrum of N3 , 1988 .

[4]  Hiroshi Nakatsuji,et al.  Energy gradient method for the ground, excited, ionized, and electron-attached states calculated by the SAC (symmetry-adapted cluster)/SAC–CI (configuration interaction) method , 1999 .

[5]  S. Langhoff,et al.  An initio calculations on C2, Si2, and SiC , 1987 .

[6]  Y. Yamaguchi,et al.  A New Dimension to Quantum Chemistry: Analytic Derivative Methods in AB Initio Molecular Electronic Structure Theory , 1994 .

[7]  Henry F. Schaefer,et al.  On the evaluation of analytic energy derivatives for correlated wave functions , 1984 .

[8]  Jerzy Leszczynski,et al.  COMPUTATIONAL CHEMISTRY: Reviews of Current Trends , 2006 .

[9]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction, valence and rydberg excitations, ionizations, and inner-valence ionizations of CO2 and N2O studied by the sac and sac CI theories , 1983 .

[10]  M. Evans,et al.  A ZEKE photoelectron study of the D and 3 satellite states of CO , 1999 .

[11]  Julia E. Rice,et al.  The elimination of singularities in derivative calculations , 1985 .

[12]  H. Nakatsuji,et al.  Theoretical study on the ionized states of ethylene by the SAC-CI (general-R) method , 1998 .

[13]  Hiroshi Nakatsuji,et al.  Exponentially generated configuration interaction theory. Descriptions of excited, ionized, and electron attached states , 1991 .

[14]  W. Jones,et al.  THE 2 700 A BANDS OF THE N3 MOLECULE , 1965 .

[15]  J. Wasilewski.  Stationary points on the lowest doublet and quartet hypersurfaces of the N3 radical: A comparison of molecular orbital and density functional approaches , 1996 .

[16]  B. Sutcliffe.  Matrix Elements between Bonded Functions , 1966 .

[17]  G. Herzberg.  Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules , 1939 .

[18]  R. Field,et al.  Ultraviolet-Optical Double-Resonance study of the predissociated C̃′ 1Ag state of acetylene , 1992 .

[19]  E W Thulstrup,et al.  Configuration interaction studies of bound, low-lying states of N2-, N2, N2+ and N22+ , 1975 .

[20]  M. Frisch,et al.  Singularity-free analytical energy gradients for the SAC/SAC-CI method: coupled perturbed minimum orbital-deformation (CPMOD)approach , 2003 .

[21]  S. Iwata,et al.  Ab initio MO study of the A, D and third 2Π states of CO+ , 2000 .

[22]  H. Nakatsuji,et al.  Ionization spectrum of CO2 studied by the SAC-CI general-R method , 1999 .

[23]  H. Nakatsuji,et al.  Elimination of singularities in molecular orbital derivatives: minimum orbital-deformation (MOD) method , 2002 .

[24]  M. Herman,et al.  The à electronic state of acetylene: Geometry and axis-switching effects , 1990 .

[25]  P. Pulay.  Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[26]  Ian M. Mills,et al.  Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations. I , 1968 .

[27]  Poul Jørgensen,et al.  Geometrical derivatives of energy surfaces and molecular properties , 1986 .

[28]  C. M. Reeves.  An algorithm for generating projective reduction formulas for matrix elements of many-electron wavefunctions , 1966, CACM.

[29]  A. Dalgarno,et al.  A perturbation calculation of properties of the helium iso-electronic sequence , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[30]  H. Nakatsuji,et al.  Analytical energy gradient of high-spin multiplet state calculated by the SAC-CI method , 2001 .

[31]  R. Mcweeny,et al.  Studies in Configuration Interaction. I. Matrix Elements between Spin-Coupled Functions , 1966 .

[32]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory , 1978 .

[33]  H. Nakatsuji,et al.  SAC-CI general-R study of the ionization spectrum of HCl , 1999 .

[34]  島内 みどり,et al.  G. Herzberg: Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, D. Van Nostrand, Prinston 1966, 745頁, 16.5×24cm, 8,000円. , 1968 .

[35]  P. Chandra,et al.  Ground and valence excited states of C2N and CN2 transients: Ab initio geometries, electronic structures, and molecular properties , 2001 .

[36]  A. Broadfoot,et al.  Electronic Transition Moment for the N2 Vegard–Kaplan Bands , 1969 .

[37]  Hiroshi Nakatsuji,et al.  Analytical energy gradient of the ground, excited, ionized and electron-attached states calculated by the SAC/SAC-CI method , 1997 .

[38]  G. Herzberg,et al.  Molecular spectra and molecular structure. Vol.3: Electronic spectra and electronic structure of polyatomic molecules , 1966 .

[39]  Peter Pulay,et al.  Second and third derivatives of variational energy expressions: Application to multiconfigurational self‐consistent field wave functions , 1983 .

[40]  Hiroshi Nakatsuji,et al.  Cluster expansion of the wavefunction. Calculation of electron correlations in ground and excited states by SAC and SAC CI theories , 1979 .

[41]  John D. Watts,et al.  Coupled‐cluster calculations on the C2 molecule and the C+2 and C−2 molecular ions , 1992 .

[42]  P. Rosmus,et al.  Quartet states in the radical cation , 1997 .

[43]  P. Bartlett.  Studies in physical and theoretical chemistry : Vol. 55, semiconductor electrodes. H.O. Finklea (Editor). Elsevier, Amsterdam, 1988, xxii + 520 pp., Dfl.340.00, US$179.00 , 1988 .

[44]  H. Nakatsuji,et al.  Symmetry‐adapted cluster–configuration interaction method applied to high‐spin multiplicity , 1993 .

[45]  H. Nakatsuji,et al.  Exponentially generated configuration interaction (EGCI) method applied to high‐spin multiplicity , 1993 .

[46]  J. Stanton,et al.  Stationary points on the S1 potential energy surface of C2H2 , 1994 .

[47]  R. Berry,et al.  The use of scaled moments of inertia in experimental structure determinations of polyatomic molecules , 1990 .

[48]  H. Nakatsuji,et al.  Fine theoretical spectroscopy using symmetry adapted cluster-configuration interaction general-R method: Outer- and inner-valence ionization spectra of CS2 and OCS , 2002 .