Fully variational optimization of modern VB wave functions using the CASVB strategy

We outline the CASVB strategy, which may be used either to generate very compact modern valence bond representations of CASSCF wave functions or to optimize general types of modern VB wave function. A simple algorithm is presented for the elimination of redundant or constrained parameters from the appropriate second-order optimization problems. Selected results for three systems—benzene, the allyl radical, and LiH—are used to illustrate various ways in which CASVB procedures can be used to perform fully variational optimizations of nonorthogonal orbitals and structure coefficients in modern VB wave functions. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 439–451, 1997

[1]  D. L. Cooper,et al.  Exact transformations of CI spaces, VB representations of CASSCF wavefunctions and the optimization of VB wavefunctions , 1996 .

[2]  Michel Dupuis,et al.  A complete active space valence bond (CASVB) method , 1996 .

[3]  David L. Cooper,et al.  Modern valence bond representations of CASSCF wavefunctions , 1996 .

[4]  D. R. Bates,et al.  Spin-coupled theory of molecular wavefunctions: applications to the structure and properties of LiH(X1∑+), BH(X1∑+), Li2(X1∑g+) and HF(X1∑+) , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Per E. M. Siegbahn,et al.  A new direct CI method for large CI expansions in a small orbital space , 1984 .

[6]  Josef Paldus,et al.  Vectorizable approach to molecular CI problems using determinantal basis , 1989 .

[7]  D. L. Cooper,et al.  The dipole moment of LiH(X1Σ+): Spin-coupled valence-bond study , 1985 .

[8]  Jeppe Olsen,et al.  Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces , 1988 .

[9]  D. L. Cooper,et al.  Spin-Coupled Valence Bond Study of the Reaction between Benzene and a Methyl Cation , 1997 .

[10]  Robert J. Harrison,et al.  An efficient implementation of the full-CI method using an (n–2)-electron projection space , 1989 .

[11]  Mario Raimondi,et al.  The electronic structure of the benzene molecule , 1986, Nature.

[12]  D. L. Cooper,et al.  Aromatic electrophilic substitution. A modern valence bond study , 1995 .

[13]  C. R. Vidal,et al.  The /A 1 Sigma +/ - /X 1 Sigma +/ system of the isotopic lithium hydrides - The molecular constants, potential energy curves, and their adiabatic corrections , 1982 .

[14]  P. Knowles,et al.  A second order multiconfiguration SCF procedure with optimum convergence , 1985 .

[15]  David L. Cooper,et al.  Expansion of the spin-coupled wavefunction in Slater determinants , 1993 .

[16]  J. M. Norbeck,et al.  Valence-bond calculation of the electronic structure of benzene , 1974 .

[17]  D. L. Cooper,et al.  Spin-Coupled Study of the Electronic Structure of Polyenyl Radicals C3H5-C9H11 , 1994 .

[18]  David L. Cooper,et al.  STUDY OF THE ELECTRONIC STATES OF THE BENZENE MOLECULE USING SPIN-COUPLED VALENCE BOND THEORY , 1994 .

[19]  David L. Cooper,et al.  Core‐valence separation in the spin‐coupled wave function: A fully variational treatment based on a second‐order constrained optimization procedure , 1992 .

[20]  D. L. Cooper,et al.  Symmetry adaptation and the utilization of point group symmetry in valence bond calculations, including CASVB , 1997 .

[21]  F. Penotti Generalization of the Optimized‐Basis‐Set Multi‐Configuration Spin‐Coupled method for the ab initio calculation of atomic and molecular electronic wave functions , 1996 .

[22]  D. L. Cooper,et al.  Study of the electronic states of the allyl radical using spin-coupled valence bond theory , 1997 .

[23]  D. L. Cooper,et al.  Spin correlation in π-electron systems from spin-coupled wavefunctions. I. Theory and first applications , 1994 .

[24]  Per-Åke Malmqvist,et al.  Calculation of transition density matrices by nonunitary orbital transformations , 1986 .

[25]  B. H. Chirgwin,et al.  The electronic structure of conjugated systems. VI , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[26]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[27]  M. Raimondi,et al.  Ab initio valence-bond calculations. 5. Benzene , 1977 .

[28]  David L. Cooper,et al.  Applications of spin-coupled valence bond theory , 1991 .

[29]  P. Knowles,et al.  An efficient second-order MC SCF method for long configuration expansions , 1985 .