An efficient reformulation of the closed‐shell self‐consistent electron pair theory

The closed‐shell SCEP method is reformulated in terms of pairwise nonorthogonal configuration state functions with particle‐hole singlet coupling. The use of a single type of external pair function instead of the usual singlet and triplet coupled pairs results in the elimination of the internal coupling coefficients in the residual vector formulas, simplifying the latter considerably. The new CI coefficients are represented as unsymmetrical quadratic matrices which are naturally adapted to the description of long‐range correlation between spatially distant localized orbitals. The number of matrix multiplications required for the interorbital pair coupling terms is reduced by half. This should lead to a reduction in the total computational effort by about 30%, except for very small molecules where intraorbital correlation dominates the computation.

[1]  A. C. Hurley.  Electron correlation in small molecules , 1976 .

[2]  Hans-Joachim Werner,et al.  The self‐consistent electron pairs method for multiconfiguration reference state functions , 1982 .

[3]  William F. Meggers,et al.  Quantum Theory of Atomic Structure , 1960 .

[4]  Peter R. Taylor,et al.  Unlinked cluster effects in molecular electronic structure. I. The HCN and HNC molecules , 1978 .

[5]  Wilfried Meyer,et al.  Theory of self‐consistent electron pairs. An iterative method for correlated many‐electron wavefunctions , 1976 .

[6]  J. S. Binkley,et al.  Electron correlation theories and their application to the study of simple reaction potential surfaces , 1978 .

[7]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[8]  C. E. Dykstra,et al.  Recent computational developments with the self‐consistent electron pairs method and application to the stability of glycine conformers , 1981 .

[9]  H. Schaefer.  Methods of Electronic Structure Theory , 1977 .

[10]  Rodney J. Bartlett,et al.  Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem , 1978 .

[11]  C. E. Dykstra,et al.  An electron pair operator approach to coupled cluster wave functions. Application to He2, Be2, and Mg2 and comparison with CEPA methods , 1981 .

[12]  R. Ahlrichs,et al.  Many body perturbation calculations and coupled electron pair models , 1979 .

[13]  J. Cizek.  On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[14]  H. Schaefer,et al.  A theory of self‐consistent electron pairs. Computational methods and preliminary applications , 1976 .

[15]  Wilfried Meyer,et al.  PNO–CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane , 1973 .

[16]  P. Jasien,et al.  The most efficacious one‐electron bases for determining and representing correlated molecular electronic wave functions. Unity in seemingly disparate electron correlation methods , 1982 .

[17]  Clifford E. Dykstra,et al.  An efficient and accurate approximation to double substitution coupled cluster wavefunctions , 1981 .