The self-consistent nonorthogonal group function approach in reduced basis frozen-core calculations

Abstract

rnThe orthogonal group function approach, as based on the Huzinaga equation, is extensively applied in reduced basis frozen-core calculations. Although the theory is developed for orthogonal electronic groups, the use of reduced basis sets prevents strict orthogonality and the formalism is complemented to take, partially, into account nonorthogonality (projection factors, projection energy). In the present article, an alternative to this approach, based on the nonorthogonal formalism, is proposed. An orbital equation is derived from the Adams-Gilbert equation and the energy is evaluated according to a recent proposal based on the power-series expansion of the overlap energy. A comparative overview of the orthogonal and nonorthogonal formalisms is presented and the results of reduced basis frozen-core calculations as obtained with the two methods are compared. It is found that the nonorthogonal formulation predicts equilibrium geometrical parameters in some cases similarly and, in other cases, slightly better than does the orthogonal one. Based on this observation and on the fact that the nonorthogonal formulation is exempt from empirical parameters (projection factors), it is concluded that the nonorthogonal formalism represents an appealing alternative in reduced basis frozen-core calculations. 0 1996 John Wiley & Sons, Inc.Hartree-Fock space.* The orthogonal formulation, as based on the Huzinga equation [5], allows the calculation of some selected canonical orbitals. The orthogonality of the groups make it possible to define independent group densities and group energies 161. If the orthogonality is combined with group-specific (also termed as reduced or local) * The theory was also developed for multiconfigurational wave hcti0m [3, 41, which will not be considered in the

A wavefunction model to chemical bonding

“…A potential solution is to use the Adams-Gilbert equation [35,36]. An approximate form and the corresponding energy expression has been proposed to obtain the orbitals [37,38]. This latter is based on the series expansion of the inverse overlap matrix and the neglect of higher order terms.…”