Convergence and computational efficiency enhancements in the iterative solution of the G-particle-hole hypervirial equation

Abstract

The G-particle-hole hypervirial (GHV) equation has been recently reported (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics Vancouver: Canada, 2008. Alcoba et al., Int J Quantum Chem 2009, 109, 3178; Valdemoro et al., Int J Quantum Chem 2009, 109, 2622). This equation is the newest member of the family of equations which can be obtained by applying a matrix-contracting mapping (Valdemoro, An R Soc Esp Fís 1983, 79, 106; Valdemoro, Phys Rev A 1985, 31, 2114; Valdemoro, in Density Matrices and Density Functionals, Reidel: Dordrecht, 1987; p 275.) to the matrix representation in the N-electron space of the Schrödinger, Liouville and hypervirial equations. The procedure that we have applied in order to solve the GHV equation exploits the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Hirschfelder and Epstein, Phys Rev 1961, 123, 1495) and follows the general lines of Mazziotti's variational approach for solving the anti-Hermitian contracted Schrödinger equation (ACSE) (Mazziotti, Phys Rev Lett 2006, 97, 143002; Mazziotti, Phys Rev A 2007, 75, 022505; Mazziotti, J Chem Phys 2007, 126, 184101). In this article, we report how the method's convergence has been significantly enhanced and how its computational scaling has been considerably reduced (in both floating-point operations and storage). The results for a variety of atomic and molecular calculations confirming these methodological improvements are reported here. Copyright © 2010 Wiley Periodicals, Inc.