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

D.R. ALCOBA; L.M. TEL; E. PEREZ-ROMERO; C. VALDEMORO

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

Wiley Periodicals, Inc.

Lugar: New Jersey; Año: 2011 vol. 111 p. 937 - 949

0020-7608

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.