The Correlation Contracted Schrödinger Equation: An Accurate Solution of the G-particle-hole Hypervirial

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

Vancouver

Congreso; 6th Congress of the International Society for Theoretical Chemical Physics (ISTCP-VI); 2008

International Society for Theoretical Chemical Physics / University of British Columbia

The equation obtained by mapping the matrix representation of the Schrödinger equation with the 2-order correlation transition matrix elements into the 2-body space is the so called correlation contracted Schrödinger equation (CCSE) [1]. The form of this equation has been known for several years. As shown by Alcoba [1], the solution of the CCSE coincides with that of the Schrödinger equation. Here the attention is focused in the vanishing hypervirial of the G-particle-hole operator (GHV) [2]. By applying a time-like Heisenberg transformation to the G-particle-hole operator, a good approximation of the expectation value of this operator as well as of the GHV is obtained. A comparative analysis of the GHV and the anti-Hermitian part of the contracted Schrödinger equation (ACSE) [3] demonstrates that the stationary conditions of the former involve more degrees of freedom than those of the latter one and, consequently, they are harder to satisfy. The method is illustrated for the case of the Beryllium isoelectronic series as well as for the Li2 and BeH2 molecules. These results show that 99.04% - 100.09% of the correlation energy is accounted for. The convergence of these calculations was more rapid when using the GHV than with the ACSE. [1] D.R. Alcoba, Phys. Rev. A 65, 32519 (2002). [2] D.R. Alcoba, C. Valdemoro, L.M. Tel, E. Pérez-Romero, submitted for publication. [3] D.A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006).