Second-order correlation energy for H2O using explicitly correlated Gaussian geminals

Abstract

The second-order pair energies are calculated for the H2O molecule employing explicitly correlated Gaussian-type geminals. The selection of the basis functions is guided by the completeness criteria for Gaussian geminal bases of C2v symmetry and by the recently developed technique [J. Chem. Phys. 100, 1366 (1994)] of crude optimization of nonlinear geminal parameters. Several simplifications have been made in the matrix elements evaluations that substantially reduce the optimization time without sacrificing numerical accuracy. The present results provide the new best upper bound to the second-order correlation energy for the water molecule. These results are compared with those obtained by Kutzelnigg and co-workers using the basis set containing terms linear in the interelectronic distance.

Theory and application of explicitly correlated Gaussians

“…The introduction of the more efficient weakorthogonality second-order energy functional (Szalewicz et al, 1982) resulted in MP2 (Szalewicz et al, 1983a) and MP3 energies (Szalewicz et al, 1983b) of He, Be, H 2 , and LiH that were the most accurate ones at that time. This approach was also applied to ten-electron systems: the Ne atom (Wenzel et al, 1986) and the water molecule (Bukowski et al, 1995).…”

“…For all practical purposes, the ECG functions form a complete basis set (King, 1967;Bukowski et al, 1995;Jeziorski, Bukowski, and Szalewicz, 1997;Hill, 1998). Issues of linear dependence can arise during calculations since the Gaussian functions used are not mutually orthogonal.…”

Second-order Møller–Plesset calculations on the water molecule using Gaussian-type orbital and Gaussian-type geminal theory

“…The MP2-R12/A values in Table 5 are lower but less trustworthy, as this approximation is known to give energies that are too low by error cancellation. The MP2-GTG value of À356.43 mE h obtained by Bukowski et al 9 is less accurate. We note that in the WO optimization of this energy the GTGs were fixed on the nuclei, rather than variationally optimized as is the normal procedure in GTG theory.…”

“…Of particular relevance to our work is the Gaussian-type geminal (GTG) method, introduced in 1982 by Szalewicz and coworkers. [6][7][8][9] With this model, a number of accurate second-order Møller-Plesset (MP2) calculations have been carried out on small systems, but applications to larger systems are difficult because of a nonlinear optimization of variational parameters (geminal centers and exponents) and the explicit evaluation of threeelectron integrals. An alternative technique is the R12 method, introduced a few years later by Kutzelnigg and Klopper.…”

“…12 We here discuss an alternative model, which uses a mixed Gaussian-type orbital (GTO) and GTG expansion, 13 avoiding the nonlinear optimization of the GTG method but otherwise closely following the approach of Szalewicz and coworkers. [6][7][8][9] In particular, we optimize the MP2 pair functions using their weak-orthogonality (WO) functional, with an explicit evaluation of three-electron integrals. 14 As in F12 theory, GTO-GTG (GG) theory uses pair functions that combine a traditional, orbital-based pair function with an explicitly correlated part, consisting of orbital products multiplied by a correlation factor.…”