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

Abstract

The Gaussian-type orbital and Gaussian-type geminal (GGn) model is applied to the water molecule, at the level of second-order Møller-Plesset (MP2) theory. In GGn theory, correlation factors are attached to all doubly-occupied orbital pairs (GG0), to all doubly-occupied and singly-excited pairs (GG1), or to all orbital pairs (GG2). Optimizing the GG2 model using a weak-orthogonality functional, we obtain the current best estimate of the all-electron MP2 correlation energy of water, À361.95 mE h . In agreement with previous observations, the GG1 model performs almost as well as the GG2 model (À361.26 mE h ), whereas the GG0 model is poorer (À351.36 mE h ). For the barrier to linearity of water, we obtain an MP2 correlation contribution of À463 AE 5 cm À1.

The geminal basis in explicitly correlated wave functions

“…The explicitly correlated pairs then take the form Q 12 f(r 12 )/ p / q , where p and q denote both occupied and virtual orbitals. This was introduced earlier to describe excited states [46] as well as in the GGn methods [18][19][20][21]. In Ref.…”

“…We are particularly interested to investigate the sensitivity of this ansatz on the function f(r 12 ). These questions are additionally motivated by a comparison of R12 theory with GGn theories [18][19][20][21], where the first order pair functions are expanded as…”

Three- and four-electron integrals involving Gaussian geminals: Fundamental integrals, upper bounds, and recurrence relations

“…46 These recurrence relations were implemented by Dahle. [47][48][49] Saito and Suzuki 50 also proposed an approach based on the work by Obara and Saika. 51,52 More recently, a general formulation using Rys polynomials [53][54][55] was published by Komornicki and King.…”

Many-Electron Integrals over Gaussian Basis Functions. I. Recurrence Relations for Three-Electron Integrals

“…26,27 Whereas VRRs for two-electron integrals have been widely studied, VRRs for three-electron integrals have not, except for GTGs. 10,[49][50][51][52][53][54] The T 1 step generates [a 3 ] m from [0] m via the 8-term VRR (see the Appendix for a detailed derivation)…”

“…Our recursive approach applies to a general class of multiplicative three-electron operators and thus generalizes existing schemes that pertain only to GTGs. 10,[49][50][51][52][53][54] Section 2 contains basic definitions, classifications of three-electron operators, and permutational symmetry considerations. In Sec.…”