Correlated geminal wave function for molecules: an efficient resonating valence bond approach

TL;DR

This paper introduces a simple yet effective correlated wave function combining Jastrow and AGP for molecules, enabling accurate electronic structure calculations with computational costs similar to traditional methods.

Contribution

It presents a novel correlated wave function approach that efficiently captures electron correlation and extends the SR method to optimize molecular geometries.

Findings

Achieves accurate total energies and bond lengths for molecules like Li_2 and benzene.

Comparable results to multi-configuration schemes with lower computational cost.

Demonstrates the method's effectiveness in describing molecular electronic structures.

Abstract

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an Antisymmetrized Geminal Power (AGP), based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several Resonating Valence Bonds (RVB) can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similarly to more conventional methods, such as Hartree-Fock (HF) or Density Functional Theory (DFT). Moreover we describe an extension of the Stochastic Reconfiguration (SR) method, that was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, that can be optimized together with the remaining ones. The method is applied to several molecules from Li_2 to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multi configuration schemes.