Geminal wavefunctions with Jastrow correlation: a first application to atoms

TL;DR

This paper introduces a generalized geminal wavefunction with Jastrow correlation for atoms, improving accuracy and convergence in quantum chemistry calculations, especially for complex atomic systems.

Contribution

The paper presents a novel wavefunction combining antisymmetric geminal and Jastrow factors, enhancing correlation energy capture with low computational cost.

Findings

Achieved good variational energies for atoms up to Z=15.

Improved wavefunction accuracy for multiconfigurational atoms.

Enhanced nodal surfaces for Monte Carlo methods.

Abstract

We introduce a simple generalization of the well known geminal wavefunction already applied in Quantum Chemistry to atoms and small molecules. The main feature of the proposed wavefunction is the presence of the antisymmetric geminal part together with a Jastrow factor. Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the many-body state: the former permits the correct treatment of the nondynamic correlation effects, the latter allows the wavefunction to fulfill the cusp conditions and makes the geminal expansion rapidly converging to the lowest possible variational energies. This ansatz is expected to provide a substantial part of the correlation energy for general complex atomic and molecular systems. The antisymmetric geminal term can be written as a single determinant even in the polarized cases. In general, therefore, the computational effort to sample this correlated wavefunction is not very demanding. We applied this Jastrow-geminal approach to atoms up to Z=15, always getting good variational energies, by particularly improving those with a strong multiconfigurational nature. Our wavefunction is very useful for Monte Carlo techniques, such as Fixed node. Indeed, the nodal surface obtained within this approach can be substantially improved through the geminal expansion.