Geminal wave functions with Jastrow correlation: A first application to atoms

Abstract

We introduce a simple generalization of the well-known geminal wave function already applied in quantum chemistry to atoms and small molecules. The main feature of the proposed wave function 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 wave function to fulfill the cusp conditions and makes the geminal expansion rapidly converge 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 wave function is not very demanding, the scaling of the algorithm with the number of atoms being comparable with the simplest Hartree–Fock calculation. We applied this Jastrow-geminal approach to atoms up to Z=14, always getting good variational energies, by particularly improving those with a strong multiconfigurational nature. Our wave function 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.