Some implications of the Hartree product treatment of the quantum nuclei in the ab initio Nuclear-electronic orbital methodology

TL;DR

This paper explores the implications of using a Hartree product nuclear wavefunction in the ab initio Nuclear-electronic orbital method, leading to a pseudo-adiabatic separation and a simplified computational approach.

Contribution

It introduces a pseudo-adiabatic separation framework and derives a computationally feasible modified Hartree-Fock set within the NEO methodology.

Findings

Nuclei are modeled as quantum oscillators.

A non-Coulombic effective Hamiltonian for electrons is developed.

Modified Hartree-Fock equations are derived and shown to be equivalent to previous multi-component versions.

Abstract

In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree-Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally.