Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization

TL;DR

This paper introduces a new exact wavefunction-based method to compute coupled nuclear and electronic behaviors on a single potential energy surface, improving the understanding of molecular bonding beyond the Born-Oppenheimer approximation.

Contribution

It formulates an exact nucleus-electron embedding potential and demonstrates its application to characterize vibrationally averaged molecular properties and electron correlation effects.

Findings

Accurately quantifies non-classical nucleus-electron couplings.

Revises molecular bonding fingerprints using the exact wavefunction.

Enables post-Hartree-Fock electron correlation calculations on coupled orbitals.

Abstract

We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We formulate an exact self-consistent nucleus-electron embedding potential from the single product molecular wavefunction, and demonstrate that the fundamental behavior of correlated nucleus-electron can be computed for mean-field electrons that are responsive to a quantal anharmonic vibration of selected nuclei in a discrete variable representation. Geometric gauge choices are discussed and necessary for formulating energy invariant biorthogonal electronic equations. Our method is further applied to characterize vibrationally averaged molecular bonding properties of molecular energetics, bond length, protonic and electron density. Moreover, post-Hartree-Fock electron correlation can be conveniently computed on the basis of nucleus-electron coupled molecular orbitals, as demonstrated to correlated models of second-order M{\o}llet-Plesset perturbation and full configuration interaction theories. Our approach not only accurately quantifies non-classical nucleus-electron couplings for revising molecular bonding properties, but also provides an alternative time-independent approach for deploying non-BO molecular quantum chemistry.