Density Matrix Renormalization Group Study of a One Dimensional Diatomic Molecule beyond the Born-Oppenheimer Approximation

TL;DR

This paper employs density matrix renormalization group techniques to study one-dimensional diatomic molecules with quantum nuclei and electrons, revealing how nuclear mass influences molecular binding beyond the Born-Oppenheimer approximation.

Contribution

It introduces a three-site DMRG algorithm and a compression method for long-range interactions to analyze 1D diatomic molecules beyond traditional approximations.

Findings

Triplet-state nuclei molecules unbind at low nuclear mass

Singlet-state nuclei molecules always bind

Quantum treatment of nuclei affects molecular stability

Abstract

We study one dimensional models of diatomic molecules where both the electrons and nuclei are treated as quantum particles, going beyond the usual Born-Oppenheimer approximation. The continuous system is approximated by a grid which computationally resembles a ladder, with the electrons living on one leg and the nuclei on the other. To simulate DMRG efficiently with this system, a three-site algorithm has been implemented. We also use a compression method to treat the long-range interactions between charged particles. We find that 1D diatomic molecules with spin-1/2 nuclei in the spin-triplet state will unbind when the mass of the nuclei reduces to only a few times larger than the electron mass, while the molecule with nuclei in the singlet state always binds, given the two electrons in their singlet state in both cases.