Quantum Proton Effects from Density Matrix Renormalization Group Calculations

TL;DR

This paper introduces a combined nuclear-electronic DMRG method that treats nuclei and electrons equally, providing highly accurate molecular properties without the Born-Oppenheimer approximation.

Contribution

It develops NEHF-DMRG, extending DMRG to nuclear-electronic systems and applying it to molecules, improving accuracy over existing methods.

Findings

Accurate proton densities and energies for HeHHe+

Reliable detection of strong correlation effects

Improved accuracy for HCN properties

Abstract

We recently introduced [J. Chem. Phys. 152 2020, 204103] the nuclear-electronic all-particle density matrix renormalization group method (NEAP-DMRG) to solve the molecular Schr\"{o}dinger equation, based on a stochastically optimized orbital basis, without invoking the Born-Oppenheimer approximation. In this work, we combine the DMRG with nuclear-electronic Hartree-Fock (NEHF-DMRG), treating nuclei and electrons on the same footing. Inter- and intra-species correlations are described within the DMRG without truncating the excitation degree of the full configuration interaction wave function. We extend the concept of orbital entanglement and mutual information to nuclear-electronic wave functions and demonstrate that they are reliable metrics to detect strong correlation effects. We apply NEHF-DMRG to the HeHHe$^+$ molecular ion, to obtain accurate proton densities, ground-state total energies, and vibrational transition frequencies by comparison with state-of-the-art data obtained with grid-based approaches and modern configuration interaction methods. For HCN, we improve on the accuracy of the latter approaches with respect to both ground-state absolute energy and proton density which is a major challenge for multi-reference nuclear-electronic state-of-the-art methods.