Sum-of-products form of the molecular electronic Hamiltonian and application within the MCTDH method

TL;DR

This paper presents two methods to express the electronic Hamiltonian in a sum-of-products form, reducing computational complexity and enabling larger molecular system simulations within the MCTDH framework.

Contribution

The paper introduces novel sum-of-products representations of the electronic Hamiltonian tailored for the MCTDH method, addressing scaling issues for larger molecules.

Findings

Successfully applied to LiH eigenenergy calculations

Extended to H2O ionization spectrum analysis

Reduced computational scaling in electronic structure calculations

Abstract

We introduce two different approaches to represent the second-quantized electronic Hamiltonian in a sum-of-products form. These procedures aim at mitigating the quartic scaling of the number of terms in the Hamiltonian with respect to the number of spin orbitals, and thus enable applications to larger molecular systems. Here we describe the application of these approaches within the multi-configuration time-dependent Hartree framework. This approach is applied to the calculation of eigen energies of LiH and electronic ionization spectrum of H2O.