# Lattice Density-Functional Theory for Quantum Chemistry

## TL;DR

This paper introduces a lattice density-functional theory approach for quantum chemistry that approximates full configuration interaction energies, demonstrating promising results for modeling strongly-correlated electrons in molecules.

## Contribution

It extends lattice density-functional theory from the Hubbard model to quantum chemistry, deriving Kohn-Sham equations for complex molecular systems.

## Key findings

- Potential energy curves align well with full configuration interaction results.
- The method outperforms standard density-functional theory in stretched bond scenarios.
- Discrepancies remain for very elongated bonds, but are reduced.

## Abstract

We propose a lattice density-functional theory for {\it ab initio} quantum chemistry or physics as a route to an efficient approach that approximates the full configuration interaction energy and orbital occupations for molecules with strongly-correlated electrons. We build on lattice density-functional theory for the Hubbard model by deriving Kohn-Sham equations for a reduced then full quantum chemistry Hamiltonian, and demonstrate the method on the potential energy curves for the challenging problem of modelling elongating bonds in a linear chain of six hydrogen atoms. Here the accuracy of the Bethe-ansatz local-density approximation is tested for this quantum chemistry system and we find that, despite this approximate functional being designed for the Hubbard model, the shapes of the potential curves generally agree with the full configuration interaction results. Although there is a discrepancy for very stretched bonds, this is lower than when using standard density-functional theory with the local-density approximation.