Quantum chemistry for solids made simple on the Clifford torus

TL;DR

This paper introduces a novel approach to quantum chemistry for solids using a Clifford torus model and a compatible Gaussian basis set, enabling accurate calculations of periodic solids.

Contribution

It develops a new theoretical framework combining Clifford torus topology with periodic basis sets for quantum-chemistry calculations on solids.

Findings

Accurately computes ground-state energy of hydrogen chains in the thermodynamic limit.

Demonstrates the approach's effectiveness compared to ring models.

Provides a practical method for applying quantum chemistry to three-dimensional solids.

Abstract

We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction of a periodic gaussian basis set that is compatible with the topology of the Clifford torus. We illustrate our approach by calculating the ground-state energy of a periodic chain of hydrogen atoms within both Hartree-Fock and coupled cluster theory. We demonstrate that our approach yields the correct ground-state energy in the thermodynamic limit by comparing it to the ground-state energy of a ring of hydrogen atoms in the same limit. Since equivalent ring-like calculations for three-dimensional solids are impossible, our approach is an excellent alternative to perform quantum-chemistry calculations of solids. Our Clifford formalism can be seamlessly combined with current implementations of quantum-chemistry methods designed for atoms and molecules to make them applicable to solids.