Quantum Chemistry for Solids Made Simple on the Clifford Torus

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.