Quantum Chemistry for Solids Made Simple on the Clifford Torus

Area of Science:

• Solid-state physics
• Quantum chemistry
• Computational materials science

Background:

• Periodic solids present unique challenges for quantum-chemistry methods.
• Existing methods struggle with the complex topology of three-dimensional solids.
• Accurate electronic structure calculations are crucial for understanding material properties.

Purpose of the Study:

• To develop a general theory for treating periodic solids using quantum-chemistry methods.
• To introduce a novel formalism applicable to solid-state systems.
• To provide an alternative to computationally intensive or impossible ring-like calculations for solids.

Main Methods:

• Modeling solids as a Clifford torus, a periodic and flat topological space.
• Introducing a compatible periodic Gaussian basis set for the Clifford torus.
• Applying Hartree-Fock and coupled cluster theories to calculate ground-state energies.

Main Results:

• The proposed Clifford formalism successfully models periodic solids.
• Ground-state energies for a periodic hydrogen chain were accurately calculated.
• Results align with theoretical predictions in the thermodynamic limit.

Conclusions:

• The Clifford torus approach offers a robust framework for quantum-chemistry calculations of solids.
• This method seamlessly integrates with existing quantum-chemistry software for molecules.
• It provides a computationally feasible and accurate alternative for solid-state electronic structure studies.