Self-Consistent Electronic Structure Calculations in the Shirley Reduced Basis: Plane-Wave Accuracy at Reduced Computational Cost

Maxwell Hutchinson, University of Chicago

For extended periodic systems, numerically converged sampling of the Brillouin zone is necessary to resolve subtle details of electronic band structure near the Fermi level, such as Dirac points, spin crossings, charge transfer, etc. When such features make significant contributions to the electron density, describing them accurately requires a self-consistent approach. The Shirley reduced basis (SRB) was originally developed to speed non-self-consistent band structure calculations by constructing a compact basis from linear combinations of Bloch states sampled coarsely over k-space. We have recently developed a self-consistent implementation, which performs more efficiently than plane-wave pseudopotential calculations for systems that require large numbers of k-points for self-consistent field convergence. The reduced basis enables explicit representation and diagonalization of the k-dependent Hamiltonian and density matrix. The accuracy of the band structure and electron density is well controlled by the basis size, down to sub-meV errors in eigen-energies, while time-to-solution can be reduced by an order of magnitude. The new methodology leads to a shift in computational workload from Fourier transforms to dense linear algebra, which matches the strengths of emerging high-performance hardware, such as graphics processing units (GPUs) and other co-processor architectures.

Abstract Author(s): Maxwell Hutchinson