Shirley Interpolation - Optimal basis sets for detailed Brillouin zone integrations revisited

TL;DR

This paper introduces an improved k-space interpolation method for electronic structure calculations that constructs an optimal basis from minimal initial data, enabling accurate and efficient Brillouin zone integrations for large systems.

Contribution

The authors generalize Shirley's interpolation scheme to reduce initial calculations and support various pseudopotentials, improving efficiency and applicability for electronic structure analysis.

Findings

Achieves eigenvalue accuracy within 0.01 eV at low computational cost.

Enables interpolation over the entire Brillouin zone from zone-center calculations.

Provides a framework for calculating optical and quasiparticle properties efficiently.

Abstract

We present a new implementation of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996). The method permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic structure calculations (based on density functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions - expressed in the optimal basis - provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.