Canonical density matrix perturbation theory

TL;DR

This paper extends density matrix perturbation theory to canonical ensembles, enabling efficient calculation of temperature-dependent response properties with linear scaling for large systems in quantum chemistry.

Contribution

It generalizes the existing theory to canonical ensembles, allowing for efficient response property calculations at finite temperatures in large-scale systems.

Findings

Enables temperature-dependent response calculations in large systems.

Achieves linear scaling complexity for non-metallic and high-temperature metallic systems.

Utilizes sparse matrix algebra for computational efficiency.

Abstract

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free energy ensembles in tight-binding, Hartree-Fock or Kohn-Sham density functional theory. The canonical density matrix perturbation theory can be used to calculate temperature dependent response properties from the coupled perturbed self-consistent field equations as in density functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large non-metallic materials and metals at high temperatures.