Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

TL;DR

This paper employs Quantum Monte Carlo methods to compute the one-body density matrix and excitation energies of silicon, demonstrating that natural orbitals closely resemble LDA orbitals and that the diagonal approximation to Extended Koopmans' Theorem is effective and scalable.

Contribution

The study introduces a QMC approach to calculate natural orbitals and excitation energies in silicon, showing the effectiveness of a diagonal approximation for larger systems.

Findings

QMC density matrix is strongly diagonally dominant.

Natural orbitals resemble LDA orbitals closely.

Diagonal approximation yields reasonable excitation energies.

Abstract

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.