Analytic second-order energy derivatives in natural orbital functional theory

TL;DR

This paper derives analytic second-order energy derivatives in natural orbital functional theory, enabling efficient computation of molecular Hessians by solving coupled-perturbed equations involving natural orbitals and occupancies.

Contribution

It introduces an alternative expression for energy derivatives in NOFT and derives the analytic second-order derivatives with respect to nuclear displacements.

Findings

Provides a method to compute analytic Hessians in NOFT.

Shifts computational effort to solving linear coupled-perturbed equations.

Simplifies the response calculation by focusing on natural orbitals and occupancies.

Abstract

The analytic energy gradients in the atomic orbital representation have recently been published (J. Chem. Phys. 146, 014102, 2017) within the framework of the natural orbital functional theory (NOFT). We provide here an alternative expression for them in terms of natural orbitals, and use it to derive the analytic second-order energy derivatives with respect to nuclear displacements in the NOFT. The computational burden is shifted to the calculation of perturbed natural orbitals and occupancies, since a set of linear coupled-perturbed equations obtained from the variational Euler equations must be solved to attain the analytic Hessian at the perturbed geometry. The linear response of both natural orbitals and occupation numbers to nuclear geometry displacements need only specify the reconstruction of the second-order reduced density matrix in terms of occupation numbers.