Analytic gradients for natural orbital functional theory

TL;DR

This paper derives analytic energy gradients for natural orbital functional theory, enabling efficient geometry optimizations comparable to Hartree-Fock, and demonstrates its application to various molecular systems.

Contribution

It introduces a method to compute natural orbital functional energy gradients analytically, avoiding linear-response theory, and applies it to optimize molecular structures.

Findings

Equilibrium geometries agree well with CCSD and empirical data.

Gradient calculations are simplified and analogous to Hartree-Fock.

Method applied successfully to 15 molecular systems.

Abstract

The analytic energy gradients with respect to nuclear motion are derived for natural orbital functional (NOF) theory. The resulting equations do not require to resort to linear-response theory, so the computation of NOF energy gradients is analogous to gradient calculations at the Hartree-Fock level of theory. The structures of 15 spin-compensated systems, composed by first- and second-row atoms, are optimized employing the conjugate gradient algorithm. As functionals, two orbital-pairing approaches were used, namely, the fifth and sixth Piris NOFs (PNOF5 and PNOF6). For the latter, the obtained equilibrium geometries are compared with coupled cluster singles and doubles (CCSD) calculations and accurate empirical data.