A density-matrix derivation of the Hartree--Fock equations in a nonorthogonal atomic-orbital basis

Thomas Kjærgaard

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arXiv · 2605.03761

A density-matrix derivation of the Hartree--Fock equations in a nonorthogonal atomic-orbital basis

Thomas Kjærgaard

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Abstract

We present a pedagogical derivation of the Hartree--Fock equations using the second-quantization atomic-orbital density-matrix formalism developed by Kj{\ae}rgaard, J{\o}rgensen, Olsen, Coriani, and Helgaker for AO-based response theory. The purpose is to introduce an alternative derivation of the Hartree--Fock equation, showing that the standard AO Hartree--Fock stationarity condition follows naturally from the exponential parametrization of the one-particle density matrix in a nonorthogonal AO basis. This route provides a compact bridge between elementary Hartree--Fock theory and the density-matrix machinery used in modern response theory and linear-scaling formulations.

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Thomas Kjærgaard. 2026-05-05. A density-matrix derivation of the Hartree--Fock equations in a nonorthogonal atomic-orbital basis. https://arxiv.org/abs/2605.03761

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