Thomas Kjærgaard | Searcharxiv

arXiv2026

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

We present a pedagogical derivation of the Hartree--Fock equations using the second-quantization atomic-orbital density-matrix formalism developed by Kjærgaard, Jørgensen, 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.

quant-ph↗

arXiv2016

CC2 oscillator strengths within the local framework for calculating excitation energies (LoFEx)

In a recent work [Baudin and Kristensen, J. Chem. Phys. 144, 224106 (2016)], we introduced a local framework for calculating excitation energies (LoFEx), based on second-order approximated coupled cluster (CC2) linear-response theory. LoFEx is a black-box method in which a reduced excitation orbital space (XOS) is optimized to provide coupled cluster (CC) excitation energies at a reduced computational cost. In this article, we present an extension of the LoFEx algorithm to the calculation of CC2 oscillator strengths. Two different strategies are suggested, in which the size of the XOS is determined based on the excitation energy or the oscillator strength of the targeted transitions. The two strategies are applied to a set of medium-sized organic molecules in order to assess both the accuracy and the computational cost of the methods. The results show that CC2 excitation energies and oscillator strengths can be calculated at a reduced computational cost, provided that the targeted transitions are local compared to the size of the molecule. To illustrate the potential of LoFEx for large molecules, both strategies have been successfully applied to the lowest transition of the bivalirudin molecule (4255 basis functions) and compared with time-dependent density functional theory.

physics.chem-ph↗