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arXiv:1011.1482

Comment on "Response calculations with an independent particle system with an exact one-particle density matrix''

Ryan Requist, Oleg Pankratov

Published Nov 5, 2010• 0 citations
arXivHTMLPDF

Abstract

We point out an error in the argument [PRL 105, 013002 (2010)] that the time independence of the occupation numbers in the adiabatic approximation follows from the invariance of the ground-state interaction energy functional with respect to changes in the phases of the natural orbitals.
DOI
10.48550/arxiv.1011.1482

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Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H2 and compare the performance of two different two-electron functionals: the phase-including Löwdin-Shull functional and the density matrix form of the Löwdin-Shull functional.
We use the natural orbitals to define an independent particle system, from which the exact one-particle density matrix can be obtained with an ensemble of degenerate determinantal ground states. Also defining explicit phases for the orbitals, and admitting functionals that are dependent on those phases, time-dependent equations for the orbitals and occupation numbers are obtained from an action principle. The wrong polarizability and lack of double excitations of straightforward adiabatic time-dependent density matrix functional theory are then corrected, and the important symmetry χ(ω)=χ{*}(-ω), lost in previous ad hoc improvements, is restored. The extension of the response calculations beyond the occupied-virtual pairs, which are the only ones admitted in time-dependent density functional theory, leads to greatly improved response properties.