Finite-size effects in response functions of molecular systems

Dupuy, Mi-Song; Levitt, Antoine

doi:10.5802/smai-jcm.87

Cited by 2 publications

(1 citation statement)

References 32 publications

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“…the atomic and molecular Hamiltonians), the spectrum is divided into discrete and continuous parts [30]. In some special cases, and for suitable f and g, the regularity of the map ω → g, χ H (ω)f along the continuous spectrum can be rigorously studied (see [16]) via the celebrated limiting absorption principle [3,17].…”

Section: Remark (Regularity Of χ H Along the Continuous Spectrum)mentioning

confidence: 99%

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

Corso

2024

Nonlinearity

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In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this setting, we derive a representation formula for the solution of the Dyson equation in terms of an operator version of the Casida matrix. While the Casida matrix is well-known in the physics literature, its general formulation as an (unbounded) operator in the N-body wavefunction space appears to be new. Moreover, we derive several consequences of the solution formula obtained here; in particular, we discuss the stability of the solution and characterise the maximal meromorphic extension of its Fourier transform. We then show that for adiabatic approximations satisfying a suitable compactness condition, the maximal domains of meromorphic continuation of the initial DDRF and the solution of the Dyson equation are the same. The results derived here apply to widely used adiabatic approximations such as (but not limited to) the random phase approximation and the adiabatic local density approximation. In particular, these results show that neither of these approximations can shift the ionisation threshold of the Kohn–Sham system.

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Section: Remark (Regularity Of χ H Along the Continuous Spectrum)mentioning

confidence: 99%

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

Corso

2024

Nonlinearity

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Computing photoionization spectra in Gaussian basis sets

Duchemin,

Levitt

2023

The Journal of Chemical Physics

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We present a method to compute the photoionization spectra of atoms and molecules in linear-response, time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set of delocalized functions, obtained as the solution of the inhomogeneous Helmholtz equation, with gaussian basis set functions as the right-hand side. The resulting scheme is able to reproduce the photoionization spectra without any need for artificial regularization or localization. We demonstrate that this Green’s function-based approach is able to produce accurate spectra for semilocal exchange-correlation functionals, even using relatively small standard gaussian basis sets.

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Finite-size effects in response functions of molecular systems

Cited by 2 publications

References 32 publications

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

Computing photoionization spectra in Gaussian basis sets

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