Use of unrestricted hartree-fock wave functions in RPA calculations

Jordan, Kenneth D.

doi:10.1002/qua.560070756

Cited by 13 publications

(3 citation statements)

References 22 publications

(7 reference statements)

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“…Since, however, the HF wave function approximates the ground-state wave function in TDHF, the de-excitation violates the Pauli exclusion principle and thus there exists an incompatibility between the wave function and the excitation operator in TDHF. Indeed, the HF ground state is often triplet unstable or yields very poor triplet excitation energies as compared to its singlet excitations [21][22][23][24][25]. In order to remedy this deficiency higher order RPA (HRPA) methods have been propsed in which the RPA ground state is the sum of the Hartree-Fock ground state and doubly excited …”

Section: Overview Of Rpa Methods Including Exchange Interactionsmentioning

confidence: 99%

Random-phase approximation correlation methods for molecules and solids

2011

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Section: Overview Of Rpa Methods Including Exchange Interactionsmentioning

confidence: 99%

Random-phase approximation correlation methods for molecules and solids

2011

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“…68 Along similar lines, it has been appreciated for a long time that TDHF specifically is prone to triplet instabilities. 90,91,[118][119][120][121][122][123][124] In fact, the appearance of imaginary excitation energies at equilibrium geometries of small molecules led Furche and Ahlrichs to conclude that this method is "rather useless. .…”

Section: Tamm-dancoff Approximationmentioning

confidence: 99%

Density Functional Theory for Electronic Excited States

Herbert¹

2022

Preprint

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This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the Kohn-Sham DFT ground state, linear-response theory affords an eigenvaluetype problem for the excitation energies in a basis of singly-excited Slater determinants, and is widely known simply as "TDDFT" despite its frequency-domain formulation. This form of TDDFT is the mostly widely-used quantum-chemical method for excited states, due to a favorable combination of low cost and reasonable accuracy. The chapter surveys the accuracy of linear-response TDDFT, which is generally more sensitive to the details of the exchange-correlation functional as compared to ground-state DFT, and also describes some known systemic problems exhibited by this approach. Some of those problems can be corrected on a case-by-case basis using orbital-optimized, excited-state self-consistent field (SCF) calculations, in what is known as excited-state Kohn-Sham theory or a "∆SCF" procedure, a class of methods that includes restricted open-shell Kohn-Sham theory. Recent successes of these approaches are highlighted, including double excitations and core-level excitations. Finally, explicitly time-dependent (or "real-time") TDDFT involves propagation of the molecular orbitals in time following an external perturbation, according to the Kohn-Sham analogue of the time-dependent Schrödinger equation. The time-dependent approach has been used to model strong-field electron dynamics, and in the weak-field limit it provides a route to broadband spectra based on the time evolution of the dipole moment function. This is useful for describing high-energy excitations (as in x-ray spectroscopy) and in systems where the density of states is high, as demonstrated by a few examples.

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“…[90][91][92] Namely, the condition that 1 Y 1 X T = − 3 Y 3 X T , which arises from the condition that the wave function is an eigenfunction of the spin-squared operator S 2 with eigenvalue zero, is not fulfilled. 47 Because of this triplet excitation energies, in contrast to singlet excitation energies, within the NRPA (timedependent Hartree-Fock) are often poor [93][94][95][96] and it has been stated by Chambaud et al that in fact triplet instabilities occur in any π -electronic system like ethylene or benzene. 97 While one possibility to overcome this deficiency is to use higher-order RPA approaches 45,47,[55][56][57][58][59][60][61] …”

Section: Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

The Journal of Chemical Physics

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Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle−hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.

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Use of unrestricted hartree-fock wave functions in RPA calculations

Cited by 13 publications

References 22 publications

Random-phase approximation correlation methods for molecules and solids

Random-phase approximation correlation methods for molecules and solids

Density Functional Theory for Electronic Excited States

Third-order corrections to random-phase approximation correlation energies

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