Higher Random-Phase Approximation as an Approximation to the Equations of Motion

Self Cite

To explain the inelastic feature at 4.5 eV in the spectrum of water and to study its spectrum in some detail, we have carried out several calculations on the excited states of water using the equations-of-motion method. We conclude that the calculated vertical excitation energy of 6.9 eV for the 3 B 1 state corresponds to the strong feature at 7.2 eV observed in low-energy electron scattering spectrum. The 4.5 eV inelastic process almost certainly does not correspond to a vertical excitation of water at the ground state geometry. The other excitation energies and oscillator strengths agree well with experiment.

Section: Discussionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 82%

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Assignments in the electronic spectrum of water

Yeager

McKoy

Segal

1974

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“…II it will be shown that the extraction of the correlation energy from the RPA is by far not unique and a number of RPA methods were developed that are exact in second order of perturbation theory, but differ in third-order. We here refer to these methods as "normal" RPA (NRPA) methods 46,55 in order to point out the difference to so called higher RPA methods 45,47,[55][56][57][58][59][60][61] (like SOPPA, second-order polarisation propagator approximation 47,62 ) in which the wave function that enters the RPA equations also contains double excitations.…”

Section: Introductionmentioning

confidence: 99%

Third-order corrections to random-phase approximation correlation energies

Heßelmann

2011

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.

“…These results are useful in explaining the appearance and ordering of states obtained in the direct open-shell SCF calculations. 4 We write the correlated ground-state wavefunction, I 0), as I 0)= 1Voee I HF);…”

Section: Introductionmentioning

confidence: 99%

Application of the RPA and Higher RPA to the V and T States of Ethylene

Shibuya

McKoy

1971

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We have applied our proposed higher random-phase approximation (HRPA) to the T and V states of ethylene. In the HRPA, unlike the RPA, one solves for the excitation frequencies and the ground-state correlations self-consistently. We also develop a simplified scheme (SHRPA) for solving the equations of the HRPA, using only molecular integrals sufficient for the usual RPA calculations. The HRPA removes the triplet instability which often occurs in the RPA. The excitation energy for the N-->T transition is now in good agreement with experiment. The N-->V transition energy increases by IS% over its RPA value. TheN--> V oscillator strength changes only very slightly. These results are also useful in explaining the appearance and ordering of states obtained in recent direct open-shell SCF calculations.