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

Abstract

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.

Multireference many-body perturbation theory

“…The proper comparison is with the basis set limit result, rather than experiment, since using a small basis set can result in poor reproduction of the experimental results even for high-quality correlated calculations. On the other hand the results obtained from the other advanced calculations i.e., higher WA [22] and the EOM-CC theory [4] point out that the correct value for this basis might be about 9 eV for the singlet in poor agreement with experiment. On the other hand the CCSDT-1 result is likely to be equivalent to the full CI (basis set limit) for the triplet [26,27], and for this state the agreement with experiment is good.…”

Third-order corrections to random-phase approximation correlation energies

“…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] …”

“…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.…”

Orbital nature in the electronic states of cyclopropene

“…The physical nature of the orbitals in the excited states of ethylene has recently been the subject of close scrutiny [6][7][8][9][10][11][12][13]. Attention is centred on the nature of the orbitals in the spectroscopic V state of ethylene which, from the earliest days of quantum mechanics, has been identified with the 1(7r, ~r*) spin-orbital electronic configuration.…”