Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory

Abstract

The symmetry-adapted-cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry-adapted excited configurations having the symmetry under consideration, and includes their higher-order effect and self-consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open-shell systems as well as closed-shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher-order effect and the self-consistency effect. We have expressed some existing open-shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo-orbital theory which is an extension of open-shell orbital theory in the SAC expansion formula.

Electronic spectra of linear HC5H and cumulene carbene H2C5

“…Adiabatic excitation energies have been computed for selected electronic states using MS(4)-CASPT2 (10/10). In addition, electronic transitions were predicted with the symmetry adapted cluster/configuration interaction (SAC-CI) method 33,34 and the ccpVTZ basis set of Gaussian09. Vibrational progressions of chosen C 5 H 2 transitions and the rotational profile of linear HC 5 H were simulated using the PGOPHER program.…”

The low-lying excited states of neutral polyacenes and their radical cations: a quantum chemical study employing the algebraic diagrammatic construction scheme of second order

“…Today, several excited state methods are already available for the investigation of large molecules, among which time-dependent density functional theory (TDDFT) [3][4][5] is by far the most widely used. Complete active-space self-consistent field (CASSCF) methods [6,7], symmetry-adapted cluster configuration interaction (SAC-CI) [8] and also approximate linear-response coupled-cluster theory of second order (RI-CC2) [9][10][11][12] are powerful wavefunction-based approaches. Nevertheless, all existing methods possess individual weaknesses and drawbacks [1,2].…”

Selected configuration interaction with truncation energy error and application to the Ne atom

“…The same may be said about the selection process in CI methods based on the symmetryadapted-cluster expansion, generically called SAC/SAC-CI methods. [9][10][11]91 Multireference CI ͑Refs. 92-96͒ continues to be actively developed.…”

“…Full CI, on the other hand, is the central referent of all orbital methods based on Hamiltonians obtained from the first principles: 6,7 highly correlated CI ͑HCCI͒, 8 symmetry-adapted-cluster 9 ͑SAC͒ and SAC-CI, [10][11][12] sizeconsistent CI, 13 coupled cluster ͑CC͒ methods, 14,15 many-is varied between R e and 3R e with R e Ϸ 1.843 45 a.u. show that in order to compete with CCSDT, a CISDTQ treatment is adequate CISDTQ Ϸ CCSDT.…”