Multiconfiguration quasi-degenerate

Multiconfigurational quasi-degenerate perturbation theory (MC-QDPT) [5,6] We have also proposed a multistate multireference perturbation theory, the QDPT with MCSCF reference functions (MC-QDPT). In this PT, state-averaged CASSCF is first performed to set reference functions, and then an elfective Hamiltonian is constructed, which is finally diagonalized to obtain the energies of interest. 

H. Moriyama, H. Tatewaki, Y. Watanabe, and H. Nakano, Molecular spinors suitable for four-component relativistic correlation calculations studies of LaF and LaF using multiconfigurational quasi-degenerate perturbation theory, Int. J. Quantum Chem. 109, 1898 - 1904 (2009). 

Here we will skip the notation details, as the relation established to the Coupled Perturbed frame allow us the shortcut of passing the references to the comprehensive works devoted to the analytic derivatives of molecular energy [9]. The recent advances in the analytic derivatives and Coupled Perturbed equations into multiconfigurational second order quasi-degenerate perturbation theory is the premise of further development in the ab initio approach of vibronic constants of JT effects [10]. 

Our multireference M0Uer-Plesset (MRMP) perturbation method [1-4] and MC-QDPT quasi-degenerate perturbation theory (QDPT) with multiconfiguration self-consistent field reference functions (MC-QDPT) [5,6] are perturbation methods of such a type. Using these perturbation methods, we have clarified electronic stmctures of various systems and demonstrated that they are powerful tools for investigating excitation spectra and potential energy surfaces of chemical reactions [7-10]. In the present section, we review these multireference perturbation methods as well as a method for interpreting the electronic structure in terms of valence-bond resonance structure based on the CASSCF wavefunction. 

Further extension of reference wavefunctions—quasi-degenerate perturbation theory with general-multiconfiguration space self-consistent field reference functions (GMC-QDPT) [36]... 

QDMBPT = quasi-degenerate many-body perturbation theory, (POL-) Cl = (polarization-) configuration interaction, MC SCF = multiconfiguration SCF, CAS SCF = complete active space SCF, MRD Cl = multireference double-excitation Cl, UHF = unrestricted Hartree-Fock, UMP2 = unrestricted Moller-Plesset perturbation method of second order. - An analytical, combined polynomial-exponential form for E(x) with x = (r-rg)/r and a figure for x= —0.98 to +0.04. 

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