Perturbation theory quasi-degenerate

Electron correlation was treated by the CIPSI multi-reference perturbation algorithm ([24,25] and refs, therein). The Quasi Degenerate Perturbation Theory (QDPT) version of the method was employed, with symmetrisation of the effective hamiltonian [26], and the Maller-Plesset baricentric (MPB) partition of the C.I. hamiltonian. 

Fig. 9. Comparison between the second-order perturbation theory and quasi-degenerate perturbation theory for the D value of ( 20) +.

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]. 

The convergence of the iterative determination of eigenvalues and eigenvectors is accelerated appreciably if spin-orbit Cl and quasi-degenerate perturbation theory procedures are combined. To this end, the perturbation matrix is set up in the basis of the most important LS contracted Cl vectors Em 1 1). The solutions of this small eigenvalue problem... 

In the basis of precalculated spin-free states of the BO Hamiltonian, SOC and SSC effect could be treated in the most accurate way using quasi-degenerate perturbation theory. This method implies construction and diagonalization of the matrix representations of //B0 + Hsoc + HSsc + Hz. 

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. 

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. 

Extension of reference wavefunctions—quasi-degenerate perturbation theory with quasi-complete active space self-consistent field reference functions (QCAS-QDPT) [35]... 

Quasi-degenerate perturbation theory is implemented in several program packages. The program GAMESS utilizes MCSCF wave functions and the full Breit—Pauli Hamiltonian... 

Fine structure splitting and transition moments for radiative and nonradiative spin-orbit coupling induced processes were calculated by Tatchen et al. for several low-lying singlet and triplet states of 4H-pyran-4-thione (7). The spin-independent properties were calculated by the DFT/MRCI method of Grimme and Waletzke, and the spin-dependent part was included at the level of quasi-degenerate perturbation theory... 

Eq.(9) in a power expansion, thus going back to a Rayleigh-Schrddinger version of the quasi-degenerate perturbation theory (QDPT (ii) use a monoelectronic definition of Ho = (Moller-Plesset definition of the... 

One may use directly the quasi-degenerate perturbation theory, or an iterative algorithm, to solve the Bloch equation, taking the main subspace S... 

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