Multiconfigurational second-order development

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]. 

Applications of the complete active space (CAS) SCF method and multiconfigurational second-order perturbation theory (CASPT2) in electronic spectroscopy are reviewed. The CASSCF/CASPT2 method was developed five to seven years ago and the first applications in spectroscopy were performed in 1991. Since then, about 100 molecular systems have been studied. Most of the applications have been to organic molecules and to transition metal compounds. The overall accuracy of the approach is better than 0.3 eV for excitation energies except in a few cases, where the CASSCF reference function does not characterize the electronic state with sufficient accuracy. 

Coupling of quantum mechanical molecular subsystems with larger classically treated subsystems has traditionally involved electronic structure models describing molecules embedded in a dielectric medium and this is a research area that has expanded tremendously over the last three decades [2-36]. Most of this work has involved electronic structure methods that have been based on uncorrelated electronic structure methods [2-12,15-19]. Accurate description of the electronic structure of molecular systems requires that the correlated electronic motion in the molecule is incorporated and therefore a number of correlated electronic structure methods have been developed such as the second order Moller-Plesset (MP2) [28,30,90,91], the multiconfigurational self-consistent reaction field (MCSCRF) [13,20] and the coupled-cluster self-consistent reaction field (CCSCRF) method [36]. 

The perturbational framework designated as MCPT has been developed in two variants the original formulation, hereafter called projected-MCPT [22] (p-MCPT) and a version which can give size-consistent correction at second order, hereafter called unprojected-MCPT [23] (u-MCPT). Both variants start with a multiconfiguration... 

The most popular way of including dynamic correlation upon a CASSCF reference wave function [54-57] is the second-order perturbation theory (CASPT2) developed by Roos and coworkers [58]. However, in contrast to the single-configurational case, where the definition of the zeroth-order Hamiltonian is universal and taken as the sum of the one-electron Fock operators, the generalization of the zeroth-order Hamiltonian to the multiconfigurational case is not straightforward [59, 60]. A different, theoretically more justified approach is to... 

Most of the theory in the present chapter is concerned with perturbational corrections to states that are dominated by a single electronic configuration, usually represented by a Hartree-Fock wave function. However, in Section 14.7, we consider multiconfigurational generalizations of Mpller-Plesset perturbation theory, in particular the second-order perturbation theory developed within the framework of CASSCF theory. 

The present contribution concerns an outline of the response tlieory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields and it gives an overview of the theoretical developments presented in the work by Poulsen et al. [7, 8, 9], The multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response method has been developed to include third order molecular properties [7, 8, 9], This contribution contains a section that describes the establisment of the energy functional for the situation where a multiconfigurational self-consistent field electronic structure method is coupled to a classical molecular mechanics field. The second section provides the necessary background for forming the fundamental equations within response theory. The third and fourth sections present the linear and quadratic, respectively, response equations for the MCSCF/MM response method. The fifth 283... 

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