Multiconfiguration self-consistent field systems

The computational model capable of yielding accurate spin-spin coupling constants is the multiconfigurational self-consistent field (MCSCF) model, and before the advent of density functional theory, spin-spin coupling constants in small systems were often... 

Nondynamical electron correlation effects are generally important for reaction path calculations, when chemical bonds are broken and new bonds are formed. The multiconfiguration self-consistent field (MCSCF) method provides the appropriate description of these effects [25], In the last decade, the complete active space self-consistent field (CASSCF) method [26] has become the most widely employed MCSCF method. In the CASSCF method, a full configuration interaction (Cl) calculation is performed within a limited orbital space, the so-called active space. Thus all near degeneracy (nondynamical electron correlation) effects and orbital relaxation effects within the active space are treated at the variational level. A full-valence active space CASSCF calculation is expected to yield a qualitatively reliable description of excited-state PE surfaces. For larger systems, however, a full-valence active space CASSCF calculation quickly becomes intractable. 

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

In the following we give a short summary of the applications of multiconfigurational self-consistent field classical mechanics response method based on the work by Poulsen and co-workers [15-17], The investigated QM/CM system is represented as a sample of 128 H20 molecules, one of which is selected as the quantum mechanical subsystem while the remaining 127 H20 molecules represent the classical subsystem. 

Also in response theory the summation over excited states is effectively replaced by solving a system of linear equations. Spin-orbit matrix elements are obtained from linear response functions, whereas quadratic response functions can most elegantly be utilized to compute spin-forbidden radiative transition probabilities. We refrain from going into details here, because an excellent review on this subject has been published by Agren et al.118 While these authors focus on response theory and its application in the framework of Cl and multiconfiguration self-consistent field (MCSCF) procedures, an analogous scheme using coupled-cluster electronic structure methods was presented lately by Christiansen et al.124... 

A structured environment model given by the multiconfigurational self-consistent field response theory for the quantum mechanical-classical system model 376... 

We start out with a section on the energy functionals and Hamiltonians that are relevant for molecular systems interacting with a structured environment. We continue with a section that briefly describes the correlated electron structure method, the multiconfigurational self-consistent field (MCSCF) electronic structure method. In the following section we cover the procedure for obtaining the correlated MCSCF response equations for the two different models describing molecules in structured environments. The final sections provide a brief overview of the results obtained using the two methods and a conclusion. 

The computationally viable description of electron correlation for stationary state molecular systems has been the subject of considerable research in the past two decades. A recent review1 gives a historical perspective on the developments in the field of quantum chemistry. The predominant methods for the description of electron correlation have been configuration interactions (Cl) and perturbation theory (PT) more recently, the variant of Cl involving reoptimization of the molecular orbitals [i.e., multiconfiguration self-consistent field (MCSCF)] has received much attention.1 As is reasonable to expect, neither Cl nor PT is wholly satisfactory a possible alternative is the use of cluster operators, in the electron excitations, to describe the correlation.2-3... 

The generalization of the HF methods toward degenerate or nearly degenerate systems is known as multiconfigurational self-consistent field (MCSCF). In this method, the MCSCF wavefunction is initially expanded in a set of many particle basis functions (Slater determinants or CSFs) [65],... 

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. 

In the multiconfigurational self-consistent field (MC SCF) method, as in Cl, it is up to us to decide which set of determinants we consider sufficient for the description of the system. 

As the next standard model of quantum chemisUy, we consider here the generalization of the Hartree-Fock wave function to systems dominated by more than one electronic configuration the multiconfigurational self-consistent field (MCSCF) wave function. This flexible model may be useful for describing the electronic structure of bonded molecular systems, in particular for excited states. Perhaps more important, however, is its ability to describe bond breakings and molecular dissociation processes. 

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