Multiconfigurational self-consistent field, MCSCF

The multiconfigurational self-consistent field ( MCSCF) method in whiehthe expeetation value < T H T>/< T T>is treated variationally and simultaneously made stationary with respeet to variations in the Ci and Cy,i eoeffieients subjeet to the eonstraints that the spin-orbitals and the full N-eleetron waveflmetion remain normalized ... 

MRCI (multireference configuration interaction) a correlated ah initio method multiconfigurational self-consistent field (MCSCF) a correlated ah initio method... 

Multiconfiguration self-consistent field (MCSCF) theory aims to optimize simultaneously the LCAO coefficients and the Cl expansion coefficients in a wavefunction such as... 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

In the mid-nineties more highly correlated methods such as CCSD and QCISD became available through distribution of the ACES and Gaussian 94 programs. Geometry optimization with these more cpu intensive programs was restricted for the most part to six heavy atoms. About this time multiconfigurational self-consistent-field (MCSCF) or... 

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. 

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... 

The method is referred to simply as GMCSC when a fixed basis set is used. In this case, it can be viewed as a non-orthogonal variant of the Multiconfiguration Self-Consistent Field (MCSCF) approach. However, GMCSC s methodological roots are firmly planted in the Modem VB camp, and more specifically in the late Joe Gerratt s Spin-Coupled theory [3]-[4]. 

Pioneering theoretical work on the formaldehyde -I- OH reaction has been reported by Dupuis and Lester [102] using multiconfiguration self-consistent-field (MCSCF) and configuration interaction (Cl) wave functions. These authors [102] predicted a large positive activation barrier of 5.5 kcal/mol. Using the ab initio Moller-Plesset method up to fourth order (MP4), Francisco [103] determine the barriers and energetic of this reaction. He obtained a small but positive barrier of... 

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 adiabatic potential energy curves for these electronic states calculated in the Born-Oppenhelmer approximation, are given in Figure 1. Since we have discussed the choice of basis functions and the choice of configurations for these multiconfiguration self-consistent field (MCSCF) computations (12) previously (] - ), we shall not explore these questions in any detail here. Suffice it to say that the basis set for Li describes the lowest 2s and 2p states of the Li atom at essentially the Hartree-Fock level of accuracy, and includes a set of crudely optimized d functions to accommodate molecular polarization effects. The basis set we employed for calculations involving Na is somewhat less well optimized than is the Li basis in particular, so molecular orbitals are not as well described for Na2 (relatively speaking) as they are for LI2. 

Several theoretical studies of diazirinyl radicals have been undertaken. Multiconfiguration self-consistent field (MCSCF) calculations have been used to investigate the stability of, and isomerization between, the diazirinyl anion 6 and the open-chain biradical anion 7 (Scheme 1) <1995JPC6548>. Dimerization of aryldiazirinyl radicals has been explored by computational and experimental methods <2004PCCP756>. Both approaches support the predominance of the N-N dimer 9 over the isomeric C-N form 8. Furthermore, bimolecular dimer decomposition was shown to be considerably more favorable than the alternative unimolecular pathways. 

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