Complete-active-space self-consistent field CASSCF method

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. 

The major problem with MCSCF methods is selecting the necessary configurations to include for the property of interest. One of the most popular approaches is the Complete Active Space Self-consistent Field (CASSCF) method (also called Full Optimized Reaction Space, FORS). Here the selection of configurations is done by partitioning the MOs into active and inactive spaces. The active MOs will typically be some of the dii rest occupied and some of the lowest unoccupied MOs from a RHF calculationr Fhe-daactive MOs either have 2 or 0 electrons, i.e. always doubly occupied or empty. Within... 

However, a reasonable quantitative treatment for TM systems seems to require a fairly high level of theory. One particularly promising approach has been developed by Roos [28] based on the Complete Active Space Self Consistent Field (CASSCF) method with a second order perturbation treatment of the remaining (dynamical) electron correlation effects, CASPT2. 

Among several types of the MCSCF method, the complete active space self-consistent field (CASSCF) method is commonly used at present. In fact, it has many attractive features (1) applicable to excited state as well as the ground state in a single framework (2) size-consistent (3) well defined on the whole potential energy surface if an appropriate active space is selected. However, CASSCF takes into account only nondynamic electron correlation and not dynamic correlation. The accuracy in the energy such as excitation energy and dissociation energy does not reach the chemical accuracy, that is, within several kcal/mol. A method is necessary which takes into account both the non-dynamic and dynamic correlations for quantitative description. 

In this section, we briefly review the use of the complete active space self-consistent field (CASSCF) method for calculating excited states. This method offers an acceptable compromise between accuracy and computational expense, but our main reason for choosing it is that it offers analytical gradients and second derivatives, which are essential for geometry optimization. As we discuss more fully below, CASSCF is often sufficient if one is interested in structure and mechanism (as we are here), but a more accurate treatment of dynamic electron correlation is often necessary for accurate energetics. 

Our group has already studied all the fluoro-, chloro-and bromo-carbenes [11-16]. We used the complete active space self-consistent field (CASSCF) method as well as complete active space second-order perturbation theory (CASPT2) and multi-reference configuration interaction (MRCI) approaches to compute the geometries, force constants, and vibrational frequencies of the (singlet) X and A states as well as the (triplet) a states. Our theoretical studies of most of these carbenes were carried out specifically to complement LIF studies that were pursued in our laboratories by Kable et al. [6]. In addition to the determination of spectroscopic constants, the spectroscopic and theoretical studies considered dynamics on the A surfaces, i.e. whether photodissociation or internal conversion to the ground state would occur. 

An important issue in MCSCF calculations is the selection of the configurations to be included in the wavefunction expansion. The most popular approach is the complete active space self-consistent field (CASSCF) method, also called full optimized reaction space (FORS). This approach starts Irom a zeroth order set of MOs, usually obtained via the Hartree-Fock method. The set of MOs is split into three subsets, as illustrated in Fig. 2.3. A first one containing occupied inactive orbitals, for which the occupation numbers are fixed to 2. A second one containing active orbitals, including both occupied and virtual orbitals of the reference Hartree-Fock configuration, in which all possible electron excitations are allowed. And a third one containing virtual inactive orbitals, for which the occupation numbers are fixed to 0. 

Further, it is understood that each matrix element consists of the components originating in the pure QM, the est and the vdW contribution. The est components are conveniently computed by the quantum chemical calculation package. For instance, in GAUSSIAN program [25], several approximate methods of electronic state calculations are available, e.g., the Hartree-Fock (HF), second-order Moller-Plesset perturbation theory (MP2), conhguration interaction field (CIS), complete active space self-consistent field (CASSCF) method, and the density functional theory (DFT) methods. On the other hand, since the vdW components are expressed as such analytical functions of the mw Cartesian coordinate variables involved in the same atom (A = B) as follows. 

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