CAS SCF method

This chapter will discuss that Complete Active Space (CAS) SCF method [1, 2] and multiconfigurational second order perturbation theory, CASPT2 [3, 4], The CASSCF method was introduced almost thirty years ago. The aim was to be able to deal with electronic structures that could not be described even qualitatively using a single electronic configuration. 

To make the NEGF-SCF step even more efficient, the restricted MO space idea is proposed. The idea is similar to the scheme of the complete active space (CAS)-SCF method in quantum chemistry [81, 82]. The MOs, whose occupation number should be determined by N EGF-SCF, are the only active MOs, and their energies cover the region dose to EF Vb/2. The inactive MOs, which are core orbitals, are always fully occupied. The MOs of much higher energy than EF are virtual MOs, and their electron occupations are always equal to zero. In typical cases, the applied bias is within a few volts, and the active MOs in the restricted MO space are only about 10% of the MOs in the whole MO space. Note that orbital relaxation is allowed for all MOs because the Hamiltonian is updated. The fixed values in the inactive and virtual MOs are only occupation numbers. 

The complete active space (CAS) SCF method has been reviewed. Current methods for optimization of an MCSCF wavefunction have been discussed with special reference to the CASSCF method. The strength of the method in solving complex electronic structure problems has been illustrated with examples from the current literature. The strength of the method lies in its simplicity. It is a pure orbital method in the sense that the user only has to worry about selecting an appropriate inactive and active orbital space in order to define the wavefunction. That this selection is far from trivial has been illustrated in some of the examples. FH, N2O4 and Ni(C2H4) give different aspects to this problem. 

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. 

The complete active space self-consistent field (CAS SCF) method is a special case of the MC SCF approach and relies on the selection of a set of spinoibitals (usually separated energetically fiom others) and on construction from them of all possible Slater determinants within the MC SCF scheme. Usually, low-energy spinoibitals are inactive during this procedure i.e.. they all occur in each Slater determinant (and are either liozen or allowed to vary). 

The most famous MCSCF method is the complete active-space (CAS) SCF method (Roos et al. 1980), which incorporates all possible excited CSFs in the set of specific valence orbitals. Since the CASSCF method may be the simplest way to take into account the nondynamical electron correlation, this method has been applied to a wide variety of systems from small molecules to biomolecules. However, this method still has various problems e.g., the number of excited CSFs exponentially increases as the size of active space increases, the SCF process is usually converged poorly in comparison with that of the Hartree-Fock calculation, and the electron correlation is ill-balanced due to the insufficient dynamical correlation. 

The studies so far made for this ESHAT employed the ab initio configuration interaction (Cl) and/or complete active space SCF (CAS-SCF) methods and examined only the two lowest coupled potential energy surfaces (and nuclear wavepacket dynamics simplified [228]). However, because of the fact that the relevant excited states are highly quasi-degenerate in reality, and in view of the complicated nature of electron dynamics associated with proton transfer as described above, it is worthwhile to re-examine the mechanism from the nonadiabatic electron wavepacket dynamics. 

J. M. Bofill and P. Pulay, J. Chem, Phys., 90,3637 (1989). The Unrestricted Natural Orbital-Complete Active Space (UNO-CAS) Method An Inexpensive Alternative to the Complete Active Space-Self-Consistent-Field (CAS-SCF) Method. 

Earlier we compared the cost of nonrelativistic and relativistic methods for perturbation and coupled-cluster calculations, and also the cost of transforming the integrals. We now turn to the cost of Cl methods, and consider the case of a full Cl, which is the basis of the complete active space (CAS) SCF method, and of a singles and doubles Cl (SDCI) calculation, which is often used for dynamic correlation from a given active space. 

Complete active space (CAS) SCF methods employ a more complete Cl expansion, incorporating all possible configurations from an active space of N electrons and M... 

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