Multiconfiguration reference function

One can further try to formulate a generalization of CEPA or rather CPF to a multiconfiguration reference function. On these lines the average coupled pair functional (ACPF) has been derived by Gdanitz and Ahlrichs [157]. A straightforward MC-CEPA method has been proposed by Fink and Staeramler [158]. This is extensive, while ACPF is only approximatively so. 

Multiconfigurational reference functions, m > 1 in number, constitute the starting point of our approximation. Vectors of Sect. 2 are associated with these... 

Nakano H (1993) Quasidegenerate perturbation theory with multiconfigurational self-consistent-field reference functions. J Chem Phys 99 7983... 

Multiconfigurational Self-Consistent-Field Reference Functions. 

These single reference-based methods are limited to cases where the reference function can be written as a single determinant. This is most often not the case and it is then necessary to use a multiconfigurational approach. Multrreference Cl can possibly be used, but this method is only approximately size extensive, which may lead to large errors unless an extended reference space is used. For example, Osanai et al. [8] obtained for the excitation energy in Mn 2.24 eV with the QCISD(T) method while SDCI with cluster corrections gave 2.64 eV. Extended basis sets were used. The experimental value is 2.15 eV. 

As a first application of a new analytical gradient method employing UHF reference functions, seven different methods for inclusion of correlation effects were employed to optimize the geometry and calculate the harmonic vibrational frequencies and dipole moments of the lowest open-shell states for three simple hydrides including 3Z i SiH2228. As the degree of correlation correction increased, results approached those from the best multiconfiguration SCF calculation. 

The present trend in calculations with correlated wave functions is to include higher than double excitations. Feasibility of CEPA calculations and their success in chemical applications belong certainly to factors which benefited development in this direction. Explicit inclusion of certain contributions due to quadruple excitations, viz, those that are due to disconnected wave function clusters of double excitations, becomes now free of complications also in MB-RSPT through fourth order. It is therefore every reason to expect that, besides Cl-SD and CEPA, MB-RSPT will soon become a method commonly used in chemical applications, A fourth order MB-RSPT approach outlined in Section 4.0. disregards triple excitations, which, however, are hardly amenable to any existing effective method. Another topical problem is a possible extension of MB-RSPT, so that it would permit convenient treatment of the correlation problem for the multiconfiguration reference state. This is difficult with MB-RSPT, but the problem is tract-... 

The doubly excited configurations in Eq. (121) are obtained by applying two-electron excitation operators to the complete reference function 4 o- If Tq is a multiconfiguration wavefunction we can write... 

A simple way to implement n-particle space truncation is to use the uncorrelated wave function (which as noted above is a very substantial fraction of the exact wave function) to classify terms in the n-particle space. If we consider the Hartree-Fock determinant, for example, we can construct all CSFs in the full n-particle space by successively exciting one, two,.., electrons from the occupied Hartree-Fock MOs to unoccupied MOs. For cases in which a multiconfigurational zeroth-order wave function is required, the same formal classification can be applied. Since only singly and doubly excited CSFs can interact with the zeroth-order wave func tion via the Hamiltonian in Eq. (1), it is natural to truncate the n-particle expansion at this level, at least as a first approximation. We thus obtain single and double excitations from Hartree-Fock (denoted SDCI) or its multiconfigurational reference analog, multireference Cl (MRCI). 

A. Banerjee, R. Shepard and J. Simons, One-particle Green s function with multiconfiguration reference states, Int. J. Quantum Chem. Quantum Chem. Symp., 12 (1978) 389. 

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. 

Multiconfigurational quasi-degenerate perturbation theory (MC-QDPT) [5,6] We have also proposed a multistate multireference perturbation theory, the QDPT with MCSCF reference functions (MC-QDPT). In this PT, state-averaged CASSCF is first performed to set reference functions, and then an elfective Hamiltonian is constructed, which is finally diagonalized to obtain the energies of interest. 

Further extension of reference wavefunctions—quasi-degenerate perturbation theory with general-multiconfiguration space self-consistent field reference functions (GMC-QDPT) [36]... 

We conclude from this little exercise that the electronic stmcture of ozone is clearly multiconfigurational. It will be difficult to treat it using methods based on a HF reference function (like CC or DFT). 

Dalgaard E and J0rgensen P 1978 Optimization of orbitals for multiconfigurational reference states J. Chem. Phys. 69 3833-44 Jensen H J Aa, J0rgensen P and A gren H 1987 Efficient optimization of large scale MCSCF wave functions with a restricted step algorithm J. Chem. Phys. 87 451-66... 

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. 

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