Multiconfigurational reference

Werner H-J, Knowles PJ (1988) An efficient internally contracted multiconfiguration reference Cl method. J Chem Phys 89 5803... 

Figure 1. Multireference problems involve both dynamical and nondynamical correlation. The nondynamical correlation is accounted for by the CASCI/CASSCF/DMRG wavefunction, which is made of multiple configurations generated in the active space with a fixed number of active electrons. The dynamical correlation is recovered on top of the multiconfigurational reference by correlating the active orbitals with orbitals in the external space (i.e., core and virtual orbitals.)...

An important question concerns the relation of the present method with the one using diabatic orbitals. Such methods are implemented in standard ab initio packages such as MOLPRO [27] with emphasis in multiconfiguration-reference Cl and related methods. These methods are based on the particle model. 

HJ.Wemer, Matrix-Formulated Direct Multiconfigurational Self Consistent Field and Multiconfiguration Reference Configuration-Interaction Methods. 

H.-J. Werner, Matrix-Formulated Direct Multiconfiguration Self-Consistent Field and Multiconfiguration Reference Configuration-Interaction Methods, in Ab Initio Methods in Quantum Chemistry - II (K.P. Lawley, ed.), John Wiley Sons Ltd, Chichester (1987). 

H.-J. Werner and P.J. Knowles, An Efficient Internally Contracted Multiconfiguration Reference Configuration Interaction Method, J. Chem. Phys. 89, 5803 (1988). 

Roos BO, Siegbahn PEM (1980) A direct Cl method with a multiconfigurational reference state. Int J Quantum Chem 17 485-500... 

The pure orbital-symmetry-conserved wavefunction has C2 = 0 and a singleconfiguration wavefunction would therefore be an acceptable reference. The pure biradical wavefunction has C2 = -Cj, necessitating a multiconfiguration reference. 

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-... 

An alternative contraction scheme which has received more attention is internally contracted multireference CISD (usually denoted simply CMRCI), which was first discussed by Meyer99 and Siegbahn.100 This method applies the single and double excitation operators to a single multiconfigurational reference wavefunction as a whole, including the reference coefficients. Thus, if the reference wavefunction is... 

MATRIX-FORMULATED DIRECT MULTICONFIGURATION SELF-CONSISTENT FIELD AND MULTICONFIGURATION REFERENCE CONFIGURATION-INTERACTION METHODS... 

III. The Internally Contracted Multiconfiguration Reference Self-consistent... 

Other multiconfiguration reference CI(SD) methods mostly used particular... 

III. THE INTERNALLY CONTRACTED MULTICONFIGURATION REFERENCE SELF-CONSISTENT ELECTRON-PAIR METHOD... 

One of the most powerful tools presently available for accurate electronic structure calculations is the multiconfiguration reference CI(SD) method. In MR-CI(SD) wavefunctions, all configurations that are singly or doubly excited relative to any of the reference eonfigurations are taken into account, and their coefficients are determined variationally. The reference wavefunctions are usually optimized by the MCSCF method. They should properly describe the dissociation of bonds and near-degeneracy effects. If the reference wavefunction includes the most important double excitations from the... 

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). 

Werner H-J. Matrix-formulated direct multiconfiguration self-consistent field and multiconfiguration reference configuration-interaction methods. Adv Chem Phys 1987 69 1-62. 

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. 

Jergensen (for excitation energies) that employs a multiconfigurational reference state within an RPA-type approximation. 

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... 

The situation is much more complicated if to 1 order a single Slater determinant is not sufficient and rather a multiconfiguration reference must be used. A completely satisfactory coupled-cluster theory for this case has not yet been formulated. This has both fundamental and practical reasons. 

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