Multireference single- and double-excitation

Modular FORTRAN programs for performing general ab initio multireference single- and double-excitation configuration interaction, averaged coupled-pair functional and linearized couple-cluster method calculations. Cray and other versions. 

MR-AQCC multireference averaged quadratic coupled-cluster MRCI multireference configuration interaction MRD-CI multireference single and double excitation Cl... 

Keywords Configuration interaction (Cl) Full Cl Multireference single- and double-excitation Cl (MRD-CI) Condon rules Slater determinants Table Cl Direct Cl Spin-orbit couphng... 

Since its introduction by Buenker and Peyerimhoff in 1974 [8, 9], the multireference single- and double-excitation... 

Estimated limits based on large uncontracted even-tempered Gaussian calculations. The Cl results for oxygen are based on the estimated full Cl energy derived from large multireference single- and double-excitation calculations. 

The calculations are CASSCF/multireference single and double excitation Cl (MRCI). The use of the MRCI method for computing potential energy surfaces is supported by full Cl studies as discussed by Bauschlicher, Langhoff, and Taylor in another article in this volume. The accuracy of this approach has also been demonstrated for reaction (2) by Walch [2], who showed that by systematically expanding the active space and basis set, the computed barrier height converged to the currently accepted value [14]. 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

MRCISD Multireference Cl including single and double excitations... 

In practice, one often has to restrict the active space to include only a few of the highest occupied and lowest unoccupied molecular orbitals. The correlation effects not included in the CASSCF calculation can then be recovered by a multireference Cl (MRCI) calculation, in which all single and double excitations from the CASSCF reference are taken into account [27], A computationally more efficient way of including dynamical electron correlation effects is perturbation theory with respect to the CASSCF reference. The most widely employed method of this type is the CASPT2 method developed by Roos and collaborators [28], The CASSCF and CASPT2 methods have been essential tools for the calculations described in this contribution. 

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... 

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). 

Multireference State-Specific Coupled Cluster Theory with Complete Account of Single and Double Excitations The CASCCSD Method... 

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