Multi-reference generalization

The multi-reference capabilities of ci contrast with the situation in many-body perturbation theory (mbpt) and coupled cluster (cc) theory, for which multi-reference generalizations are substantially more difficult than their... 

In general it is found that GGA methods often give geometries and vibrational frequencies for stable molecules of the same or better quality than MP2, at a computational cost similar to HE For systems containing multi-reference character, where MP2 usually fails badly, DFT methods are often found to generate results of a... 

They showed that the dimerized bond should be considered as a singlet diradical. Therefore, a qualitatively correct description of the dimer requires at least a generalized valence bond, GVB-PP132, or a two configuration self-consistent field (TCSCF)33 wave function. More recently, Paulus29 performed a more exhaustive multi-reference analysis of silicon clusters and reconfirmed this conclusion. 

MOLCAs, like DALTON, is something of an experts code . It is described as a code for the ab initio treatment of very general electronic structure problems for molecular systems in both ground and excited states . It is particularly for electronic structure problems requiring a multi-reference treatment. 

The first-order interacting space restriction is generally used to reduce the number of double substitutions included in single- or multi-reference CISD... 

Most studies limit the Cl space to single and double substitutions from a single reference (CISD). Occasionally, when one reference does not provide a sufficient zeroth-order wavefunction, the multi-reference CISD method will be employed. The applications of such methods are too numerous to discuss here their general performance has already been described in section 2. We consider studies which go beyond CISD for one or a few references such highly correlated wavefunctions are useful when very accurate results are desired or when several electron configurations are needed for a qualitatively correct reference wavefunction (such as when multiple bonds are broken). We will limit our attention to methods which select the Cl space in an a priori fashion based on the distribution of electrons among various orbital subspaces. 

Because of its size-extensivity and faster convergence with respect to excitation level Coupled cluster theory has replaced Cl theory as the dominant approach in ab initio correlation calculations. Like MBPT the theory is still mainly applied in cases where the exact wave function is dominated by a single determinant, but multireference methods have been formulated and begin to enter mainstream quantum chemistry. Generalization of the algorithms to the relativistic no-pair level can again be achieved via the spinorbital formulation of the methods. I will first discuss the single reference method and then consider the Fock space method [40] that uses multi-reference wavefiinctions for ionized or excited states. 

Although the approach described above is presented in its most general form, using a multiple coupled-cluster Ansatz for the SS-MRCC formalism, suitable approxi-mants to it such as the state-specific multi-reference perturbation theory (SS-MRPT) or state-specific multi-reference CEPA (SS-MRCEPA) can be generated by straightforward approximations. Since the new closed component of the wave operator for IMS appear first at the quadratic power, it is evident that the expressions we have derived in this and the earlier papers for the CAS will remain valid if the quadratic powers of are ignored in the approximants to SS-MRCC for IMS. This implies that all the SS-MRPT... 

Before closing this section, the extensions of the SAC/SAC-CI method to the quasi-degenerate and multi-reference cases are described. The first such proposal was made in 1985 as the MR-SAC method, in which the reference function was extended from the Hartee-Fock single-determinant to a general Cl type wave function [34]. Further, based on the consideration on the nature of electron correlations in quasidegenerate situations, a generalization of the exponential operator was made i.e. 

The effects of intruder states are generally more severe for molecules than for atoms, due to more dense energy levels. Therefore, even if there are ways of avoiding - or at least reducing - the effect of intruder states in the multi-reference approach, it is when the interest lies entirely in one or a few particular states, more advantageous to study one state at a time in a state-specific approach. 

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