Wave-function based methods multireference

Our recently developed reduced multireference (RMR) CCSD method [16, 21, 22, 23, 24, 25] represents such a combined approach. In essence, this is a version of the so-called externally corrected CCSD method [26, 27, 28, 29, 30, 31, 32, 33, 34] that uses a low dimensional MR CISD as an external source. Thus, rather than neglecting higher-than-pair cluster amplitudes, as is done in standard CCSD, it uses approximate values for triply and quadruply excited cluster amplitudes that are extracted by the cluster analysis from the MR CISD wave function. The latter is based on a small active space, yet large enough to allow proper dissociation, and thus a proper account of dynamic correlation. It is the objective of this paper to review this approach in more detail and to illustrate its performance on a few examples. 

This problem was intensively studied both experimentally and theoretically. The quantum chemical calculations were carried out using various methods at different levels. The earlier calculations for the Cope reanangement based on a CASSCF wave function for six electrons in the bonds rearranged were found to overestimate the diradical character of the wave funclion- --. More recently, MP2 methods for the multireference wave function have been developed whose application to an estimate of the energy of the chair transition state has been described. AMI calculations of altemative transition states for the Cope rearrangement of 1,5-hexadiene derivatives have been discussed by Dewar and colleagues i -217... 

Finally, it should be pointed out that the perturbation-theoretic methods [25] (MP2, etc.), used with such success for molecules near their equilibrium geometries, are much less satisfactory when used to compute a PES. Obviously, where several reference configurations are required these single-reference treatments cannot be expected to perform well, and it does not seem possible to overcome such problems by the use of unrestricted Hartree-Fock (UHF) methods to define a single reference CSF the UHF PES itself will often display discontinuities from spontaneous symmetry breaking, and this inevitably compromises the subsequent perturbation theory treatment. Recent efforts [26] to devise projected UHF-based schemes may overcome these problems, but this is simply another approach to generating a multireference wave function. 

This is not to say that the CCSD(T) method provides an accurate description of the ground states of all molecules. The coupled cluster method is based on a Hartree-Fock reference wave function and thus will fail when the HF wave function does not provide an adequate zero-order description of the molecule. The development of multireference coupled cluster methods is being actively pursued by several groups. 

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