MRCI-CASSCF

The notation for denoting this type of calculation is sometimes more specihc. For example, the acronym MCSCF+1+2 means that the calculation is a MRCI calculation with single and double Cl excitations out of an MCSCF reference space. Likewise, CASSCF+1+2 and GVB+1+2 calculations are possible. 

Just as single reference Cl can be extended to MRCI, it is also possible to use perturbation methods with a multi-detenninant reference wave function. Formulating MR-MBPT methods, however, is not straightforward. The main problem here is similar to that of ROMP methods, the choice of the unperturbed Hamilton operator. Several different choices are possible, which will give different answers when the tlieory is carried out only to low order. Nevertheless, there are now several different implementations of MP2 type expansions based on a CASSCF reference, denoted CASMP2 or CASPT2. Experience of their performance is still somewhat limited. 

CASSCF [138] CASPT2 [138] CASPT2 [143] CASPT2 [164] CASPT2 [141] MCQDPT [264] MRCI [210] CIPSI[219]... 

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

Table 5.2 shows the N2 dissociation energy obtained with a sequence of ANO basis sets at the MRCI level [68]. We should note that all ten valence electrons are correlated in these calculations, which are based on a six-electron six active orbital CASSCF reference. 

It is essential to use selection of reference configurations in the MRCI procedure with the larger basis set, as the MRCI(CAS) calculation would involve several million CSFs. The result labelled Valence(0.025) is obtained with only the valence configurations — that is, it is the MRCI(0.025) wave function with all excitations to the virtual orbitals omitted. This wave function will be considerably smaller than the CASSCF wave function, but if we are to describe the nondynamical correlation acceptably it should produce similar results. This is one reason for not using a selection threshold of (0.05) the Valence(0.05) binding energy was found to be quite different from the CASSCF value [74]. 

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