Paired-excitation MCSCF

The second possible contraction scheme was first proposed by Meyer , and discussed in the context of the direct Cl method by Siegbahn ". In this case all configurations which have the same external but different internal parts are contracted, and the scheme is therefore called the internal contraction. The internally contracted configurations are generated by applying pair excitation operators to the complete MCSCF reference function. Therefore, the number of contracted configurations and variational parameters is independent of the number of reference configurations. It only depends on the number of correlated internal orbitals and the size of the basis set. ... 

Amos [354] has used pair replacement MCSCF wave function to calculate electric dipole polarizability and polarizability derivatives for HF. Double excitations from the single determinant (Hartree-Fock) wave functions from the valence orbital is used. The MCSCF calculations yielded the following values for the mean polarizability and polarizability anisotropy (in units of A )... 

The lowest A, excited states of C3H2are of Rydberg type, arising from the promotion of one electron from the carbene lone pair orbital to 3s and 3p Rydberg orbitals, are better represented by orbitals generated by a MCSCF/SD treatment (Table 9). 

However, when this is done the HF orbitals are no longer the best orbitals for the new physical situation, with (partially) correlated electron pairs. Accordingly, the occupied orbitals should be reoptimized, which corresponds to a new mixing with the virtual (unoccupied) orbitals. This is done in a MCSCF method, but not in methods such as MP that describe Just dynamic electron correlation. Instead, single (S) excitations f are mixed (via D excitations) into the wavefunction these describe orbital relaxation effects, i.e., the orbitals are partially readjusted to accommodate correlated electron pairs. S excitations cannot compensate for an orbital reoptimization within a MCSCF calculation, however they represent an useful orbital relaxation correction, which compared to pair correlation effects is considerably smaller. 

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