Active-external space correlations

Figure 1. Multireference problems involve both dynamical and nondynamical correlation. The nondynamical correlation is accounted for by the CASCI/CASSCF/DMRG wavefunction, which is made of multiple configurations generated in the active space with a fixed number of active electrons. The dynamical correlation is recovered on top of the multiconfigurational reference by correlating the active orbitals with orbitals in the external space (i.e., core and virtual orbitals.)...

Nondynamic correlation is associated with active-active space correlations, while dynamic correlation is associated with correlations between the active-external and external-external spaces. 

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. 

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