SDTQ-CI expansions

Since the triply and quadruply excited configurations are truncated separately, it is usually possible to shorten the Cl expansion somewhat further, if this should be desirable, by applying the procedure described in Section 2.3 to the total calculated truncated SDTQ-CI wavefunction obtained as described in this section. Thus, for the SDTQ[ 18/18] wavefunction of NCCN, an accuracy of 1 mh is achieved with 49,033 determinants by the estimation method, and with 43,038 determinants by the just mentioned additional improvement, reducing the truncation from 6.32% to 5.54% of the 776,316 determinants of the full SDTQ-CI expansion. 

Figure 2. Rate of convergence of truncated SDTQ-CI expansions based on a priori a posteriori ordering and error assessment. Filled circles Truncations based on anticipated a priori estimates. Open circles Truncations determined a posteriori from the full wavefunctions.

The final step is the orbital optimization for the truncated SDTQ-CI expansion. We used the Jacobi-rotation-based MCSCF method of Ivanic and Ruedenberg (55) for that purpose. Table 1 contains the results for the FORS 1 and FORS2 wavefiinctions of HNO and NCCN, obtained using cc-pVTZ basis sets (51). In all cases, the configurations were based on split-localized orbitals. For each case, four energies are listed corresponding to (i) whether the full or the truncated SDTQ-CI expansion was used and (ii) whether the split-localized orbitals were those deduced from the SD naturals orbitals or were eventually MCSCF optimized. It is seen that... 

A two-pronged approach has been discussed for dealing with electron correlation in large systems (i) An extension of zeroth-order full-valence type MCSCF calculations to larger systems by radical a priori truncations of SDTQ-CI expansions based on split-localized orbitals in the valence space and (ii) the recovery of the remaining dynamic correlation by means of a theoretically-based simple semi-empirical formula. 

Figure 1. Rate of convergence of SDTQ-CI truncated expansions for FORS1 and FORS2 active spaces for HNO and NCCN molecules (a) Open-circles correspond to Cl configurations generated from SD-CI natural orbitals ...

Next, SDTQ-CI calculations are performed for a few truncated quadruple expansions with quadruple truncation degrees in the expected range (around 10% of all quadruple space products). Furthermore, using our estimation formula (2.6), the quadruple normalization deficiencies of these wavefimctions relative to the full SDTQ wavefiinction are readily estimated as... 

Use of a complete set of CSFs in the expansion (7) is referred to as the complete or full configuration interaction (FCI). Since FCI calculations are computationally very demanding, they are only feasible for small orbital sets and a small number of electrons. In chemical applications of the Cl method we are therefore confined to considerably smaller expansions. Standard levels of the Cl method are termed according to the extent of the Cl expansion CI-S, CI-SD, CI-SDT, and CI-SDTQ correspond to expansions through singly, doubly, triply, and quadruply excited CSFs, respectively. 

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