Nonparallelity errors

Figures 7 and 8 plot deviations of total energies from FCI results for the various methods. It is clear that the CASSCF/L-CTD theory performs best out of all the methods smdied. (We recall that although the canonical transformation operator exp A does not explicitly include single excitations, the main effects are already included via the orbital relaxation in the CASSCF reference.) The absolute error of the CASSCF/L-CTD theory at equilibrium—1.57 mS (6-31G), 2.26 m j (cc-pVDZ)—is slightly better than that of CCSD theory—1.66m j (6-31G), 3.84 m j (cc-pVDZ) but unlike for the CCSD and CCSDT theories, the CASSCF/L-CTD error stays quite constant as the molecule is pulled apart while the CC theories exhibit a nonphysical turnover and a qualitatively incorrect dissociation curve. The largest error for the CASSCF/L-CTD method occurs at the intermediate bond distance of 1.8/ with an error of —2.34m (6-3IG), —2.42 mE j (cc-pVDZ). Although the MRMP curve is qualitatively correct, it is not quantitatively correct especially in the equilibrium region, with an error of 6.79 mEfi (6-3IG), 14.78 mEk (cc-pVDZ). One measure of the quality of a dissociation curve is the nonparallelity error (NPE), the absolute difference between the maximum and minimum deviations from the FCI energy. For MRMP the NPE is 4mE (6-3IG), 9mE, (cc-pVDZ), whereas for CASSCF/ L-CTD the NPE is 5 mE , (6-3IG), 6 mE , (cc-pVDZ), showing that the CASSCF/L-CTD provides a quantitative description of the bond breaking with a nonparallelity error competitive with that of MRMP.

Comparing the different methods we see once again that the CASSCF/L-CTD method yields the most accurate description of the potential energy curve out of aU the theories. The error at equilibrium (5.99 mEh) is better than that of CCSD (11.03 mEh) and once again this error stays roughly constant across the curve, while that of the CC-based approaches exhibit a nonphysical turnover. For comparison, the MRMP error at equilibrium is 15.41 mEh. The nonparallelity errors for CASSCF/L-CTD and MRMP are 8.9 and 8.3 mEh, respectively, demonstrating again that CASSCF/L-CTD yields quantitatively accurate curves with NPEs competitive with that of MRMP theory. 

Table II. The SR, 2R, 4R and (2/2)R CISD ground state energies together with various Davidson-type corrections relative to the FCI energy (in mH) for the DZP H4 model with 0 < a < 0.5. The nonparallelism errors (NPE) are givenin the last two rows. See the text for details. 

Ref. [79] These results do not involve any size-extensivity corrections. Nonparallelism error for a restricted interval 0.01 < a < 0.5. 

Table 1. Comparison of the SR CCSD, RMR CCSD, and ASTQ CCSD energies with the exact FCI result for the X2If state of OH at three internudear separations R, R = Re = 1.832 bohr, R = l.5Re> and R = 2Re. Except for the SCF and FCI total energies, which are reported as — (E + 75) (in hartree), the energy differences (in millihartree) relative to the FCI result are given in all cases. The nonparallelism error (NPE) for the interval R e [Re, 2Re] (in millihartree) is also given for easier comparison (see the text for details) ...

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