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Figure 11.6 RMP2, UMP2 and PUMP2 dissociation curves for H2O near the instability point

The UMP2 energy is higher than the RMP2, although the UHF energy is lower than the RHF. At the HF level, the UHF energy is lowest owing to a combination of spin contamination and inclusion of electron correlation (Section 4.8.2). Since the MP2 procedure recovers most of the electron correlation, only the energy rising effect due to spin contamination remains, and the UMP2 energy becomes higher than RMP2. Removing the unwanted spin components makes the PUMP2 energy very similar to RMP2 for elongations less than ~1 A, but is significantly better at longer bond lengths owing to the correct dissociation of the UHF wave function. The RMP2 energy follows the "exact" curve closely out to a AR of ~0.5A, and is in respectable agreement out to ~1.0A. RMP2 activation energies are therefore often in quite reasonable agreement with experimental or higher level theoretical values. It should also be noted that the discontinuity at the PUHF level essentially disappears when the projection is carried out on the MP2 wave function.

Figure 11.7 and 11.8 show the effect of extending the perturbation series at the RMP and UMP levels.

Addition of more terms in the perturbation series improves the results, although the effect of MP3 compared with MP2 is minute. As the bond is stretched more than ~1.5 A, the perturbation series breaks down owing to the RHF wave function becoming a too poor reference, and the energies start to decrease. The RMP4 method performs well out to an elongation of ~1.0A, and in the TS region where the bond is stretched 0.5-0.8A, the MP4 error is less than a few kJ/mol. Although real transition structures usually have more than one breaking/forming bond, and therefore are more sensitive to correlation effects, it is often found that the MP4 method with a suitable large basis can reproduce activation energies to within a few kJ/mol.

The improvement by extending the perturbation series beyond second order is small when a UHF wave function is used as the reference, i.e. the higher order terms do very

Figure 11.7 RMP2, RMP3 and RMP4 dissociation curves for H2O

Figure 11.7 RMP2, RMP3 and RMP4 dissociation curves for H2O

Figure 11.8 UMP2, UMP3 and UMP4 dissociation curves for H2O

Figure 11.8 UMP2, UMP3 and UMP4 dissociation curves for H2O

little to reduce the spin contamination. In the dissociation limit the spin contamination is inconsequential, and the MP2, MP3 and MP4 results are all in reasonable agreement with the "exact" CASSCF result (but too high compared with the experimental result due to basis set limitations).

Figures 11.9 and 11.10 compare the performance of the CCSD and CCSD(T) methods, based on either an RHF or UHF reference wave function.

ARoe(A)

Figure 11.9 RCCSD and RCCSD(T) dissociation curves for H2O

ARoe(A)

Figure 11.9 RCCSD and RCCSD(T) dissociation curves for H2O

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