PUHF method

For the UHF calculations the undectet implies = 5 (septet implies 3z = 3) and the electrons are assigned as suggested by the ROHF calculation. For the 5 = 0 case the electrons are assigned to be AF coupled. The Projected Unrestricted Hartree-Fock (PUHF) energies correspond to the fully projected UHF values with 3 = 5. A brief overview of the PUHF method is given below, a more detailed description can be found in Reference 4. 

Table 1. The 72-atom model examined by different theoretical methods. The energy differences (AE in kcal/mol) are calculated with respect to the lowest SCF energy. q(Fe) stands for Mulliken population charges on the Fe atoms q(S) and SS(b.i.) are the Mulliken population charges and the bond index for the bridging S atoms, respectively AEq is the calculated Mossbauer quadrupole splitting constant [mm/sec]. The PUHF spin states are those projected from the UHF wavefunction with 5 = 5,. 

The challenge with unrestricted methods is tire simultaneous minimization of spin contamination and accurate prediction of spin polarization . The projected UHF (PUHF, see Appendix C) spin density matrix catr be employed in Eq. (9.36), usually with somewhat improved results. 

To reduce or eliminate spin contamination problems in unrestricted wave functions, spin projection methods have been developed diat annihilate the contributions of certain spin states higher than the desired one. As derived in Appendix C, the PUHF energy for a wave function that has had contamination from the next higher spin state annihilated is computed as... 

Herivatives of the PUHF energy are not eontinnons at the RffF/UHF instability point. Projeetion of the wave function after electron correlation has been added, however, turns out to be a viable pathway. This has mainly been used in coimection with perturbation methods, to be described in Section 4.8.2. 

The corresponding curves based on a UHF reference are shown in Figure 11.13. It is immediately clear that DFT methods do not have the spin contamination problem in the intermediate region, indeed spin contamination is not well defined in DFT." Removing the spin contamination by projection methods gives rise to discontinuous derivatives and artificial minima, analogously to the PUHF case in Figures 11.3 and... 

The constants ajso(N) and ajso(F) were obtained by a number of ab initio studies UHF ( Nesbet ) [14], UHF and UHFASA [15 to 19], comparison of the UHF, PUHF, PO, and SECI methods [20], RHF + CI [19], and some semiempirical calculations MNDO [21], MINDO within UHF and UHFASA formalisms [22], and INDO (s-electron spin densities aiso/a ef only given, see p. 233) [23]. 

Table 3 shows that, as in the case of square CB, UHF and MBPT methods based on one-configuration UHF wavefunctions for the singlet states do not work well for TMM, which is not surprising in view of the inherent inappropriateness of the zero-order wavefunction. Following projection of the first high-spin contaminants from the singlet and triplet wavefunctions, Bj is erroneously predicted to lie lower than the triplet at both the PUHF and PUMP2 levels of theory. 

PUHF Projected (—>) UHF method, whereby higher spin contaminants are removed from the UHF wavefunction. 

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