UHF calculations

Calculated transition structures may be very sensitive Lo the level of theory employed. Semi-empirical methods, since they are parametrized for energy miriimnm structures, may be less appropriate for transition state searching than ab initio methods are. Transition structures are norm ally characterized by weak partial" bonds, that is, being broken or formed. In these cases UHF calculations arc necessary, and sometimes even the inclusion of electron correlation effects. 

IXDCf is faster than MINDO/3, MNDO, AMI, and PM3 and, unlike C XDO, can deal with spin effects. It is a particularly appealing choice for UHF calculations on open-shell molecules. It is also available for mixed mode calculations (see the previous section ). IXDO shares the speed and storage advantages of C XDO and is also more accurate. Although it is preferred for numerical results, it loses some of the simplicity and inierpretability of C XDO. 

Choose UHF (spin Unrestricted Hartree-Fock) or RHF (spin Restricted Hartree-Fock) calculations according to your molecular system. HyperChem supports UHF for both open-shell and closed-shell calculations and RHF for closed-shell calculations only. The closed-shell UHF calculation may be useful for studying dissociation of molecular systems. ROHF (spin Restricted Open-shell Hartree-Fock) is not supported in the current version of HyperChem (for ab initio calculations). 

When computing UV visible spectra, you should do a Cl singles calculation. RHF or UHF calculations are sufficient to reproduce the proper order of molecular orbitals in most complexes. 

At this point, we might expect that a UHF calculation would be sufficient. However, when we perform a UHF StablesOpt calculation, the predicted wavefunction is again found to be unstable ... 

Here is the input file for an optimization of the transition structure for the reaction H3CO —t H2COH (a simple 1,2 hydrogen shift reaction). We specify a UHF calculation (open shell) since the molecular system is a doublet ... 

Table 18.4 Hyperfine coupling constants/mT for the vinyl radical. UHF calculations ...

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 4 Methanal Ti(n,x ) excited state. Comparison of HPHF and UHF calculations and experimental data.

The conclusions from this rather elementary survey of the symmetry constraint problem all point in the same general direction. The imposition of symmetry constraints (other than the Pauli principle) on a variationally-based model is either unnecessary or harmful. Far from being necessary to ensure the physical reality of the wave function, these constraints often lead to absurd results or numerical instabilities in the implementation. The spin eigenfunction constraint is only realistic when the electrons are in close proximity and in such cases comes out of the UHF calculation automatically. The imposition of molecular spatial symmetry on the AO basis is not necessary if that basis has been chosen carefully — i.e. is near optimum. Further, any breakdowns in the spatial symmetry of the AO basis are a useful indication that the basis has been chosen badly or is redundant. 

A first quantitative assessment of the effect by ab initio calculations was presented by Schleyer s group (Crans et al. 1980). They used unrestricted Hartree-Fock (UHF) calculations at the fully geometry optimized, split valence, 4-3IG basis-set level to investigate the interaction of a ic-donor and a Jt-acceptor both bonded to a CH radical centre. The existence of a... 

An ab initio RHF/3-21 G study has shown that the decomposition of 3-hydroxy-3-methylbutan-2-one is a concerted process with hydrogen transfer and bond breaking via a five-membered cyclic transition state.AMI and PM3 methods using UHF calculations were applied to study the thermolysis of 2-cyanofuroxan. The reaction proceeds via a two-step pathway in which the second step is rate determining. The effect of solvent in the thermal decomposition reaction of fran -3,3-dimethyl-5,6-tetramethylene-l,2,4-trioxacyclohexane was studied. ... 

The results obtained up to this point show that the amount of spin contamination was crucial to obtain good results for this system. We found that even small spin contamination leads, in some cases, to disparate charge distributions. Thus, we used the restricted open shell procedure (ROHF) to calculate an initial guess for the UHF calculation. Since the ROHF solution has the correct value of the spin, it was found that it provides a better starting point for the UHF procedure. Unfortunately it is not a final solution to this problem because we found some cases where even this procedure leads to a very large spin contamination. 

At the ROHF level, the unpaired spin is located in the Cu02 planes on oxygens, 02 and 03. The picture is drastically changed when we include the electron correlation. According to Table 6, in both at the UHF level as well as at the MP2 level, the unpaired spin is located in chains on the Cul. In previous ECM calculations [22,29] at the UHF level, the unpaired spin was indicated in planes on Cu2. The reasons for this contradiction are not clear, because in our calculations the location of unpaired spin at the UHF level is the same as at the MP2 one. Note that the location of the unpaired spin is found to be very sensitive to the spin contamination in the UHF calculation. In our case. 

The inherent spin-impurity problem is sometimes fixed by using the orbitals which are obtained in the UHF calculation to subsequently form a properly spin-adapted wavefunction. For the above Li atom example, this amounts to forming a new wavefunction (after the orbitals are obtained via the UHF process) using the techniques detailed in Section 3 and Appendix G ... 

This wavefunction is a pure S = 1/2 state. This prescription for avoiding spin contamination (i.e., carrying out the UHF calculation and then forming a new spin-pure ) is referred to as spin-projection. 

The most general version of Hartree-Fock (HF) theory, in which each electron is permitted to have its own spin and spatial wave function, is called unrestricted HF (UHF). Remarkably, when a UHF calculation is performed on most molecules which have an equal number of alpha and beta electrons, the spatial parts of the alpha and beta electrons are identical in pairs. Thus the picture that two electrons occupy the same MO with opposite spins comes naturally from this theory. A significant simplification in the solution of the Fock equations ensues if one imposes this natural outcome as a restriction. The form of HF theory where electrons are forced to occupied MOs in pairs is called restricted HF (RHF), and the resulting wave function is of the RHF type. A cal-... 

When a spin-contaminated wave function is obtained from a UHF calculation, the desired spin state is inevitably the one of lower spin (otherwise one would have constructed the high-component of the higher spin state). The contaminated wave function can be improved... 

For our SCF calculation the way to obtain such a solution is to optimize the orbitals not for the energy of determinant 7.6, but for the average energy of both determinants. This is termed the imposition of symmetry and equivalence restrictions. It involves imposing a constraint on a variational calculation, and consequently the symmetry and equivalence restricted solution will have an energy no lower than the broken symmetry solution it will usually have a higher energy. We may note that in a UHF calculation we impose neither spin nor spatial symmetry and equivalence restrictions — the -terms restricted and unrestricted were first used in exactly this context of whether to impose symmetry constraints on the wave function. 

The allyl radical (Figure 18.6) has been the subject of very many studies. It has been prepared in the liquid phase by electron irradiation of cyclopropane. The sign of the CH proton coupling constant was deduced by comparison with a single-crystal study of the radical CH(COOH)2 formed by y-irradiation of a single crystal of malonic acid. A straightforward UHF calculation gives a wavefunction... 

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