Restricted Hartree-Fock activation energies

The second approach to treating nondynamical correlation has an air of the ostrich about it ignore the spin symmetry of the wave function and use unrestricted Haxtree-Fock (UHF) theory as the single configuration description [7]. Since the UHF wave function comprises one spin-orbital for each electron, a molecular UHF wave function should dissociate to atomic UHF wave functions, for example. This is certainly not the case for spin-restricted Hartree-Fock (RHF) molecules and atoms in general. And there is an attractive simplicity about UHF — no active orbitals to identify, and so forth. However, where nondynamical correlation would be important in an RHF-based treatment, the UHF method will suffer from severe spin-contamination, while where nondynamical correlation is not important the RHF solution may be lower in energy than any broken-symmetry UHF solution, so potential curves and surfaces may have steps or kinks where the spin symmetry is broken in the UHF treatment. 

Despite these restrictions, the GVB and SC methods generally provide energies that are much closer in quality to CASSCF than to Hartree Fock (19), and wave functions that are close to the CASSCF wave function having the same number of electrons and orbitals in the active space. This property has been used to devise a fast method to get approximate SC wave functions. 

A somewhat modified MO LCAO scheme, without restriction on the identity of spin orbitals (p and

unrestricted Hartree-Fock (UHF) method and is usually used to treat open-shell systems (free radicals, triplet states, etc.). Electron correlation is partially taken into account in this method, and therfore it can be expected to be more efficient than the RHF method when applied to calculate potential energy surfaces of chemical rearrangements whose intermediate or final stages may involve the formation of free- or bi-radical structures. The potentialities of the UHF method are now under active study in organic reaction calculations. Also, it is successfully coming into use in chemisorption computations (6). 

This procedure suffers from a high degree of arbitrariness in the choice of just which configurations are deemed important. The calculation can be made somewhat more objective by including all excitations between a subset of occupied MOs and a subset of vacant orbitals. (These excitations are subject to certain restrictions as to multiplicity or order of excitation.) The orbitals chosen for the excitations are referred to as the active space , and the method is dubbed Complete Active Space Self Consistent Field (CASSCF) - ". Both MCSCF and CASSCF provide a certain fraction of the correlation energy, relative to a single configuration, Hartree-Fock, calculation. 

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