Improper HF Asymptotic Behaviour

Corrections for Improper HF Asymptotic Behaviour.—There are two techniques which may be used to obtain results at what is essentially the Hartree-Fock limit over the complete range of some dissociative co-ordinate in those cases where the single determinants] approximation goes to the incorrect asymptotic limit. These techniques are (i) to describe the system in terms of a linear combination of some minimal number of determinantal wavefunctions (as opposed to just one) 137 and (ii) to employ a single determinantal wavefunction to describe the system but to allow different spatial orbitals for electrons of different spins - the so-called unrestricted Hartree-Fock method. Both methods have been used to determine the potential surfaces for the reaction of an oxygen atom in its 3P and 1Z states with a hydrogen molecule,138 and we illustrate them through a discussion of this work. 

All three component wavefunctions involve double occupation of the 3m (= log of Ha) orbital. The description of Of1/)) is given by the linear combination IF with the 3m orbital omitted. Hence, XP as written above corresponds to an (antisymmetrized) product of the Hartree-Fock wavefunctions for Ha and Of1/)). 

It is generally found that if one increases the flexibility of a single-determinantal wavefunction by allowing each space orbital to assume an independent form (rather than insisting on double occupation by an and a (1 electron for those orbitals which would otherwise be so occupied as dictated by the electronic configuration) that the asymptotic difficulties of the wavefunction are removed. Thus, the unrestricted Hartree-Fock method usually predicts the correct dissociation products of a molecular system.140 The symmetrical (C2 ,) insertion of Of3P) into Ha yields the 33i state of the HaO system. The electronic configuration of this state expressed in terms of the unrestricted set of orbitals is 

The singlet insertion reaction was determined using the limited configuration interaction treatment outlined above.138 The singlet abstraction reaction 

The symmetrical insertion of 0(3P) into H2 results in a barrier of approximately 335 kJ mol-1 and yields a linear metastable intermediate. For distances of approach of 0(SF) to H2 less than 3.0 a.u., the triplet insertion path is unstable to an unsym-metrical motion of the nuclei which leads to OH(aII) and H(2S). The energy minimum on the symmetric triplet path is therefore, a saddle point and does not represent a stable nuclear configuration for triplet water. 

---