Unrestricted Hartree-Fock dissociation limit

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. 

The electronic structure methods are based primarily on two basic approximations (1) Born-Oppenheimer approximation that separates the nuclear motion from the electronic motion, and (2) Independent Particle approximation that allows one to describe the total electronic wavefunction in the form of one electron wavefunc-tions i.e. a Slater determinant [26], Together with electron spin, this is known as the Hartree-Fock (HF) approximation. The HF method can be of three types restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF) and restricted open Hartree-Fock (ROHF). In the RHF method, which is used for the singlet spin system, the same orbital spatial function is used for both electronic spins (a and (3). In the UHF method, electrons with a and (3 spins have different orbital spatial functions. However, this kind of wavefunction treatment yields an error known as spin contamination. In the case of ROHF method, for an open shell system paired electron spins have the same orbital spatial function. One of the shortcomings of the HF method is neglect of explicit electron correlation. Electron correlation is mainly caused by the instantaneous interaction between electrons which is not treated in an explicit way in the HF method. Therefore, several physical phenomena can not be explained using the HF method, for example, the dissociation of molecules. The deficiency of the HF method (RHF) at the dissociation limit of molecules can be partly overcome in the UHF method. However, for a satisfactory result, a method with electron correlation is necessary. 

We have only discussed the restricted Hartree-Fock dissociation problem for the minimal basis model of H2. The ideas presented are not limited to H2, however, and very similar effects will occur for other closed-shell systems when a bond is stretched. In H2, the onset of unrestricted solutions... 

Numerous steps have been undertaken in order to overcome these shortcommings of the standard CCSD method. The simplest way to achieve a proper dissociation limit (size-consistency) is to employ the unrestricted Hartree-Fock (UHF) reference. This often works rather well, except that UHF solution(s) exist(s) only in a limited range of internuclear separations and, at the onset of the RHF triplet instability the computed energies display a nonanalytic behavior. Of course, in more general situations, the UHF solution may dissociate to a wrong limit [cf., e.g. Refs. 4J0)]. not to mention the multiplicity and often haphazard behavior of various broken-spin-symmetry solutions, spin contamination, etc 4), Thus, this approach is usually reserved for computation of dissociation energies rather than for the generation of accurate PESs. 

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