Attempts at an Exact Theory

There have been several attempts to develop methods that will eliminate the BSSE a priori and not a posteriori, as do most of the methods discussed later. In all a priori cases, operators are set up which eliminate the extraneous contributions of the atomic centers to the total wavefunction, consistent with the overall antisymmetry. Those operators are often quite complex and make calculations more lengthy. 

in a series of papers, developed a theory called the chemical Hamiltonian approach (CHA), which was based on observables, such as charge densities. Beginning with two 1983 papers, he developed a non-Hermitian perturbation theory that was able to separate out the energy components that comprise the BSSE. He was able to show that there are both over- and undercorrection effects, and later we demonstrate that overcorrection typically is small in most cases. Using a complete analysis of a four-orbital, two-electron model, Mayer and Turi were able to separate out and display all the BSSE terms. Their paper contains the most extensive discussion of the origins of BSSE and the most elaborate presentation of the theory. 

Calculations have been performed by Mayer, Surjan, and their coworkers on small systems such as He2, (LiH)2, (H20)2, and (HF)2. Mayer and Vibo k also developed a separate self-consistent field (SCF) theory that excluded BSSE effects, and Mayer et al. recently applied the CHA approach to density functional theory.  

In 1991 Sadlej proposed another perturbation theory that is Hermitian but requires some major constraints on the wavefunctions. This method must be slightly modified in real problems to make sure that the wavefunctions of the subsystem descriptions are not made poorer by the process.  

Another method, by Cullen, uses the monomer s own basis set, which is a very localized valence bond description. This method is complicated in its implementation and also does not include the important charge transfer effects in its treatment. 

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