A preliminary
account is given of a perturbation method for calculating interatomic and intermolecular interaction energies in which the wave function is expanded in terms of product functions. The results obtained are compared with those found using &her expansions.
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Introduction
Recently there has been a revival of interest in the calculation of interatomic and intermofecular intractions particularly for distances intermediate between those where chemical interactions are impormt and those where only London-Van der Wadis interactions need be considered [1-S]. Almost invaribly (ref. [3] is the exception) the calculations have used perturbation theory with antisymmetrized proucts of the wave functions for the individual atoms or molecules as basis functions. We have recently eveloped a significantly different perturbation theory in which only the zero order wave function is Ken to be the antisymmetrized product and the other members of the basis set are just the simple roducts. The first purpose of this note is to give a preliminary account of the new theory, full details f which will be published later [?'I. Secondly we wish to show that the results agree with those of the leery using antisymmetric functions when that theory has been correctly applied [6,8] and we also men-.on the errors and potential ambiguities which appear in the various othe+-treatments of the problem l-51. . THEORY Consider the atoms or molecules A, B, . . . N and let ( @,A}, {QzB) etc. be the complete set of orthoormal wave functions for each atom or molecule. The product functions * 111 =fb.AlfJ.B... . 2 3
vhere the single index m stands for the ordered set i, j ,k . . . ) will form a complete, and not overcomlete, set of functions for the interacting system. The Hamiltonian U can be written as H = Ho f V where r. is that Ho*m = E m\k,, where E, = EVA + EJB + . . . in the obvious notation. It is impossible to apply ertwbation theory directly using the function (1) since, if, for example, we zre interested in the ground tate, the function \k, = @oA@oB.. . will not be a good zero order function as it is not antisymmetric [9]. However, an operator & which antisymmetrizes 'k. and normalizes the resulting function at infinite sepration can be defined so that &'Eo can be taken as a valid zero order function. If a perturbation solution ; looked for in the form (unnormalized) * Research