Density and Potential Distribution in Molecules

Having discussed the basic equations of the density description and their application to atomic ions we turn now to the much more difficult problem of molecules. Even the simplest density description afforded by the TF theory presents severe computational problems for multicentre problems, as well as some conceptual difficulties on which we shall attempt to throw light in the ensuing discussion. 

From the practical standpoint, the first attempt to solve the self-consistent TF equation for a diatomic molecule was made by Hund.82 Following this, the density method was applied to the benzene molecule and compared with both the molecular orbital prediction for the density and with relevant experiments.88 Various other early molecular calculations are discussed in ref. 16 we refer here to the recent studies of Dreizler and his co-workers.84 The importance of such self-consistent calculations will be emphasized below, even though we shall not use them in any detail in the ensuing discussion. 

Indeed, we shall focus on generalizing much of the above discussion of atoms to molecules, especially in their equilibrium configuration. With regard to atoms, the important questions which arise are then  

All these questions, as we shall see, can be discussed fruitfully from the density description of molecules. But because, as we have already emphasized, the multicentre problem is difficult to tackle even in the simplest TF density description, we shall attempt to tackle questions (i)—(iii) above by turning immediately to a central field model which was solved by March86 in the TF density description. The model was set up with tetrahedral and octahedral molecules in mind, for example GeH4, UF6 etc. It has been used recently by Mucci and March88 in a discussion of energy relations for molecules at equilibrium. We shall summarize their main results below, after discussing the solution of the central field model.85 

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