Loge partitioning

Figure E7.1 illustrates the search for the best spherical loge in a two-loge partitioning of the six-electron BH(X ) molecule. Plotted in this figure are...

Bader, R. F. W. (1975) Comparison of Loge and Virial Methpds of Partitioning Molecular Charge Distributions, in O. Chalvet, R. Daudel, S. Diner and J. P. Malrieu (eds.) Localization and Delocalization in Quantum Chemistry, Reidel Publishing Company, Dordrecht, Vol. 1 pp. 15-38. 

Abstract The paper presents maximum probability domains (MPDs). These are regions of the three dimensional space for which the probability to find a given number of electrons is maximal. In order to clarity issues hidden by numerical uncertainties, some simple models are used. They show that MPDs reproduce features which one would expect using chemical intuition. For a given number of electrons, there can be several solutions, corresponding to different chemical situations (e.g. different bonds). Some of them can be equivalent, by symmetry. Symmetry can produce, however, alternative solutions. The models show that MPDs do not exactly partition space, and they can also be formed by disjoint subdomains. Finally, an example shows that a partition of space, as provided by loge theory, can lead to situations difficult to deal with, not present for MPDs. 

MPDs remind of Daudel s loges [21,22] which also use pv D). There, the idea is to partition molecular space into domains, called loges , and look for ail different possibilities to distribute electrons into them. After some initial trials it was decided to minimize the missing information function. 

For few atoms and molecules, the procedure (utilizing the high synunetry of the system) yielded space partitioning into loges which could be coimected with atomic cores, bonds, and lone pairs with electron populations close to the expectation of a chemist. It was concluded by Bader and Stephens [34] ... 

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