Molecular shape electron-group distributions

Point symmetry groups provide at least a partial characterization of molecular shapes. This characterization can be improved considerably by extending the family of point symmetry operators to a much larger family of continuous transformations. Symmorphy is a particular extension of the point symmetry group concept of finite point sets, such as a collection of atomic nuclei, to a complete algebraic shape characterization of continua, such as a three-dimensional electron distribution of a molecule. 

Bioisosteres are compounds or groups that essentially possess near equal molecular shapes and volumes, approximately the same distribution of electrons, and that exhibit similar physical characteristics, such as hydro-phobicity. Bioisosteric compounds affect the same biochemically associated systems as agonists or antagonists and thereby produce biological properties that are more or less related to each other . 

Compounds or groups that possess near-equal molecular shapes and volumes, approximately the same distribution of electrons, and which exhibit similar physicochemical properties... ... 

A different approach to mention here because it has some similarity to QM/MM is called RISM-SCF [5], It is based on a QM description of the solute, and makes use of some expressions of the integral equation of liquids (a physical approach that for reasons of space we cannot present here) to obtain in a simpler way the information encoded in the solvent distribution function used by MM and QM/MM methods. Both RISM-SCF and QM/MM use this information to define an effective Hamiltonian for the solute and both proceed step by step in improving the description of the solute electronic distribution and solvent distribution function, which in both methods are two coupled quantities. There is in this book a contribution by Sato dedicated to RISM-SCF to which the reader is referred. Sato also includes a mention of the 3D-RISM approach [6] which introduces important features in the physics of the model. In fact the simulation-based methods we have thus far mentioned use a spherically averaged radial distribution function, p(r) instead of a full position dependent function p(r) expression. For molecules of irregular shape and with groups of different polarity on the molecular periphery the examination of the averaged p(r) may lead to erroneous conclusions which have to be corrected in some way [7], The 3D version we have mentioned partly eliminates these artifacts. 

Structural criteria are based on SAR analysis. Two basic approaches may be used firstly, structural analogies with established types of chemical carcinogens, and, secondly, considerations of molecular size, shape and symmetry, and of electron distribution and steric factors in and around functional groups, independently from any possible analogy with other compounds. Some of the structural criteria (see Appendix V of ref. 5 for details) are listed below ... 

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