A Shape Representation of Macromolecules

An early approach to the local shape problem was based on the Shape Group Methods as applied to truncated surfaces, where the truncation was selected using essentially arbitrary criteria for deciding which part of the molecule belongs to a local region. The purpose of the study was to analyze the influence of various substituents on the local shape of the rest of the molecule. 

A simple, additive fragmentation approach to the molecular electronic density, proposed by the author, can be used for the construction of electronic densities and density-based shape representations for macromolecules. The simplest of these approaches is motivated by Mulliken s population analysis technique,and can be regarded as a natural generalization of Mulliken s approach a formal population analysis without integration. This method, the Mulliken-Mezey approach, is the simplest realization of a more general, additive fuzzy density fragmentation (AFDF) principle.  

The same Mulliken-Mezey method, and the more elaborate alternative partitioning schemes serve as the basis of the ALDA (adjustable local density assembler) method and the ADMA (adjustable density matrix assembler) technique. The ALDA and ADMA methods generate geometry-adjustable electronic densities and macromolecular density matrices. The ADMA macromolecular density matrices can be computed without determining a macromolecular wave function, a feature advantageous in the macromolecular application of a variety of quantum-chemical 

According to the Mulliken-Mezey AFDF method, the set of nuclei of the molecule are divided into m mutually exclusive families 

These nuclear families serve as reference for m fuzzy, additive density fragments, Fi, F2. Fj, . where these fuzzy molecular fragments correspond to fragment density functions 

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