Molecular electron density analysis

These electron densities provide detailed information that gives important insight into the fundamentals of molecular structure and a better understanding of chemical reactions. The results of electron density analysis are used in a variety of applied fields, such as pharmaceutical drug discovery and biotechnology. 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

In representations of electron densities, the presence or lack of boundaries plays a crucial role. A quantum mechanically valid electron density distribution of a molecule cannot have boundaries, nevertheless, artificial electron density representations with actual boundaries provide useful tools of analysis. For these reasons, among the manifold representations of molecular electron densities, manifolds with boundaries play a special role. 

R.F. Nalewajski, E. 6witka, A. Michalak, Information distance analysis of molecular electron densities, Int. J. Quantum Chem. 87 (2002) 198. 

The additive fuzzy electron density fragmentation scheme of Mezey is the basis of the Molecular Electron Density Lego Assembler (MEDLA) method [67,70-72], reviewed in section 4. of this report, where additional details and applications in local shape analysis are discussed. The MEDLA method was used for the generation of the first ab initio quality electron densities for macromolecules such as proteins [71,72] and other natural products such as taxol [66],... 

The alternative approach is to count the number of electrons in an atom s space. The question is how to define the volume an individual atom occupies within a molecule. The topological electron density analysis (sometimes referred to as atoms-in-molecules or AIM) developed by Bader uses the electron density itself to partition molecular space into atomic volumes. 

Information-distance analysis of molecular electron densities 165... 

INFORMATION-DISTANCE ANALYSIS OF MOLECULAR ELECTRON DENSITIES... 

The main tool for a systematic, topological shape and similarity analysis of molecules is the shape group analysis of molecular electron density clouds [13-25]. The shape group methods are not restricted to molecular electron densities however, in the present context, we shall phrase our brief review of these techniques in terms of electron densities. 

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. ... 

Earlier density extension results were proven only for parts of artificial molecular electron densities, where the complete molecule was assumed to be confined to a finite, bounded region of the three-dimensional space [21], a condition that violates quantum mechanics. However, the new Holographic Electron Density Fragment Theorem quoted here proves the unique extension property of parts of quantum-mechanically correct, boundaryless electron densities of molecules. This new theorem is of special importance with respect to transferability, establishing that for complete, boundaryless molecular electron densities no actual fragment density of sharp boundaries is perfectly transferable. This result has implications on using averaged electron densities for similarity analysis [162]. 

The world consists of individuals that are composed of less-extensive components and also are parts of more-extensive coherences. With appropriate technology, any item can be analyzed to yield stable materials— however those stable products of analysis need not have been components of the analyzed individual. Similarly, It is possible to partition molecular electron-density distributions into atomic constituents (Bader 2011), but those hypothetical pieces are not the same as corresponding uncombined atoms would be (if such could be prepared). 

The Hirshfeld analysis has been discussed previously [1, 2], so we will outline the process as it applies to the current study. Hirshfeld [2] suggested that if one wanted to partition the molecular electron density among the constituent atoms in a molecule, one does so by allotting density to each atom in proportion to the density that atom would have in the promolecule. For PCI, one would define the... 

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