From Functional Groups to Extended Molecular Regions

FROM FUNCTIONAL GROUPS TO EXTENDED MOLECULAR REGIONS 

Two important tools of electron density modeling and shape analysis are the concepts of molecular isodensity contour, MIDCO G(K,a) and the associated density domain DD(K,a) [27], Here the nuclear arrangement (also called the nuclear configuration) is denoted by K, whereas the electron density threshold is denoted by a. Each MIDCO G(K,a) is the collection of all those points r of the three-dimensional space where the electron density p(K,r) of the molecule M of conformation K is equal to the threshold a. The density domain DD(K,a) is the collection of all points r where the electron density p(K,r) is greater than or equal to the threshold a. Using formal notations, 

The MIDCO G(K,a) can be regarded as the boundary surface of the density domain DD(K,a). 

Quantum chemical functional groups have been defined as fuzzy electron density fragments (AFDF fragments) associated with a family of nuclei fk, 

Consider a macromolecule M of some nuclear configuration K. For an electron density threshold a, the family of functional groups 

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