Local shape interacting functional groups

Two choices for the representation of a local molecular moiety will be discussed. For the first choice, describing the local shapes of non-interacting functional groups within a molecule, we define a FIDCO for a fragment A in a molecule AB as follows ... 

Figure 1. Illustration of the local shape description of non-interacting and interacting functional groups. See text for definitions of symbols.

In most interactions between two reactants, local shape complementarity of functional groups is of importance. A local shape complementarity of molecular electron densities represented by FIDCOs implies complementary curvatures for complementary values of the charge density threshold parameters a. For various curvature domains of a FIDCO, we shall use the notations originally proposed for complete molecues [2], For example, the symbol D2(b),i(a, Fj) stands for the i-th locally convex domain of a FIDCO G(a) of functional group Fj, where local convexity, denoted by subscript 2(b), is interpreted relative to a reference curvature b. For locally saddle type and locally concave domains relative to curvature b, the analogous subscripts 1(b) and 0(b) are used, respectively. 

If a contact density threshold ao can be chosen for a given interaction between two functional groups, then the local shape complementarity between G(ao, Fj) and G(a<), F2) is clearly of importance. However, complementarity should also manifest itself within a whole range of density thresholds. One may consider the local shape complementarity of FIDCOs G(ao-a, F[) and G(ao+a, F2) in a density interval containing the contact density threshold ao,... 

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