Molecular isodensity contours MIDCO

One approach to the approximate representation of molecular bodies is based on molecular isodensity contours, MIDCOs, defined with respect to some fixed nuclear configuration K and some electron density threshold a. A MIDCO G(a,K) is defined (in the fixed nuclear configuration approximation) as the collection of all those points r of the three-dimensional space where the electronic density is equal to the threshold a ... 

The fundamental principle we shall follow in the local shape analysis of functional groups and local molecular moieties is a strict analogy with the shape analysis of complete molecules. Accordingly, instead of molecular isodensity contour (MIDCO) surfaces, the main tool of analysis will be the fragment isodensity contour (FIDCO) surfaces. Some of the ideas and concepts described in this section are illustrated in Figure 1. 

Figure 1.2 The three-dimensional, fuzzy "body" of the charge density distribution of allyl alcohol can be represented by a series of "nested" molecular isodensity contours (MIDCO s). Along each MIDCO the electronic density is a constant value. Three such MIDCO s are shown for the constant electron density values of 0.2, 0.1, and 0.01 (in atomic units), respectively. A contour surface of lower density encloses surfaces of higher density. These MIDCO s are analogous to a series of Russian wooden dolls, each larger doll enclosing a smaller one. These ab initio MIDCO s have been calculated for the minimum energy conformation of allyl alcohol using a 6-31C basis set.

If molecular shape is represented by the electronic density, then the shape analysis can be performed on the molecular isodensity contours (MIDCO s) of the calculated density. Some of the elementary properties of MIDCO s have been... 

According to a recent proposal [4,8,9], chemical bonding within formal molecular bodies can be described by molecular isodensity contour (MIDCO) surfaces and by density domains (DD) that are the formal bodies enclosed by... 

An important fact has been pointed out by Parr and Berk the bare nuclear potential Vn(r) shows many similarities with the electronic density function p(r). The computed isopotential contours of the composite nuclearpotential VnC lwere remarkably similar to some of the molecular isodensity contours (MIDCOs) of the electronic ground states in several simple molecules. One may regard the composite nuclear potential as the harbinger of electronic density, and isopotential contours of the composite nuclear potential V (r) can serve as surprisingly good approximations of MIDCOs. The nuclear potential contours (NUPCOs) are suitable for an inexpensive, approximate shape representation of molecules. 

Whereas in the rigorous quantum chemical sense, the interpretation of the concept of molecular shape is nontrivial, a natural interpretation is based on the shape of the electronic density cloud. For each fixed nuclear configuration K and density threshold value a, a molecular isodensity contour (MIDCO) surface G(K, a) is the collection of all points r of the 3D space where the electronic density p(K, r) is equal to the constant value a,... 

A typical discrete set of chemical importance is a nuclear arrangement in the clamped nucleus version of the Bom-Opp-enheimer approximation. A single molecular isodensity contour (MIDCO) surface is a crisp continuum set. A simple generalization of the CSM approach from finite, discrete point sets to continua is provided by the crisp average of sets. 

---