Nuclear potential contours NUPCO

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. 

This observation of Parr and Berk provides the basis for a simple approach to molecular shape analysis and molecular similarity analysis, described below. Although the molecular shapes, as defined by the electronic density, differ somewhat from the shapes of the nuclear potentials, their similarity can be exploited the nuclear potential contour surfaces provide a simple approximation of the shape of molecules. We shall refer to the isopotential surfaces of the nuclear potential contours as NUPCO surfaces. These surfaces have a major advantage the computation of NUPCO s is a trivially simple task as compared to the calculation of electronic densities. Furthermore, nuclear potential is a useful molecular property in its own right, without any reference to electronic density a comparison of NUPCO s of various molecules can provide a valid tool for evaluating molecular similarity. The superposition of potentials of different sets of nuclei can result in similar composite potentials, consequently, the comparison of NUPCO s is better... 

Isopotential contours of the composite nuclear potentials (NUPCO s, see Chapter 4), provide an inexpensive, approximate shape representation that can be computed easily even for very large molecules. Although NUPCO s only approximate the MIDCO s of molecules, the family of NUPCO s of a molecule describes an important molecular property that has a major effect on the actual molecular shape. Consequently, NUPCO s can be used for direct comparisons between molecules, and similar NUPCO s are likely to be associated with similar molecular shapes. All the shape analysis techniques originally developed for MIDCO s are equally applicable to NUPCO s. The shape groups, the (a,b) parameter maps [where a is the nuclear potential threshold of a NUPCO G(a)], the shape matrices, shape codes, and the shape globe invariance maps of NUPCO s of molecules can serve as inexpensive methods for the detection and evaluation of a particular aspect of molecular similarity. 

Isopotential contours of the composite nuclear potentials (NUPCO s), provide an inexpensive approximate shape representation that can be computed easily even for very large molecules. 

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