Isoproperty surfaces

For convenience, we shall classify the molecular models according to their topological dimensionality, p. A molecular conformation defined by the set of nuclear position vectors is a zero-dimensional (OD) model. A one-dimensional (ID) model corresponds to a molecular skeleton, defined by the set of nuclear positions and their connectivity (bond) matrix. Contour surfaces of one-particle molecular properties such as electron density or electrostatic potential are topologically two-dimensional (2D) models embedded in three dimensions. Finally, we find a true three-dimensional (3D) model whenever an entire one-electron property over all space is involved. This model can be regarded as the continuum of all 2D isoproperty surfaces. The difference among the models is summarized in Figure 1. We shall deal with pD models in this work (p = 0,1, 2, 3). Each of them requires a different type of shape descriptor. 

The shape of isoproperty surfaces (Eq. [25]) can be analyzed in detail by using a 2D map of shape descriptors. The key notion is as follows the truncated surface G a, K) can be specified by two parameters the density value a, and a reference curvature value b, defining the criterion for truncation. 

The boundary surfaces G a) of level sets F a) are the isoproperty contours (IPCOs) defined as... 

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