Abstract
Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.
Highlights
This is a companion paper to [7] and [4] on the derivatives of the weighted volume and of the weighed area of a space- lling diagram, and of [1] on the derivative of the weighted mean curvature, with which this paper shares the notation
Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy
The main result of this paper is an explicit formula for the derivative of the weighted Gaussian curvature of a space- lling diagram, and an analysis of the cases in which this derivative either does not exist or is not continuous
Summary
This is a companion paper to [7] and [4] on the derivatives of the weighted volume and of the weighed area of a space- lling diagram, and of [1] on the derivative of the weighted mean curvature, with which this paper shares the notation. Getting its inspiration from the theory of intrinsic volumes, this approach writes the solvation free energy as a linear combination of the weighted volume, the weighted area, the weighted mean curvature, and the weighted Gaussian curvature. Compare this with Hadwiger’s characterization theorem, which asserts that any measure of convex bodies in R that is invariant under rigid motion, continuous, and additive is a linear combination of the four (unweighted) intrinsic volumes [9].
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