Toward a global maximization of the molecular similarity function: Superposition
of two molecules
P. Constans, L. Amat, and R. Carbó-Dorca. Toward a global maximization of
the molecular similarity function: Superposition of two molecules. Journal of
Computational Chemistry, 18, 826-846 (1997).
Abstract
A quantum similarity measure between two molecules is normally identified with the
maximum value of the overlap of the corresponding molecular electron densities. The
electron density overlap is a function of the mutual positioning of the compared
molecules, requiring the measurement of similarity, a solution of a multiple-maxima
problem. Collapsing the molecular electron densities into the nuclei provides the
essential information toward a global maximization of the overlap similarity
function, the maximization of which, in this limit case, appears to be related to
the so-called assignment problem. Three levels of approach are then proposed for a
global search scanning of the similarity function. In addition, atom]atom similarity
Lorentzian potential functions are defined for a rapid completion of the function
scanning. Performance is tested among these three levels of simplification and the
Monte Carlo and simplex methods. Results reveal the present algorithms as accurate,
rapid, and unbiased techniques for density-based molecular alignments.
Keywords
Molecular quantum similarity measures MQSM, atomic shell approximation ASA, global
maximization, molecular alignments, N-dimensional representation, diffusion equation
method, Lennard-Jones atoms, dissimilar molecules, optimum structures, quantum
objects, orbital bases, drug design, correspondences, deformation.
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 Molecular Quantum Similarity Measures
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