P. Constans et al., TOWARD A GLOBAL MAXIMIZATION OF THE MOLECULAR SIMILARITY FUNCTION - SUPERPOSITION OF 2 MOLECULES, Journal of computational chemistry, 18(6), 1997, pp. 826-846
A quantum similarity measure between two molecules is normally identif
ied with the maximum value of the overlap of the corresponding molecul
ar electron densities. The electron density overlap is a function of t
he mutual positioning of the compared molecules, requiring the measure
ment of similarity, a solution of a multiple-maxima problem. Collapsin
g the molecular electron densities into the nuclei provides the essent
ial information toward a global maximization of the overlap similarity
function, the maximization of which, in this Limit case, appears to b
e related to the so-called assignment problem. Three levels of approac
h are then preposed for a global search scanning of the similarity fun
ction. In addition, atom-atom similarity Lorentzian potential function
s are defined for a rapid completion of the function scanning. Perform
ance is tested among these three levels of simplification and the Mont
e Carlo and simplex methods. Results reveal the present algorithms as
accurate, rapid, and unbiased techniques for density-based molecular a
lignments. (C) 1997 by John Wiley & Sons, Inc.