By R. Carbó-Dorca, P.G. Mezey

This quantity highlights a few of the advances in molecular similarity. Molecular similarity study is a dynamic box the place the swift move of rules and methodologies from the theoretical, quantum chemical and mathematical chemistry disciplines to effective algorithms and laptop courses utilized in industrially very important purposes is mainly obtrusive. those functions frequently function motivating components towards new advances within the basic and theoretical fields, and the combo of highbrow problem and functional software presents mutual merits to theoreticians and experimentalists. the purpose of this quantity is to provide an outline of the present methodologies of molecular similarity reports, and to show new demanding situations, unsolved difficulties, and parts the place vital new advances might be anticipated.

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Extra resources for Advances in Molecular Similarity, Volume 2

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Molecular point-clouds can also be constructed by means of the eigenvectors of matrix Z. This is possible because the set of QSM [Sjj] can be considered a set of scalar products between density function pairs. In this manner, the QSM matrix Z is somehow a kind of Gram matrix, constructed using the elements of the density set D. The Z matrix column eigenvector coordinates are to be considered, in any case, a set of point-molecules possessing a canonical behavior. They are normalized vectors orthogonal to the rest of the molecular point-cloud elements.

Novoa, J. J. J. Mol. Struct. 1983, 95, 15-33. ; Calabuig, B. Comput. Phys. Commun. 1989, 52, 345-354. 24. ; Calabuig, B. J. Comput. Chem. 1992,13,155-159. 25. ; Carbo, R. J. Comput. Chem. 1994, 75 ,1113-1120. 26. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1970. 27. ; Piskorz, P J. Chem. Phys. 1997,106, 3607-3612. 28. G. Potential Energy Hypersurfaces. Studies in Physical and Theoretical Chemistry, Vol. 53; Elsevier: Amsterdam, 1987. 29. Jacobi, C. G. J. J. Peine Angew. Math.

This dependence, which can also be attached to the kernel, produces as a result a DIT dependence of this vector too: A^(R, R„) = r(pJ = J K(R, r, R,)p^(r, R^)dr (44) Usual calculations consider the dependence of all of the involved functions on the coordinate vector RQ as implicit, and in this way it is not explicitly written in the developed formulas. In any case, if DIT are used over a density function set P = {p^}, obtained over a QOS S = {sj}, the corresponding elements of the DIT set D = {Aj} can be considered as sound representations of the set S elements as the former density function set can be.

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