Download Advances in Molecular Similarity, Volume 1 (Advances in by R. CarbA?-Dorca, P.G. Mezey PDF

By R. CarbA?-Dorca, P.G. Mezey

The purpose of this article is to supply experiences and monographs on themes regarding molecular similarity, starting from the basic actual homes underlying molecular behaviour to purposes in industrially very important fields corresponding to pharmaceutical drug layout and molecular engineering. The editors wish that this sequence will inspire new rules and techniques, support to systematize the quickly collecting new chemical details, and make chemistry larger understood and higher utilized.

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J. Am. Chem. Soc. 1992,114,4773 . 20. D. J. Am. Chem. Soc. 1991, H3,64. 21. ; Challacombe, M. Int. J. Quant. Chem. 1991,25,81. 22. ; Cioslowski, J. Chem. Phys. Utt. 1991,185,270. 23. ; Surjin, PR. J. Mol. Struct. (Theochem) 1992,255,9. 24. ; Stmad, M. Collect. Czech. Chem. Commun. 1990,55,2583. 25. ; Stmad, M. / Phys. Org. Chem. 1991,4,701. 26. Ponec. ; Stmad. M. Int. J. Quantum Chem. 1992,42,501. 27. ; Stmad, M. Croat. Chem. Acta 1991,66,123. 28. Ponec, R. J. Chem. Inf Comput. Sci. 33, 805. 29.

When the parameters in the Eq. 32 take the values K = 1 and X = 0 the Hodgkin-Richards index is obtained, whereas the Tanimoto index appears naturally when K-X-\. As a function of the D-class index of infinite order described in Eq. 31, the Petke index^* can also be defined as having the form: <%,= z„rD,,r' (33) C. QMSI in the Molecular Point-Cloud n-Dimensional Representation The polyhedron nature of the molecular point-cloud has not been used so far. Here, the columns of the similarity matrix Z can be taken directly to obtain new index forms.

From the quantum mechanical point of view, given any observable O, and the associated hermitian operator Q, the expectation value , of the system described by the density function p^ may be formally obtained as: ,= = J n p, dr (61) Then, to the operator Q one can assign the discrete vector representation w, using the same basis set contained in P 0 D, in such a way that both vectors u, and w belong to the same discrete n-dimensional space representation. Using these results, the following scalar product, ,-'W^u^ (62) can be associated to the approximate expectation value computed within the discrete space where the molecular point-cloud belongs.

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