By R. Carbó-Dorca, P.G. Mezey

ISBN-10: 0762302585

ISBN-13: 9780762302581

This quantity highlights a few of the advances in molecular similarity. Molecular similarity learn is a dynamic box the place the speedy move of principles and methodologies from the theoretical, quantum chemical and mathematical chemistry disciplines to effective algorithms and machine courses utilized in industrially vital purposes is principally obtrusive. those purposes frequently function motivating elements towards new advances within the basic and theoretical fields, and the mix of highbrow problem and useful software offers mutual benefits to theoreticians and experimentalists. the purpose of this quantity is to give an summary of the present methodologies of molecular similarity reviews, and to indicate new demanding situations, unsolved difficulties, and parts the place vital new advances might be anticipated.

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**Additional resources for Advances in Molecular Similarity, Volume 2**

**Sample text**

1989, 20, 375-441. ; 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.

All of them are widely discussed in Ref. 44. To compute TI, it is just necessary to define some auxiliary matrices as shown in Table 1. The TI definition and the relationship with the matrix elements, shown in Table 1 is summarized in Table 2. Table 1, Definition of Matrices Used in TI Calculations^ Matrix Elements Definition ^ in^ n) Classical topological matrix: J _ j1 if atoms / and j are bonded u [0 otherwise D (n X n) V in) Djj'. topological length of shortest path from atom / to atom j Vf.

Then, the BD set 5 = {P^}, can be normalized using the above integral, that is, Pf(R) = 'a7^P/R) (108) the original or the new normalized BD set B may, then, be used to compute QSM in the same way as in the usual electronic density distribution framework. That is, a Boltzmann similarity measure (BSM) involving two QO, {A, fi}, corresponds to the integral \x^^(Q) = J P^(R)Q(R)P^(R)^ (109) just as in Eq. 1, Q(R) is a weighting operator and the densities used here are the associated BD (P^, P^}. Thus, everything said in the realm of electronic density distributions can be repeated here.