Computable similarity function, molecular

The overall form of each of these equations is fairly simple, ie, energy = a constant times a displacement. In most cases the focus is on differences in energy, because these are the quantities which help discriminate reactivity among similar stmctures. The computational requirement for molecular mechanics calculations grows as where n is the number of atoms, not the number of electrons or basis functions. Immediately it can be seen that these calculations will be much faster than an equivalent quantum mechanical study. The size of the systems which can be studied can also substantially ecHpse those studied by quantum mechanics. 

Constans P, Amat L, Carbo-Dorca R. Toward a global maximization of the molecular similarity function superposition of two molecules. J Comput Chem 1997 18 826-846. 

Vector-based methods can use combinations of ID, 2D, and 3D descriptors vide supra) and are considerably faster computationally than function-based methods (cf. [100]) for two reasons. First, summations over vector components are generally faster than integrations over whole molecules. In one case, fast 3D similarity searches were carried out using a vector-like representation whose components were derived from a set of molecular shape-based criteria [100]. 

How does this example apply to the use of multiple similarity methods Each of the similarity methods can be considered to be equivalent to an independent judge, since none of the values produced by the other methods have an explicit impact on the value produced by a given method. This may not always be the case, for example, if two methods use MACCS key fingerprints, but one uses the Tanimoto (Jacard) and the other a closely related similarity function (see Table 15.3). As shown by Gower [76], some molecular similarity functions are monotonically related. Thus, comparisons of these functions based on the same molecular representation will produced linear correlations of the values computed by the two functionally similarity functions. Hence, only one of the functions should be used. 

For metal clusters, it is now possible, through first principle theoretical (calculational) approaches, to predict and better understand vibrational spectra, optical band gaps, polarizability, quantum confinement, and stmctural predictions. One modern approach is to use pseudopotential density functional methods (PDFM), in particular to predict optical and dielectric properties. Similarly, using molecular dynamics simulations, it is possible to create models for cluster structures. This has been especially valuable for predicting a three-dimensional image for mixed metal clusters. Figure 6 illustrates computed stmctures for Cu-Ru bimetallic clusters. Note that in this case the dynamics simuiation predicted an enrichment of Cu at the edges and corners of the polyhedral structure. Indeed, this prediction was supported by later experimental catalysis data. 

C, E E Hodgkin and Richards W G 1993. The Utilisation of Gaussian Functions for the Rapid nation of Molecular Similarity. Journal of Chemical Information and Computer Science 32 188-192. C and I D Kuntz 1995, Investigating the Extension of Pairwise Distance Pharmacophore sures to Triplet-based Descriptors, Journal of Computer-Aided Molecular Design 9 373-379. 

In light of the differences between a Morse and a harmonic potential, why do force fields use the harmonic potential First, the harmonic potential is faster to compute and easier to parameterize than the Morse function. The two functions are similar at the potential minimum, so they provide similar values for equilibrium structures. As computer resources expand and as simulations of thermal motion (See Molecular Dynamics , page 69) become more popular, the Morse function may be used more often. 

Monte Carlo calculations are somewhat similar to the molecular (or Langevin) dynamics calculations discussed earlier. All function by repeated application of a computational algorithm that generates a new configuration from the current configuration. The... 

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