Similarity index

During its historical development, chemistry has introduced a number of useful qualitative notions and concepts in terms of which a wealth of empirical experimental data could be rationalized and classified. An example of such a usefiil 

Because of normalization, the values of this index are bounded by the inequality 

The maximum value of unity attains this index for two identical structures, i.e. when A = B, and with increasing deviations between the structures its value monotonously decreases. 

Within the framework of the topological approximation [91] allowing to eliminate some problems with the invariance of this index to the distance and the mutual orientation of the molecules, the above general definition (68) can be 

The usefulness of this index, especially for the applications to chemical reactivity, can be best demonstrated by formally incorporating the eq.(70) into the framework of the generalized overlap determinant method, where structures A and B are identified 

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Consequently, we can construct a similarity measure intuitively in the following way all matches c -i- d relative to all possibilities, i.e., matches plus mismatches (c+ d) + (a -I- h), yields (c -t- d) / a + b+ c + d), which is called the simple matching coefficient [18], and equal weight is given to matches and mismatches. (Normalized similarity measures are called similarity indices or coefficients see, e.g.. Ref. [19].) When absence of a feature in both objects is deemed to convey no information, then d should not occur in a similarity measure. Omitting d from the above similarity measure, one obtains the Tanimoto (alias Jaccard) similarity measure (Eq. (8) see Ref. [16] and the citations therein) ... 

Statistically, a similar Indication of precision could be achieved by utilising the 95% probability level if the results fell on a "Gaussian" curve, viz., the confidence would lie within two standard deviations of the mean. R 2 x SD = 56.3 24.8... 

The ultraviolet spectra provide further evidence for the predominance of the hydroxycoumarin structure. The spectra of 4-hydroxycoumarin (20, R = H) and 20 (R = Me) are very similar, indicating that the former exists in the hydroxy form, and this formulation is supported by more recent ultraviolet spectral data." Later, the ultraviolet spectra of 26 (R = H) and 26 (R = Me) were reported to differ, this difference being considered to indicate that 4-hydroxycoumarins exist in a keto form in ethanoP however, this... 

Select a set of compounds resolved on a given CSP, calculate the similarity indices between all possible molecule pairs, and then use these indices to build a similarity matrix containing relevant information about the structural diversity within the set of samples separated on this CSP. 

Both dehydrogenases of the pentose phosphate pathway can be classified as adaptive enzymes, since they increase in activity in the well-fed animal and when insulin is given to a diabetic animal. Activity is low in diabetes or starvation. Malic enzyme and ATP-citrate lyase behave similarly, indicating that these two enzymes are involved in lipogenesis rather than gluconeogenesis (Chapter 21). 

Fig. 4 shows c.d.-difference spectra that are due to the presence of a hydroxymethyl group in one member of the pair. The pairs of pyranoses have the same conflguration about each asymmetric carbon atom that is part of the ring. Three related pairs have the same conflguration at the carbon atoms near the hydroxymethyl group and give very similar difference spectra. The similarity indicates that the rotameric distribution for the hydroxymethyl group is similar for each of these pairs. This is to be expected, as all three sugars have 4-hydroxyl groups oriented equatorially, but the relationship is certainly not obvious from the c.d. spectra themselves (see Fig. 3). In contrast, when the conflguration near the hydroxymethyl group...

When the same [NiI (NHC)2] complexes are employed as alkene dimerisation catalysts in ionic liquid (IL) solvent [l-butyl-3-methylimidazolium chloride, AICI3, A-methylpyrrole (0.45 0.55 0.1)] rather than toluene, the catalysts were found to be highly active, with no evidence of decomposition. Furthermore, product distributions for each of the catalyst systems studied was surprisingly similar, indicating a common active species may have been formed in each case. It was proposed that reductive elimination of the NHC-Ni did indeed occur, as outlined in Scheme 13.8, however, the IL solvent oxidatively adds to the Ni(0) thus formed to yield a new Ni-NHC complex, 15, stabilised by the IL solvent, and able to effectively catalyse the dimerisation process (Scheme 13.9) [25-27],... 

There are many alternative indices of similarity, but Gower s is considered to be fairly general and can be related to several other similarity indices [47]. 

The UV spectra of 292 were studied. The spectra of 292 (Y = OEt) with substituents R1 = R2 = Me R1 =Ph, Rz = Me and R1 = Ph, R2 = Me were very similar, indicating that the chromophore was little influenced by the presence or position of the Ph group, which is forced out of planarity by the large C02Et group <1996EJM663>. 

Klebe, G. (1998). Comparative Molecular Similarity Indices CoMSIA In 3D QSAR in Drug Design.., H. Kubinyi, G. Folkers, and Y.C. Martin (eds). Kluwer Academic Publishers, London, UK. 3 87. 

Studies of the energetics and dynamics of Cu2 and Ag2 in rare gas solids have also been completed (31,34). The absorption and fluorescence spectra are similarly indicative of strong guest-host interactions in the low lying states of Cu2 and Ag2 Rather than presenting the spectroscopic and photolytic details, a summary of the observed radiative relaxation processes of visible and uv excited Cu2 and Ag2 in rare gas solids is shown below ... 

From Table 4 it is evident that several natural and modified polyanions did not induce insulinoma cell detachment. Furthermore, the DNA content, a quantitative metric of cell viability, was in general near the baseline (100%) observed in the control studies with PBS. In generalboth the cell attachment and DNA indices gave similar indications of cytotoxicity. Therefore, in an effort to unify these measures the third column of Table 4 reports an overall ranking of the polymer... 

For the low-spin t2g aqua ions [Ru(H20)6]2+, [Rh(H20)6]3+, and [Ir(H20)e]3+ a d-activation mode would a priori be predicted. The approach of a seventh water molecule towards a face or edge of the coordination octahedron is electrostatically disfavored by the filled t2g orbitals which are spread out between the ligands. Rate constants for anation reactions of Cl-, Br-, and I- on [Ru(H20)e]2+ are very similar, indicating identical steps to reach the transition state, namely the dissociation of a water molecule (130). An extension of this study to a large variety of ligands demonstrated clearly that the rate determining... 

The five vials on the bench top are also then applied to a fresh HPTLC plate to examine any degradation of the drug substance in solution. In this case, the plates looked very similar, indicating similar degradation in solution within 1 hour also. 

Many applications of QSM use not the MQSM values as such but similarity indices. There exist many such indices and for a review, the reader is referred to Willett et al. [54]. One example that was touched upon above is the Carbo index. The Carbo index is one of the so-called C-class descriptors giving a value between 0 and 1 where a higher value indicates higher similarity. Although originally defined for overlap MQSM, it can be generalized to different operators f so that the Carbo index becomes... 

Other examples of similarity indices include the Petke [57] and Tanimoto [58] indices, both of which have been investigated in the QSM context. Several studies have shown that mutual relationships between these different indices exist [59-62],... 

Cioslowski et al. used fragment similarity indices to compute the degree of similarity between atoms of the same element in different molecules, where the atoms were those derived from Bader s atoms in molecules theory [68,69]. They introduced a novel atomic similarity index for atom A in molecule X and atom B in molecule Y defined as [70]... 

This similarity indicator, in fact, precedes Parr and Bartolotti s introduction of the shape function terminology [59]. In general, it seems that the shape function is preferred to the electron density as a descriptor of molecular similarity whenever one is interested in chemical similarity. Similarity measures that use the electron density will typically predict that fluorine resembles chlorine less than it resembles sodium, oxygen, or neon using the shape function helps one to avoid conflating similarity of electron number with chemical similarity [53,57]. 

Formulas 21.1 through 21.3 are designed for Hartree-Fock wave functions. There are some attempts to define similar indices using wave functions obtained via methods including electron correlation [19]. Similarly, to the situation with respect to basis set improvement, the results based on correlated wave functions do not necessarily make the qualitative picture of bonding easier to understand. An exception is when there is a significant nondynamical correlation in the system,... 

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