Arbitrary molecular similarity

Keywords Arbitrary molecular similarity Hierarchical molecular overlay ... 

Basak SC, Gute BD, Mills D, Hawkins DM. Quantitative molecular similarity methods in the property/toxicity estimation of chemicals a comparison of arbitrary versus tailored similarity spaces. J Mol Struct (Theochem) 2003 622 127-45. 

This chapter has dealt with introducing the main concepts within a theory called MQS. It has discussed the different steps to be taken to evaluate and quantify a degree of similarity between molecules in some molecular set but also fragments in molecules. QSM provides a scheme that relieves the arbitrariness of molecular similarity by using the electron density function as the sole descriptor, in agreement with the Hohenberg-Kohn theorems. It also addressed the different pitfalls that are present, for example the dependence on proper molecular alignment. 

The eluates from the Sephadex and Styragel experiments were combined to give four arbitrary molecular weight fractions (a) <1000, (b) 1000-4000, (c) 4000-8000 and (d) 8000-22000. The relative proportions of the four fractions were determined by weighing after evaporation of the solvent. Similar separations were carried out on the resins and the methanol-soluble component. 

Benzene is the prototypical aromatic molecule with 6 n electrons, perfect Z)6h symmetry, aromatic stabilization energy of about 36 kcal/mol, a NICS value of roughly -9 ppm and an appreciable amount of diamagnetic ring current. Aromaticity of an arbitrary molecule is some times judged through its resemblance with benzene via parameters like Polansky index, molecular similarity, Clar s sextet etc. 

In drug design, one uses the molecular similarity concept to select analogs of interesting leads. Such selections are usually made based on user-defined methods. Therefore, such methods are always biased. We have come up with the idea of tailored similarity , where the property of interest is used to create a structure space that is relevant to that specific property. The results indicate that such tailored methods outperform arbitrary, user-defined QMSA techniques. 

This section attempts a brief review of several areas of research on the significance of phases, mainly for quantum phenomena in molecular systems. Evidently, due to limitation of space, one cannot do justice to the breadth of the subject and numerous important works will go unmentioned. It is hoped that the several cited papers (some of which have been chosen from quite recent publications) will lead the reader to other, related and earlier, publications. It is essential to state at the outset that the overall phase of the wave function is arbitrary and only the relative phases of its components are observable in any meaningful sense. Throughout, we concentrate on the relative phases of the components. (In a coordinate representation of the state function, the phases of the components are none other than the coordinate-dependent parts of the phase, so it is also true that this part is susceptible to measurement. Similar statements can be made in momentum, energy, etc., representations.)... 

The main idea of the 3D-LogP descriptor approach is to sample the molecular surface and then to sum the area of those points with similar MLP values. The 3D-LogP descriptor proposed here is a vector V with NBINS elements each element of which V, is the sum of the area of all surface elements whose MLP lies between two arbitrary discrete values. The number of bins to be used was chosen after experimentation with various values and 200 was found to be appropriate here, because it allowed the population of the bins with a significant number of area elements for both hydrophilic (MLP < 0) and hydrophobic (MLP > 0) surfaces. However, other values for NBINS may be more suitable in particular cases. In order to simplify things, in the following description it is... 

Similar analysis can be made for particles with an arbitrary initial charge multiplicity Z. If, in particular, a particle is originally neutral, tunneling will occur in an attractive electric field. It can be readily seen that, in the general case, the activation energy is ET + (Z+ 1)A.FT. The assumption that the molecular affinity EA is independent of the electric field of charged particles is quite reasonable, because at Z < 3 this field is still considerably weaker than the local electric fields associated with the chemisorption process. 

Figure 6.12. Coordinate system for the hydrogen molecular ion. O is the arbitrary space-fixed origin, CM is the centre-of-mass of the system, and G is the geometric centre of the nuclei. This diagram, although similar to figure 2.1, differs in some important aspects.

Several points concerning the above prescription should be emphasized. First of all, it is an arbitrary construction that is not derivable from the postulates of quantum mechanics. Second, since the presence of a sufficient number of the aforementioned maxima cannot be guaranteed in general, this prescription is by no means universal. Third, since atoms and molecules have infinite extends, similar considerations cannot be employed in a definition of molecular shape. In summary, although isolated molecules possess neither classical structures nor shapes [3], their geometries can be defined under certain conditions. 

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