Molecular quantum similarity computational measurement

Finally, in the last chapter (Chapter 12) of Part II of this book, Ramon has studied the molecular quantum similarity (QS) measures involving three density functions. The necessary algorithms have been described here. General theory and computational feasibility of a h3q)ermatricial or tensorial representation of molecular structures associated to any molecular quantum object set (MQOS) have been nicely explained in this chapter. Secondly, generalized Carbo similarity indices (CSI) have also been studied. The theoretical and computational approaches have been supported by various suitable applicative examples. 

Robert, D. and Carb6-Dorca, R. (1998a). A Formal Comparison Between Molecular Quantum Similarity Measures and Indices. J.Chem.Inf.Comput.Sci., 38, 469 75. 

Molecular quantum similarity measures tuned 3D QSAR an antitumoral family validation study./. Chem. Inf. Comput. Sci., 38, 624—631. 

Robert D, Amat L, Carbo-Dorca R. Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures prediction of the corticosteroid-binding globulin binding affinity for a steroid family. J Chem Inf Comput Sci 1999 39 333-344. 

Amat L, Carbo-Dorca R, Ponec R. Molecular quantum similarity measures as an alternative to log P values in QSAR studies. J Comput Chem 1998 19 1575-1583. 

A firm theoretical basis has been estabHshed for molecular quantum similarity, and many computational tools have been developed that allow for the evaluation and quantification of molecular quantum similarity measures among sets of molecules or atoms. Molecular quantum similarity is also the basis of quantum QSAR, another active field of research. 

In the next two subsections, we describe collections of calculations that have been used to probe the physical accuracy of plane-wave DFT calculations. An important feature of plane-wave calculations is that they can be applied to bulk materials and other situations where the localized basis set approaches of molecular quantum chemistry are computationally impractical. To develop benchmarks for the performance of plane-wave methods for these properties, they must be compared with accurate experimental data. One of the reasons that benchmarking efforts for molecular quantum chemistry have been so successful is that very large collections of high-precision experimental data are available for small molecules. Data sets of similar size are not always available for the properties of interest in plane-wave DFT calculations, and this has limited the number of studies that have been performed with the aim of comparing predictions from plane-wave DFT with quantitative experimental information from a large number of materials. There are, of course, many hundreds of comparisons that have been made with individual experimental measurements. If you follow our advice and become familiar with the state-of-the-art literature in your particular area of interest, you will find examples of this kind. Below, we collect a number of examples where efforts have been made to compare the accuracy of plane-wave DFT calculations against systematic collections of experimental data. 

Carb6, R. and Calabuig, B. (1992d). Quantum Similarity Measures, Molecular Cloud Description, and Structure-Properties Relationships. J.Chem.Inf.Comput.Sci.,32,600-606. 

Field-based similarities are usually evaluated by the cosine or correlation function similarity measure employed initially by Carbo and co-workers (67) to compute molecular similarities based upon quantum mechanical wavefunctions. Such a measure, which is usually called a Carbo similarity index, is given by... 

Although QS has started within such similarity-dissimilarity index premises, essentially the fact is that the elementary QS computational element building block reduces to the well-known scalar product of two DFs, a so-called similarity measure. Indeed, given two quantum systans, say [A,B), the familiar quantum mechanical theoretical basis permits to obtain their attached wavefunctions via solving the respective Schrbdinger equations. From the system wavefunctions, a pair of associated DF p,4(r),pg(r) can be simply set up, with the vector r representing some number of particle coordinates. In molecular QS studies, the usual DF chosen is the first-order one thus, vector r = (x,y,z) corresponds to one-electron position coordinate only. Then, the similarity measure between the system pair of DF is simply defined as the overlap similarity integral ... 

Combined Quantum Mechanical and Molecular Mechanical Potentials Hyperconjugation M0ller-Plesset Perturbation Theory Ifatural Bond Orbital Methods Rotational Barriers and Molecular Mechanics Corrections Rotational Barriers Ab Initio Computations Spectroscopy Computational Methods Structural Similarity Measures for Database Searching. 

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