Structure quantum similarity measures

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

Lobato, M., Amat, L., Besalil, E. and Carbd-Dorca, R. (1997). Structure-Activity Relationships of a Steroid Family Using Quantum Similarity Measures and Topological Quantum Similarity Indexes. Quant.Struct.-Act.Relat., 16,465-472. 

Robert, D, Amat, L. and Carb6-Dorca, R. (1999). Three-Dimensional Quantitative Structure-Activity Relationships from Timed Molecular Quantum Similarity Measures Prediction of the Corticosteroid-Binding Globulin Binding Affinity for a Steroid Family. J.Chem.Inf.Comput.Sci., 39, 333-344. [R]... 

Lobato M, Amat L, Besalu E, Carbo-Dorca R. Structure-activity relationships of a steroid family using quantum similarity measures and topological quantum similarity indices. Quant Struct-Act Relatsh 1997 16 465-472. 

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. 

Finally, three further studies on QSAR of artemisininoids applying a variety of quantum-chemical and conventional molecular descriptors [105], molecular quantum-similarity measures (MQSM, [111]) and topological descriptors based on molecular connectivity [112] have led to models of quite satisfactory statistical performance. However, apart from showing the applicability of the respective QSAR approaches to this type of compounds both studies offer comparatively little new information with respect to structure-activity relationships. 

Molecular Similarity and QSAR. - In a first contribution on the design of a practical, fast and reliable molecular similarity index Popelier107 proposed a measure operating in an abstract space spanned by properties evaluated at BCPs, called BCP space. Molecules are believed to be represented compactly and reliably in BCP space, as this space extracts the relevant information from the molecular ab initio wave functions. Typical problems of continuous quantum similarity measures are hereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para- and me/a-substituted benzoic acids. On the basis of the author s definition of distances between molecules in BCP space, the experimental sequence of acidities determined by the well-known a constant of a set of substituted congeners is reproduced. Moreover, the approach points out where the common reactive centre of the molecules is. The generality and feasibility of this method will enable predictions in medically related Quantitative Structure Activity Relationships (QSAR). This contribution combines the historically disparate fields of molecular similarity and QSAR. 

Density Functions play a fundamental role in the definition of Quantum Theory, due to this they are the basic materials used in order to define Quantum Objects and from this intermediate step, they constitute the support of Quantum Similarity Measures. Here, the connection of Wavefunctions with Extended Density Functions is analysed. Various products of this preliminary discussion are described, among others the concept of Kinetic Energy Distributions. Another discussed set of concepts, directly related with the present paper, is constituted by the Extended Hilbert Space definition, where their vectors are defined as column structures or diagonal matrices, containing both wavefunctions and their gradients. The shapes of new density distributions are described and analysed. All the steps above summarised are completed and illustrated, when possible, with practical application examples and visualisation pictures. 

Analyzing the main information-theoretic properties of many-electron systems has been a field widely studied by means of different procedures and quantities, in particular, for atomic and molecular systems in both position and momentum spaces. It is worthy to remark the pioneering works of Gadre et al. [62,63] where the Shannon entropy plays a fundamental role, as well as the more recent ones concerning electronic structural complexity [27, 64], the connection between information measures (e.g., disequilibrium, Fisher information) and experimentally accessible quantities such as the ionization potentials or the static dipole polarizabilities [44], interpretation of chemical phenomena from momentum Shannon entropy [65, 66], applications of the LMC complexity [36, 37] and the quantum similarity measure [47] to the study of neutral atoms, and their extension to the FS and CR complexities [52, 60] as well as to ionized systems [39, 54, 59,67]. 

After the seminal structure building of the QS formalism, several additional studies appeared over time, which developed new theoretical details. Especially noteworthy is the concept of vector semispace (VSS). This mathematical construction will be shown to be the main platform on which several QS ideas are built, related in turn, to probability distributions and hence to quantum mechanical probability density functions. Such quantum mechanical density distributions form a characteristic functional set, which can be easily connected to VSS properties. Construction of the so-called quantum objects (QO) and their collections the QO sets (QOS) (see, for example, Carbo-Dorca ), easily permit the interpretation of the nature of quantum similarity measures for relationships between such quantum mechanically originated elements. Within quantum similarity context, QOS appear as a particular kind of tagged sets, where objects are submicroscopic systems and their density functions become tags. 

Using Molecular Quantum Similarity Measures as Descriptors in Quantitative Structure-Toxicity Relationships. 

Applied Sciences and Engineering (ECCOMAS 2000), CDROM edited by Facultat d ln-formatica de Barcelona (FIB)— Universitat Politecnica de Catalunya (UPC)—International Centre for Numerical Methods in Engineering (CIMNE) Barcelona, 2000, Computational Chemistry Section, Chapter 12. Quantum Quantitative Structure-Activity Relationships (QQSAR) A Comprehensive Discussion Based on Inward Matrix Products, Employed as a Tool to Find Approximate Solutions of Strictly Positive Linear Systems and Providing QSAR-Quantum Similarity Measures Connections. 

IT-IQC-02-17, 2002. Brief Theoretical Description, With Appropriate Application Examples, of Density Eunctions Structure and Approximations, Leading to the Eoundation of Quantum Similarity Measures and Conducting Towards Quantum Quantitative Structure-Properties Relationships. 

R. Carbo and B. Calabuig,/. Chem. Inf. Comput, Sci. 32, 600 (1992). Quantum Similarity Measures, Molecular Cloud Description and Structure-Property Relationships. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

Carb6, R., Besalu, E., Amat, L. and Fradera, X. (1995). Quantum Molecular Similarity Measures (QMSM) as a Natural Way Leading towmds a Theoretical Foundation of Quantitative Structure-Properties Relationships (QSPR).J.Math.Chem., 18,237-246. 

Carbo R, Besalu E, Amat L, Fradera X. Quantum molecular similarity measures (QMSM) as a natural way leading towards a theoretical foundation of quantitative structure-properties relationships (QSPR). J Math Chem 1995 18, 237-246. 

In quantum chemistry, the state of a physical system is usually described by a wave function in the position space. However, it is also well known that a wave function in the momentum space can provide complementary information for electronic structure of atoms or molecules [1]. The momentum-space wave function is especially useful to analyse the experimental results of scattering problems, such as Compton profiles [2] and e,2e) measurements [3]. Recently it is also applied to study quantum similarity in atoms and molecules [4]. In the present work, we focus our attention on the inner-shell ionization processes of atoms by charged-particle impact and study how the electron momentum distribution affects on the inner-shell ionization cross sections. 

Vol. 1, R. Carbo-Dorca and P. G. Mezey, Eds., JAI Press, London, 1996, pp. 1-42. Quantum Molecular Similarity Measures Concepts, Definitions, and Applications to Quantitative Structure-Property Relationships. 

Type-A measures are appropriate for measuring the similarity between one or, at most, a few pairs of structures that are characterized by quantum-mechanical descriptions of various sorts. Following the pioneering studies of Carbo et al.io a large number of similarity measures have been described that fall in this class (see, e.g.. Refs. 11—14). Here, a molecule is described by an electron probability density function, and the similarities between pairs of molecules are calculated with measures that describe the overlap of their density functions. Work in this area is exemplified by that of Manaut et al.i" who describe a procedure to align two molecules so as to maximize the similarity... 

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. 

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. 

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