Quantum similarity measures applications

Gallegos Sahner, A. and Girones, X. (2005) Topological quantum similarity measures applications in QSAR. /. Mol Struct. (Theochem), 727, 97-106. 

Amat, L. and Carbo-Dorca, R. (1999) Fitted electronic density functions from H to Rn for use in quantum similarity measures cis-diamminedichloroplatinum(II) complex as an application example. 

R. Modeling antimalarial activity application of kinetic energy density quantum similarity measures as descriptors in QSAR./. Chem. Inf. Comput. Sci. 2000, 40, 1400—1407. 

Carbo, R. and Calabuig, B. (1992b). Molecular Quantum Similarity Measures and N-Dimen-sional Representation of Quantum Objects. II. Practical Applications. InU.Quant.Chem., 42, 1695-1709. 

A general definition of the Quantum Molecular Similarity Measure is reported. Particular cases of this definition are discussed, drawing special attention to the new definition of Gravitational-like Quantum Molecular Similarity Measures. Applications to the study of fluoromethanes and chloro-methanes, the Carbonic Anhydrase enzyme, and the Hammond postulate are presented. Our calculations fully support the use of Quantum Molecular Similarity Measums as an efficient molecular engineering tool in order to predict physical properties, lMok>gical and pbarraacdogical activities, as well as to interpret complex chemical problems. 

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. 

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. 

The actual discussion has the aim to adopt this previous spirit, but obviously choosing a much more modest point of view, attached to Quantum Similarity Measures (QSM). This work is focused to explore the various possible extensions for the study of DF, the auxiliary building block elements of QSM [16-38]. In order to fulfil such a purpose, this study will start analysing a sound formal basis as a first step to understand the role of momentum operators in computational Quantum Chemistry. From this introductory position, it will be finally obtained a general pattern enveloping the whole area of DF study, beginning at the basic aspects and ending over the final applications of extended DF definitions. 

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]. 

As a final note, on several occasions, alignment-free methods have been used to quantify molecular similarity in the field of molecular quantum similarity, these methods have not yet fovmd extensive application. One method to obtain molecular quantum similarity measures without the need for molecular alignment was published by Boon et al. They use statistical techniques, more specifically, the autocorrelation function. This technique offers an interesting alternative method for similarity studies by removing completely the important obstacle of molecular alignment. 

Application of Eq. [86] in the general definition of a molecular quantum similarity measure then gives ... 

Modeling Antimalarial Activity Application of Kinetic Energy Density Quantum Similarity Measures as Descriptors in QSAR. 

Density Functions from FI to Rn for Use in Quantum Similarity Measures Cis-Diammine, Dichloroplatinum(II) Complexes as an Application Example. 

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. 

In recent years, the present authors have developed an interest in obtaining chemical information from atonic density functions. The application of concepts from quantum chemistry shows that some particular aspects of physical and chemical interest can be read from the density functions. In particular the comparison of density functions using quantum similarity measures or functionals from information theory plays an important role. The original goal of the work was to find a way of regaining the periodicity in Mendeleev s table through the comparison of density functions. 

As to the content of Volume 25, the Editors thank the authors for their contributions, which give an interesting picture of part of the current state of the art of the quantum theory of matter From nonlinear-optical calculations, over a study of ion motion in molecular channels, a treatment of molecular integrals over Gaussian basis functions, and an investigation of soliton dynamics in franr-polyacetylene, to applications of quantum molecular similarity measures. 

As mentioned, the application of molecular descriptors with quantum mechanical origins was proposed several years ago, ° but the first ideas about quantum similarity (QS) and QS measures (QSM) were published aroimd 1980. However, it has been not until recently that the mathematical and physical foundations of QS have been developed in a series of publica-... 

Quantum Chemical to Phenomenological Approaches, R. Carbo, Ed., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995, pp. 89-111. General Suggestions and Applications of Quantum Molecular Similarity Measures from Ab Initio Fitted Electron Densities. 

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. 

Among the many applications of molecular similarity measures to the analysis of electronic wavefunctions, those associated with the taxonomy of chemical reactions and the assessment of accuracy of various quantum chemical methods are particularly worth mentioning. Quantification of similarities among reactants, products, and transition states of chemical reactions has afforded a rigorous formulation of the Hariimond postulate. Accuracies of Koopmans theorem and various approaches to the electron correlation problem have been assessed with the help of the NOEL similarity measure applied to the one-electron reduced density matrices obtained at the respective levels of theory. The use of similarity measures in analysis of excited-state wavefunctions has already been mentioned in Section 7. 

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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