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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computer aided molecular design 13 (1999), S. 259-270 
    ISSN: 1573-4951
    Keywords: log P ; molecular quantum similarity measures ; quantitative structure-properties relationships (QSPR) ; substituent effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Since the dawn of quantitative structure-properties relationships (QSPR), empirical parameters related to structural, electronic and hydrophobic molecular properties have been used as molecular descriptors to determine such relationships. Among all these parameters, Hammett σ constants and the logarithm of the octanol- water partition coefficient, log P, have been massively employed in QSPR studies. In the present paper, a new molecular descriptor, based on quantum similarity measures (QSM), is proposed as a general substitute of these empirical parameters. This work continues previous analyses related to the use of QSM to QSPR, introducing molecular quantum self-similarity measures (MQS-SM) as a single working parameter in some cases. The use of MQS-SM as a molecular descriptor is first confirmed from the correlation with the aforementioned empirical parameters. The Hammett equation has been examined using MQS-SM for a series of substituted carboxylic acids. Then, for a series of aliphatic alcohols and acetic acid esters, log P values have been correlated with the self-similarity measure between density functions in water and octanol of a given molecule. And finally, some examples and applications of MQS-SM to determine QSAR are presented. In all studied cases MQS-SM appeared to be excellent molecular descriptors usable in general QSPR applications of chemical interest.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computer aided molecular design 13 (1999), S. 597-610 
    ISSN: 1573-4951
    Keywords: Atomic Shell Approximation (ASA) density functions ; Carbó index ; classical scaling ; Cramer steroids ; facet theory ; quantum similarity ; quantitative structure-activity relationships (QSAR) ; toxicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The objective of this work is to demonstrate that an appropriate treatment of quantum similarity matrices can reveal hidden data grouping related to relevant structural features and even to biological properties of interest. Classical scaling is used here to extract the information contained in the similarity relationships between the elements of a molecular set. Facet theory is invoked to relate, in a qualitative way, the spatial regions to structural characteristics as well as to properties of interest. Two application examples are discussed: the Cramer steriod set and a benzene, toluene and xylene derivatives set.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computer aided molecular design 14 (2000), S. 477-485 
    ISSN: 1573-4951
    Keywords: electron-electron repulsion energy ; molecular descriptor ; molecular quantum similarity measures ; QSAR ; QSPR
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Electron-electron repulsion energy (〈 Vee〉) is presented as a new molecular descriptor to be employed in QSAR and QSPR studies. Here it is shown that this electronic energy parameter is connected to molecular quantum similarity measures (MQSM), and as a consequence can be considered as a complement to steric and electronic parameters in description of molecular properties and biological responses of organic compounds. The present strategy considers the molecule as a whole, thus there is no need to employ contributions of isolated fragments as in many calculations of molecular descriptors, like log P or the Free–Wilson analysis. The procedure has been tested in a widespread set of molecules: alcohols, alkanamides, indole derivatives and 1-alkylimidazoles. Molecular properties, as well as toxicity, are correlated using 〈 Vee〉 as a parameter, and extensions to the method are given for handling difficult systems. In almost all studied cases, satisfactory linear relationships were finally obtained.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 21 (1997), S. 395-412 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract An iterative method based on perturbation theory in matrix form is described as a procedure to obtain the eigenvalues and eigenvectors of square matrices. Practical vector notation and elementary schematic algorithm codes are given. The particular programming characteristics of the present computational scheme are based upon eigenvector corrections, obtained through a simple Rayleigh–Schrödinger perturbation theory algorithm. The proposed methodological processes can be used to evaluate the eigensystem of large matrices.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Starting from previous work, where Rayleigh–Schrödinger perturbation theory has been reformulated in matrix form, a practical algorithm implementation is described using both full matrix and vector alternatives. An heuristic convergence sufficiency criterion based on Gershgorin discs is also presented. Some numerical examples related to atomic CI computations are reported to illustrate the theoretical framework.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 22 (1997), S. 143-147 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The fuzzy set structure is analysed from the point of view of a new definition: Boolean tagged sets, which are constructed as a straightforward generalisation of the fuzzy set concept, but fully adapted to computational purposes. Boolean tagged sets are simply structured as sets whose members are tagged by a binary string, attached in turn to the vertices of a unit hypercube. Boolean tagged sets are so designed as to become useful in any field of applied mathematics, but they can also be seen as obviously prepared for chemical applications, associated to molecular information gathering and manipulation.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 28 (2000), S. 59-70 
    ISSN: 1572-8897
    Keywords: quantum chemistry ; Sobolev spaces ; Schrödinger equation ; extended wavefunctions ; kinetic energy ; Sobolev transformation ; SCF theory ; generalised secular equations ; LCAO-MO theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Extended wavefunctions, including the wavefunction gradient, and the norm induced Sobolev spaces are presented as a mathematical structure well adapted to the approximate quantum-chemical formalism, customarily used to handle the Schrödinger equation. A useful application, related to the solution of SCF Euler equations in matrix form, is also analysed.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 20 (1996), S. 247-261 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Maxwell-Boltzmann statistics provides the adequate mathematical background allowing to define similarity measures involving molecular energy surfaces and electrostatic potential maps. Boltzmann similarity measures are described and various illustrative examples are used to show the practical viability of the theory. A new molecular similarity index is also presented. Finally, hybrid measures involving Boltzmann and density distributions are defined.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 20 (1996), S. 263-271 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Based on Jacobi elementary rotations, a simple, elegant procedure to obtain approximate CI wavefunctions is discussed. Essentially, a sequence of (2 x 2) matrices is builtup, and the eigenvector attached to the lowest eigenvalue is used to construct a stepwise set of coefficients, which become a very good approximation to theexact Cl result. Full CI calculations could easily be reached in this way. An example formed by some atoms of the He isoelectronic sequence is provided in order to test the flexibility and accuracy of the procedure. A Fortran 90 code is available.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 23 (1998), S. 327-351 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Quantum similarity is a useful tool to establish comparisons between elements of a quantum object set and, so far applied successfully to molecular physics, is applied here to atomic nuclei. Quantum Similarity Measures (QSM) and Indices (QSI) are introduced to study an arbitrary set of 20 nuclei. From this study, relationships between nuclear overlap‐like self‐similarities and size‐like properties are found. A bidimensional projection of the set is performed, and Mendeleev conjecture is invoked to predict qualitatively some nuclear ground‐state properties, such as total binding energy per nucleon, nuclear radius, nuclear volume, total and partial energies, etc.
    Type of Medium: Electronic Resource
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