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  • 1
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    Distance between natural numbers based on their prime signature (2021)
    Elsevier
    Details
    Publication Date: 2021-10-01
    Print ISSN: 0022-314X
    Electronic ISSN: 1096-1658
    Topics: Mathematics
    Published by Elsevier
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    PAPER CURRENT
  • 2
    Electronic Resource
    Electronic Resource
    Comprehensive conformational analysis of the four- to twelve-membered ring cycloalkanes: identification of the complete set of interconversion pathways on the MM2 potential energy hypersurface (1993)
    s.l. : American Chemical Society
    Journal of the American Chemical Society 115 (1993), S. 2107-2119 
    Details
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ja00059a003
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Compare Conformer: a program for the rapid comparison of molecular conformers based on interatomic distances and torsion angles (1992)
    s.l. : American Chemical Society
    Journal of chemical information and modeling 32 (1992), S. 191-199 
    Details
    ISSN: 1520-5142
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ci00007a003
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  • 4
    Electronic Resource
    Electronic Resource
    A similarity measure for chemical data: Applications to cluster analysis (1990)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 4 (1990), S. 255-266 
    Details
    ISSN: 0886-9383
    Keywords: Similarity measure ; Cluster analysis ; Riemannian space ; Metric tensor ; Curvature ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The results of unsupervised pattern recognition methods are critically dependent on the measure of similarity used for clustering objects. There is little a priori information available on the relative utility of various similarity measures. We introduce here an alternative similarity measure based on the metric tensor measure (MTM). Two standard clustering strategies are tested with the proposed similarity measure: hierarchical clustering and the K-median method. As data we use the ARCH obsidian data, a data set on Hungarian coal, and trace element data on Hungarian paprika. Differences from the Mahalanobis distance measure are described for intraclass relations.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180040306
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  • 5
    Electronic Resource
    Electronic Resource
    On the degeneracy of the Hessian matrix (1992)
    Springer
    Journal of mathematical chemistry 9 (1992), S. 359-367 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A widespread notion in the computational chemistry literature about the Hessian matrix has been revisited, namely, that the Hessian matrix over Cartesian space is sixfold degenerate due to the three translational and three rotational degrees of freedom. It has been shown that this is true only at critical points on the potential energy hypersurface, otherwise the Hessian matrix is only threefold degenerate. The rotational degrees of freedom generally do not cause degeneracy in the Hessian matrix away from critical points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01166099
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  • 6
    Electronic Resource
    Electronic Resource
    Information theory and electron density (1996)
    Springer
    Journal of mathematical chemistry 19 (1996), S. 393-399 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The intriguing concept of inherent uncertainty of probability schemes in information theory and statistical inference is applied to the molecular electron density. The electron density function is treated as a multimodal, three-dimensional probability density function describing the distribution of the electrons of a molecule in real space. A simple theory is proposed to introduce the amount of information associated with perturbations of the nuclear geometry such as molecular vibrations and reaction paths, in particular. It is shown by computations that the amount of information associated with the normal modes of vibration is related to the reduced mass. The proposed theory also suggests a novel Riemannian nuclear configuration space which is completely defined by the observable electron density of a molecular system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01166728
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  • 7
    Electronic Resource
    Electronic Resource
    Evaluation of quantitative structure-activity predictions. Comparison of the predictive power of an artificial intelligence system with human experts (1990)
    Springer
    Journal of mathematical chemistry 5 (1990), S. 389-407 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract In this paper, we present three new mathematical techniques for evaluating the predictive skills of structure-activity experts. The question addressed in this paper is how to evaluate the predictive ability of structure-activity experts in identifying the most active compounds of a set of drug candidates. The three proposed mathematical techniques are based on the Phi-square Distance, the Rank Comparison, and the Shuffle method, respectively. They have been used to evaluate the performance of a new computer system and three human experts in predicting the antibacterial potencies of a series of chemical compounds in five different biological tests. The expert system, an artificial intelligence structure-activity program called MULTICASE, performed significantly better than one of the human experts and somewhat better than the other two.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164858
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  • 8
    Electronic Resource
    Electronic Resource
    Torsional flexing: Conformational searching of cyclic molecules in biased internal coordinate space (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 14 (1993), S. 691-698 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A new stochastic (Monte Carlo) procedure, termed torsional flexing, has been devised for searching the conformational space of cyclic molecules. Torsional flexing causes a local, torsion angle-biased, distortion of a ring bond in a cyclic molecule. Because torsional flexing does not cause large atomic movements, even when it is applied to several bonds simultaneously, subsequent energy minimization generally proceeds rapidly. Nevertheless, the torsional flexing method is prone to generate structures that cross energy barriers so that the structure resulting after energy minimization is frequently a different conformer of the cyclic molecule. Conformational searches on cycloheptadecane, oxobrefeldin A, cyclopenta-L-alanine, and rifamycin SV based upon torsional flexing indicated that torsional flexing is among the best methods yet devised for searching the conformational space of flexible cyclic molecules. © 1993 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540140610
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  • 9
    Electronic Resource
    Electronic Resource
    Theoretical study of intramolecular hydrogen bonding and molecular geometry of 2-trifluoromethylphenol (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 17 (1996), S. 1804-1819 
    Details
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The conformational behavior of 2-trifluoromethylphenol was investigated by means of theoretical calculations. Four characteristic structures have been found on the potential energy hypersurface of the compound: anti form (local minimum), in which the hydroxy hydrogen points away from the trifluoromethyl group; and three syn forms (the hydrogen points towards the trifluoromethyl group), with different trifluoromethyl torsions (global minimum, one low and another one high lying saddle-point). The geometry of these conformers were optimized by ab initio calculations using 6-31G** basis set. The effects of electron correlation were investigated by MP2 and various DFT methods. To investigate the intramolecular interaction in the syn forms, the electron density distribution was calculated at the MP2 level of theory. In the structure corresponding to the global minimum at the MP2/6-31G** level a bond critical point was found in Bader's sense between the hydroxy hydrogen and a fluorine of the trifluoromethyl group indicating hydrogen bonding interaction. The length of the hydrogen bond, 1.98 Å, corresponds to medium strength interaction. The O(SINGLE BOND)H bond is slightly twisted and the C(SINGLE BOND)F bond, interacting with it, is considerably twisted out of the plane of the benzene ring to the same side of the ring. The most pronounced geometrical consequence of the hydrogen bond is the 0.02-Å lengthening of the C(SINGLE BOND)F bond participating in its formation. All the other geometrical changes in 2-trifluoromethylphenol, as compared with trifluoromethylbenzene and phenol, are also consistent with the phenomenon of resonance-assisted hydrogen bonding. © 1996 by John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.2
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  • 10
    Electronic Resource
    Electronic Resource
    Simple tests for density functional methods (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 1534-1545 
    Details
    ISSN: 0192-8651
    Keywords: self-interaction error ; hybrid functionals ; H2, total energy ; equilibrium bond length ; electron density ; KS potential ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The performance of the currently used generalized gradient approximation density functionals is analyzed using several simple, yet critical requirements. We analyze the effects of the self-interaction error, the inclusion of the exact exchange, and the parameter settings used in the popular three-parameter hybrid density functionals. The results show that the elimination of the self-interaction error from the current density functionals lead to very poor results for H2. The inclusion of the exact exchange does not significantly influence the self-interaction corrected results. The variation of the A, B, and C parameters of a hybrid DFT method influences the H(SINGLE BOND)H equilibrium bond length through a very simple linear equation, and it is possible to reproduce the experimental H(SINGLE BOND)H distance with appropriate selection of these parameters, although an infinite number of solutions exists. Similar results were obtained for the total energy and the electron density along the internuclear axis. The analysis of the exact KS potential at the bond critical point of the dissociating H2 molecule shows that, for this property, the second order Moller-Plesset perturbation theory yields a better potential than the density functionals studied in this article.   © 1997 John Wiley & Sons, Inc.   J Comput Chem 18: 1534-1545, 1997
    Additional Material: 5 Ill.
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