Abstract
The principle of“Geometrical Similarity as Topological Equivalence“ (the GSTE Principle) has been proposed and applied to the problems of molecular similarity in several studies (see, e.g. refs. 1–3 and references therein). The basic idea behind this principle is simple: similarity between two geometrical constructions can be expressed as a topological equivalence within a suitable chosen topology.
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References
Mezey, P.G. (1993) Shape in Chemistry: An Introduction to Molecular Shape and Topology, VCH Publishers, New York.
Mezey, P.G. (1997) Quantum Chemistry of Macromolecular Shape, Internat. Rev. Phys. Chem., 16, 361–388.
Mezey, P.G. (1997) Shape in Quantum Chemistry. In Conceptual Trends in Quantum Chemistry, Vol. 3, Calais, J.-L.; Kryachko, E.S. (eds.), Kluwer Academic Publ., Dordrecht, The Netherlands, pp 519–550.
Mezey, P.G. (1991) The Degree of Similarity of Three-Dimensional Bodies; Applications to Molecular Shapes, J. Math. Chem., 7, 39–49.
Mezey, P.G. (1999) Shape-Similarity Relations Based on Topological Resolution, J. Math. Chem., in press.
Mezey, P.G. (1995) Macromolecular Density Matrices and Electron Densities with Adjustable Nuclear Geometries, J. Math. Chem., 18, 141–168.
Mezey, P.G. (1997) Quantum Similarity Measures and Löwdin’s Transform for Approximate Density Matrices and Macromolecular Forces, Int. J. Quantum Chem., 63, 39–48.
Walker, P.D., and Mezey, P.G. (1994) Ab initio Quality Electron Densities for Proteins: A MEDLA Approach, J. Am. Chem. Soc., 116, 12022–12032.
Walker, P.D., and Mezey, P.G. (1994) Realistic, Detailed Images of Proteins and Tertiary Structure Elements: Ab Initio Quality Electron Density Calculations for Bovine Insulin, Can J. Chem., 72, 2531–2536.
Walker, P.D., and Mezey, P.G. (1995) A New Computational Microscope for Molecules: High Resolution MEDLA Images of Taxol and HIV-1 Protease, Using Additive Electron Density Fragmentation Principles and Fuzzy Set Methods, J. Math. Chem., 17, 203–234.
Mezey, P.G. (1998) Generalized Chirality and Symmetry Deficiency, J. Math. Chem., 23, 65–84.
Mezey, P.G. (1999) The Holographic Electron Density Theorem and Quantum Similarity Measures, Mol. Phys., 96, 169–178.
Hohenberg, P., and Kohn, W. (1964) Inhomogeneous electron gas. Phys. Rev. 136, B864-B871.
Levy, M. (1996) Elementary Concepts in Density Functional Theory. In Recent Developments and Applications of Modern Density Functional Theory, Theoretical and Computational Chemistry, Vol. 4; J.M. Seminario, Ed.; Elsevier Science B.V.: Amsterdam, pp 3–24.
Mezey, P.G. (1999) Holographic Electron Density Shape Theorem and Its Role in Drug Design and Toxicological Risk Assessment, J. Chem. Inf. Comput. Sci., 39, 224–230.
Mezey, P.G., Ponec, R., Amat, L., and Carbo-Dorca, R. (1999) Quantum Similarity Approach to the Characterization of Molecular Chirality, Enantiomers, in press.
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Mezey, P.G. (2001). Topological Similarity of Molecules and the Consequences of the Holographic Electron Density Theorem, an Extension of the Hohenberg-Kohn Theorem. In: Carbó-Dorca, R., Gironés, X., Mezey, P.G. (eds) Fundamentals of Molecular Similarity. Mathematical and Computational Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3273-3_8
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DOI: https://doi.org/10.1007/978-1-4757-3273-3_8
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