Using only numerical differences of descriptors of entries in databases and the subsequent generation of iterated difference sequences, a simple similarity characterization and efficient approximate similarity measures can be obtained for the database entries, and for some families of functional relations among databank entries, information on the dominant power dependence of such functions interrelating the database entries can be obtained, without the involvement of any fitting algorithm. After the dominant power dependence has been determined by this simple approach, and if more precise functional relations are needed, this knowledge allows one to choose better trial functions fulfilling this constraint, instead of a ``trial and error'' approach more commonly used for the determination of unknown functions describing the relations among the database entries with respect to the given property.
MezeyP.G., Iterated Similarity Sequences and Shape ID Numbers for Molecules, J. Chem. Inf. Comp. Sci.34 (1994), 244-247.
2.
MezeyP.G., Shape in Chemsitry; An Introduction to Molecular Shape and Topology, VCH (Wiley) Publisshers, New York, 1993.
3.
Carbo-DorcaR. and MezeyP.G., eds, Advances in Molecular Similarity, Vol.1 and Vol. 2, JAI Press Inc., Greenwich, CT, 1996 and 1998.
4.
Carbo-DorcaR., GironesX. and MezeyP.G., eds, Fundamentals of Molecular Similarity, Kluwer Academic/Plenum Publ., New York, USA, 2001.
5.
CarboR., ArnauJ. and LeydaL., How similar is a molecule to another? An electron density measure of similarity between two molecular structures, Int. J. Quantum Chem.17 (1980), 1185-1189.
6.
Carbo'R. and ArnauM., Molecular Engineering: A General Approach to QSAR, in Medicinal Chemistry Advances, ed., F.G. de las Heras and S. Vega, Pergamon Press, Oxford, 1981.
7.
HodgkinsE.E. and RichardsW.G., A semi-empirical method for calculating molecular similarity, J. Chem. Soc. Chem. Commun. (1986), 1342-1344.
8.
JohnsonM.A. and MaggioraG.M., Concepts and applications of molecular similarity, Wiley, Minneapolis, 1990.
9.
CarboR. and CalabuigB., Quantum Similarity Measures, Molecular Cloud Descriptors and Structure-Property Relationships, J. Chem. Inf. Comput. Sci.32 (1992), 600-606.
10.
CarboR. and CalabuigB., Molecular quantum similarity measures and n-dimensional representation of quantum objects, I. Theoretical foundations, Int. J. Quantum Chem.42 (1992), 1681-1693.
11.
CarboR. and CalabuigB., Molecular quantum similarity measures and n-dimensional representation of quantum objects, II. Practical applications, Int. J. Quantum Chem.42 (1992), 1695-1709.
12.
GoodA.C., HodgkinE.E. and RichardsW.G., Similarity screening of molecular data sets, J. Comput-Aided Mol. Des.6 (1992), 513-520.
13.
CarboR., CalabuigB., VeraL. and BesaluE., Molecular Quantum Similarity: Theoretical Framework, Ordering Principles, and Visualization Techniques, in Advances in Quantum Chemistry, ed. P.-O. Löwdin, J.R. Sabin and M.C. Zerner, Academic Press, New York, 1994, vol. 25.
14.
BesaluE., CarboR., MestresJ. and SolaM., Foundations and Recent Developments on Molecular Quantum Similarity, in Topics in Current Chemistry, Molecular Similarity, ed. K. Sen, Springer-Verlag, Heidelberg, 1995, vol. 173.
15.
Carbo-DorcaR. and BesaluE., A general survey of Molecular Quantum Similarity, THEOCHEM451 (1998), 11-23.
16.
ConstansP., AmatL. and Carbo-DorcaR., Toward a Global Maximization of the Molecular Similarity Function: Superposition of Two Molecules, J. Comput. Chem.18 (1997), 826-846.
17.
PonecR., AmatL. and Carbo-DorcaR., Molecular basis of quantitative structure - properties relationships (QSPR): A quantum similarity approach, J. Comput-Aided Mol. Des.13 (1999), 259-270.
18.
AmatL., Carbo-DorcaR. and PonecR., Simple Linear QSAR Models Based on Quantum Similarity Measures, J. Med. Chem.42 (1999), 5169-5180.
19.
Carbo-DorcaR., BesaluE. and GironesX., Extended Density Functions, Adv. Quantum Chem.38 (2000), 1-63.
20.
AmatL., BesaluE., Carbo-DorcaR. and PonecR., Identification of Active Molecular Sites Using Quantum-Self-Similarity Measures, J. Chem. Inf. Model.41 (2001), 978-991.
21.
Carbo-DorcaR. and GironesX., Foundation of Quantum Similarity Measures and Their Relationship to QSPR: Density Function Structure, Approximations, and Application Examples, Int. J. Quantum Chem.101 (2005), 8-20.
22.
Carbo-DorcaR. and BesaluE., Communications on Quantum Similarity (2): A Geometric Discussion on Holographic Electron Density Theorem and Confined Quantum Similarity Measures, J. Comput. Chem.31 (2010), 2452-2462.
23.
HararyF. and MezeyP.G., Embedding and Characterization of Quantum Chemical Reaction Graphs on Two-Dimensional Orientable Surfaces, Discrete Appl. Math.19 (1988), 205-214.
24.
MezeyP.G., Semi-Similarity of Molecular Bodies: Scaling-Nesting Similarity Measures, Int. J. Quantum Chem.51 (1994), 255-264.
25.
MezeyP.G., Methods of Molecular Shape-Similarity Analysis and Topological Shape Design, in ``Molecular Similarity in Drug Design'', Ed. P.M. Dean, Chapman & Hall - Blackie Publishers, Glasgow, U.K., 1995, pp. 241-268.
26.
MezeyP.G., Molecular Similarity Measures for Assessing Reactivity, in Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, Ed. R. Carbó, Kluwer Academic Publ., Dordrecht, The Netherlands, 1995, pp. 57-76.
27.
WalkerP.D. and MezeyP.G., Towards Similarity Measures for Macromolecular Bodies: MEDLA Test Calculations for Substituted Benzene Systems, J. Comput. Chem.16 (1995), 1238-1249.
28.
HararyF., RandolphW. and MezeyP.G., A Study of Maximum Unit-Circle Caterpillars - Tools for the Study of the Shape of Adsorption Patterns, Discrete Appl. Math.67 (1996), 127-136.
29.
MezeyP.G., Theorems on Molecular Shape-Similarity Descriptors: External T-Plasters and Interior T-Aggregates, J. Chem. Inf. Comp. Sci.36 (1996), 1076-1081.
30.
HararyF. and MezeyP.G., Cell-Shedding Transformations, Equivalence Relations, and Similarity Measures for Square-Cell Configurations, Int. J. Quantum Chem.62 (1997), 353-361.
31.
MezeyP.G., A Proof of the Metric Properties of the Symmetric Scaling-Nesting Dissimilarity Measure and Related Symmetry Deficiency Measures, Int. J. Quantum Chem.63 (1997), 105-109.
32.
MezeyP.G., Quantum Similarity Measures and Löwdin's Transform for Approximate Density Matrices and Macromolecular Forces, Int. J. Quantum Chem.63 (1997), 39-48.
33.
MezeyP.G., FukuiK., ArimotoS. and TaylorK., Polyhedral Shapes of Functional Group Distributions in Biomolecules and Related Similarity Measures, Int. J. Quantum Chem.66 (1998), 99-105.
34.
MezeyP.G., The Holographic Electron Density Theorem and Quantum Similarity Measures, Mol. Phys.96 (1999), 169-178.
35.
MezeyP.G., Molecular Similarity and Host-Guest Interactions, Theor. and Comput. Chem.6 (1999), 593-612.
36.
MaggioraG.M. and MezeyP.G., A Fuzzy Set Approach to Functional Group Comparisons Based on an Asymmetric Similarity Measure, Int. J. Quant. Chem74 (1999), 503-514.
37.
MezeyP.G., Shape-Similarity Relations Based on Topological Resolution, J. Math. Chem.27 (2000), 61-69.
38.
MezeyP.G., Molecular Informatics and Topology in Chemistry, in ``Topology in Chemistry'', Eds. R.B. King and D.H. Rouvray, Ellis Horwood Publ., Chichester, U.K., 2002, pp. 316-332.
39.
MezeyP.G., The Role of Imperfect Symmetry in Nature, Art, Mathematics, and Chemistry: Approximate Symmetry and Symmetry Deficiency Measures, J. Internat. Soc. Interdisc. Study Symmetry.2004 (2004), 166-169.
40.
MezeyP.G., SimilarityM., TopologyQ. and Shape, In ``Computational Medicinal Chemistry and Drug Discovery'', Eds. Patrick Bultinck, Jan P. Tollenaere, Hans De Winter, and Wilfried Langenaeker, Marcel Decker Inc., New York, 2004, pp. 345-364.
41.
MezeyP.G., Quantitative Shape - Activity Relations (QShAR): Electron Density Foundations and Applications, Symmetry: Culture and Science (Special volume in memoriam Jacques-Émile Dubois and André Rassat)16 (2005), 311-320.
42.
MezeyP.G., Graph Representations of Molecular Similarity Measures Based on Topological Resolution, Journal of Computational Methods in Sciences and Engineering (JCMSE)5 (2005), 109-114.
43.
MezeyP.G., Rules on the Changes of Approximate Symmetry Measures Along Reaction Paths, Molec. Phys.104 (2006), 723-729. Corrigendum, Molec. Phys., 104, 2575 (2006). (Special Volume dedicated to Prof. Michael A. Robb).
44.
WangL., WangL., ArimotoS. and MezeyP.G., Large-Scale Chirality Measures and General Symmetry Deficiency Measures for Functional Group Polyhedra of Proteins, J. Math. Chem.40 (2006), 145-153.
45.
MezeyP.G., Molecular Symmetry Deficiency and Shape Deviation Measures, l'Actualité Chimique320-321 (2008), 56-60. (Hommage à Jacques-Emile Dubois, Special Volume honoring Professor Jacques-Emile Dubois).
46.
MezeyP.G., Natural Molecular Fragments, Functional Groups, and Holographic Constraints on Electron Densities, Phys. Chem. Chem. Phys.14 (2012), 8516-8522.
47.
SimonE. and MezeyP.G., Imperfect Periodicity and Systematic Changes of Some Structural Features Along Linear Polymers: The Case of Rod-Like Boron/Nitrogen Nanostructures, Theor Chem Acc (2012) 131:1097 (honoring Prof. Akira Imamura, invited paper). Published online 10 February 2012, DOI 10.1007/s00214-012-1097-y.
48.
MezeyP.G., Fuzzy Electron Density Fragments in Macromolecular Quantum Chemistry, Combinatorial Quantum Chemistry, Functional Group Analysis, and Shape - Activity Relations, Accounts of Chem. Research47 (2014), 2821-2827, invited paper.
49.
AntalZ. and MezeyP.G., Substituent Effects and Local Molecular Shape Correlations, Phys. Chem. Chem. Phys.16 (2014), 6666-6678.
50.
AntalZ., WarburtonP.L. and MezeyP.G., Electron Density Shape Analysis of a Family of Through-Space and Through-Bond Interactions, Phys. Chem. Chem. Phys.16 (2014), 918-924.
51.
MezeyP.G., Relations Between Real Molecules Through Abstract Molecules: The Reference Cluster Approach, Invited paper, Theor. Chem. Accounts (Surjan Festschrift) (2015), 134:134 DOI 10.1007/s00214-015-1728-1.
52.
MezeyP.G., Compensation Effects in Molecular Interactions and the Quantum Chemical le Chatelier Principle, Invited paper to the Jacopo Tomasi Festschrift, J. Phys. Chem. A119 (2015), 5305-5312.
