Part of the Lecture Notes in Chemistry book series (LNC, volume 73)


Molecular similarity attempts to give a quantitative answer to the question: how similar are two molecules? It is clear that this is an interesting problem, and that it has no unique answer. The possible solutions will be associated to the type of molecular aspect that one wants to analyze. Due to the fact that molecules are objects ruled by the laws of quantum mechanics, it seems that one of the satisfactory answers to the question ought to be found within this specific discipline. Following this line of thought, the first quantitative measure of the similarity between two molecules, based on quantum-mechanical basic elements, was formulated by Carbó in 1980 [1]. Carbó proposed that a numerical comparative measure between two molecules could be derived from the superposed volume between their respective electronic distributions. This original definition still holds, and constitutes the fundamental tool of the present work. The seminal idea was developed by this author and collaborators [2, 3, 4, 5, 6], and the present state-of-the-art can be obtained from various review articles [7, 8, 9, 10]. These papers deepen in the quantum-mechanical nature of the definition, connect it with several subjects of chemical and mathematical interest and show a broad amount of possible applications.


QSAR Model Quantum Object Molecular Similarity Quantum Similarity QSAR Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Carbó R, Leyda L, Arnau M (1980) How similar is a molecule to another? An electron density measure of similarity between two electronic structures. Int J Quantum Chem 17:1185–1189CrossRefGoogle Scholar
  2. 2.
    Carbó R, Domingo L (1987) LCAO-MO similarity measures and taxonomy. Int J Quantum Chem 23:517–545CrossRefGoogle Scholar
  3. 3.
    Carbó R, Calabuig B (1989) MOLSIMIL-88: Molecular similarity calculations using a CNDO-like approximation. Comput Phys Commun 55:117–126CrossRefGoogle Scholar
  4. 4.
    Carbó R, Calabuig B (1992) Molecular quantum similarity measures and n-dimensional representation of quantum objects. I. Theoretical foundations. Int J Quantum Chem 42:1681–1693CrossRefGoogle Scholar
  5. 5.
    Carbó R, Calabuig B (1992) Molecular quantum similarity measures and n-dimensional representation of quantum objects. II. Practical applications. Int J Quantum Chem 42:1695–1709CrossRefGoogle Scholar
  6. 6.
    Carbó R, Calabuig B, Besalü E, Vera L (1994) Molecular quantum similarity: theoretical framework, ordering principle and visualization techniques. Adv Quantum Chem 25:255–313Google Scholar
  7. 7.
    Besalú E, Carbó R, Mestres J, Solà M (1995) Foundations and recent developments on molecular quantum similarity. Top Curr Chem 173:31–62CrossRefGoogle Scholar
  8. 8.
    Carbó-Dorca R, Besalú E (1998) A general survey of molecular quantum similarity. J Mol Struct (Theochem) 451:11–23CrossRefGoogle Scholar
  9. 9.
    Carbó-Dorca R, Amat L, Besalú E, Lobato M (1998) Quantum similarity. In: Carbó-Dorca R, Mezey PG (eds) Advances in molecular similarity. JAI Press, Greenwich, Vol 2, pp 1–42Google Scholar
  10. 10.
    Carbó-Dorca R, Amat L, Besalü E, Gironés X, Robert D (1999) Quantum mechanical origin of QSAR: theory and applications. J Mol Struct (Theochem) in pressGoogle Scholar
  11. 11.
    Cioslowski J, Fleischmann ED (1991) Assessing molecular similarity from results of ab initio electronic structure calculations. J Am Chem Soc 113:64–67CrossRefGoogle Scholar
  12. 12.
    Cioslowski J, Challacombe M (1991) Maximum similarity orbitals for analysis of the electronic excited states. Int J Quantum Chem 25:81–93CrossRefGoogle Scholar
  13. 13.
    Ortiz JV, Cioslowski J (1991) Molecular similarity indices in electron propagator theory. Chem Phys Lett 185:270–275CrossRefGoogle Scholar
  14. 14.
    Cioslowski J (1992) Differential density matrix overlap: an index for assessment of electron correlation in atoms and molecules. Theor Chim Acta 81:319–327CrossRefGoogle Scholar
  15. 15.
    Cooper DL, Allan NL (1989) A novel approach to molecular similarity. J Comput-Aided Mol Design 3:253–259CrossRefGoogle Scholar
  16. 16.
    Cooper DL, Allan NL (1992) Molecular dissimilarity: a momentum-space criterion. J Am Chem Soc 114:4773–4776CrossRefGoogle Scholar
  17. 17.
    Allan NL, Cooper DL (1992) A momentum space approach to molecular similarity. J Chem Inf Comput Sci 32:587–590CrossRefGoogle Scholar
  18. 18.
    Allan NL, Cooper DL (1995) Momentum-space electron densities and quantum molecular similarity. Top Curr Chem 173: 85–111CrossRefGoogle Scholar
  19. 19.
    Cooper DL, Allan NL (1995) Molecular similarity and momentum space. In: Carbó R (ed) Molecular similarity and reactivity: from quantum-chemical to phenomenological approaches. Kluwer, Amsterdam, pp 31–55Google Scholar
  20. 20.
    Measures PT, Allan NL, Cooper DL (1996) Momentum-space similarity: some recent applications. In: Carbó R, Mezey PG (eds) Advances in molecular similarity. JAI Press, Greenwich, Vol 2, pp 61–87CrossRefGoogle Scholar
  21. 21.
    Allan NL, Cooper DL (1998) Quantum molecular similarity via momentum-space indices. J Math Chem 23:51–60CrossRefGoogle Scholar
  22. 22.
    Bowen-Jenkins PE, Richards WG (1985) Ab initio computation of molecular similarity. J Phys Chem 89:2195–2197CrossRefGoogle Scholar
  23. 23.
    Hodgkin EE, Richards WG (1987) Molecular similarity based on electrostatic potential and electric field. Int J Quantum Chem 14:105–110CrossRefGoogle Scholar
  24. 24.
    Meyer AM, Richards WG (1991) Similarity of molecular shape. J Comput-Aided Mol Design 5:426–439CrossRefGoogle Scholar
  25. 25.
    Richards WG (1995) The dominant role of shape similarity and dissimilarity in QSAR. In: Sanz F, Manaut F (eds) QSAR and molecular modelling: concepts, computational tools and biological applications. Prous Science, Barcelona, pp 364–373Google Scholar
  26. 26.
    Herndon, WC (1988) Graph codes and a definition of structural similarity. Comput Math Applic 15:303–309CrossRefGoogle Scholar
  27. 27.
    Mezey PG (1993) Shape in Chemistry: an introduction to molecular shape and topology. VCH, New YorkGoogle Scholar
  28. 28.
    Mezey PG (1988) Shape group studies of molecular similarity: shape groups and shape graphs of molecular contour surfaces. J Math Chem 2:299–323CrossRefGoogle Scholar
  29. 29.
    Arteca GA, Mezey PG (1989) Molecular similarity and molecular shape changes along reaction paths: a topological analysis and consequences on the Hammond postulate. J Phys Chem 93:4746–4751CrossRefGoogle Scholar
  30. 30.
    Mezey PG (1991) The degree of similarity of three-dimensional bodies: applications to molecular shapes. In: Mezey PG (ed) Mathematical Modeling in Chemistry. VCH, New York, pp 39–49Google Scholar
  31. 31.
    Mezey PG (1992) Shape-similarity measures for molecular bodies: a 3D topological approach to QShAR. J Chem Inf Comput Sei 32:650–656CrossRefGoogle Scholar
  32. 32.
    Ponec R (1987) Topological aspects of chemical reactivity. On the similarity of molecular structures. Collect Czech Chem Commun 52:555–561CrossRefGoogle Scholar
  33. 33.
    Ponec R, Strnad M (1990) Similarity approach to chemical reactivity. Specificity of multibond reactions. Collect Czech Chem Commun 55:2583–2589CrossRefGoogle Scholar
  34. 34.
    Ponec R, Strnad M (1991) Topological aspects of chemical reactivity. Evans/Dewar principle in terms of molecular similarity approach. J Phys Org Chem 4:701–705CrossRefGoogle Scholar
  35. 35.
    Ponec R, Strnad M (1992) Electron correlation in pericyclic reactivity: a similarity approach. Int J Quantum Chem 42:501–508CrossRefGoogle Scholar
  36. 36.
    Ponec R, Strnad M (1993) Position invariant index for assessment of molecular similarity. Croat Chem Acta 66:123–127Google Scholar
  37. 37.
    Mezey PG, Ponec R, Amat L, Carbó-Dorca R (1999) Quantum similarity approach to the characterization of molecular chirality. Enantiomeres 4:371–378Google Scholar
  38. 38.
    Constans P, Amat L, Carbó-Dorca R (1997) Toward a global maximization of the molecular similarity function: superposition of two molecules. J Comput Chem 18:826–846CrossRefGoogle Scholar
  39. 39.
    Solà M, Mestres J, Carbó R, Duran M (1994) Use of ab initio quantum similarity measures as an interpretative tool for the study of chemical reactions. J Am Chem Soc 116:5909–5915CrossRefGoogle Scholar
  40. 40.
    Solà M, Mestres J, Caibó R, Duran M (1996) A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods. J Chem Phys 104:636–647CrossRefGoogle Scholar
  41. 41.
    Forés M, Duran M, Solà M (1997) A procedure for assessing the quality of a given basis set based on quantum molecular similarity measures. Theor Mol Mod Electr Conf 1:50–56Google Scholar
  42. 42.
    Carbó R, Besalú E, Amat L, Fradera X (1995) Quantum molecular similarity measures (QMSM) as a natural way leading towards a theoretical foundation of quantitative structure-properties relationship. J Math Chem 18:237–246CrossRefGoogle Scholar
  43. 43.
    Fradera X, Amat L, Besalú E, Carbó-Dorca R (1997) Application of molecular quantum similarity to QSAR. Quant Struct-Act Relat 16:25–32CrossRefGoogle Scholar
  44. 44.
    Lobato M, Amat L, Besalú E, Carbó-Dorca R (1997) Structure-activity relationships of a steroid family using quantum similarity measures and topological quantum similarity indices. Quant Struct-Act Relat 16:465–472CrossRefGoogle Scholar
  45. 45.
    Amat L, Robert D, Besalu E, Carbó-Dorca R (1998) Molecular quantum similarity measures tuned QSAR: An antitumoral family validation study. J Chem Inf Comput Sci 38:624–631CrossRefGoogle Scholar
  46. 46.
    Amat L, Carbó-Dorca R, Ponec R (1998) Molecular quantum similarity measures as an alternative to log P values in QSAR studies. J Comput Chem 19:1575–1583CrossRefGoogle Scholar
  47. 47.
    Robert D, Amat L, Carbó-Dorca R (1999) Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures: Prediction of the corticosteroid binding globulin binding affinity for a steroid family. J Chem Inf Comput Sci 39:333–344CrossRefGoogle Scholar
  48. 48.
    Ponec R, Amat L, Carbó-Dorca R (1999) Molecular basis of quantitative structure-properties relationship (QSPR): A quantum similarity approach. J Comput-Aided Mol Design 13:259–270CrossRefGoogle Scholar
  49. 49.
    Ponec R, Amat L, Carbó-Dorca R (1999) Quantum similarity approach to LFER: Substituent and solvent effects on the acidities of carboxylic acids. J Phys Org Chem 12:447–454CrossRefGoogle Scholar
  50. 50.
    Amat L, Carbó-Dorca R, Ponec R (1999) Simple linear models based on quantum similarity measures. J Med Chem 42:5169–5180CrossRefGoogle Scholar
  51. 51.
    Robert D, Gironés X, Carbó-Dorca R (1999) Facet diagrams for quantum similarity data. J Comput-Aided Mol Design 13:597–610CrossRefGoogle Scholar
  52. 52.
    Robert D, Carbó-Dorca R (1999) Aromatic compounds aquatic toxicity QSAR using molecular quantum similarity measures. SAR QSAR Environ Res 10:401–422CrossRefGoogle Scholar
  53. 53.
    Gironés X, Amat L, Carbó-Dorca R (1999) Using molecular quantum similarity measures as descriptors in quantitative structure-toxicity relationships. SAR QSAR Environ Res, in pressGoogle Scholar
  54. 54.
    Cioslowski J, Stefanov BB, Constans P (1996) Efficient algorithm for quantitative assessment of similarities among atoms in molecules. J Comput Chem 17:1352–1358CrossRefGoogle Scholar
  55. 55.
    Solà M, Mestres J, Oliva JM, Duran M, Carbó-Dorca M (1996) The use of ab initio quantum molecular self-similarity measures to analyze electronic charge density distributions. Int J Quantum Chem 58:361–372CrossRefGoogle Scholar
  56. 56.
    Robert D, Carbó-Dorca R (1998) On the extension of quantum similarity to atomic nuclei: nuclear quantum similarity. J Math Chem 23:327–351CrossRefGoogle Scholar
  57. 57.
    Robert D, Carbó-Dorca R (1999) Structure-property relationships in nuclei. Prediction of the binding energy per nucleon using a quantum similarity approach. Nuovo Cimento Alll:1311–1321Google Scholar
  58. 58.
    Fradera X, Duran M, Mestres J (1998) Second-order quantum similarity measures from intracule and extracule densities. Theor Chem Acc 99:44–52CrossRefGoogle Scholar
  59. 59.
    Quoted in: Borman S (1990) New QSAR techniques eyed for environmental assessments. Chem Eng News 68:20–23Google Scholar
  60. 60.
    Cram-Brown A, Fraser TR (1868) On the connection between chemical constitution and physiological action. Part 1. On the physiological action of the ammonium bases, derived from Strychia, Brucia, Thebaia, Codeia, Morphia and Nicotia. Trans Royal Soc Edinburgh 25:257–274Google Scholar
  61. 61.
    Richet C (1893) C R Seances Soc Biol 9:775Google Scholar
  62. 62.
    Meyer H (1899) Theorie der Alkoholnarkose, welche Eigenschaft die Anästhetica bedingt ihre narkotische Wirkung Arch Exp Pathol Pharmakol 42:109–118CrossRefGoogle Scholar
  63. 63.
    Overton E (1901) Studien über die Narkose. Gustav Fischer, JenaGoogle Scholar
  64. 64.
    Ferguson J (1939) The use of chemical potentials as indicators of toxicity. Proc Royal Soc London B127:387CrossRefGoogle Scholar
  65. 65.
    Hammett LP (1937) The Effect of Structures upon the Reactions of Organic Compounds. Benzene Derivatives. J Am Chem Soc 59:96CrossRefGoogle Scholar
  66. 66.
    Hammett LP (1940) Physical Organic Chemistry. McGraw-Hill, New YorkGoogle Scholar
  67. 67.
    Taft RW (1952) J Am Chem Soc 74:3120–3128CrossRefGoogle Scholar
  68. 68.
    Free SM, Wilson JW (1964) A mathematical contribution to structure-activity studies. J Med Chem 7:395–399CrossRefGoogle Scholar
  69. 69.
    Hansch C, Fujita T (1964) ρ-σ-π analysis. A method for the correlation of biological activity and chemical structure. J Am Chem Soc 86:1616–1626CrossRefGoogle Scholar
  70. 70.
    Kubinyi H (1993) QSAR: Hansch analysis and related approaches. VCH, WeinheimCrossRefGoogle Scholar
  71. 71.
    Wiener H (1947) Structural determination of paraffin boiling points. J Chem Phys 69:17–20Google Scholar
  72. 72.
    Kier LB, Hall LH, Murray WJ, Randic M (1975) Molecular connectivity. I: Relationship to nonspecific local anaesthesia. J Pharm Sci 64:1971–1974CrossRefGoogle Scholar
  73. 73.
    Randic M (1975) On characterization of molecular branching. J Am Chem Soc 97:6609–6615CrossRefGoogle Scholar
  74. 74.
    Kier LB, Hall LH (1976) Molecular connectivity in chemistry and drag research. Academic Press, New YorkGoogle Scholar
  75. 75.
    Kier LB, Hall LH (1986) Molecular Connectivity in Structure-Activity Analysis. Research Studies Press, LetchworkGoogle Scholar
  76. 76.
    Cramer III RD, Paterson DE, Bunce JD (1988) Comparative molecular field analysis (CoMFA). 1. Effect of shape on binding of steroids to carrier proteins. J Am Chem Soc 110:5959–5967CrossRefGoogle Scholar
  77. 77.
    Klebe G, Abraham U, Mietzner T (1994) Molecular similarity indices in a comparative analysis (CoMSIA) of drag molecules to correlate and predict their biological activity. J Med Chem 37:4130–4146CrossRefGoogle Scholar
  78. 78.
    Silverman BD, Platt DE (1996) Comparative molecular moment analysis (CoMMA): 3D-QSAR without molecular superposition. J Med Chem 39:2129–2140CrossRefGoogle Scholar
  79. 79.
    Jain AN, Koile K, Chapman D (1994) Compass: predicting biological activities from molecular surface properties. Performance comparisons on a steroid benchmark. J Med Chem 37:2315–2327CrossRefGoogle Scholar
  80. 80.
    Bravi G, Gancia E, Mascagni P, Pegna M, Todeschini R, Zaliani A (1997) MS-WHIM, new 3D theoretical descriptors derived from molecular surface properties: A comparative 3D QSAR study in a series of steroids. J Comput-Aided Mol Design 11:79–92CrossRefGoogle Scholar
  81. 81.
    Kellogg GE, Kier LB, Gaillard P, Hall LH (1996) E-state fields-Applications to 3D QSAR. J Comput-Aided Mol Design 10:513–520CrossRefGoogle Scholar
  82. 82.
    Luque FJ, Sanz F, Illas F, Pouplana R, Smeyers YG (1988) Relationships between the activity of some H2-receptor agonists of histamine and their ab initio molecular electrostatic potential (MEP) and electron density comparison coefficients. Eur J Med Chem 23:7–10CrossRefGoogle Scholar
  83. 83.
    Richard AM (1991) Quantitative comparison of molecular electrostatic potentials for structure activity studies. J Comput Chem 12:959–969CrossRefGoogle Scholar
  84. 84.
    Rum G, Herndon WC (1991) Molecular similarity concepts. 5. Analysis of steroid-protein binding constants. J Am Chem Soc 113:9055–9060CrossRefGoogle Scholar
  85. 85.
    Good AC, So SS, Richards WG (1993) Structure-activity relationships from molecular similarity matrices. J Med Chem 36:433–438CrossRefGoogle Scholar
  86. 86.
    Good AC, Peterson SJ, Richards WG (1993) QSAR’s from similarity matrices. Technique validation and application in the comparison of different similarity evaluation methods. J Med Chem 36:2929–2937CrossRefGoogle Scholar
  87. 87.
    Good AC, Richards WG (1996) The extension and application of molecular similarity to drug design. Drug Information Journal 30:371–388CrossRefGoogle Scholar
  88. 88.
    Carbó R, Calabuig B (1992) Quantum similarity measures, molecular cloud description and structure-properties relationships. J Chem Inf Comput Sci 32:600CrossRefGoogle Scholar
  89. 89.
    Besalú E, Amat L, Fradera X, Carbó R (1995) An application of the molecular quantum similarity: Ordering of some properties of the hexanes. In: Sanz F, Manaut M (eds) QSAR and molecular modelling: concepts, computational tools and biological applications. Prous Science: BarcelonaGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  1. 1.Institute of Computational Chemistry, Campus MontiliviUniversity of GironaGironaSpain

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