Skip to main content
SpringerLink
Log in

Configurational dependence of molecular shape

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Some of the topological techniques developed for the description of molecular shape are studied, formulated as a problem of embedding nuclei within electronic clouds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Primas, in:Quantum Dynamics of Molecules; The New Experimental Challenge to Theorists, ed. R.G. Woolley, NATO ASI B 57 (Plenum, New York, 1980).

    Google Scholar 

  2. R.G. Woolley, Struct. Bonding 52 (1982)1.

    Google Scholar 

  3. F.M. Richards, Ann. Rev. Biophys. Bioeng. 6 (l977)151.

    Google Scholar 

  4. R. Langridge, T.E. Ferrin, I.D. Kuntz and M.L. Connolly, Science 211 (1981)661.

    PubMed  Google Scholar 

  5. P.A. Basch, N. Pattabiraman, C. Huang, T.E. Ferrin and R. Langridge, Science 222 (1983)1325.

    Google Scholar 

  6. M.L Connolly, J. Amer. Chem. Soc. 107 (1985)1118.

    Google Scholar 

  7. R.S. Pearlman, in:Partition Coefficient: Determination and Estimation, ed. W.J. Dunn, J.H. Brock and R.S. Pearlman (Pergamon, New York, 1986).

    Google Scholar 

  8. J.C. McGowan and A. Mellors,Molecular Volumes in Chemistry and Biology: Applications Including Partitioning and Toxicology (Horwood, Chichester, 1986).

    Google Scholar 

  9. A.Y. Meyer, Chem. Soc. Rev. 15 (1986)449.

    Google Scholar 

  10. H.R. Karfunkel and V. Eyraud, J. Comput. Chem. 10 (1989)628.

    Google Scholar 

  11. L Schäfer, J. Mol. Struct. 100 (1983)51.

    Google Scholar 

  12. P.G. Mezey, Molecular surfaces, in:Reviews in Computational Chemistry, ed. K.B. Lipkowitz and D.B. Boyd (VCH, New York, 1990).

    Google Scholar 

  13. P.G. Mezey,Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).

    Google Scholar 

  14. P.G. Mezey, Int. J. Quant. Chem. QBS 12 (1986)113.

    Google Scholar 

  15. P.G. Mezey, J. Comput. Chem. 8 (1987)462.

    Google Scholar 

  16. G.A. Arteca and P.G. Mezey. Int. J. Quant. Chem. QBS 14 (1987)113.

    Google Scholar 

  17. G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem. QBS 15 (1988)33.

    Google Scholar 

  18. P.G. Mezey, J. Math. Chem. 2 (1988)299.

    Google Scholar 

  19. P.G. Mezey, J. Math. Chem. 2 (1988)325.

    Google Scholar 

  20. G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem. QCS 23 (1989)305.

    Google Scholar 

  21. G.A. Arteca and P.G. Mezey, J. Phys. Chem. 93 (1989)4746.

    Google Scholar 

  22. G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem. 38 (1990)7l3.

    Google Scholar 

  23. W.G. Richards, Quantum Pharmacology, 2nd. ed. (Butterworths, London, 1983).

    Google Scholar 

  24. I. Motoc, Steric and other structural parameters for QSAR, in:Steric Fit in Quantitative Structure-Activity Relationships, ed. A.T. Balaban, A. Chiriac, I. Motoc and Z. Simon, Lecture Notes in Chemistry No. 15 (Springer, Berlin, 1980).

    Google Scholar 

  25. A.J. Stuper, W.E. Brügger and P.C. Jurs,Computer-Assisted Studies of Chemical Structures and Biological Function (Wiley, New York, 1979), ch. 3.

    Google Scholar 

  26. J.M. Blaney, E.C. Jorgensen, M.L. Connolly, T.E. Ferrin, R. Langridge, S.T. Oatley, J.M. Burridge and C.C.F. Blake, J. Med. Chem. 25 (1982)785.

    PubMed  Google Scholar 

  27. R. Franke,Theoretical Drug Design Methods, Pharmacochemistry Library Vol. 7(Elsevier, Amsterdam, 1977).

    Google Scholar 

  28. J.C Dearden (ed.),Quantitative Approaches to Drug Design, Pharmacochemistry Library, Vol. 6 (Elsevier, Amsterdam, 1983).

    Google Scholar 

  29. R. Bonaccorsi, E. Strocco and J. Tomasi, in:Chemical and Biochemical Reactivity, ed. E.D. Bergmann and B. Pullman (Reidel, Dordrecht, 1974).

    Google Scholar 

  30. E. Strocco and J. Tomasi, Topics Curr. Chem. 42 (1973)95; Adv. Quant. Chem. ll(1978)115.

    Google Scholar 

  31. J. Tomasi, On the use of electrostatic molecular potentials in theoretical investigations on chemical reactivity, in:Quantum Theory of Chemical Reactions, Vol. 1, ed. R. Daudel, A. Pullman, L. Salem and A. Veillard (Reidel, Dordrecht, 1979).

    Google Scholar 

  32. H. Weinstein, R. Osman, J.P. Green and S. Topiol, Electrostcic potentials as descriptors of molecular reactivity, in:Chemical Applications of Atomic and Molecular Electrostatic Potentisl, ed. P. Politzer and D.G. Truhlar (Plenum, New York, 1981), pp. 309–334.

    Google Scholar 

  33. J.J. Kaufman, P.C. Hariharan, F.C. Tobi and C. Petrongolo, Electrostatic molecular potential contour maps from ab initio calculations, in:Chemical Applications of Atomic and Molecular Electrostatic Potentials, ed. P. Pulitzer and D.G. Truhlar (Plenum, New York, 1981), pp. 335–380.

    Google Scholar 

  34. A. Pullman and B. Pullman, Electrostatic molecular potential of the nucleic acids, in:Chemical Applications of Atomic and Molecular Electrostatic Potentials, ed. P. Politzer and D.G. Truhlar (Plenum, New York, 1981), pp. 381–405.

    Google Scholar 

  35. P. Politzer and K.C. Daiker, Models for chemical reactivity, in:The Force Concept in Chemistry, ed. B.M. Deb (Van Nostrand, New York, 1981).

    Google Scholar 

  36. J.R. Rabinowtiz and S.B. Little, Int. J. Quant. Chem. QBS 13 (1986)9.

    Google Scholar 

  37. J.C. Culberson, G.D. Purvis III, M.C. Zerner and B.A. Seiders, Int. J. Quant. Chem. QBS 13 (1986)267.

    Google Scholar 

  38. G. Náray-Szabó and P.R. Surján, Computational methods for biological systems, in:Theoretical Chemistry of Biological Systems, ed. G. Náray-Szabó (Elsevier, Amsterdam, 1986).

    Google Scholar 

  39. G.D. Purvis III and C. Culberson, Int. J. Quant. Chem. QBS 13 (1986)216.

    Google Scholar 

  40. R.F. Hout and W.J. Hehre, J. Amer. Chem. Soc. 105 (1983)3728.

    Google Scholar 

  41. M.M. Francl, R.F. Houtand W.J. Hehre, J. Amer. Chem. Soc. 106 (1984)563.

    Google Scholar 

  42. J.M. Blaney, E.C. Jorgensen, M.L. Connolly, T.E. Ferrin, R. Langridge, S.J. Oatley, J.M. Burridge and C.C.F. Blake, J. Med. Chem. 25 (1982)785.

    PubMed  Google Scholar 

  43. P.K. Weiner, R. Langridge, J.M. Blaney, R. Schaefer and P.A. Kollman, Proc. Nat. Acad. Sci. USA 79 (1982)3754.

    PubMed  Google Scholar 

  44. L.H. Pearl and A. Honegger, J. Mol. Graph. 1 (1983)9.

    Google Scholar 

  45. M.L. Connolly, Science 221 (1983)709.

    PubMed  Google Scholar 

  46. M.L. Connolly, J. Mol. Graph. 3 (1985)19.

    Google Scholar 

  47. G.A. Arteca and P.G. Mezey, Folia Chim. Theor. Lat. 15 (1987)115.

    Google Scholar 

  48. P.G. Mezey, Three-dimensional topological aspects of molecular similarity, in:Molecular Similarity, ed. G. Maggiora and M.S. Johnson (Wiley, New York, 1990).

    Google Scholar 

  49. F. Harary,Graph Theory (Addison-Wesley, Reading, MA, 1969).

    Google Scholar 

  50. R.J. Wilson and L.W. Beinecke (eds.),Applications of Graph Theory (Academic Press, London, 1978)

    Google Scholar 

  51. A.T. Balaban (ed.),Chemical Applications of Graph Theory (Academic Press, London, 1976).

    Google Scholar 

  52. N. Trinajstić,Chemical Graph Theory (CRC Press, Boca Raton, 1983).

    Google Scholar 

  53. I. Gutman and O.E. Polansky,Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986).

    Google Scholar 

  54. M. Randić, J. Amer. Chem. Soc. 97 (1975)6609.

    Google Scholar 

  55. D. Rouvray, J. Comput. Chem. 8 (1987)470.

    Google Scholar 

  56. R.B. King (ed.),Chemical Applications of Topology and Graph Theory (Elsevier, Amsterdam, 1983).

    Google Scholar 

  57. H. Hosoya and N. Ohkami, J. Comput. Chem. 4 (1983)585.

    Google Scholar 

  58. L.B. Kier and L.H. Hall,Molecular Connectivity in Chemistry and Drug Research (Academic Press, New York, 1976).

    Google Scholar 

  59. R.E. Merrifield and H.E. Simmons,Topological Methods in Chemistry (Wiley, New York, 1989).

    Google Scholar 

  60. M. Randić, Int. J. Quant. Chem. QBS 15 (1988)201.

    Google Scholar 

  61. F. Harary and P.G. Mezey, J. Math. Chem. 2 (1988)377.

    Google Scholar 

  62. G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem. 34 (1988)517.

    Google Scholar 

  63. G.A. Arteca and P.G. Mezey, Theor, Chim. Acta 75 (1989)333.

    Google Scholar 

  64. P.G. Mezey, Int. J. Quant. Chem. QBS 14 (1987)127.

    Google Scholar 

  65. See, for instance: J.R. Munkres, Elements of Algebraic Topology (Addison-Wesley, Menlo Park, 1984);

    Google Scholar 

  66. E.H. Spanier, Algebraic Topology (McGraw-Hill, New York, 1966).

    Google Scholar 

  67. G.A. Arteca and P.G. Mezey, J. Comput. Chem. 9 (1988)554.

    Google Scholar 

  68. G.A. Arteca and P.G. Mezey, J. Mol. Struct. 166 (1988)11.

    Google Scholar 

  69. P.D. Walker, G.A. Arteca and P.G. Mezey, J. Comp. Chem. 12 (1991)220.

    Google Scholar 

  70. J.S. Richardson, Adv. Protein Chem. 34 (1981)167.

    PubMed  Google Scholar 

  71. J.S. Richardson, Meth. Enzymol. 115 (1985)359.

    PubMed  Google Scholar 

  72. M. Carson and C.E. Bugg, J. Mol. Graph. 4 (1986)121.

    Google Scholar 

  73. M. Carson, J. Mol. Graph. 5 (1987)103.

    Google Scholar 

  74. H. Lass,Vector and Tensor Analysis (McGraw-Hill -Kogakusha, Tokyo, 1950).

    Google Scholar 

  75. M. Delbrück, Proc. Symp. Appl. Math. 14 (1962)55.

    Google Scholar 

  76. F.B. Fuller, Proc. Symp. Appl. Math. 14 (1962)64.

    Google Scholar 

  77. F.B. Fuller, Proc. Nat. Acad. Sci. USA 68 (1971)815.

    PubMed  Google Scholar 

  78. M. Le Bret, Biopolymers 18 (1979)1709.

    PubMed  Google Scholar 

  79. P. De Santis, S. Morosetti and A. Palleschi, Biopolymers 22 (1983)37.

    PubMed  Google Scholar 

  80. M.-H. Hao and W.K. Olson, Biopolymers 28 (1989)873.

    PubMed  Google Scholar 

  81. G.A. Arteca and P.G. Mezey, J. Mol. Graph. 8 (1990)66.

    PubMed  Google Scholar 

  82. G.A. Arteca, O. Tapia and P.G. Mezey, J. Mol. Graph 9 (1991)148.

    PubMed  Google Scholar 

  83. See, for example: R.H. Crowell and R.H. Fox,Introduction to Knot Theory (Springer, Berlin, 1977).

    Google Scholar 

  84. K.B. Lipkowitz, B. Barker and R. Larter, J. Amer. Chem. Soc. 111 (1989)7750.

    Google Scholar 

  85. R.G. Pearson,Symmetry Rules for Chemical Reactions, Orbital Topology, and Elementary Processes (Wiley, New York 1976).

    Google Scholar 

  86. P. Pechukas, J. Chem. Phys. 64 (1976)1516.

    Google Scholar 

  87. P.G. Mezey, J. Amer. Chem. Soc. 112 (1990)3791.

    Google Scholar 

  88. P.G. Mezey, Non-visual molecular shape analysis: Shape changes in electronic excitations and chemical reactions, in:Computational Advances in Organic Chemistry, ed. C. Ogretir and I.G. Csizmadia (Kluwer, Dordrecht, 1991).

    Google Scholar 

  89. G.S. Hammond, J. Amer. Chem. Soc. 77 (1955)335.

    Google Scholar 

  90. L. Melander,The Transition State (Royal Chemical Society Special Publ., London, 1962).

    Google Scholar 

  91. J.C. Polanyi, J. Chem. Phys. 31 (1959)1338.

    Google Scholar 

  92. M.H. Mok and J.C. Polanyi, J. Chem. Phys. 51 (1969)1451.

    Google Scholar 

  93. N. Agmon, J. Chem. Soc. Faraday Trans. II 74 (1978)388.

    Google Scholar 

  94. A.R. Miller, J. Amer. Chem. Soc. 100 (1978)1984.

    Google Scholar 

  95. J.R. Murdoch, J. Amer. Chem. Soc. 105 (1983)2667.

    Google Scholar 

  96. G.A. Arteca and P.G. Mezey, J. Comput. Chem. 9 (1988)728.

    Google Scholar 

  97. G.A. Arteca, G.A. Heal and P.G. Mezey, Theor. Chim. Acta 76 (1990)377.

    Google Scholar 

  98. M.J. Frisch, J.S. Binkley, H.B. Schlegel, K. Raghavachari, C.F. Melius, R.L. Martin, J.J.P. Stewart, F.W. Bobrowicz, C.M. Rohlfing, L.R. Kahn, D.J. Defrees, R. Seeger, R.A. Whiteside, D.J. Fox, E.M. Fleuder and J.A. Pople,Caussian'86 (Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh, 1984).

    Google Scholar 

  99. R.G. Woolley, Chem. Phys. Lett. 125 (1986)200.

    Google Scholar 

  100. A. Gavezzotti, J. Amer. Chem. Soc. 105 (1983)5220.

    Google Scholar 

  101. G.A. Arteca and P.G. Mezey,Proc. 11th Conf. IEEE EMBS, Vol. 11 (1989), p. 1907.

    Google Scholar 

  102. P.K. Pearson, H.F. Schaefer III and U. Wahlgren, J. Chem. Phys. 62 (1975)350.

    Google Scholar 

  103. R.A. Poirier, D. Majlessi and T.J. Zielinsky, J. Comput. Chem. 7 (1986)464.

    Google Scholar 

  104. X. Luo, G.A. Arteca and P.G. Mezey, Int. J. Quant. Chem., in press.

  105. D.M. Walba, Stereochemical topology, in:Chemical Applications of Topology and Graph Theory, ed. R.B. King (Elsevier, Amsterdam, 1983).

    Google Scholar 

  106. V.F.R. Jones, Bull. Amer. Math. Soc. (NS) 12 (1985)103.

    Google Scholar 

  107. P. Freyd, D. Yetter, J. Hoste, W.B.R. Lickorish, K. Millett and A. Ocneanu, Bull. Amer. Math. Soc. (NS) 12 (1985)239.

    Google Scholar 

  108. D.M. Walba, Tetrahedron 41 (1985)3161.

    Google Scholar 

  109. S.A. Wasserman and N.R. Cozzarelli, Science 240 (1986)110.

    Google Scholar 

  110. M.L. Connolly, I.D. Kuntz and G.M. Crippen, Biopolymers 19 (1988)1l67.

    Google Scholar 

  111. T. Kikuchi, G. Némethy and H.A. Scheraga, J. Comput. Chem. 7 (1986)67.

    Google Scholar 

  112. J. Simon, J. Comput. Chem. 9 (1987)718.

    Google Scholar 

  113. D.W. Sumners, J. Math. Chem. 1 (1987)1.

    Google Scholar 

  114. P.G. Mezey, J. Amer. Chem. Soc. 108 (1986)3976.

    Google Scholar 

  115. K.C. Millett, J. Comp. Chem. 8 (1987)536.

    Google Scholar 

  116. M. Karplus and J.A. McCammon, Ann. Rev. Biochem. 53 (1983)263.

    Google Scholar 

  117. F. Colonna-Cesari, D. Perahia, M. Karplus, H. Eklund, C.I. Brändén and O. Tapia, J. Biol. Chem. 261 (1986)15273.

    PubMed  Google Scholar 

  118. O. Tapia, H. Eklund and C.I. Brändén, Molecular, electronic, and structural aspects of the catalytic mechanism of alcohol dehydrogenase, in:Steric Aspects of Biornolecular interactions, ed. G. Náray-Szabó and K. Simon (CRC Press, West Palm Beach, 1987).

    Google Scholar 

  119. P.L. Chau and P.M. Dean, J. Mol. Graph. 5 (1987)97.

    Google Scholar 

  120. L. Caccianotti, Istituto “G. Donegani” Preprint, Novara, Italy (1989).

  121. M.A. Johnson, J. Math. Chem. 3 (1989)117.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry and Department of Mathematics, University of Saskatchewan, S7N 0W0, Saskatoon, Saskatchewan, Canada

    Gustav A. Arteca & Paul G. Mezey

Authors
  1. Gustav A. Arteca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul G. Mezey
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arteca, G.A., Mezey, P.G. Configurational dependence of molecular shape. J Math Chem 10, 329–371 (1992). https://doi.org/10.1007/BF01169181

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01169181

Keywords

Search

Navigation