Spectral moments of the edge-adjacency matrix of molecular graphs. 2. Molecules containing heteroatoms and QSAR applications

Journal of Chemical Information and Computer Sciences

Volumn 37, Issue 2, 1997, Pages 320-328

  Estrada, Ernesto ^a  

^a CENTRAL UNIVERSITY OF LAS VILLAS   (Cuba)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000125522     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci960113v     Document Type: Article

References (74)

1. Rouvray, D. Taking a Short Cut to Drug Design. New Scientist 1993, May 29, 35-38.
2. Balaban, A. T. Applications of Graph Theory to Chemistry. J. Chem. Inf. Comput. Sci. 1985, 25, 334-343.
3. Hansen, P. J.; Jurs, P. C. Chemical Applications of Graph Theory. Part I. Fundamentals and Topological Indices. J. Chem. Educ. 1988, 65, 574-580.
4. Mihalic, Z.; Trinajstić, N. A Graph-Theoretical Approach to Structure-Property Relationships. J. Chem. Educ. 1992, 69, 701-712.
5. Sabljic, A.; Trinajstić, N. Quantitative Structure-Activity Relationships: The Role of Topological Indices. Acta Pharm. Jugosl. 1981, 31, 189-214.
6. Albert, A. Selective Toxicity: The Physico-chemical Basis of Therapy; Chapman and Hall: London, 1984.
7. Cvetkovic, D. M.; Doob, M.; Sach, H. Spectra of Graphs; VEB: Berlin, 1982.
8. Randić, M. Characterization of Atoms, Molecules and Classes of Molecules Based on Path Enumeration. MATCH 1979, 7, 5-64. Randić, M.; Wilkins, C. L. Graph Theoretical Study of Structural Similarity in Benzomorphans. Int. J. Quantum Chem.: Quantum Biol. Symp. 1979, 6, 55-71. Wilkins, C. L.; Randić, M. A Graph Theoretical Approach to Structure-Property and Structure-Activity Correlations. Theor. Chim. Acta 1980, 58, 45-68.
9. Randić, M. Characterization of Atoms, Molecules and Classes of Molecules Based on Path Enumeration. MATCH 1979, 7, 5-64. Randić, M.; Wilkins, C. L. Graph Theoretical Study of Structural Similarity in Benzomorphans. Int. J. Quantum Chem.: Quantum Biol. Symp. 1979, 6, 55-71. Wilkins, C. L.; Randić, M. A Graph Theoretical Approach to Structure-Property and Structure-Activity Correlations. Theor. Chim. Acta 1980, 58, 45-68.
10. Randić, M. Characterization of Atoms, Molecules and Classes of Molecules Based on Path Enumeration. MATCH 1979, 7, 5-64. Randić, M.; Wilkins, C. L. Graph Theoretical Study of Structural Similarity in Benzomorphans. Int. J. Quantum Chem.: Quantum Biol. Symp. 1979, 6, 55-71. Wilkins, C. L.; Randić, M. A Graph Theoretical Approach to Structure-Property and Structure-Activity Correlations. Theor. Chim. Acta 1980, 58, 45-68.
11. Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Search for Self-avoiding Path for Molecular Graphs. Comput. Chem. 1979, 3, 5-13. Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Use of Self-avoiding Path for Characterization of Molecular Graphs with Multiple Bonds. Comput. Chem. 1980, 4, 27-32.
12. Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Search for Self-avoiding Path for Molecular Graphs. Comput. Chem. 1979, 3, 5-13. Randić, M.; Brissey, G. M.; Spencer, R. B.; Wilkins, C. L. Use of Self-avoiding Path for Characterization of Molecular Graphs with Multiple Bonds. Comput. Chem. 1980, 4, 27-32.
13. Randić, M. Random Walks and Their Diagnostic Value for Characterization of Atomic Environment. J. Comput. Chem. 1980, 1, 386-399.
14. Barysz, M.; Knop, J. V.; Pejakovic, S.; Trinajstić, N. Characterization of Branching. Polish J. Chem. 1985, 59, 405-432.
15. Randić, M. Representation of Molecular Graphs by Basic Graphs. J. Chem. Inf. Comput. Sci. 1992, 32, 57-69.
16. Estrada, E. Spectral Moments of Edge Adjacency Matrix in Molecular Graphs. 1. Definition and Applications to the Prediction of Physical Properties of Alkanes. J. Chem. Inf. Comput. Sci. 1996, 36, 844-849.
17. Randić, M. Novel Graph Theoretical Approach to Heteroatoms in Quantitative Structure-Activity Relationships. Chemom. Intell. Lab. Syst. 1991, 10, 213-217.
18. Kier, L. B.; Hall, L. H. Molecular Connectivity in Chemistry and Drug Research; Academic Press: New York, 1976.
19. Kupchik, E. J. General Treatment of Heteroatoms with the Randic Molecular Connectivity Index. Quant. Struct.-Act. Relat. 1989, 8, 98-103.
20. Estrada, E.; Montero, L. A. Bond Order Weighted Graphs as Structure-Property Indices. Mol. Eng. 1993, 2, 363-373.
21. Estrada, E.; Ramirez, A. Edge Adjacency Relationships and Molecular Topographic Descriptors. Definition and QSAR Applications. J. Chem. Inf. Comput. Sci. 1996, 36, 837-845.
22. Estrada, Three-Dimensional Molecular Descriptors Based on Electron Charge Density Weighted Graphs. J. Chem. Inf. Comput. Sci. 1995, 35, 708-713.
23. Grossman, S. C.; Jerman-Blazic Dzonova, B.; Randić, M. A Graph Theoretical Approach to Quantitative Structure-Activity Relationship. Int. J. Quantum Chem.: Quantum Biol. Symp. 1986, 12, 123-139.
24. Estrada, E. Edge Adjacency Relationships in Molecular Graphs Containing Heteroatoms: A New Topological Index Related to Molar Volume. J. Chem. Inf. Comput. Sci. 1995, 35, 701-707.
25. Estrada, E. Edge Adjacency Relationships and A New Topological Index Related to Molecular Volume. J. Chem. Inf. Comput. Sci. 1995, 35, 31-33.
26. Rouvray, D. H. In Chemical Applications of Graph Theory. Balaban, A. T., Ed.; Academic Press: London, 1976; pp 180-181. Trinajstić, N. Chemical Graph Theory; CRC Press: Boca Raton, FL, 1983; 2nd ed. 1992; pp 32-33.
27. Rouvray, D. H. In Chemical Applications of Graph Theory. Balaban, A. T., Ed.; Academic Press: London, 1976; pp 180-181. Trinajstić, N. Chemical Graph Theory; CRC Press: Boca Raton, FL, 1983; 2nd ed. 1992; pp 32-33.
28. Gutman, I.; Estrada, E. Topological Indices Based on Line Graph of the Molecular Graphs. J. Chem. Inf. Comput. Sci. 1996, 36, 541-543.
29. Jiang, Y.; Tang, A.; Hoffmann, R. Evaluation of Moments and their Application in Hückel Molecular Orbital Theory. Theoret. Chim. Acta 1984, 66, 183-192. Cioslowski, J. Decomposition of the Total pielectron Energy of Polycyclic Hydrocarbons into Benzene Ring Increments. Chem. Phys. Lett. 1985, 122, 234-236. Cioslowski, J. The Generalized Padé Approximants and the Chemical Graph Theory. Int. J. Quantum Chem. 1988, 34, 217-224.
30. Jiang, Y.; Tang, A.; Hoffmann, R. Evaluation of Moments and their Application in Hückel Molecular Orbital Theory. Theoret. Chim. Acta 1984, 66, 183-192. Cioslowski, J. Decomposition of the Total pielectron Energy of Polycyclic Hydrocarbons into Benzene Ring Increments. Chem. Phys. Lett. 1985, 122, 234-236. Cioslowski, J. The Generalized Padé Approximants and the Chemical Graph Theory. Int. J. Quantum Chem. 1988, 34, 217-224.
31. Jiang, Y.; Tang, A.; Hoffmann, R. Evaluation of Moments and their Application in Hückel Molecular Orbital Theory. Theoret. Chim. Acta 1984, 66, 183-192. Cioslowski, J. Decomposition of the Total pielectron Energy of Polycyclic Hydrocarbons into Benzene Ring Increments. Chem. Phys. Lett. 1985, 122, 234-236. Cioslowski, J. The Generalized Padé Approximants and the Chemical Graph Theory. Int. J. Quantum Chem. 1988, 34, 217-224.
32. Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982.
33. Schlick, T. Optimization Methods in Computational Chemistry. In Reviews in Computational Chemistry; Lipkowitz, B., Boyd, B., Eds.; VCH Publishers: New York, 1992; Vol. 3, Chapter 1.
34. Potapov, V. M. Stereochemistry. MIR Publ.: Moscow, 1978. Montero, L. A. HAVPAC: User Manual; Universidad de La Habana: Havana, 1991.
35. Potapov, V. M. Stereochemistry. MIR Publ.: Moscow, 1978. Montero, L. A. HAVPAC: User Manual; Universidad de La Habana: Havana, 1991.
36. Randić, M. Generalized Molecular Descriptors. J. Math. Chem. 1991, 7, 155-168.
37. Belsey, D. A.; Kuh, E.; Welsch, R. E. Regression Diagnostics; Wiley: New York, 1980.
38. Randić, M. Search for Optimal Molecular Descriptors. Croat. Chem. Acta 1991, 64, 43-54. Miyashita, Y.; Ohsako. H.; Okuyama, T.; Sasaki, S.; Randic, M. Computer-Assisted Studies of Structure-Property Relationships Using Graph Invariants. Magn. Res. Chem. 1991, 29, 362-365.
39. Randić, M. Search for Optimal Molecular Descriptors. Croat. Chem. Acta 1991, 64, 43-54. Miyashita, Y.; Ohsako. H.; Okuyama, T.; Sasaki, S.; Randic, M. Computer-Assisted Studies of Structure-Property Relationships Using Graph Invariants. Magn. Res. Chem. 1991, 29, 362-365.
40. Smolenskii, E. A. Utilization of the Theory of Graphs for the Calculation of Structure-Additive Properties of Hydrocarbons. Zh. Fiz. Khim. 1964, 38, 1288-1291.
41. Klein, D. J. Chemical Graph-Theoretic Cluster Expansions. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 153-171. Poshusta, R. D.; McHughes, M. C. Embedding Frequencies of Trees. J. Math. Chem. 1989, 3, 193-215. McHughes, M. C.; Poshusta, R. D. Graphtheoretic Cluster Expansions. Thermodynamic Properties of Alkanes. J. Math. Chem. 1990, 4, 227-249. Schmalz, T. G.; Klein, D. J.; Sandleback, B. L. Chemical Graph-Theoretical Cluster Expansion and Diamagnetic Susceptibility. J. Chem. Inf. Comput. Sci. 1992, 32, 54-57. Kvasnicka, V.; Pospíchal, J. Simple Construction of Embedding Frequencies of Trees and Rooted Trees. J. Chem. Inf. Comput. Sci. 1995, 35, 121-128.
42. Klein, D. J. Chemical Graph-Theoretic Cluster Expansions. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 153-171. Poshusta, R. D.; McHughes, M. C. Embedding Frequencies of Trees. J. Math. Chem. 1989, 3, 193-215. McHughes, M. C.; Poshusta, R. D. Graphtheoretic Cluster Expansions. Thermodynamic Properties of Alkanes. J. Math. Chem. 1990, 4, 227-249. Schmalz, T. G.; Klein, D. J.; Sandleback, B. L. Chemical Graph-Theoretical Cluster Expansion and Diamagnetic Susceptibility. J. Chem. Inf. Comput. Sci. 1992, 32, 54-57. Kvasnicka, V.; Pospíchal, J. Simple Construction of Embedding Frequencies of Trees and Rooted Trees. J. Chem. Inf. Comput. Sci. 1995, 35, 121-128.
43. Klein, D. J. Chemical Graph-Theoretic Cluster Expansions. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 153-171. Poshusta, R. D.; McHughes, M. C. Embedding Frequencies of Trees. J. Math. Chem. 1989, 3, 193-215. McHughes, M. C.; Poshusta, R. D. Graphtheoretic Cluster Expansions. Thermodynamic Properties of Alkanes. J. Math. Chem. 1990, 4, 227-249. Schmalz, T. G.; Klein, D. J.; Sandleback, B. L. Chemical Graph-Theoretical Cluster Expansion and Diamagnetic Susceptibility. J. Chem. Inf. Comput. Sci. 1992, 32, 54-57. Kvasnicka, V.; Pospíchal, J. Simple Construction of Embedding Frequencies of Trees and Rooted Trees. J. Chem. Inf. Comput. Sci. 1995, 35, 121-128.
44. Klein, D. J. Chemical Graph-Theoretic Cluster Expansions. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 153-171. Poshusta, R. D.; McHughes, M. C. Embedding Frequencies of Trees. J. Math. Chem. 1989, 3, 193-215. McHughes, M. C.; Poshusta, R. D. Graphtheoretic Cluster Expansions. Thermodynamic Properties of Alkanes. J. Math. Chem. 1990, 4, 227-249. Schmalz, T. G.; Klein, D. J.; Sandleback, B. L. Chemical Graph-Theoretical Cluster Expansion and Diamagnetic Susceptibility. J. Chem. Inf. Comput. Sci. 1992, 32, 54-57. Kvasnicka, V.; Pospíchal, J. Simple Construction of Embedding Frequencies of Trees and Rooted Trees. J. Chem. Inf. Comput. Sci. 1995, 35, 121-128.
45. Klein, D. J. Chemical Graph-Theoretic Cluster Expansions. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 153-171. Poshusta, R. D.; McHughes, M. C. Embedding Frequencies of Trees. J. Math. Chem. 1989, 3, 193-215. McHughes, M. C.; Poshusta, R. D. Graphtheoretic Cluster Expansions. Thermodynamic Properties of Alkanes. J. Math. Chem. 1990, 4, 227-249. Schmalz, T. G.; Klein, D. J.; Sandleback, B. L. Chemical Graph-Theoretical Cluster Expansion and Diamagnetic Susceptibility. J. Chem. Inf. Comput. Sci. 1992, 32, 54-57. Kvasnicka, V.; Pospíchal, J. Simple Construction of Embedding Frequencies of Trees and Rooted Trees. J. Chem. Inf. Comput. Sci. 1995, 35, 121-128.
46. Needham, D. E.; Wei, I-C.; Seybold, P. G. Molecular Modeling of the Physical Properties of the Alkanes. J. Am. Chem. Soc. 1988, 110, 4186-4194.
47. Franke, R. Theoretical Drug Design Methods; Elsevier: Amsterdam, 1984.
48. Hansch, C. A Quantitative Approach to Biochemical Structure-Activity Relationships. Acc. Chem. Res. 1969, 2, 232-239.
49. See ref 35 Chapter 11, pp 254-274.
50. Stuper, A. J.; Brugger, W. E.; Jurs, P. C. Computer Assisted Studies of Chemical Structure and Biological Function; Wiley-Interscience: New York, 1979.
51. Cramer III, R. D.; Patterson, D. G.; Bunce, J. D. Comparative Molecular Field Analysis (CoMFA). 1. Effect of Shape on Binding of Steroids to Carrier Proteins. J. Am. Chem. Soc. 1988, 110, 5959-5967.
52. Kier, L. B. Molecular Orbital Studies in Chemical Pharmacology; Springer-Verlag: Berlin, 1970. Sadlej, J. Semi-empirical Methods of Quantum Chemistry. Ellis Horwood: Chichester, 1985; Chapter 10.
53. Kier, L. B. Molecular Orbital Studies in Chemical Pharmacology; Springer-Verlag: Berlin, 1970. Sadlej, J. Semi-empirical Methods of Quantum Chemistry. Ellis Horwood: Chichester, 1985; Chapter 10.
54. Randić, M. Nonempirical Approach to Structure-Activity Studies. Int. J. Quantum Chem.: Quantum Biol. Symp. 1984, 11, 137-153.
55. Kier, L. B.; Hall, L. H. Molecular Connectivity in Structure-Activity Analysis; Wiley: New York, 1986.
56. Trinajstić, N.; Randic, M.; Klein, D. J. On the Quantitative Structure-Activity Relationships in Drug Research. Acta Pharm. Jugosl. 1986, 36, 267-279.
57. Carter, D. V.; Carlton, P. T.; Fenton, A. H.; Housley, J. R.; Lessel, B. The Preparation and the Antibacterial and Antifungal Properties of Some Substituted Benzyl Alcohols. J. Pharm. Pharmacol. 1958, 10, Suppl. 147T-159T.
58. PC Index. J. Pharm. Sci. 1980, 69, 1034-1039.
59. A detailed discussion about the use of each substituent parameters is given in ref 35. Original works defining each of these parameters are as follows: Fujita, T.; Iwasa, J.; Hansch, C. A New Substituent Constant, π, Derived from Partition Coefficients. J. Am. Chem. Soc. 1964, 36, 5175-5180. Swain, C. G.; Lupton, E. C. Field and Resonance Components of Substituent Effects. J. Am. Chem. Soc. 1968, 90, 4328-4337. Verloop, A.; Hoogenstraaten, W.; Tipker, J. In Drug Design, Vol VII; Ariens, E. J., Ed.; Academic Press: New York, 1976; p 165.
60. A detailed discussion about the use of each substituent parameters is given in ref 35. Original works defining each of these parameters are as follows: Fujita, T.; Iwasa, J.; Hansch, C. A New Substituent Constant, π, Derived from Partition Coefficients. J. Am. Chem. Soc. 1964, 36, 5175-5180. Swain, C. G.; Lupton, E. C. Field and Resonance Components of Substituent Effects. J. Am. Chem. Soc. 1968, 90, 4328-4337. Verloop, A.; Hoogenstraaten, W.; Tipker, J. In Drug Design, Vol VII; Ariens, E. J., Ed.; Academic Press: New York, 1976; p 165.
61. A detailed discussion about the use of each substituent parameters is given in ref 35. Original works defining each of these parameters are as follows: Fujita, T.; Iwasa, J.; Hansch, C. A New Substituent Constant, π, Derived from Partition Coefficients. J. Am. Chem. Soc. 1964, 36, 5175-5180. Swain, C. G.; Lupton, E. C. Field and Resonance Components of Substituent Effects. J. Am. Chem. Soc. 1968, 90, 4328-4337. Verloop, A.; Hoogenstraaten, W.; Tipker, J. In Drug Design, Vol VII; Ariens, E. J., Ed.; Academic Press: New York, 1976; p 165.
62. Kubinyi, H. QSAR: Hansch Analysis and Related Approaches (Methods and Principles in Medicinal Chemistry; Mannhold, R., Krogsgaard-Larsen, P., Timmerman, H., Eds.; VCH: Weinheim, 1993; Vol. I.
63. Trinajstić, N.; Klein, D. J.; Randic, M. On Some Solved and Unsolved Problems of Chemical Graph Theory. Int. J. Quantum Chem.: Quantum Chem. Symp. 1986, 20, 699-742.
64. Dewar, M. J. S. Quantum Mechanical Molecular Models. J. Phys. Chem. 1985, 89, 2145-2150.
65. Dewar, M. J. S. Chemical Implications of σ Conjuation. J. Am. Chem. Soc. 1984, 106, 669-682.
66. See, for instances: Laurencelle, N.; Pacey, P. D. Simple Electrostatic Model for Enthalpies of Formation of Singly Substituted Alkanes. J. Am. Chem. Soc. 1993, 115, 625-631.
67. Bykov, G. V. Dipole Moments of Bonds in Organic Compounds. Russ. J. Phys. Chem. 1969, 43, 310-313.
68. Pauling, L. The Nature of the Chemical Bond; Cornell University Press: New York, 1960.
69. Kier, L. B.; Hall, L. H. An Electrotopological State Index for Atoms in Molecules. Pharm. Res. 1990, 7, 801-807. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: Structure Information at the Atomic Level for Molecular Graphs. J. Chem. Inf. Comput. Sci. 1991, 31, 76-82. Hall, L. H.; Kier, L. B. An Index of Electrotopological State for Atoms in Molecules. J. Math. Chem. 1991, 7, 229-241. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: An Atom Index for QSAR. Quant. StructAct. Relat. 1991, 10, 43-51.
70. Kier, L. B.; Hall, L. H. An Electrotopological State Index for Atoms in Molecules. Pharm. Res. 1990, 7, 801-807. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: Structure Information at the Atomic Level for Molecular Graphs. J. Chem. Inf. Comput. Sci. 1991, 31, 76-82. Hall, L. H.; Kier, L. B. An Index of Electrotopological State for Atoms in Molecules. J. Math. Chem. 1991, 7, 229-241. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: An Atom Index for QSAR. Quant. StructAct. Relat. 1991, 10, 43-51.
71. Kier, L. B.; Hall, L. H. An Electrotopological State Index for Atoms in Molecules. Pharm. Res. 1990, 7, 801-807. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: Structure Information at the Atomic Level for Molecular Graphs. J. Chem. Inf. Comput. Sci. 1991, 31, 76-82. Hall, L. H.; Kier, L. B. An Index of Electrotopological State for Atoms in Molecules. J. Math. Chem. 1991, 7, 229-241. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: An Atom Index for QSAR. Quant. StructAct. Relat. 1991, 10, 43-51.
72. Kier, L. B.; Hall, L. H. An Electrotopological State Index for Atoms in Molecules. Pharm. Res. 1990, 7, 801-807. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: Structure Information at the Atomic Level for Molecular Graphs. J. Chem. Inf. Comput. Sci. 1991, 31, 76-82. Hall, L. H.; Kier, L. B. An Index of Electrotopological State for Atoms in Molecules. J. Math. Chem. 1991, 7, 229-241. Hall, L. H.; Mohney, B.; Kier, L. B. The Electrotopological State: An Atom Index for QSAR. Quant. StructAct. Relat. 1991, 10, 43-51.
73. Feguson, L. N. The Modern Structural Theory of Organic Chemistry Prentice-Hall: NJ, 1963; pp 53-55.
74. Estrada, E. Spectral Moments of Edge Adjacency Matrix in Molecular Graphs. 3. Applications to the Prediction of Diamagnetic Susceptibilities. Manuscript in preparation.