Systematic search for new types of chemical interconversions: Mathematical models and some applications

Journal of Chemical Information and Computer Sciences

Volumn 38, Issue 3, 1998, Pages 331-348

  Tratch, Serge S ^a   Zefirov, Nikolai S ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001638930     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci960099m     Document Type: Article

References (85)

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17. (a) Tratch, S. S.; Zefirov, N. S. Problems of Molecular Design and Computers. 7. Formal-Logical Approach to Organic Reactions. Main Notions and Terminology. Zh. Org. Khimii 1982, 18, 1561-1583 [in Russian],
18. (b) Zefirov, N. S.; Tratch, S. S. Problems of Molecular Design and Computers. 8. Reaction Fragments and Classification Equations in Formal-Logical Approach to Organic Reactions. Zh. Org. Khimii 1984, 20, 1121-1142 [in Russian],
19. (c) Tratch, S. S.; Baskin, I. I.; Zefirov, N. S. Problems of Molecular Design and Computers. 13. Systematic Analysis of Organic Processes Characterized by Disclosed Topologies of Bond Redistribution. Zh. Org. Khimii 1988, 24, 1121-1133 [in Russian],
20. (d) Tratch, S. S.; Baskin, I. I.; Zefirov, N. S. Problems of Molecular Design and Computers. 14. Systematic Analysis of Organic Processes Characterized by Linear-Cyclic Topology of Bond Redistribution. Zh. Org. Khimii 1989, 25, 1585-1606 [in Russian].
21. Zefirov, N. S.; Gordeeva, E. V.; Tratch, S. S. Problems of Molecular Design and the Computer. 11. The FLAMINGOES Program System for the Nonempirical Solution of Structural Problems of Organic Chemistry. The BASIC Program Oriented for Microcomputer. J. Chem. Inf. Comput. Sci. 1988, 28, 188-193.
22. (b) Zefirov, N. S.; Tratch, S. S. Symbolic Equations and Their Application to Reaction Design. Anal. Chim. Acta 1990, 235, 115-134.
23. (c) Zefirov, N. S.; Baskin, I. I.; Palyulin, V. A. SYMBEQ Program and Its Application in Computer-Assisted Reaction Design. J. Chem. Inf. Comput. Sci. 1994, 34, 994-999.
24. (a) Zefirov, N. S.; Tratch, S. S.; Gamziani, G. A. Problems of Molecular Design and Computers. 9. Formal-Logical Approach to Organic Reactions. General Description of the Processes with Linear Electron Transfer. Zh, Org. Khimii 1986, 22, 1341-1359 [in Russian],
25. (b) Tratch, S. S.; Gamziani, G. A.; Zefirov, N. S. Problems of Molecular Design and Computers. 10. Enumeration and Generation of Equations Characterizing Ionic, Radicalic, and Oxidation-Reduction Processes with Linear Electron Transfer. Zh. Org. Khimii 1987, 23, 2488-2507 [in Russian].
26. (c) Zefirov, N. S.; Tratch, S. S.; Gamziani, G. A. Description of Organic Reactions in Frame of the Formal-Logical Approach; Metsniereba Press: Tbilisi, 1993; 208 pp [in Russian].
27. (a) Tratch, S. S.; Podimova, E. V,; Zefirov, N. S. An Algorithm Generating Nonequivalent Labelings for Sets with Given Permutation Groups. Solution Methods and Programs for Optimization Problems on Graphs and Networks (Proceedings of the 2nd All-Union Conference); Novosibirsk, 1982; Part 1, pp 210-213 [in Russian].
28. (b) Tratch, S. S.; Podimova, E. V.; Zefirov, N. S. An Algorithm Generating Complete Sets of Equations Which Describe Possible Reactions of Organic Compounds. Application of Computers in Molecular Spectroscopy and Chemical Investigations (Proceedings of the 6th All-Union Conference); Novosibirsk, 1983; pp 205-206 [in Russian].
29. (c) Tratch, S. S.; Zefirov, N. S. A Mathematical Model of Generation Problems for Structural Equations and Directed Search for Degenerate Rearrangements. Applications of Computers in Molecular Spectroscopy and Chemical Investigations (Proceedings of the 8th All-Union Conference); Novosibirsk, 1989; pp 315-316 [in Russian].
30. G: Application of Burnside's Lemma and Expanded Cycle Indices of Permutation Groups. Molecular Graphs in Chemical Investigations (Proceedings of the High-School Conference); Kalinin, 1990; pp 104-105 [in Russian].
31. (e) Tratch, S. S.; Zefirov, N. S. The Methodology of Solution for Some Enumeration Problems of Organic Chemistry on the Base of Burnside's Lemma and Expanded Cycle Indices of Permutation Groups. Molecular Graphs in Chemical Investigations (Proceedings of the High-School Conference); Kalinin, 1990; pp 106-107 [in Russian].
32. Tratch, S. S. Logical-Combinatorial Approaches to Design Problems for Organic Structures, Reactions, and Configurations (Doctoral Dissertation); Moscow, 1993; Vol. 1, pp 10-153; Vol. 2, pp 5-178 [in Russian].
33. Tratch, S. S. Logical-Combinatorial Approaches to Design Problems for Organic Structures, Reactions, and Configurations (Doctoral Dissertation); Moscow, 1993; Vol. 1, pp 10-153; Vol. 2, pp 5-178 [in Russian].
34. Tratch, S. S.; Zefirov, N. S. A Hierarchical Classification Scheme for Chemical Reactions. J. Chem. Inf. Comput. Sci. 1998, 38, 349-366.
35. Chemical interconversions in which no bonds change their multiplicity are not considered. Thus, all stereochemical transformations as well as "one-centered" oxidation equation presented processes are beyond the scope of the Formal-Logical Approach. Additionally, this approach needs all nonclassical bonds (e.g., decentralized bonds in organometallic compounds) to be formally represented by ordinary, double, or triple bonds.
36. The "monocentric" cation - radicals are important for mass-spectroscopy but are not typical intermediates in the great majority of real organic transformations. On the other hand, it is evident that taking into account doubly signed centers (dications, dianions, cation - radicals, and anion - radicals) would drastically increase the number of results produced by a computer. Most of the resulting equations (as well as practically all "processes" with 4, 6, 8, ⋯ SRCs) are of no interest to an organic chemist and hence are not considered in the "generating part" of the Formal-Logical Approach.
37. In elementary homolysis (equation presented) and heterolysis (equation presented) processes and also in elementary oxidation-reduction processes (cf. note 11), the total number of signs in both systems is always even. All multicentered reactions can evidently be represented by sequences of two-centered dissociation - recombination and one-centered oxidation-reduction processes.
38. (a) Schank, K. Base Catalyzed Rearrangement of α-Acetoxy-β-Oxosulfones. Signs for the Intermediate Existence of Valence Tautomeric α-Acetoxyketenes. Chem. Ber. 1970, 103, 3093-3103.
39. (b) Franzen, V.; Driessen, H. E. Methylenation with Sulfonium Ylides. Tetrahedron Lett. 1962, 661-662.
40. Note that in reaction or skeletal equations, "free" valencies to other atoms as well as lone pairs of oxygen, nitrogen, sulfur, etc. atoms can be either drawn or omitted (see Charts 1b,e and 2a,b with no lone pairs but with "free" valences being explicitly shown). These details must, however, be absent in any symbolic or structural equation because all necessary information related to valence reorganization of each unspecified atom is hidden in its designation (unsigned or signed symbol ○, O, X, X, X′, X′, X″, X″, etc.). Additionally, underlining symbols of pseudospecific centers should in no case be mixed with lone electron pairs.
41. 2a,c
42. 5a,9 On the other hand, the most "elementary" (e.g., "no mechanism") reactions are described by canonical, single mode bond redistributions which in principle cannot correspond to nonelementary topology contours.
43. (a) Balaban, A. T.; Fǎrcasiu, D.; Harary, F. Chemical Graphs. 9. Isotope-Isomerism of Multiply-Labelled Compounds. J. Labelled Comp. 1970, 6, 211-223.
44. (b) Zefirov, N. S.; Tratch, S. S.; Tchizhov, O. S. Cage and Polycyclic Compounds. Molecular Design Based on Isomorphic Substitution Principle (Itogi Nauki i Tekhniki, Ser. Org. Khim., No. 3); VINITI Press: Moscow, 1979; 88 pp [in Russian],
45. (c) Masinter, L. M.; Sridharan, N. S.; Carhart, R. E.; Smith, D. H. Applications of Artificial Intelligence for Chemical Inference. 13. Labeling of Objects Having Symmetry. J. Am. Chem. Soc. 1974, 96, 7714-7723.
46. (d) Balaban, A. T. Chemical Graphs. 45. Edge-Labelled Graphs as Unsaturated Valence Isomers of Annulenes; Applications of Polya's Theorem. Rev. Roum. Chim. 1986, 31, 695-708.
47. (e) Balaban, A. T. Chemical Graphs. 46. Enumeration of Valence Isomers of Adamantane Using Polya's Theorem. Rev. Roum, Chim. 1986, 31, 795-810.
48. (f) Traten, S. S.; Lomova, O. A.; Sukhachev, D. V.; Palyulin, V. A.; Zefirov, N. S. Generation of Molecular Graphs for QSAR Studies: An Approach Based on Acyclic Fragment Combinations. J. Chem. Inf. Comput. Sci. 1992, 32, 130-139.
49. At first sight, this list seems to be incomplete, e.g., due to absence of the signed graph equation presented The corresponding labeling is, however, equivalent to that represented in Chart 4d (because in any labeling related to a reverse process, all labels "+" must be substituted by "(+)" and vice versa). The mathematical nature of the mentioned equivalency relation is completely clarified in sections 5 and 6.
50. Some doubts about completeness of this list can also arise, e.g., due to absence of the edge-labeled graph equation presented At a glance, this graph is not identical to the graph of Chart 5b. The corresponding labelings are, however, equivalent and relate to just the same symbolic equation in which initial and final systems are interchanged. In order to recognize this equivalence (which is completely explained in sections 5 and 6), one must convert all labels into their counterparts, i.e., "+" into "(+)", "(+)" into "+", and "1/ 0" into "0/1".
51. (a) Balaban, A. T. Chemical Graphs. 3. Reactions with Cyclic Six-Membered Transition States. Rev. Roum. Chim. 1967, 12, 875-898.
52. (b) Hendrickson, J, B. The Variety of Thermal Pericyclic Reactions. Angew. Chem., Int. Ed. Engl. 1974, 13, 47-76.
53. (c) Fujita, S. A Novel Approach to the Enumeration of Reaction Types by Counting Reaction-Center Graphs Which Appear as the Substructures of Imaginary Transition Structures. Bull Chem. Soc. Jpn. 1988, 61, 4189-4206.
54. (d) Fujita, S. Formulation of Isomeric Reaction Types and Systematic Enumeration of Six-Electron Pericyclic Reactions. J. Chem. Inf. Comput. Sci. 1989, 29, 22-30.
55. (e) Fujita, S. Formulation and Enumeration of Five-Center Organic Reactions. Bull. Chem. Soc. Jpn. 1989, 62, 662-667.
56. 1) form the subset M°.
57. (a) Harary, F.; Palmer, E. The Power Group Enumeration Theorem. J. Combin. Theory 1966, 1, 157-173.
58. (b) Faradgev, I. A. Constructive Enumeration of Combinatorial Objects. In Algorithmic Investigations in Combinatorics; Faradgev, I. A., Ed.; Nauka Press: Moscow, 1978; pp 3-11 [in Russian],
59. (c) Alexandrov, P. S. Introduction to Group Theory; Nauka Press; Moscow, 1980; 143 pp [in Russian].
60. 25c was the first in mathematical chemistry who used "symmetry types of functions" in order to formalize graph generation problems.
61. (a) Tratch, S. S. Mathematical Models in Stereochemistry. 1. Combinatorial Characteristics of Composition, Connectivity, and Configuration of Organic Molecules. Zh. Org. Khimii 1995, 31, 1320-1351 [in Russian],
62. (b) Tratch, S. S.; Zefirov, N. S. Algebraic Chirality Criteria and Their Application to Chirality Classification in Rigid Molecular Systems. J. Chem. Inf. Comput. Sci. 1996, 36, 448-464.
63. (d) Kerber, A. On Graphs and Their Enumeration. MATCH 1975, 1, 5-10.
64. 4 and a, b, c, b*, a* for labels - are used in these examples in order to avoid further confusions in the course of chemical interpretation of the obtained results (which actually relate to different, not completely independent, generation steps, cf. section 6).
65. 15, c.; cf. Chart 7a) and also "unpaired" functions for which antipodes cannot be constructed. The arrow schemes related to unpaired functions are absent in Chart 7a because the subset M° is considered to be empty in this example.
66. The remaining signed graphs relate to three-centered dioxidation - direduction processes (see c/a. cc/n. and aa/n subcategories in subsection 4.1 of ref 10). The generation of these graphs could be suppressed if the additional restriction (related to allowed pairs of labels, cf. step 1 in section 4) and corresponding predicate p(φ) were taken into account.
67. k], k = 3, 11, consist of permutations (1)(2)(3), (1, 3)(2) and are isomorphic to the automorphism group of the "parent" graph, i.e., that of Chart 4a.
68. 0}) must be transformed into edge-labeled graphs; the label set consists of symbols "0/1", "1/2", "2/1", and "1/0" in both cases. The resulting symbolic equations relate to three-centered single mode rr/n-radicalic and ca/n-ionic processes, respectively. These equations are listed in ref 7b together with chemically reasonable examples.
69. 6b,c,9), the correctly formulated groups, i.e., Aut[χ], are, however, taken into account.
70. (a) Pólya, G. Combinatorial Calculations for Groups, Graphs, and Chemical Compounds. Acta Math. 1937, 68, 145-254.
71. (b) Harary, F.; Palmer, E. M. Graphical Enumeration; Academic Press: New York, 1973.
72. (c) Klin, M. H.; Pöschel, R.; Rosenbaum, K. Applied Algebra for Mathematicians and Informaticians. Introduction to oup-Theoretical and Combinatorial Methods; VEB Deutscher Verlag den Wissenschaften: Berlin, 1988.
73. H and to its subgroup Γ″. The calculation of these polynomials needs the special, "expanded" cycle indices of the groups H to be initially constructed.
74. 35a was probably the first who differentiated reaction planning and reaction design from synthesis planning (and synthesis design, respectively). In the former case, the target is the (new) reaction or reaction type, while in the latter case, the target is a molecule to be synthesized by a sequence of (known) chemical transformations.
75. (a) Herges, R. Reaction Planning (Computer Aided Reaction Design). In Chemical Structures: The International Language of Chemistry Warr, W. A., Ed.; Springer - Verlag: Berlin, 1988, pp 385-398.
76. (b) Bauer, J.; Ugi, I. Chemical Reactions and Structures without Precedent Generated by Computer Program. J. Chem. Res. 1982, (S) 11, 298.
77. (c) Bauer, J.; Herges, R.; Fontain, E.; Ugi, I. IGOR and Computer Assisted Innovation in Chemistry. Chimia 1985, 39, 43-53.
78. (d) Bauer, J.; Fontain, E.; Forstmeyer, D.; Ugi, I. Interactive Generation of Organic Reactions by IGOR2 and the PC - Assisted Discovery of a New Reaction. Tetrahedron Comput. Methodol. 1988, 1, 129-132.
79. (e) Bauer, J. IGOR2: a PC-Program for Generating New Reactions and Molecular Structures. Tetrahedron Comput. Methodol. 1989, 2, 269-293.
80. (f) Herges, R. Reactionsplanung: Computer Aided Reaction Design (Dissertation Dr. rer. nat. habil.); Erlangen - Nürnberg: 1990; 289 pp.
81. 37c
82. (a) Doering, W. v. E.; Roth, W. R. A Rapidly Reversible Degenerate Cope Rearrangement. Bicyclo[5.1.0]octa-2,5-diene. Tetrahedron 1963, 19, 715-737.
83. 4,6]deca-2,7,9-triene (Bullvalene). Chem. Ber. 1964, 97, 3140-3149.
84. (c) Živković, T. P. Bullvalene Reaction Graph. Croat. Chem. Acta 1996, 69, 215-222.
85. These procedures correspond to specific selection criteria, especially to those which must ensure all constructed structural equations to represent only highly degenerate rearrangement processes.