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New Approaches to Degenerate Interconversions of Organic Structures: 1. Levels of Structural Degeneracy and Computer-Aided Search for Degenerate Rearrangements*

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New Approaches to Degenerate Interconversions of Organic Structures: 1. Levels of Structural Degeneracy and Computer-Aided Search for Degenerate Rearrangements* CROATICA CHEMICA ACTA CCACAA 79 (3) 339¿353 (2006) ISSN-0011-1643 CCA-3099 Original Scientific Paper New Approaches to Degenerate Interconversions of Organic Structures: 1. Levels of Structural Degeneracy and Computer-aided Search for Degenerate Rearrangements* Serge S. Tratch,a,** Marina S. Molchanova,b and Nikolai S. Zefirova aDepartment of Chemistry, Moscow State University, Leninskie Gory, Moscow 119992, Russia bZelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Leninskii prospekt 47, Moscow 119991, Russia RECEIVED OCTOBER 4, 2005; REVISED NOVEMBER 8, 2005; ACCEPTED JANUARY 26, 2006 The general methodology of systematic search for degenerate interconversions must be based on a certain hierarchy of degeneracy. The levels and sublevels of the proposed hierarchy are represented by topological and structural types and subtypes of degeneracy, which correspond to specific equations and to graphs identifying them. Graph operations that enable an efficient Keywords search for arbitrary types of organic reactions are formulated, and problems specific to genera- degenerate interconversions tion of degenerate transformations are considered. In conclusion, results of computer-aided graph-based classification search (using the ARGENT–1 software) for new heteroderivatives and structural analogs of the reaction design problems Cope reaction are discussed. Many of the rearrangements thus found (especially [3,3]-shifts in ARGENT–1 software cations and anions, which have not been studied to date) can be subjects of experimental in- new "Cope-like" rearrangements vestigations. INTRODUCTION one-stage processes, or final results of more complicated, two- or multistage interconversions.1 Examples are such Degenerate transformations (DTs) are reversible inter- well-known DTs as the [1,2]-shift in the 2-norbornyl ca- conversions in which chemical and/or spatial structures of the initial reagents (educts) and reaction products can- tion (Figure 1a), which is one of the stages of the Wag- not be distinguished from each other. Degenerate trans- ner-Meerwein rearrangement; the Cope rearrangement in formations of individual species (neutral molecules, ca- hexadiene-1,5 (Figure 1b), which is a concerted six-cen- tions, anions, or radicals) with breaking/formation of tered process; and prototropic tautomerizations of carboxy- chemical bonds are referred to as degenerate rearrange- lic acids (Figure 1c), for which a dissociative mecha- ments. In the discussion of such rearrangements, the nism with intermediate formation of carboxylate anions spatial structure of the rearranging particle is usually dis- is usually postulated. The degenerate (at R' = R'') isome- regarded. From the standpoint of their mechanism, DTs rization of a-pyrones2 (Figure 1d) can serve as an example can represent elementary stages of reactions, concerted of a multistage reaction whose primary products (ketenes) * The paper represents the ''chemist-oriented'' part of the investigation reported at MATH/CHEM/COMP 2005 (Dubrovnik, June 20–25, 2005). The main ideas of the second, more mathematically involved part of our report are briefly outlined in the last section of the paper. ** Author to whom correspondence should be addressed. (E-mail: [email protected]) 340 S. S. TRATCH et al. 7 7 (a) H C H C (b) (c) 2 2 2 2 CH HC 2 4 4 1 3 1 3 2 5 CH H C CH H C CH O O 5 CH 3 H C 3 2 2 2 2 H C 2 + CH 1 3 1 3 2 CH CH 2 6 6 R C H R C H HC + 2 1 H C CH H C CH H C CR H C CR 2 2 2 2 O O 2 1 2 4 4 6 CH HC 4 4 6 2 2 55 (d) HH H HH H R’ CR’’ R’ C R’’ R’ CR’’ R’ C R’’ R’ CR’’ R’ C R’’ C C C C C C C C C C C C C C C C C C C C C C C C H O O H O O H H O O H O O H O O O O (e) (f) CH CH CH CH CH CH CH CH HC CH HC CH HC HC HC HC CH HC CH HC CH HC CH HC CH CH CH CH CH CH CH HC CH CH HC CH HC CH HC CH HC CH HC CH HC CH HC CH HC CH Figure 1. Interconversions of identical structures in an (a) elementary act of a skeletal rearrangement, (b) concerted process, (c) two-stage dissociation–recombination reaction, and (d) series of constitutional isomerization and stereoisomerization processes. The (e) multiply de- generate rearrangement of hypostrophene and its (f) reaction graph. are formed and then disappear as a result of a nonde- examples is the graph in Figure 1f, whose five vertices generate [6]-electrocyclic process. correspond to interconverted hypostrophene structures Methods used for the experimental study of DTs and five edges correspond to rearrangement processes in make it possible either to distinguish educts from Figure 1e. reaction products (owing to the presence of isotopic There are presently many published papers discus- labels or specially selected substituents) or to recognize sing the methods of construction, the metric properties, degeneracy according to a decrease in the number of and the automorphism groups of reaction graphs that signals in NMR spectra. For example, the process in correspond to multiply degenerate rearrangements and Figure 1a is nondegenerate at R ≠ H and degenerate at especially to stereoisomerization processes (in the latter R = H; in the latter case, degeneracy must be manifested processes, the chemical constitution remains unchanged by merging of signals from protons of the C1H and C2H and degeneracy is associated with molecular motions that groups (and also from protons of the C3H and C7H convert the stereoisomers in question into themselves). groups), which become equivalent in the case of a DT. Since analysis of these results lies beyond the scope of Note that in the case of a multiply or highly degenerate this work, here we provide only some references to pa- rearrangement (a reversible process involving more than pers on the best studied reaction graphs,5–10 as well as to two identical interconvertible particles), even all atoms or more special studies on the general properties of these groups of atoms can become equivalent. As an example, graphs.11–14 Figure 1e depicts five structures of hypostrophene,3 which Among the works dealing with DTs, irrespective of consecutively pass into each other due to the Cope reac- the properties of their reaction graphs, we can distinguish tion. As easily seen, the multiply degenerate process in numerous studies of permutational isomerization proces- this case leads to the equivalence of all ten CH groups, 15–20 a fact that enabled the authors of Ref. 3 to recognize de- ses; see several fundamental papers on this topic. In generacy while studying the PMR spectra of dideutero- these (not necessarily degenerate) processes, the conver- substituted hypostrophene. sion of the initial structural or spatial isomer into the fi- nal one is associated with a certain permutation, which Although the phenomenon of degeneracy has been determines the renumbering of atoms. For example, let receiving significant attention of chemists over recent 123456 decades, the main theoretical results were obtained just us consider the permutation , which for multiply degenerate rearrangements, such as the one 321654 in Figure 1e. More specifically, the principal objects of interconverts atoms 1 and 3, as well as atoms 4 and 6, studies in mathematical chemistry were reaction graphs4 but leaves atoms 2 and 5 as they are. When applied to the of such rearrangements, i.e., graphs whose vertices cor- Cope rearrangement (Figure 1b), this permutation converts respond to the rearranging particles while edges corres- the "initial" double bonds 1–2 and 5–6, as well as single pond to transitions between them. One of the possible bonds 2–3, 3–4, and 4–5, into "final" bonds of the same Croat. Chem. Acta 79 (3) 339¿353 (2006) NEW APPROACHES TO DEGENERATE INTERCONVERSIONS 341 multiplicity (3–2, 5–4 and 2–1, 1–6, 6–5, respectively). In the second of the aforementioned papers,26 its This implies that the permutation in question really trans- authors made an attempt to find such new modes of the forms the initial structure of hexadiene-1,5 in Figure 1b Cope reaction that would lead to "averaging" of all car- into an identical final structure. It is significant that many bon atoms in the rearranging particle. For this purpose, results obtained by theoretical analysis of "permutamer" in- they developed a heuristic criterion, which enabled them terconversions (the term is taken from Ref. 17) turned out to reveal (among valence isomers of annulenes CnHn, 19,20 to be extremely helpful for dynamic stereochemistry n ≤ 18, and polycarbons Cn, n = 6, 8, obtained by various but have rarely been applied to degenerate transformations techniques) quite a number of structures for which mul- of constitutional isomers. In this connection, mention should tiply degenerate [3,3]-shifts are possible from the formal be made of the use of permutation theory for solving se- standpoint. Unfortunately, it turned out that none of such veral systematization problems. Classification of degene- structures, except for those mentioned earlier in Ref. 25, rate processes according to their chirality or achirality21 can undergo the concerted process of the [3,3]-sigmatro- and self-inverseness22 or non-self-inverseness, as well as pic shift because of their extremely unfavorable rigid classification considering both factors,23 have been illu- geometries. strated in literature almost exclusively by examples of In our opinion, systematic search for DTs should by stereoisomer interconversions. no means be reduced to designing new concerted pro- On the other hand, the permutation group theory is cesses belonging to a single type selected in advance.
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