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THE ALTERNATION RULE: AN OLD HEURISTIC PRINCIPLE OR A NEW CONSERVATION LAW E. V. Babaev Zhurnal Ross. Khim. Ob-va im. D. I. Mendeleeva, Vol. 38, No. 6, pp . 54-65 UDC 541 INTRODUCTION In relation to natural sciences, mathematics was and is an unattainable standard of accuracy, for which any science, studying natural phenomena, strives. One of the key features of mathematical thinking consists in separation of ideal sets, closed in relation to some operation of changes in the objects themselves of this set. Thus, a set of numbers, matrices, or polynomials can be examined, on which operations are determined (different types of addition, multiplication, etc.), not going beyond the limits of the initial sets. Examples of mathematical structures, determined by namely this way, can be algebra, groups, rings, fields, etc., generating a rich arsenal of mathematical subjects. Closed mathematical structures play an enormous role in natural science. A special case of such structures groups - is formalized by the qualitative concept of the symmetry of objects, expressing in symbolic form intuitive concepts of proportionality, harmonics, and order of parts of the whole. The well-known applications of group theory in chemistry [1,2] clearly show namely of what use can be analysis of the symmetry of wave functions or the symmetry of the location of atoms in molecules as points in space. In addition, the use of the idea of group theory in physics gives an example of a fundamentally different possibility of use of the apparatus of closed sets in natural science. Physicists have long noted that the presence in an object of certain symmetry, described by a closed group structure, is equivalent to the presence of a certain (explicit or latent) property of invariance, i.e., the law of conservation. In the last decade chemistry has accumulated a rich arsenal of algebraic models, successfully used for the solution of problems of the "structure-property" type, used in computer synthesis or focused on determination of the degree of molecular similarity (e.g., see collections [2-4] and bibliographic review [5]). However, we note that of the known algebraic models not one example is known to us in which such a model would have led to the formulation of some new conservation principles. It can be stated that chemistry is generally extraordinarily poor in invariants and conservation laws. Thus, if the invariance of mass, charge, and energy is discarded (conservation laws, physical in their nature), then only the law of conservation of orbital symmetry [6] and the principle of invariance of the Euler characteristic remain [7]. We will attempt in this paper to find an example of a closed set where it was earlier not looked for or was not noted. We will show that among structures, habitual to the glance of organic chemists, a class of molecules can be mathematically rigidly separated, possessing certain "rhythmic" similarity of electronic structure, associated with alteration of polar (donor and acceptor) centers. As an example of the operation of changes of such objects (called superconsonant below), we will examine general polar reactions, including stages of heterolytic formation and/or cleavage of bonds. The main idea of this approach is that the indicated set with certain assumptions can in fact be considered "almost closed" in relation to the indicated operation of changes. In its turn, such an assertion is equivalent to a new principle, nontrivial for organic chemistry, of retention of the topological property of polar bipartition (charge alternation) in polar processes. The formulation of the model is preceded by a review of early papers, devoted to the principle of alternation and the problem of consonance, in no way finding reflection to date in the domestic literature.

1995 by Allerton Press, Inc.

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1. PRINCIPLE OF ALTERNATION: HISTORY AND MODERN STATE OF THE PROBLEM 1.1. Alternation of polarities as a structural feature. In 1920 a Manchester professor, Arthur Lapworth, published (although in a relatively inaccessible journal) an excellent paper [8], stimulating very contradictory responses of both contemporaries and descendants. We will recall that the question concerned the so-called principle of alternating polarities, according to which a heteroatom, connected to (completely or partially) a conjugated hydrocarbon chain, causes alternation of positive and negative polarities of atoms along this chain. Such alternation explained numerous facts of the chemical behavior of conjugated systems (orientation upon substitution in benzenes, addition to polar multiple bonds, the effect of substituents on the CH-acidity, vinylogy, etc.). The heteroatom of both donor and acceptor groups (for example, the oxygen heteroatom of a carbonyl or nitro group or the nitrogen atom of a nitrile group, in the last case) was examined as the key atom, responsible for such alternation. The idea of Lapworth was confirmed by a series of scientists, particularly Robinson, who proposed a similar model [9]. The apparent universality combined with vagueness of formulations made the Lapworth model very vulnerable, which gave rise to a prolonged dispute between Lapworth and Robinson, on one hand, aqd with Ingold, on the other hand. A series of factors seemed to contradict the rule, which Ingold attempted to demonstrate in a series of papers under the name Th e nature of the alternation effect in the carbon chain" [10], directed toward refuting this model. In the connection that Ingold incorrectly interpreted the initial principles of the model, and thus himself allowed a series of errors (including experimental), the discussion assumed very sharp and emotional character [11]. In 1926 the British Royal Society found a very original way out of the situation, imposing a unique veto on continuation of the dispute, calling it "games in chemical x's and o's," and refusing "henceforth to examine and publish papers, devoted to the mysticism of polarities" [12]. Terminating the discussion, Lapworth and Robinson actually stopped the further development of the model, while the language of electronic displacements, introduced by Ingold, completely displaced the terminology of alternation. Materials of science historians on this question were published relatively recently [13,14], and attention of chemists was first drawn [15] to the name of Lapworth only in 1972 (a year after the death of Ingold). We note that the actual ban of the further development of the idea in the British Isles did not weaken the interest in it of the world society. In addition to Lapworth, for example, similar ideas were stated by other European [16,17] and American chemists [18,19]. A series of pupils up to the middle of the century referred to the principle of alternation not only from a critical point of view, but also as a useful theoretical model [20-22]. It is clear that the concepts of mesomerism and alternation are deeply synonymous and are useful to an equal degree for the description of electron-density redistribution in x-systems with heteroatoms. Nonetheless, the majority of data confirmed the model, introduced by Ingold, of damping of the effect of the polar group along the saturated chain. In addition, the attractive paradigm of alternation as a unique "idea-phantom," continued to be rediscovered anew by experimenters and episodically arose and disappeared from the visual field of theoreticians. The effect of alternation in a saturated chain, observed experimentally for individual classes and confirmed by both spectral and kinetic investigations, attracted [19,23-26] and continues to attract special attention [27-32]. However, the expected effect was not observed in a series of cases [33,34]. We will not dwell on known examples of alternation of physical properties [35], typical, for example, in the alkane series [36]. Understandably the idea of alternation of polarities did not remain unnoticed from the direction of quantum chemistry. Alternation of charges in alternant p-system s with heteroatoms is even displayed in the simplest MOX method. Less trivial is the appearance of a charge with the opposite sign on the central atom in the allyl cation and anion, appearing upon the use of PMO (perturbation of molecular orbitals) theory [37]. The unique renaissance of the principle of alternation in the 1970s can be associated with the appearance of a paper by Pople and Gordon [38], when the first testing of the semiempirical CNDO/2 method on a broad class of structures showed clear alternation of charge, including in saturated chains. The same result was confirmed later by calculations by the ab initio method [39] (also see the critical analysis and bibliography in [40]). The reasons for the phenomenon are possibly more profound from a physical point of view [41]. Interesting results were obtained during the analysis of the alternation principle from the thermodynamic point of view. Thermochemical data indicate [42] that for small molecules the proximity of functions, similar in polarity, near one atom (i.e., pairs of donors of pairs of acceptors, leading to an alternating sequence) is energetically more favorable than is proximity of functions of opposite nature (i.e., with disturbance of alternation), which is reflected in the direction of disproportionation reactions. Analogously the stability of substituted olefins or benzenes is primarily determined by the alternating or nonalternating surrounding of the double bond (benzene nucleus) with polar groups. In particular, a result of this rule [43] is the unexpectedly higher stability of cross-

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Scheme 1 Evans Classification of Bifunctional Structures [47]

Consonant structures

Dissonant structures

conjugated fragments over systems with normal conjugation, displayed particularly clearly in the case of carbanions. Deserving attention are the recently published review and monographs of Ho, a famous American synthetic chemist [44, 45]. An attempt was made in his developed approach to use the alternation principle as an instrument to explain the most diverse facts of reactivity and regioselectivity in organic chemistry on the basis of the assumption that an alternating arrangement of functions around an atom is always more energetically favorable than upon the absence of such alternation. The discussed group of facts includes, for example, the problem of substrate activation (by both an increase and disturbance of alternation), the explanation of the observedregioselectivityin substitution, oxidation, addition, and cycloaddition processes, and the driving force or rearrangements. The author himself proposes that the principle of alternation be regarded as a convenient mnemonic rule, making it possible to solve specific problems. 1.2. Principle of alternation and design of synthesis. The principle of alternation has evidently found the greatest number of applications in the field of the design of organic synthesis. The inception is assumed to be the paper of Corey [46], in which the retrosynthesis operation was introduced, i.e., the imaginary heterolytic separation of the whole structure into arbitrary subunits of synthones. Such separation was defined as "logical" or "illogical" (logical and illogical disconnection) as a function of how much the polar structure of the formed synthone corresponded to the normal distribution of polarities in the structure of the actual reactant (comp. "logical" acylium cation and "illogical'' acyl anion). From this definition it was just a step to analysis of interrelations between alternation of polarities in the whole structure with such alternation in its precursors. In May 1971 D . A . Evans presented a paper at a university seminar [47], which had a decisive effect on formation of a whole series of mathematical models of organic synthesis. The manuscript of Evans was occasionally circulated among many chemists, but was never published; nevertheless, this paper has repeatedly between referenced (e.g., see [48,49]), and there is detailed commentary on it in the Catalonian language [50]. In this paper Evans proposed a simple and elegant classification of bifunctional (i.e., containing two polar functions) molecules into consonant and dissonant molecules. Consonant structures permit marking of carbon atoms in such a way so that they resemble a preset pattern (charge affinity pattern) with an alternating sequence of electro- and nucleophile centers. Such a presentation is not possible in dissonant molecules (Scheme 1). We note that the fundamental restrictions to chain saturation (as in the Lapworth model) were not imposed. Evidently Evans was one of the first to formulate strictly mathematically how namely the maximum use can be obtained of functionalities, already available in the molecule, during the design of its synthesis, having noted that the synthesis of a consonant structure (or a consonant chain of a complex molecule) is conveniently achieved from consonant precursors. It is significant that not only an electronegative heteroatom (N, O, F as in Lapworth), but also a heteroorganic fragment (with a metal of group 1 or 2, aluminum or silicon), having the opposite polarization of centers in the chain, can act as terminal groups of the bifunctional molecule or pattern with Evans. The nitro group and functions, containing sulfur, phosphorus, boron, and other elements, which led to an ambiguous distribution of polarities in the chain, separating the same atom simultaneously with electro- and nucleophiles, were separated into a special class. In experimental papers Evans [51] discussed other methods, making it possible to invert the
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initial consonance of the alternating chain. The famous review of Seebach appeared slightly later [52], in which (with reference to a private communication of Evans) a more simplified and alternative terminology was derived for separation of polar structures into "normal" structures (i.e., with an alternating sequence of donor-acceptor centers in the chain) and structures, containing an "umpolung" (inversion of polarity of some donor or acceptor carbon center in relation to the heteroatom at the end of the chain). Limiting himself to an examination of only nitrogen and oxygen as the heteroatoms, Seebach superficially mentioned the synthesis of structures of normal construction from other normal precursors (reactions of the aldol or Claisen condensation type, the Prince, Mannich, and Michael reactions), considering this regularity a unique synthetic restriction. The main merit of Seebach is the detailed analysis of methods (a series of which was first proposed by his investigative group), with the use of which an umpolung can be created. We note that a double meaning is incorporated into this term from the very beginning: an umpolung as a structural feature (e.g., parity of the chain between a pair of heteroatoms) and an umpolung as a process, in which the donor or acceptor nature of the atom is inverted. Namely which methods make it possible to create an umpolung are fundamental for our further analysis. In the opinion of Seebach, six such methods should be distinguished: (1) 1,2N-oxidation; (2) exchange and modification of the heteroatom; (3) homologization and its reversal; (4) the use of cyclopropanes; (5) the use of acetylenes; (6) redox reactions. It is understood that the initial reactants in relation to all of these methods appear as structures of normal construction. The concept of a straight umpolung (e.g., in carbon monoxide, isonitriles, etc.) is formulated as a structural feature as the limiting case of an umpolung. Finally, reversal of the umpolung is regarded as a process, leading to structures of normal construction. It is not by chance that the dichotomous classification of structures and reactants into consonant and dissonant (or normal and with an umpolung), constructed on a purely mathematical definition, attracted the attention of specialists in the field of computer synthesis. The first of the TOSCA programs was developed by specialists of the German concern Hoechst AG over a period of five years [49] and led to the prediction of new ways of synthesis of artificial sweeteners with a consonant structure. A detailed formalization of the transition from consonant synthones to actual structures of reactants is used in the STRATOS program [53]. Finally, a third computer program CHAOS [54], based on analysis of ways of synthesis of bifunctional molecules, has recommended itself as a convenient medium for the study of principles of computer synthesis. Using the alternation model for creation of computer programs, the authors introduced refinements and more clearly defined the field of applicability of the initial model. This pertains in particular to [49], where it was emphasized that the most promising model of consonant and dissonant reactants can be found in the field of heterocyclic synthesis, where polar processes (e.g., cyclocondensation) play a key role. We note that the principle of alternation for design of a heterocyclic synthesis has clearly been insufficiently recognized in heterocyclic chemistry itself. The only time the alternation rule was slipped in was recently mentioned by the authors of a review [55] during an attempt to generalize data on methods of construction of six-membered hetarenes. Such a situation stimulated the author of the present paper to carry out a detailed analysis of the types of polar structure of reactants, used any time for the construction of the pyridine nucleus. The results of a literature analysis made it possible to create a computer data base [56, 57], the analysis of which led to the conclusion that in 95% of the cases a magic "structure-synthesis" rule [58] is observed, namely, that the alternating polarity of centers of the pyridine nucleus is rigidly determined by the polarity of acyclic reactants. Only in isolated cases were reagents with an umpolung used for the synthesis of rings (frequently with side formation of pyrroles), or a process of umpolung reversal occurred. This rule (also strictly observed for quinolines) was used as the base of the Heterocycland computer program [59], making it possible to enumerate polar types of reactants for the synthesis of hetarenes and to predict earlier unknown ways of synthesis. The experimental confirmation of the model was achieved in a new, earlier unknown synthesis of quinolines [60]. 2 . CRITICAL OBSERVATIONS AND THE NECESSITY FOR THE FURTHER DEVELOPMENT OF THE ALTERNATION PARADIGM A conducted analysis of literature on the problem of alternation clearly shows the existence of a significant 81


Scheme 2

phenomenon, observed in very remote fields of both theoretical and experimental chemistry. Unfortunately, the frequent absence of mutual references by authors of the approaches hinders the development of a single terminology. The authors of programs, for example, preferred to describe the structure of molecules in terms of consonance and dissonance, using the term umpolung namely to describe reactions. (The terminology, introduced by H o [45], who proposed the use of the terms "conjoint" and "disjoint" for consonant and dissonant structures, additionally complicates the language problem.) Since, in our opinion, the "musical-linguistic" terms consonance and dissonance are most easily formalized, we will also follow the terminology of Evans. Let us now examine namely what aspects of the alternation problem are not completely elucidated and deserve further development. First, it is not completely clear if consonance should be considered a local property of the atom (e.g., due to its environment), a local property of the chain or fragment (bifunctional relation between the pair of polar functions), or a global property of the polyfunctional molecule as a whole. Second, a very serious aspect of the problem is the disregard or neglect of the degree of chain unsaturation. It was asserted beginning with Lapworth that the alternation effect is displayed most strongly in a conjugated chain; nevertheless, attempts to generalize the applicability of the effect to partially unsaturated or completely saturated chains have not ceased to date. However, in saturated chains with a polar group at the end competition between the alternation effect and the quenching effect is resolved in favor of the latter. The maximum, which can be recorded experimentally, is the saw-tooth dependence of the alternation effect, quenching at approximately the fifth unit of the saturated chain [23-32]. Analogously, during the design of the synthesis of a quite long (assume that it is consonant, but saturated) chain the selection between consonant or dissonant precursors may not be fundamental. The third problem, virtually not touched upon on the cited approaches, can be formulated thus: is a powerful (electropositive or electronegative) noncarbon substituent in fact necessary for manifestation of alternation. Chemistry is full of examples, in which an expressed polar effect is displayed, for example, by alkyl, alkenyl, or alkyl groups. In addition, charged carbon fragments (carbocations and carbanions), i.e., synthones without heteroatoms, are the reality of modern organic synthesis. The above-cited review of Klein [43] indicates that the alternation rule has prospects of application in the field of p-system s of low polarity. A feasible approach, which would make it possible to answer the set questions, should consider in some way the polarity of the C-H bonds. We note that this question was asked yet by Lapworth, who thought that hydrogen can be conditionally considered to be an electropositive atom, equivalent to other "key" heteroatoms. Anticipating the model of consonant and dissonant structures, Lapworth proposed the examination of "homogeneous" and "heterogeneous" [8] methods of the mutual arrangement of hydrogen and heteroatoms in the chain (also see the commentary of Robinson [9] on this approach). Thus, acetic acid is a homogeneous structure, since it permits unambiguous marking of atoms by plus and minus signs, while formic acid is heterogeneous and can be marked by two methods as a function of which atom, hydrogen or oxygen, is taken as the key atom (Scheme 2). Lapworth limited himself to the possibility of introduction of such a classification and did not return to its development.
3 . PRINCIPLE OF SUPERCONSONANCE

3.1. Mathematical model of polar homogeneity. Let us examine to what the joint examination of the qualitative concept "homogeneity" according to Lapworth and the stricter formulation "nonconsonance" according to Evans can lead. We will take an arbitrary organic structure, containing the N, O and F heteroatoms, in addition to C and H atoms. (Restriction to namely these elements, organogens, has a clear meaning; see concluding section.) We will assume that as normally a conditional minus sign can always be placed on the heteroatom (by virtue of its electronegativity), while we will always write a formal plus sign on the hydrogen atom; carbon atoms will be considered "neither," i.e., passive conductors of effects of "key atoms," H, N, O, and F. It is clear that polar homogeneity (the possibility to mark unambiguously with plus and minus signs carbons in the molecule) is only
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Scheme 3

permissible upon strict fixation of the mutual arrangement of terminal hydrogen atoms and heteroatoms. We will call a certain chain between the arbitrary pair of key atoms in the structure homogeneous if: 1) the chain is odd between any pair of heteroatoms; 2) the chain is even between any of the heteroatoms (N, O, F) and the hydrogen atom; 3) the chain is odd between any pair of hydrogen atoms. We will consider as a special case the odd chain of a one-carbon fragment and will include its absence in determination of the even chain (i.e., direct vicinity of the function). It is understood that all carbon atoms of a homogeneous chain permit a strict unambiguous marking with alternating signs (let us say, with the same pluses and minuses). Definition 1. Molecules, constructed only from homogeneous chains, will be called homogeneous. It is evident that a long chain can be made up of smaller chains and that a ring can also be presented as a closed chain. Consequently, rings (including connected) or structures, containing a heteroatom inside the chain (particularly heterocycles), can be included in the examination. Two ways exist of construction of sets of such homogeneous molecules. The first way is analytical: having an innumerable set of structures, we establish a filter on the basis of definition 1, separating homogeneous structures from those which are not homogeneous. The second way is constructive generation of homogeneous structures on the basis of an increase by an arbitrary (saturated or unsaturated) chain of new atoms in order that exclusively homogeneous chains (rings) are formed. It is seen from comparison of homogeneous structures with consonant structures that these sets intersect only partially. Thus, tert-butanol, acetone, and acetic and carbonic acid are homogeneous and consonant, while methanol, formaldehyde, acetaldehyde, or formic acid are consonant, but not homogeneous. In addition, by virtue of the definition the group of homogeneous structures should include slightly polar or nonpolar structures of the propyne, isobutylene, or neopentane type, generally not described in terms of consonance. However, the Lapworth model, obtained by refining to a logical end, leaves a certain feeling of dissatisfaction, without answers to all questions, set above in Section 2. First, the definition does not include a concept of charged species, as a result of which it is necessary to identify formally isostructural cations and anions, fundamentally differing in their polarity and reactivity (cf. an "illogical" acyl anion and a "logical" acylium cation, electrophilic OH or NH2 cations, and nucleophilic hydroxyl and amide anions). Finally, carbenoid (methylene, difluoromethylene, nitrene) and noncarbene species are in no way distinguished in the model. Thus, it is necessary that the classification include in explicit form a concept of the mutual arrangement of centers of Lewis acidity and basicity, i.e., vacancies and unshared pairs. Let us examine how the necessary results can be attained. 3.2. Generalization of the model of polar homogeneity for ions. To describe transfer of certain polar effects of hydrogen or a heteroatom chemists long ago devised a convenient methodical procedure: imaginary heterolytic dissociation of the bond with formation of a limiting (unbonded) resonance structure of two ions. For example, we can cleave the C-H bond in the methyl group of isobutylene (into a proton and a carbanion portion) or the C-F bond in perfluorobutylene (into fluoride ion and a carbonation part) for a graphic explanation of the effect of the methyl or trifluoromethyl group. Formally nothing interferes with the repetition of this procedure many times until the covalent structure is separated into a multiply charged carbon skeleton, surrounded by a group of external ions (protons or fluoride ions in our example), see Scheme 3. In the general case this operation can also be used for
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heteroatoms of the oxygen and nitrogen type (generating saturated oxide- and nitride-ion structures). In the case of such separation of homogeneous structures the formed carbon skeleton possesses a remarkable property. According to the definition, the carbon atoms in such structures already have the plus and minus signs, and upon separation of ions the localized charge has the same sign as the initial mark. Since an alternating structure is again generated, nothing prevents the bringing of the procedure of ionic separation to a logical end by heterolytically cleaving the C-C bond with formation theorem 1 is valid: any homogeneous molecules can be mentally broken up into an alternating set of ions (C4+, H + ) and (C 4- , N 3- , O 2- , F - ) . It is evident that a nonhomogeneous molecule cannot be presented in this way - an "extra" ion will compulsorily appear, in addition to the enumerated six (cf. structures of hydrazine, ethane, or methylamine). In addition, the procedure of separation into ions can be reversed, and the sequence of assembly of a certain molecule from the indicated set of ions can be examined in such a way so that a cation and anion are always adjacent. It can be proposed that after such assembly reorganization of the hypothetical ionic bonds will occur to the normal covalent (polar or nonpolar) bonds of the necessary multiplicity in accordance with the normal valence laws. It is not difficult to show that the following (opposite) theorem 2 will be valid in this case: any homogeneous molecule can be assembled mentally from the supply of (C4+, H+) and (C4-, N3-, O2-, F-) ions, during which each cation is connected to an anion. Thus, polar homogeneous structures can be constructively generated not only on the basis of evenness of chains between the "key" atoms, giving the carbon atoms a passive role, but also, purely formally, on the basis of the concept of two (cationoid and anionoid) carbon atoms as equitable subunits of homogeneous structures. In addition, the implicit requirement for electroneutrality of resulting structures becomes extremely optional: one can decide on an arbitrary mono- or polycharged ion or a zwitter ion. The obtained set is already a certain qualitatively new object, for which a new name can be proposed. Definition 2 . Molecules and ions, which can be mentally separated exclusively into (C4+, H + ) and (C4-, N3-, O2-, F-) ions or can be assembled form these ions so that each cation is connected to an anion will be called strongly consonant or superconsonant. (We will use these same terms for the initial supply of ions). A mathematician could say that a certain proportion of equivalence is introduced by this definition into the set of molecular structures. In fact, any molecule is strictly either superconsonant (and then equivalent to other such structures) or not. 4. STRUCTURAL FEATURES OF SUPERCONSONANT MOLECULES The concept of covalent molecules as a group of ions has a long tradition: namely thus in the past did Robinson attempt to visualize a picture of transfer of the substituent effect [9] and namely thus did Fijans [19], including two types of carbon ions, draw himself a picture of alternation. The problem was that this principle was given too broad an interpretation, and it was used in those cases when it possibly was not very applicable. (See [20] for the reasons for criticism of concepts of Robinson on "growth and disintegration of octets" along the alternating chain.) Our problem is different: having given a strict definition of a certain class, to determine the qualitative features of the electronic structure, the activity, and methods of synthesis of structures of this class. 4.1. Main features. The first purely topological feature of superconsonant structures is that any such structure is described by a bipartite graph. As is known from graph theory [61], a graph is called bipartite if the set of its apices can be broken up into two nonintersecting subsets (let us say, of different color), so that the edge of the graph connects compulsorily apices of different color. Bipartition of a graph automatically includes odd rings. With the use of our earlier introduced symbolism [58, 62] to assign color to charge ("philicity"), we will agree graphically to present a cationic center by a white apex in the graph and an anionoid center by a black apex. We will show below that bipartition generates a very elegant genetic relation side the class of superconsonant structures. The second features pertain to the mutual arrangement of actually charged centers, unshared pairs, and heteroatoms. In the simplest cases the carbocationic center of such structures, by definition, is surrounded by atoms with unshared pairs, and the carbanio