An Extension of the Hückel 4N + 2 Rule to Polycyclic Non-alternant Conjugated Hydrocarbons

Abstract

JERZY KRUSZEWSKI and TADEUSZ MAREK KRYGOWSKI. Can. J. Chem. 53,945 (1975) A general rule of aromatic stability of non-alternant polycyclic conjugated hydrocarbons has been detailed and using aromatic stability indices, corroborated. The n-electron system is said t o be relatively more stable if the difference between number of 4N + 3-type rings minus number of 4 N + 1-type rings is 0 or divisible by 4 . If not, the system is assumed t o be relatively unstable. The presence of benzene rings does not affect the rule. A further extension for intramolecular H-bonded systems is also suggested. The rule suggested permits prediction of substituent effects on stability as well as the ionic form being most stable if the rule is not fulfilled.JERZY KRUSZEWSKI et TADEUSZ MAREK KRYGOWSKI. Can. J. Chem. 53,945 (1975). On a dCveloppC une regle gCnCrale permettant d'kvaluer la stabilite aromatique des hydrocarbures polycycliques conjugues mais non alternants; cette regle a Ct C corroboree en faisant appel aux indices de stabilitk aromatique. On dit gCnCralement que le systeme d'klectrons n est relativement plus stable si la diffkrence entre le nombre des cycles du type 4 N + 3 moins le nombre des cycles du type 4 N + 1 est 0 ou divisible par 4 . Si tel n'est pas le cas, on fait I'hypothtse que le systeme est relativement instable. La presence de noyaux benzkniques n'affecte pas cette rigle. On suggere aussi une autre extention pour les systemes contenant des ponts hydrogkne intramolCculaires. La rkgle suggCrCe permet aussi de prkdire l'effet des substituants sur la stabilitk de mEme que la forme ionique est la plus stable si la regle n'est pas suivie.[Traduit par le journal]The Huckel4N + 2 rule (1) is one of the best known and most useful rules for predicting the aromatic stability of monocyclic n-electron systems (2). An extension of this rule to polycyclic conjugated hydrocarbons has not been successfully developed. Some indirect applications, taking into account only peripheral n-bonds of these systems, led to rather good results (3), but most often in the case of alternant systems. Recently a number of authors have reviewed the problem of aromatic stability (see e.g. refs. 4-8, 11-24, 35) and have suggested various quantitative measures of "aromaticity". The most advantageous seem to be those coming from quantum chemical calculations like the Hess-Schaad REPE (1 3) (Resonance Energy per Pi Electron) or other (7, 10, 11,14) estimates of resonance energy. However, these calculations cannot always be carried out especially by those 'Visiting Professor at the Department of Chemistry, University of Guelph, Guelph, Ontario, NIG 2W1. concerned with the practical aspects of organic chemistry such as synthesis; moreover, the quantum mechanical calculations are not always sufficiently reliable. It is clear that a simple rule as a qualitative guide to aromatic stability is needed in the area of non-alternant polycyclic conjugated hydrocarbon chemistry.The main purpose of this paper is t o present an attempt to extend the Huckel4...

Crystallographic studies and physicochemical properties of π-electron compounds. III. Stabilization energy and the Kekulé structure contributions derived from experimental bond lengths

“…(i) Geometries of non-alternant systems are those of their substituted species, with the substituent strongly interacting with the odd ring (i.e. a ring containing an odd number of atoms) and stabilizing it according to the 4N + 2 aromaticity rule, or its extension for polycyclic non-alternant systems (Kruszewski & Krygowski, 1975). This effect is especially well seen for derivatives of fulvene.…”

Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems

“…The following theorem about bk s has been proved by bk{G) = bk(G-e) + bk-dG-(e)) (27) -i (-l)("(í)-|)/2-Mí)x«(s) (17) •sGSoddB y utilizing eq 17 the above expression for (ref structure) becomes X+°°H y -In |//ac(G,x)| (18) Substitution of the formulas 15 and 16 back into eq 1 yields an expression for the Dewar resonance energy. Since it is in fact a topological definition of DRE, we feel that the name topological resonance energy, TRE, is justified to be used.…”

Structural Aspects of Aromaticity

“…The Hu ¨ckel rule was extended onto polycyclic nonalternant systems: 39 Defining F and S as numbers of five-and seven-membered rings in a fused system, the molecule is more stable when S ) F and less stable for other cases. This rule was then demonstrated and proved by use of the topological theories of aromaticity.…”