Ringstrom bei cyclischen Polyenen mit alternierenden und ausgeglichenen Bindungsabständen

Abstract

The ring current effect in NMR has generally been used to distinguish between equal and alternant bonds in cyclic ;r-electron systems, assuming a strong ring current in equal-bonds-hydrocarbons and no ring current in alternant-bonds-hydrocarbons. A calculation of the ring current is presented based on the one dimensional electron gas model. The effect of bond alternation is considered by a sine curve potential.Proceeding from a model with equal bonds to a model with alternant bonds the ring current is strongly reduced in rings with more than 10 members; it is reduced by 24% and 51% only in 6 and 10 membered rings, respectively. In non-HücKEL type rings with 4 to 16 carbon atoms the ring current is directed opposite to the classical current and is strongest in cyclobutadiene. The contribution of the ^-electrons to the susceptibility of these compounds is therefore paramagnetic and ring current shifts opposite to those in HÖCKEL rings are to be expected. These results are confirmed by the proton chemical shifts in the NMR spectrum of [16]-Annulene.Das Verhalten eines Ji-Elektronensystems ist entscheidend davon abhängig, ob alternierende Einfachund Doppelbindungen vorliegen oder ob die Bindungslängen ausgeglichen sind. Im Fall der offenkettigen Polyene wurde früher angenommen daß bei kurzen Ketten Bindungslängenalternanz auftritt und daß sich mit wachsender Kettengliederzahl die Bindungslängen zunehmend ausgleichen. Auf Grund des Elektronengasmodells wurde jedoch dann gezeigt 2 , daß die Alternanz von Einfach-und Doppelbindungen bis zu beliebigen Kettenlängen aufrechterhalten bleibt. Aus dem Ergebnis folgt sofort, daß auch bei cyclischen Polyenen mit 4 N Kohlenstoffatomen (N -ganze Zahl) unabhängig von der Ringgröße Bindungsalternanz anzunehmen ist. Im Fall der cyclischen Polyene mit (4 A^ + 2) C-Atomen ist nach HÜCHEL Bindungslängenausgleich zu erwarten, nach dem erwähnten Ergebnis der Elektronengasmethode muß aber für sehr große Kettengliederzahl auch hier Bindungsalternanz auftreten, da ein unendlich langes offenkettiges Polyen und ein unendlich vielgliedriger Ring nicht zu unterscheiden sind.

Synthesis, Characterization, and Electrochemistry of σ-Bonded Cobalt Corroles in High Oxidation States

“…Paratropic behavior, as is seen for [(OEC)Co(C 6 H 5 )]ClO 4 , is a characteristic feature of cyclic π systems with 4 n π electrons …”

Unified theory of resonance energies, ring currents, and aromatic character in the (4n + 2).pi.-electron annulenes

“…Given the complementary nature74 of the Peierls63 and superconducting46 transitions in solid-state physics, we felt that it might be worthwhile to seek an eigenvalue problem bearing a similar relationship to the Binsch, Heilbronner, and Murrell71 treatment of the second-order Jahn-Teller effect as expressed in eq 32. This would be provided by Wñrs.tu ~(frs ~Prs)5rs.tu\\ = 0 (38) which from eq 21 and 22 may be reduced to \\(Prs/N)rS,,u-Xrs5rs,,u\\ =0 (39) This is similar to the eigenvalue equation implicated in the BCS theory.46-75 All the matrix elements have a common value (Prs/N). and the eigenvalue spectrum (shown for benzene in Table IV) has an energy gap (prs) between the ground state and the manifold of excited states.…”

The “Anthracene Problem”: Closed-Form Conjugated-Circuit Models of Ring Currents in Linear Polyacenes

“…In these reduced units, the current taken from parametrized calculations by Baer et al 42 is 36 À2.189, +1, À1.273, +0.721, À0.691, +0.375, À0.375, +0.165, À0.1, and 0 for the annulenes with k = 4, 6, 8, 10, 12, 14, 16, 18, 20, and g22 carbon centers, respectively (where ( signs indicate diatropic/paratropic circulation). This raw current is divided by the area of the idealized polygonal annulene (i.e., k cot(π/k)/6 √ 3) to give an areanormalized current, j(C), which is then multiplied by the area enclosed by C. In the first publication, 36 pairings of perfect matchings that give rise to sets of disjoint conjugated circuits are apparently not included in the calculation, whereas in later calculations ("model 4a") they are.…”