Ring Currents in Pentacyclic Hydrocarbons

Abstract

McWeeny's modification of London's molecular orbital theory of π-electron ring currents has been used to calculate the individual currents in the 15 pentacyclic hydrocarbons. The results, useful in themselves for the calculation of NMR chemical shifts, are also significant in the light of what they shed on the question of the range of validity of the assumption that the current in each ring is approximately equal to the benzene ring current.

On the magnetic properties of conjugated molecules

“…the same induced-current distribution results as when the gauge factor defined in equation (2) (1) and (3)) are exactly those implicit in the London method [1,2] (based on equations (1) and (2)) which can predict only the total magnetic susceptibility of a conjugated, polycyclic molecule, and not that (formally) associated with each individual ring. (This statement can be verified if, for example, [26] 'ring currents' calculated [4,[14][15][16][17][18][19][20]25] …”

“…the ~" which describes the molecule in the presence of the uniform, external, magnetic field only (as, indeed, other approaches have done [10][11][12][13].) However, within the last decade, many calculations have been made [4,[14][15][16][17][18][19][20][21][22][23][24][25] based on the original McWeeny ' test-dipole ' approach, using equations (1) and (3)--involving the computation of relative 'ring current' intensities [4,[14][15][16][17][18][19][20][21] in conjugated molecules, and/or the estimation of secondary fields (and, hence, nuclear screening constants) due to these 'ring currents' [4,19,[21][22][23][24][25]. It is, therefore, of interest to consider the repercussions of this recent critique [3] on the status and validity of these calculations.…”

“…(1) Those calculations which have used the original McWeeny method [4] to estimate relative ' ring current' intensities [4,[14][15][16][17][18][19][20][21]25], are unaffected by the insertion of a dipole contribution into the gauge factor (equation (3)), remain inviolate to this recent critique [3] and are, therefore, entirely as valid (or otherwise) as the results of the London [1,2] and Pople [31] approaches, which use the simpler gauge factors defined by equations (1) and (2).…”

“…The two expressions differ only in the thirdorder term, important for small values of ri~ (such as occur, for example, in the benzene, naphthalene 1 and, to a lesser extent, naphthalene 2 situations), but not important for more-distant points from ring centres. In calculating the Ji (' ring current ') factors required for the application of equation (22) (the expression for which is implied by equations (7)- (9)), the following explicit general formulation is useful, for any particular set of' circuits ' [4,19,36] constructed from any arbitrary ' open-chain' [4,19,36] Hence, with the KBS(ri) terms from equation (21), and Ji terms via equation (25) (or, in appropriate cases, from the literature [4,[14][15][16][17][18][19][20][21]), equation (22) can now be applied to all the sterieally-non-hindered [25] protons (66 in all) in the sixteen molecules studied ; following previous treatments [4-8, 19, 23-25], we calculate the quantity H'/H'ben~en e (where H'benzen e is obtained from equation (22), in which Ji=Jbenzene (= 1/9 [4]), and --KBS(rbenzene)=0"6583 (table 1)) and then regress this quantity against the corresponding experimental proton chemical shifts [37,38] (r values). The resulting regression line is shown in figure 2, and the details are given in table 2, where ' sigma ratios ' calculated [23][24][25] by the original McWeeny method [4] are also included for comparison.…”

Coding and Ordering Kekule Structures.

“…It is worth pointing out a remarkable coincidence with the ratio 1:0.25 obtained from the calculated π-electron "ring-current" intensities in the outer rings (0.970) and the inner ring (0.239). 16 The class of fully arenoid benzenoids is of research interest because of the possibility that there are among them molecules possessing a favorable π-electronic structure for semiconductivity. 17 If we consider, for example, the thio-derivatives of perylene, that is, a class of thio-conjugated systems generated by a gradual replacement of six-membered rings in perylene with thiophene-like five-membered rings, the inner sixmembered ring is loosing its π-electron content.…”