The calculation of chemical shifts in conjugated molecules

Abstract

Within the context of pi-electron theory an expression for the proton chemical shifts in conjugated molecules is derived via a current density approach. Using London integral approximations the method is applied to benzene and naphthalene. Provided a particular form of the London Approximation is used, theoretical values in good agreement with experiment are obtained.

On the magnetic properties of conjugated molecules

“…I~=8rr213c -~c SH~ (12) which is equivalent to the formula obtained by Pople [31], making use, in the final stages of his calculation, of a test dipole, but basically using the ' London' gauge factors defined by equations (1) and (2), i.e. not including the dipole effect on the LCAO basis functions.…”

“…McWeeny concludes, therefore [3], that what shouM be evaluated by first-order perturbation theory is the coupling energy between the 'test' dipole and the required secondary field, using, as the unperturbed wave-function, qe+, the set of {$+} defined by equations (1) and (2)--i.e. 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].…”

“…In his original paper [4], McWeeny used the ' test-dipole ' approach, whilst Slichter [10] and Pople [11] and, recently, Amos and Roberts [12], have adopted the so-called 'current-density' formalism in which direct appeal is made to the current-density operator ; in this latter method, for an N-electron system (such as the rr-electron system of a planar, conjugated molecule), if W(rl, r~, . .., rj, .…”

“…In this assessment, we shall invoke the ' classical line current ' concept introduced by Salem [26], and will show that use of such a procedure, though it has unattractive, classical features, is, in fact, not only algebraically analogous to ineluding the dipole term in the gauge factor (as in equation (3)) in the entirely quantum-mechanical McWeeny approach [4,26], but is also actually numerically equivalent, even when the secondary fields at points relatively close (> 3 AJ-) to a conjugated ring, are considered. Before doing this, however, since the methodology of this semi-classical theory is very much in the spirit of the entirely quantum-mechanical current-density formalism [10][11][12], we briefly discuss the latter approach (and its relation to the test-dipole method) in the next Section 9…”

The calculation of chemical shifts in conjugated molecules

“…(The jargon adopted here follows that introduced in the preceding paper [1]. The latter will, henceforward, be denoted by I.)…”