Extended London theory of diamagnetism. I. General theory and saturated hydrocarbons

Abstract

In this paper a method is proposed to calculate diamagnetic susceptibilities of organic compounds. This method uses the extended Hückel formalism generalized to include the perturbation due to a magnetic field ℋ. Parameters are varied to obtain agreement with experimental results. The diamagnetic properties of the alkanes are examined and all the terms contributing to the susceptibility are analyzed. The importance of a coupling term between matrix elements of first order in ℋ and London terms is shown. Some results are discussed, particular to methane and the cycloalkanes.

Extended Hückel calculation of proton chemical shifts with the aid of gauge invariant atomic orbitals. Application to hydrocarbons

“…H+H.E 2~ n.w+ .... (1) where E ~ represents the unpertiarbed energy. The magnetic susceptibility and magnetic shielding tensors, X and a are deduced by equating expression (1) with E=E~ H-g.. (1-a).…”

“…The diamagnetic susceptibility theory leads to a London term (equation (16) [1]) depending on SktH by equation (6) of reference [1]. Coupling this term, proportional to H, with the O.~kt ~ terms involving the integrals of equation (28 c),…”

“…In the general theory, a coupling term between the external magnetic field and the nuclear moment has to be calculated. So, we use for the magnetic field the expansions given previously [1] and for the magnetic moment perturbation similar expressions. Basically less justified than ab initio Hartree-Fock theories (coupled perturbation) [2,3], the method presented here can still treat relatively large molecules such as aromatics for which, to our knowledge, no ab initio calculation has so far been performed.…”