Uncoupled Hartree–Fock Calculations of the Ring-Current Contribution to the Magnetic Susceptibilities of Conjugated Molecules

Abstract

Uncoupled Hartree–Fock perturbation theory is used to compute the ring-current contributions to the magnetic susceptibilities of several conjugated hydrocarbons. In the usual form of the perturbation theory this leads to an origin dependent result, but when corrections are included this origin dependence is removed. The final results agree very well with those calculated using the more complicated coupled Hartree–Fock method, and, when empirical values are used for the local contributions to the susceptibility, the theoretical values for the components, the mean value, and the anisotropy of the susceptibility are in excellent agreement with experiment.

Anisotropy of the Diamagnetic Susceptibility in 3,5-dibromo-p-amino and 3,5-dibromo-p-hydroxybenzoic Acids

“…The calculated values are -60.90 [6], -60.24 [25] and -60.00 [8], while the experimental value is -59.70 [8,23]. In the present work the magnetic anisotropy is taken as -60.00.…”

“…where K|| is the in-plane susceptibility wlose value can be determined from the sum of the atomic susceptibilities of the molecule as discussed by Hoarau [ΙΙ] or from the local values of in-plane susceptibilities x|| (Αv) as worked out by Mason [12], Amos and Roberts [6], and by Long and Memory [13]. In our recent paper [1A] these two different methods that are used for the calculation of K|| have been outlined.…”

“…The strong anisotropy of the diamagnetic susceptibility of benzenoid compounds is usually explained in terms of ring current [1][2][3][4][5][6][7][8][9]. An interesting discussion with the use of ring current concept has been given by Gomes [10].…”

Shielding Theory: GIAO Method

“…Essentially all of the problems in calculating shielding constants arise from the paramagnetic contribution. For an atom at the origin, the diamagnetic contribution, say the zz component, is given, according to equations (10), (13), and (16), as the expectation value of the operator 1 2 α 2 (r 2 − z 2 )/r 3 , and thus the isotropic average is the expectation value of 1 3 α 2 r −1 . As this is essentially the electron-nucleus attraction energy, it is very accurate (even with mediocre basis sets) and stable.…”

Calculations of electric dipole polarizabilities of polyatomic molecules

“…Several equivalent formulations of the Coupled Hartree-Fock (CHF) scheme were proposed [5-131 and a few encouraging results have been attained for small polyatomic molecules [ l l , 13-19]; at any rate, since CHF equations are usually solved by iteration, which has been often considered a nuisance [6,20], alternative simpler uncoupled schemes were proposed [5, to reduce the computational effort involved in the calculation of second-order properties.…”