Nuclear versus electronic ring currents in oriented torsional molecules induced by magnetic fields. II. Electronic currents of toluene

Abstract

The theory of nuclear ring currents of torsional molecules induced by an external magnetic field along the torsion axis was developed in the preceding paper [D. Jia et al., preceding paper, Phys. Rev. A 106, 042801 (2022)]. Here we study the magnetically induced electronic current density (MIC) for toluene in the presence of an external magnetic field that is aligned with the torsion axis of the methyl group. Properties of the MIC are studied in detail at the density-functional theory (DFT) level using our gauge-including magnetically induced current method, the derivation of which is briefly outlined. The strength of the MIC is determined by numerical integration and compared to the estimated strength of the magnetically induced nuclear ring current reported in the preceding paper. Spatial contributions to the diatropic and paratropic MICs are discussed in detail, where the diatropic MIC flows in the classical direction and the paratropic MIC flows in the opposite direction. The MIC in the vicinity of the methyl group is mainly diatropic, whereas the phenyl group ring is dominated by a paratropic MIC of $\ensuremath{-}14.90\phantom{\rule{4pt}{0ex}}\mathrm{nA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$ localized to the carbon atoms. The strength of the MIC near the methyl group is $10.41\phantom{\rule{4pt}{0ex}}\mathrm{nA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$, which is of about the same size as the strength of the ring current of benzene when the magnetic field is perpendicular to the molecular ring. The strength of the magnetically induced nuclear ring current of the whole toluene molecule is $19.9\phantom{\rule{4pt}{0ex}}\mathrm{pA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$, which is two orders of magnitude smaller than the electronic one of $\ensuremath{-}1.93\phantom{\rule{4pt}{0ex}}\mathrm{nA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$ calculated for the eclipsed structure at the employed DFT level. This value is in perfect agreement with the current strength of $\ensuremath{-}1.93\phantom{\rule{4pt}{0ex}}\mathrm{nA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$ calculated at the coupled-cluster singles and doubles level with a perturbative treatment of the triple excitations. The current strength calculated at the second-order M\o{}ller-Plesset perturbation level is $1.20\phantom{\rule{4pt}{0ex}}\mathrm{nA}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$, which is of the same size with opposite sign.