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

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