Gauge invariance and origin independence of electronic charge density and current density induced by optical fields

Abstract

Expressions for the first-order polarization charge density ρ(1) and current density J(1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ(1) and J(1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J(1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules

“…Using Equation ( 13 ), the off-diagonal hypervirial relationships ( 19 ), and the condition of completeness , one finds [ 36 , 37 ]: This result, directly arrived at via definitions ( 12 ) and ( 13 ), and the r.h.s. of Equation ( 16 ), is fully consistent with the l.h.s.…”

“…If the intensity of is weak enough, first-order time-dependent perturbation theory [ 31 ] can be applied to describe the interacting system [ 36 ]. For instance, the total electronic charge density can be expressed as a truncated series, introducing polarization densities of increasing order induced by the impinging wave.…”

“…Together with the polarization density defined by the scalar , an electronic current density vector field is induced by the oscillating optical field [ 36 , 37 ]. Its effects on molecular response are dealt with via practical computational procedures based on a dynamic, second-rank, current density tensor (CDT), obtained by differentiation [ 36 , 37 ], It is expressed as a sum of paramagnetic and diamagnetic terms within the conventional common-origin (CO) assumption [ 38 ], …”

“…The time derivative of the electric field associated to the monochromatic light shining on the molecule induces an electronic current density [ 22 ] . A corresponding CDT, to first order in the electric field, is obtained by differentiating, It is cast in the form [ 36 ]: …”

“…A useful connection between alternative approaches to the molecular response, allowing either for scalar polarization densities or vectorial current densities, is available within the framework of recent suggestions [ 36 ], introducing the interaction Lagrangian density and a perturbative expansion for the moments of the polarization charge density function , in relation to corresponding moments of the current density J , via the general relationship [ 22 , 37 ]: In Section 4 , we will make use of Equation ( 16 ), allowing for the definition of electronic charge density vector , Equation ( 11 ), and current density tensor , Equation ( 13 ).…”