The multipole Hamiltonian and magnetic circular dichroism

The Power–Zienau–Woolley transformation in molecular quantum electrodynamics is carried out for a molecule in an external static magnetic field. From the gauge-independent multipole Hamiltonian thus obtained the Einstein B coefficients for the absorption of left and right circularly polarized photons by an oriented molecule in a uniform magnetic field are evaluated. The B coefficients are related to the macroscopic absorption coefficients by treating the line shapes phenomenologically and by introducing a Boltzmann factor. A familiar expression for magnetic circular dichroism in a dilute medium is thereby recovered; the calculation is extended beyond the electric dipole approximation so as to include the leading contribution of natural circular dichroism. A simple use of the appropriate Kramers–Kronig dispersion relation leads to the deduction of the optical rotatory dispersion, both natural and magnetic, in spectral regions far removed from absorption bands.