  Quantum mechanical perturbative expressions for second order dynamical
magnetoelectric (ME) susceptibilities have been derived and calculated for a
small molecular system using the Hubbard Hamiltonian with SU(2) symmetry
breaking in the form of spin-orbit coupling (SOC) or spin-phonon coupling.
These susceptibilities will have signatures in second harmonic generation
spectra. We show that SU(2) symmetry breaking is the key to generate these
susceptibilities. We have calculated these ME coefficients by solving the
Hamiltonian for low lying excited states using Lanczos method. Varying the
Hubbard term along with SOC strength, we find spin and charge and both
spin-charge dominated spectra of dynamical ME coefficients. We have shown that
intensities of the peaks in the spectra are highest when the magnitudes of
Hubbard term and SOC coupling term are in similar range.
