where µ V α and m β are respectively the α and β Cartesian components of the velocity gauge electric and magnetic dipoles, represented as vectors over all orbital pairs in the given basis. D ω = Ω -1 is the linear response matrix for the perturbation frequency ω and D 0 is the zero frequency response matrix. The second term in Eq. 3 is the spurious static limit that must be subtracted out in the velocity gauge. For a general self consistent field (SCF) wavefunction, we can write the matrix elements more explicitly as