Analytical calculations of frequency-dependent hypermagnetizabilities and Cotton–Mouton constants using London atomic orbitals

We present the first gauge-origin-independent, frequency-dependent calculations of the hypermagnetizability anisotropy, which determines the temperature-independent contribution to magnetic-field-induced linear birefringence, the so-called Cotton-Mouton effect. A density-matrix-based scheme for analytical calculations of frequency-dependent molecular properties for self-consistent field models has recently been developed, which is also valid with frequency- and field-dependent basis sets. Applying this scheme to Hartree-Fock wave functions and using London atomic orbitals in order to obtain gauge-origin-independent results, we have calculated the hypermagnetizability anisotropy. Our results show that the use of London orbitals leads to somewhat better basis-set convergence for the hypermagnetizability compared to conventional basis sets and that London orbitals are mandatory in order to obtain reliable magnetizability anisotropies.