Calculation of spin-current densities using gauge-including atomic orbitals.

The gauge-including magnetically induced current method for calculating the components of the current-density tensor using gauge-including atomic orbitals has been extended to treating open-shell molecules. The applicability of the method is demonstrated by calculations of first-order induced current densities on cyclobutadiene, Al(3), and B(3) at correlated ab initio levels of theory. For comparison, current-density calculations were also performed on the lowest closed-shell singlet state of cyclobutadiene as well on the closed-shell Al(3)(-) and B(3)(-) anions. The ring-current susceptibilities of the open-shell species are computed at the Hartree-Fock self-consistent-field, second-order Møller-Plesset perturbation theory, and coupled-cluster singles and doubles levels, whereas for the closed-shell systems also density functional theory calculations were employed. Explicit values for the current strengths caused by α and β electrons as well as the difference, representing the spin current, were obtained by numerical integration of the current-density contributions passing a plane perpendicular to the molecular ring. Comparisons of the present results to those recently obtained for the lowest triplet state of biphenyl emphasize that electron correlation effects must be considered for obtaining an accurate description of spin-current densities.