The spin polarized linear response from density functional theory: Theory and application to atoms

Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N-s] and [N-alpha, N-beta] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N-alpha, N-beta] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated chi(r, r') to a quantity chi(r, r'), circumventing the theta and phi dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, chi(alpha beta)(r, r'), chi(beta alpha)(r, r'), and chi(SS)(r, r') plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, alpha(alpha alpha), alpha(alpha beta), alpha(beta alpha), and alpha(beta beta) have been calculated. (C) 2014 AIP Publishing LLC.