Analytical GGA exchange-correlation kernel calculation in auxiliary density functional theory

The general working equations for the analytical calculation of the kernel of gradient corrected functionals within auxiliary density functional theory (ADFT) are presented. This formulation improves even further the computational performance for the calculation of second-order energy derivatives already achieved within the ADFT framework. To show this, we present benchmark polarisability calculations of alkane chains and fullerenes. As a specific example, for a gradient corrected functional, the PW86-P86 functional was used. In comparison to finite-difference kernel calculations, we observe speed-ups of at least a factor of 2 with the new analytical kernel evaluation. The here presented implementation will be of particular importance for indirect spin-spin coupling constant and vibrational frequency calculations in the framework of ADFT. [GRAPHICS] .