Analytic second derivatives from auxiliary density perturbation theory.

The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary density functional theory (ADFT) are presented. The needed perturbations are calculated with auxiliary density perturbation theory (ADPT) which is extended to perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.