Nuclear second analytical derivative calculations using auxiliary basis set expansions

We present an efficient implementation of second order analytical derivatives (force constants) within density functional theory which applies to non-hybrid functionals. The dominant step in force constant treatments concerns the solution of the coupled perturbed Kohn–Sham equations (CPKS). We employ an auxiliary basis expansion, the RI-J technique (resolution of the identity for the interelectronic Couomb energy J), to accelerate the solution of the CPKS equations. This results in pronounced reductions of computational work and implies insignificant losses in accuracy as is shown by extensive tests. A force constant calculation of cyanocobalamin is reported as a demonstrative application.