An implementation of analytic second derivatives of the gradient-corrected density functional energy

We report an implementation of analytic second derivatives with respect to nuclear displacement of the Kohn–Sham energy for gradient-corrected functionals. The second derivative equations are given in a form well-suited for computer implementation, and the exchange-correlation contributions are discussed in detail. The algorithms presented have favorable asymptotic exchange-correlation cost scaling requirements relative to other aspects of the calculation. The results obtained show that analytic calculation of Kohn–Sham second derivatives is indeed a viable technique in practice.