ANALYTIC 2ND DERIVATIVES OF THE POTENTIAL-ENERGY SURFACE

One of J.A. Pople's leading contributions in ab initio quantum chemist ry was his 1979 paper in which he and his colleagues presented calcula tions for the analytic second derivatives of the Self Consistent Field Potential Energy surface. This led to the automatic characterization of stationary points as minima or transition states. Recently there ha s been an upsurge of interest in computational density functional theo ry (DFT). Here we describe our implementation of analytic gradients an d second derivatives for the Kohn-Sham potential energy surface. This parallels similar developments by Pople and his coworkers. We examine Pople's idea of differentiating the weights in the quadrature scheme t o ensure that the energy gradient is exactly zero at the energy minimu m. We present some calculations on small molecules which are as near ' exact' as possible for the LDA and BLYP functionals which we use. In o ther words we use large basis sets and a large number of quadrature po ints to evaluate the extra (nonanalytical) integrals. We do not use an y fitting procedures and no other approximations are introduced.