Development, Implementation, and Application of an Analytic Second Derivative Formalism for the Normalized Elimination of the Small Component Method.

Analytical second derivatives for the normalized elimination of the small component (NESC) method are derived for the first time and implemented for the routine calculation of NESC vibrational frequencies and other second order molecular properties using the scalar relativistic form of NESC. Using response theory, the second derivatives of the transformation matrix U connecting the large and the pseudolarge components of the relativistic wave function are correctly derived. The 24 derivative terms involving the NESC Hamiltonian and the NESC renormalization matrix are individually tested, and their contributions to the energy Hessian are calculated. The influence of a finite nucleus model and that of the picture change is determined. Different ways of speeding up the calculation of the NESC second derivatives are tested. It is shown that second order properties can routinely be calculated in combination with Hartree-Fock, density functional theory, Moller-Plesset perturbation theory, and any other electron correlation corrected quantum chemical method provided analytic second derivatives are available in the nonrelativistic case. The general applicability of the analytic NESC Hessian is demonstrated by benchmark calculations for NESC/DFT calculations involving up to 1500 basis functions.