Derivative studies in hartree-fock and møller-plesset theories

The complete spin-orbital formulation of the analytical first and second derivatives of the Hartree-Fock (HF) energy as well as the analytical first derivative of the correlated second-order Moller-Plesset perturbation energy (MP2) is presented. Some features of an efficient computational method to calculate these derivatives are described. The methods are applied to calculate the harmonic vibrational frequencies of ethylene, and the results are compared with experiment.