Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory

Based on the orbital invariant formulation of Mo/ller–Plesset (MP) perturbation theory, analytical energy gradients have been formulated and implemented for local second order MP (LMP2) calculations. The geometry-dependent truncation terms of the LMP2 energy have to be taken into account. This leads to a set of coupled-perturbed localization (CPL) equations which must be solved together with the coupled-perturbed Hartree–Fock (CPHF) equations. In analogy to the conventional non-local theory, the repeated solution of these equations for each degree of freedom can be avoided by using the z-vector method of Handy and Schaefer. Explicit equations are presented for the Pipek–Mezey localization. Test calculations on smaller organic molecules demonstrate that the local approximations introduce only minor changes of computed equilibrium structures.