More accurate solutions to the electronic problem

At this point we must mention that there exist more accurate approximations to the electronic problem. These are usually referred as the post-Hartree-Fock methods or electron correlation methods. Starting from the HF equations we can include more configurations (determinants) to the wavefunction. The solution is progressively improved variationally or by perturbation theory. Mainly there are three categories in the post-HF methods, the Configuration Interaction (CI or MCSCF), the Many-Body perturbation theory and Coupled Cluster theory. An alternative to the post-HF methods, although very expensive, are the promising Quantum Monte Carlo methods[46] which give the most accurate results in small molecular systems.

Unfortunately these more sophisticated tools are still too expensive to be applied to condensed phase reactions where the systems are too big and many energy and gradient evaluations are required. Although this field occupies a significative part of theoretical chemistry they will not be commented further. Related to this topic some very good reviews and books have been published [11,28,47].