5. Post-Hartree Fock Methods: CI and MPn#
In the limit of a complete basis, the Hartree-Fock (HF) energy in the complete basis set limit (\(E_{CBS}^{HF}\)) yields an upper boundary to the physical energy of the system:
where the difference between the total and the Hartree-Fock energy is given by effects due to electron correlation, \(E^{corr}\). The neglect of electron correlation in Hartree-Fock is a consequence of the restriction to a single Slater determinant. In weakly correlated systems, this may be a reasonable approximation; in the majority of the cases, however, this approximation breaks down more or less drastically. In such cases, it is inevitable to include electron correlation; Hartree-Fock results may, in the worst case, be almost (or even totally) meaningless, since the the contribution of correlation is significant in these systems.
Inclusion of correlation can be based on e.g. Post-Hartree-Fock methods, such as Configuration Interaction (CI) or Møller Plesset Perturbation Theory of n\(^{th}\) order (MPn). In this set of exercises, you will compare the performance of HF, CI and MPn in describing a bond dissociation energy, and you will assess the influence of electron correlation on structural parameters (bond lengths and angles).
🎯 Learning goals
Understanding what is correlation energy
Getting familiar with some Post-HF method and their advantages/disadvantages
📖 Chapter in script
Chapter 5 - An introduction to configuration interaction theory
Chapter 6 - Many-body perturbation theory
📚 Resources
An Introduction to Configuration Interaction Theory - David Sherrill
Jensen, F. (2017). Introduction to computational chemistry. John wiley & sons.
Chapter 4.8.1 - Møller–Plesset perturbation theory