One way to know if standard models are failing for bond breaking reactions, diradicals, etc, is to compare the predictions to experiment. Unfortunately, however, these comparisons are usually indirect. Is the error due to the presence of nearly degenerate electron configurations, or merely due to an insufficiently large basis set? Is the error coming from the equilibrium, intermediate, or broken bond parts of the potential energy curve? These questions are much easier to ask if we can compare the model to exact theoretical results computed at the same geometry and the same basis set.
The exact analytical solution of the electronic Schroedinger equation is, of course, impossible except for very simple systems like the harmonic oscillator or the hydrogen atom. However, we can obtain numerically exact results, within some small tolerance, using full configuration interaction (full CI), which solves the problem variationally using all possible electron configurations that can be generated consistent with the symmetry, number of electrons, etc., of the molecule. Since the number of configurations grows factorially with the size of the molecule or the basis set, full CI computations are extremely challenging and are only possible for very small molecules containing no more than about a dozen electrons. Nevertheless, for such small molecules, the availability of full CI results allows an unambiguous assessment of approximate methods for challenging problems like bond breaking reactions.
Our group has developed one of the few efficient full CI computer programs available. This program, called DETCI, is based on important work by Handy, Olsen, and others, is described in a review article, ``The Configuration Interaction Method: Advances in Highly Correlated Approaches,'' C. D. Sherrill and H. F. Schaefer, Adv. Quantum Chem. 34, 143-269 (1999). The DETCI program is capable of solving for full CI wavefunctions including more than a billion determinants on a Linux PC. This program is being used to obtain exact results by which the approximations may be judged.
