Configuration interaction is the only certain way to get a calculation to converge toward the exact solution of the many-body Schrödinger equation (within the approximations used for the framework of the method). In such calculations, the wave function is expanded in all possible electron configurations, and will therefore often take too long to be practical. For full CI, all dynamical correlation is recovered.
In truncated CI, part of the dynamical correlation is recovered. The wave function expansion is, for example, limited to include only single and double excitations (CISD).
In a CASSCF calculation, a subset of all orbitals is chosen, and the wave function is expanded in all possible electron configurations within this subset of orbitals. However, here it is said that no dynamical correlation is recovered. This is stated so often I suspect it is common knowledge for computational chemists, but I can provide references if someone want them.
It is my understanding that the CI method recovers dynamical correlation in allowing electrons to be moved into virtual orbitals (and hence "react" to the instantaneous coulombic repulsion from other electrons). In allowing for higher a number of excitations, a larger portion of the dynamical correlation is recovered (CISDT > CISD).
So, why is no dynamical correlation recovered in the CASSCF method? Imagine a good set of orbitals are chosen for the active space, such that no important configurations are left outside of the wave function expansion, surely dynamical correlation is described? What if we extend this to the generalized actice space (GAS) formulation. In developing GAS, the original authors aimed to remove the "deadwood" of configuration state functions; that is, exclude CSF's with near-zero coefficients. So now a larger active space can be used, and hence a larger number of excitations can be used. Why is not more dynamical correlation recovered?
If indeed CASSCF recovers no dynamical correlation, a CASSCF calculation should give the same energy as a HF calculation. Is this the case?