I would like to know what exact property of the wave function these terms refer to. It would also be helpful to have a clear definition of 'reference' and 'configuration'. I'll try to explain below where my problems are in clearly understanding/defining these terms:
Starting with Hartree-Fock, it is obvious that the wave function in HF is both single-reference and 'single-configurational': there is only one Slater determinant.
Going to configuration interaction methods, the wave function now becomes a linear combination of several Slater determinants. The additional Slater determinants are excitations of the ground state determinant: virtual orbitals from HF are taken and replace previously occupied orbitals in the determinant. However, these orbitals still have the same coefficients as in HF - only the coefficients in front of the Slater determinants are optimized for the linear combination. If I'm correct, 'configuration' here refers to one particular Slater determinant - a method is therefore 'multi-configurational' if the wave function that is used has two or more (different) Slater determinants, correct? That also means that none of the CI methods (be it CIS, CISD, ... , or Full CI) are multireference methods?
Continuing with CASSCF, this method is basically Full CI limited to the chosen active space of orbitals. It is therefore multi-configurational. At the same time, it is also often referred to as being 'multireference'. The only difference to CI, however, seems to be the optimization of the coefficients in the Slater determinants themselves, hence, this must be the defining criterion for 'multireference'? What does 'reference' here refer to?
Now there is also multireference-CI. From the above definition, I would expect this to be a form of CI where I also optimize the orbitals, but that does not seem to be the case. The Wikipedia article on MRCI starts with:
In quantum chemistry, the multireference configuration interaction (MRCI) method consists of a configuration interaction expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinants which correspond to excitations of the ground state electronic configuration but also of some excited states. The Slater determinants from which the excitations are performed are called reference determinants.
This is confusing to me: Is 'excitation of the ground state electronic configuration' vs. 'excited states' referring to the optimization of the Slater determinants themselves? Or does 'excited state' refer to configurations with different total spin? That would be a different definition of 'reference', but then CASSCF would only be a multireference method if it uses the corresponding SA-CSFs, regardless whether the Slater determinants are optimized or not?