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The CASSCF method is perhaps the most commonly used theoretical method for studying difficult chemical systems exhibiting multi-reference character or non-dynamical/static/strong correlation. CASSCF is quite similar to CI, in the sense that a full CI wavefunction is generated within the active space used in the CASSCF method.

However, the CI method is a so-called ground state method, while the CASSCF method is multi-configurational. My question is simply "Why?". I feel it may be related to that during the CASSCF optimization, both the orbitals and CSF expansion coefficients are optimized, while in CI only the expansion coefficients are optimized. But I fail to understand how optimizing the orbitals gives the CASSCF method its multi-configurational nature.

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    $\begingroup$ I think it is just a convention.. If we put HF and MCSCF into equal footing. They both serve a common starting point to include dynamical correlation. HF->CI; MCSCF->MRCI. We name HF: single configurational, CI: single reference method; MCSCF: multi configurational; MRCI: multi reference method. $\endgroup$ – Rodriguez May 4 '16 at 18:50
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When you say multiconfigurational I think you mean that the ground state wavefunction does not have one single dominant MO configuration.

CI can be multiconfigurational depending on the type of excitation included. For example, Full CI is of course multiconfigurational since it is the exact solution for the basis set used. However, CIS (single excitations) or CISD (single + double excitations) calculations are the only two CI methods that are computationally efficient enough to be used in practice. So that’s probably what you mean when you say CI. You also probably mean CIS or CISD based on an RHF wavefunction, to distinguish it from multi-reference CI.

The lowest energy solution of CIS based on RHF is the RHF energy, so you can think of the SCF procedure as a form of CIS.

So a CASSCF(2,2) calculation (e.g. where the active space is HOMO, LUMO) is a bit like a CISDT calculation. For example, there will be contributions to the wavefunction where the LUMO is doubly occupied and another MO outside the active space is “singly excited”. Thus, the LUMO is allowed to change when electrons are put into it, which becomes more and more important as the HOMO-LUMO gap decreases. CISD cannot account for this, so in that sense it is not multiconfigurational.

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  • $\begingroup$ CASSCF(2,2) can never have a triple excitation, because it will never have a change in orbitals that are not in the active space. It would not make sense to define an active space and then construct configurations outside of it. $\endgroup$ – Martin - マーチン May 4 '16 at 7:50
  • $\begingroup$ The orbitals outside the active space are also SCF optimised. They are optimised by mixing in virtual orbitals, which has the same net effect as a single excitation. $\endgroup$ – Jan Jensen May 4 '16 at 7:56
  • $\begingroup$ I did, it does not make any sense to me. In a CASSCF(2,2) you have four configurations, which only differ in the occupation within the active space. There will only be doubly occupied and unoccupied orbitals outside the active space. Or I simply too stupid to understand the words you use. $\endgroup$ – Martin - マーチン May 4 '16 at 8:04
  • $\begingroup$ @JanJensen Perhaps I should not have used multiconfigurational, but instead multi-reference. Or, like this: truncated CI is said to be a "ground state" method, right? While CASSCF is not. $\endgroup$ – Yoda May 5 '16 at 9:23
  • $\begingroup$ @AndersMB yes, multi-reference is more accurate. I knew what you meant though. Bottom line: whether CI can handle multi-reference problems depends on the number of dominant MO configurations in the ground state and the number of type of excitations in the CI. A minimum of CISDT is needed and that's already too expensive for most molecules $\endgroup$ – Jan Jensen May 5 '16 at 18:07

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