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I'm not sure the exact difference between the MCSCF and CASSCF methods. I know that the CASSCF method proceeds by optimizing both the CSFs and MOs (I mean the coefficients), but I don't know if this is also the case in MCSCF calculations.

My guess is that in MCSCF only the coefficients of CSFs will be optimized, but the HF reference MOs would be the same.

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Both methods optimize orbitals and CI coefficients. MCSCF is the more general term, while CASSCF is a special type of MCSCF.

As the name Multi-Configurational Self Consistent Field already implies, it combines the Configuration Interaction method with the SCF method (Hartree-Fock). Since this combination increases complexity of the wave function, one usually applies restrictions to both sets of parameters (CI and orbital coefficients). For example core orbitals may be kept fixed (frozen) or only a small subset of configurations is considered.

Regarding the selection of configurations, there are various possible approaches. For example:

  • hand selecting configurations using chemical intuition or some other a priori knowledge
  • selecting a subset of orbitals, which should at least cover the HOMO and LUMO. In this active space one considers all possible configurations, hence Complete Active Space Self Consistent Field (CASSCF)
  • restricting configurations only to certain excitation levels (e.g. Singles and Doubles) within the active space: Restricted Avtive Space Self Consistent Field (RASSCF)

So CASSCF is a special variant of MCSCF, therefore there is not really a difference between the two. Although not every MCSCF is necessarily a CASSCF, the later is the most common type.

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  • $\begingroup$ I still cannot understand the difference. You are saying that MCSCF calculations are different in the orbitals, but in what way? I completely understand that CASSCF is based on orbital selection and you do a full-CI in the active space, but what MCSCF is based on I don't get it. It would be great if you could elaborate more on the MCSCF. thanks $\endgroup$
    – Gilli
    Jul 10, 2018 at 17:20
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    $\begingroup$ Your question is like asking about the difference between an apple and a fruit. There is no difference, because an apple is always a fruit, but there are also other kinds of fruits. I hope I made this more clear now in my answer. $\endgroup$
    – Feodoran
    Jul 10, 2018 at 18:32
  • $\begingroup$ MCSCF: "Pick some orbitals, and inside that, pick some configurations." It could be all the configurations, or not. CASSCF: "Pick some orbitals, and inside that, do EVERY configuration". It's specifically all of them. $\endgroup$
    – iammax
    Jul 10, 2018 at 20:19
  • $\begingroup$ MCSCF is just "pick some configurations", you don't need to explicitly pick orbitals first (although you do implicitly). $\endgroup$
    – Feodoran
    Jul 10, 2018 at 21:43
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CASSCF is a particular type of MCSCF in which there is a set of orbitals (active space) for which all possible configurations (complete set) are included.

There are types of MCSCF that are not CASSCF:

  • RASSCF (restricted active space SCF): some of the CAS configurations are restricted in a particular way, such as allowing single and double excitations into and out of a smaller CAS.
  • FCIQMC-SCF: like CASSCF but rather than doing FCI on the CAS you do FCIQMC, which includes configurations with all possible levels of excitation, but only the most important configurations survive a Monte Carlo sampling process.
  • DMRG-SCF: like FCIQMC-SCF but with deterministic DMRG used instead of Monte Carlo FCI.
  • GASSCF (generalized active space SCF).

MC just means multi-configurational, so it is like HF-SCF, but with not just one configuration.

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