Reliable frequency and Raman for some specific states.

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It is difficult to provide a general answer to that question, and I suggest you spend sometime searching the literature for background and other examples of the method you plan on using. If you are breaking spin symmetry (i.e. an unrestricted wave function) you are inevitably going to get mixing of higher spin states into your wave function (this is going to be true of the lowest energy state as well as all higher energy states whether calculated through an SCF procedure or TDDFT). I am not very familiar with CDFT, so I cannot provide any insight there; although, I am unsure if the constraints are properly accounted for in all of the modules beyond the SCF module and the gradient module (for charge constraints). You would still be able to get frequencies through a numerical procedure, but if the constraints aren't accounted for in the CPHF routines, I would not expect a Raman calculation to work/provide meaningful results.

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