[Columbus] Molecular orbital energies

[Shepard, Ron]

I agree with the previous emails, but I wanted to point out that there is an extended Koopmans Theorem that does apply to general MCSCF wave functions. It involves the eigenvalue equation FC=DCE where F is one of the fock matrices we compute in COLUMBUS and D is the 1-RDM. The eigenvalues E correspond to ionization potentials.

As for orbital energies in general, we compute two different fock matrices in the MCSCF code in COLUMBUS, one we call F and the other we call Q. They both map to the closed-shell RHF fock matrix in that limit, but they generally differ otherwise. We use the Q matrix to bring the doubly occupied and virtual (unoccupied) orbitals to a canonical form. It is possible for CASSCF wave functions to also diagonalize the active orbitals and to represent the wave function in those orbitals. However, these orbitals generally do not correspond to any kind of optimal mean field conditions, so they are otherwise less useful than the closed-shell RHF case.  As Felix said, we rather more typically diagonalize the 1-RDM rather than a fock matrix to define the active orbitals.

-Ron

On 3/24/25, 5:20 AM, "Columbus" <columbus-bounces+shepard=tcg.anl.gov at lists.osc.edu> wrote:
Dear Yincheng, Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs. In most cases, when discussing MCSCF, we talk about
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Dear Yincheng, Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs. In most cases, when discussing MCSCF, we talk about

Dear Yincheng,
Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs.
In most cases, when discussing MCSCF, we talk about natural orbitals (NOs). NOs have occupations, because we diagonalised the density matrix. But NOs don't have energies.
If you want MO energies, then you have to diagonalise the Fock matrix. This will give you some indication about where the orbitals are. But you should realise that there is no such thing as Koopmans theorem for MCSCF. Therefore, it is not so common to report orbital energies, because they don't actually have a physical meaning.
Best
Felix

On 23/03/2025 16:39, Hans Lischka via Columbus wrote:

**

Dear Yincheng, Look into the file mcscfls, there you will find the orbital energies of the mcscf calculation. Best regards, Hans On 3/22/2025 6: 11 AM, Yicheng Zhu via Columbus wrote: Dear Columbus Admins: Is there a way for me to obtain molecular

Dear Yincheng,
Look into the file mcscfls, there you will find the orbital energies of the mcscf calculation.
Best regards, Hans

On 3/22/2025 6:11 AM, Yicheng Zhu via Columbus wrote: Dear Columbus Admins: Is there a way for me to obtain molecular orbital energies from running MCSCF calculations? If so, which file should I look into? Best, Yicheng _______________________________________________ Columbus mailing list Columbus at lists.osc.edu<mailto:Columbus at lists.osc.edu> <mailto:Columbus at lists.osc.edu<mailto:Columbus at lists.osc.edu>> https://lists.osu.edu/mailman/listinfo/columbus  <https://urldefense.com/v3/__https://urldefense.us/v3/__https:/*lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$__;Lw!!KGKeukY!ylrqTUVhHjJQGacBWlmK5ku8DlLL3Ioguvaon_Il7HHBcOhkmeR12mpoNP8B5qyef4WHFbkP801IgDyPR-i1Ci63$ <https://urldefense.com/v3/__https://urldefense.us/v3/__https:/lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$__;!!KGKeukY!ylrqTUVhHjJQGacBWlmK5ku8DlLL3Ioguvaon_Il7HHBcOhkmeR12mpoNP8B5qyef4WHFbkP801IgDyPRzkGEcUu$ >>


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