I have calculated the absolute redox potentials of some molecules in Orca Software, using the Gibbs free energy difference of the DFT/CAM-B3LYP/TZVP-optimized structures of the neutral structures and the corresponding ions.
The gaps between the redox processes match my experimental data quite well, even closely resembling the optical gap obtained by spectroscopy (only in different units, of course, because it partially considers the electron charge).
I would like to know if there is a way, from these absolute redox potential data, which are already relative to the vacuum scale, to estimate the HOMO or LUMO energies, or the ionization potential?
A bibliographic citation would be very helpful to understand if this is something commonly done in the literature.
Thanks in advance.
If you have used an SCF calculation and it converged, you have already calculated the HOMO energy and the redox potential you calculated is derived from that.
You can use openbabel to convert the output into something your preferred structure+orbital viewer can display.
Regarding the ionization potential: within the approximation of Koopmans' theorem, the HOMO energy would already approximate that quantity. I am not proficient with ORCA, so I can't say which more sophisticated methods it offers.
Greetings!
In restricted Hartree-Fock (RHF) theory using Slater determinants, Koopmans' theorem is valid and can sometimes reproduce experimental ionization energies. Specifically, the negative of the HOMO energy corresponds to the first ionization energy. This approximation holds reasonably well for systems where electron correlation effects are negligible—typically those with low multireference character—since the single-determinant description fails for strongly correlated systems.
In DFT, an analogous result is given by Janak’s theorem, which states that the first vertical ionization energy equals the HOMO energy. However, DFT’s accuracy in predicting orbital energies is limited by the approximations used for the exchange-correlation functional. Consequently, while DFT can yield good agreement with experiment, this depends heavily on the choice of functional and may not be consistently reliable.
Both Koopmans’ and Janak’s theorems are theoretically valid, but deviations from experimental values arise due to inherent limitations in the underlying methods—such as the neglect of electron correlation in Hartree-Fock or the approximate nature of exchange-correlation functionals in DFT.
In regards to the references or citations, a quick search on those theorems will afford several papers.
Good luck!
Dear Dr Jürgen Weippert and Lucas Gian Fachini
Thank you both very much for your valuable response. Yes, I did perform SCF calculations, and from there I can obtain the molecular orbital energies. However, when I optimize the structures of the neutral molecule and the ions, and apply the relationship between the Gibbs free energy difference, the absolute redox potential, and the Faraday constant, the theoretical gaps I obtain match quite well with the electrochemical gaps determined by CV. Additionally, the optical gaps obtained by UV-Vis are also very similar.
The issue is that if I optimize only the ground-state structure and then try to obtain the orbital energies and the gap from that, the result doesn't resemble the experimentally observed (spectroscopic) optical gap at all.
My question was whether I can use the absolute redox potentials I already calculated (via the Gibbs free energy difference between the ion and the neutral molecule) to estimate the HOMO or LUMO energy levels—depending on whether I’m using the oxidation or reduction potential—by applying some kind of correlation. This is particularly relevant because the four systems I'm analyzing are electrochemically reversible and involve redox processes with only a one-electron transfer.
I wanted to know if this is a commonly used approach, since if I proceed this way, all the data—electrochemical, theoretical, and spectroscopic—would be in very good agreement.
Also, thank you for the information about the theorems; I will look into that!
Erick Alfonso Sánchez , I've come across a couple of papers that use a similar approach to what you described. You may find these references useful:
- Capobianco, Amedeo; Velardo, Amalia; Peluso, Andrea. "DFT predictions of the oxidation potential of organic dyes for opto-electronic devices." Computational and Theoretical Chemistry 1070 (2015): 68-75.
- Xing, Lidan; Borodin, Oleg. "Oxidation-induced decomposition of ethylene carbonate from DFT calculations—importance of explicitly treating surrounding solvent." Physical Chemistry Chemical Physics 14.37 (2012): 12838-12843.
- Konezny, Steven J., et al. "Reduction of systematic uncertainty in DFT redox potentials of transition-metal complexes." The Journal of Physical Chemistry C 116.10 (2012): 6349-6356.
The procedure could work, provided that the Gibbs free energy is modeled correctly for your system.