I guess so. It is fine to calculate like this.

By the way I have found these formula as following:

E (HOMO) =-e [Eox (onset) + 4.4]

E (LUMO) =-e [Ered (onset) + 4.4]

by Bredas et al.

As you mentioned there two ways to calculate the HOMO, LUMO and Eg. Cyclic voltammetry and optical spectroscopy. In CV, in oxidation state of material or molecule, we take out the first electron in HOMO and in reduction state we put an electron in LUMO, so the potentials Eox and Ered give us the information on HOMO and LUMO. I think you can calculate these values directly from the formulas.

Dear Dena, thanks for sharing the comment :)

In case when the polymer has no reduction peak in the limits of electrolytic solution, HOMO level is calculated from the onset of oxidation peak. The band gap is evaluated from the onset of pi-pi* absorption band. This value is subtracted from HOMO level value to obtain LUMO level.

If, however, when the polymer has both oxidation and reduction values, then one can use onsets of these peaks to calculate HOMO-LUMO levels directly from CV measurements.

Dear Dr. Ahmet. Thanks for your clear explanation.

Yes it is OK if you dont have reduction peak. Then you can calculate the HOMO from oxidation potential.

ordan, A. N.; Das, S.; Siraj, N.; de Rooy, S. L.; Li, M.; El-Zahab, B.; Chandler, L.; Baker, G. A.; Warner, I. M., Anion-controlled morphologies and spectral features of cyanine-based nanoGUMBOS - an improved photosensitizer. Nanoscale 2012, 4 (16), 5031-5038

One must be, of course, careful when predicting the LUMO energy from electronic absorption spectra in case the cathodic potential is not available (for example due to the limited cathodic window of the electrolyte/solvent used). The same applies for oxidation and the HOMO energy. Even if the lowest electronic transition (e.g., pi-to-pi*) has a 'pure' HOMO-to-LUMO character (this can be checked by TDDFT calculations) the molecule in the excited state could actually absorb more energy than is corresponding to the HOMO-LUMO gap determined for the v=0 and v' = 0 vibrational sublevels. The vertical Franck-Condon excitation often leads to 'hot' excited states at v' > 0 (especially if the molecule becomes significantly distorted) and the extra energy is dissipated by vibrational cooling.

Dear Siraj and Hartl, thank you for sharing informative comment.

I want to calculate homo lumo of reduced graphene oxide. I have a doubt in choosing the electrolyte.

Lavanya, try using anhydrous acetonitrile (CH3CN) using 0.1 M lithium perchlorate as a supporting electrolyte under nitrogen atmosphere ..

Thank you sir

What if the energy gaps determined from CV data and from absorption spectra are significantly different? What does it mean? Which method to use to determin HOMO and LUMO then?

Hi Olga,

The bandgap obtained from the optical (UV) spectra is often overestimated compared to bandgap from CV data. As much as possible the two methods should be separate and if you have two sets values then you should report both sets of values indicating the method of measurement for each

But this is not always the case as one may not always see a reduction peak. Then you get the E(HOMO) from CV, get the bandgap from UV-vis (in the same solvent) and then figure out the E(LUMO)

As Hartl has said above, if you can use TDDFT to give you the band gap in addition to your data. This is good practice

Here is a good paper discussing briefly how the Bredas equation was arrived at (pg6-7)as well as comparing the CV bandgap (obtained from onset potentials and peak potentials) and optical band gap (Fig 8).

S. Admassie et al., Synthetic Metals 156 (2006) 614–623

http://www.sciencedirect.com/science/article/pii/S0379677906000567#

Dear all,

I have to oppose some of the comments here. There is a fundamental difference in determining the band gap from optical vs. electronic (or in this case electrochemical) methods. I have already commented on this in another question. ("What is the basic difference between optical band gap and electrical band gap?")

In a optical spectroscopy experiment, the molecule always stays in a neutral charge state. In an electronic spectroscopy experiment (photoemission, inverse photoemission, tunneling spectroscopy or cyclic voltammetry) an electron is either taken out of the molecule to detect the HOMO) or added to it (for the LUMO), i.e., the initial state is neutral (n electrons) but the final state is charged (n-1 or n+1 electrons, respectively). In order to add an electron to a molecule, it needs more energy than the HOMO-LUMO separation of the neutral molecule: the electron also has to overcome the electrostatic repulsion, the Coulomb energy. Therefore, the electronically measured HOMO-LUMO gap (also called transport gap), will always be larger compared to an optical measurement (optical gap). (And this is exactly what the above cited paper shows, although the authors obviously did not state the obvious reason.)

How large the difference is, depends on the spatial charge and orbital distribution. If the HOMO and LUMO are delocalized pi-orbitals and if the molecule is large, then the Coulomb repulsion won't be strong. The effect will even be further reduced if molecules aggregate and form delocalized states, or when a molecule is adsorbed on a metal surface (where the molecular orbitals hybridize and become delocalized; in that case, the HOMO-LUMO gap can even be significantly reduced due to electronic polarization and screening effects - but that is another topic). However, for small molecules (e.g. the widely studied pentacene and PTCDA; cf. the attached publications), the difference between optical and transport gaps is already almost 1 eV. In an organometallic molecule with strongly localized 3d-orbitals, the effect can even be several eV!

All that said, I would never advise to mix data from optical experiments and electronic experiments!

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Dear  Prof. Wegner

                              Thank you for the detailed and informative answer. 

The equation for the LUMO would then be LUMO = HOMO - Excitation energy(eV) , and the output values for HOMO and LUMO would be in Volts vs. your reference. Note: Many people use CV to get the oxidation and reduction potentials, subtract them, and see that as the HOMO-LUMO gap.

Please see following link:

https://www.youtube.com/watch?v=CMSD264DoFo