# Cyclic Voltammetry - HOMO and LUMO levels

I'm a physicist, so I apologize if these are obvious questions.

I've carried out CV measurements on a few different types of material (with a ferrocene reference). I am interested in determining the HOMO and LUMO levels of the material.

My CV measurements result in a current-voltage curve (IV curve). It has been explained to me I just need to measure the mV difference between the peak of the ferrocene and the oxidation or reduction curve, then subtract/add that onto the reference for ferrocene (4.8eV) to get the HOMO/LUMO levels.

Sounds simple, right?

But:

• Do I measure to the onset of the oxidation/reduction curve or the peak?

• What justification do I use to convert the voltage to an energy? How can I say that a difference in mV corresponds to eV? Maybe this might make sense if it was a one electron process, but how do I know that?

• Are these peaks even the HOMO/LUMO levels at all? In this eminent paper it warns me

" Often cyclic-voltammetry-based ionization potentials and electron affinities are inappropriately referred to as "HOMO" and "LUMO" energies"

Yes, you can "convert" this way, but you're correct to be skeptical. (figure from Wikipedia)

Note that the "peak" actually has two sides. When you sweep the potential with CV, the cathodic peak ($E_{pc}$) and the anodic peak ($E_{ac}$) won't exactly line up. If you have a well-behaved, reversible redox species, the two peaks will be separated by $E_{pa}-E_{pc}=\frac{56.5\text{ mV}}{n}$ for $n$ electrons.

Do I measure to the onset of the oxidation/reduction curve or the peak

You do neither. Instead, you take $E^0 = (E_{pa}-E_{pc})/2$ - the average of the anodic and cathodic peaks. This is the standard potential for that redox reaction.

You mention that you're including ferrocene as an in-situ reference potential, so you would compare the $E^0$ potential of your redox couple to the $E^0$ of ferrocene.

What justification do I use to convert the voltage to an energy? How can I say that a difference in meV corresponds to eV?

In principal, you're monitoring an oxidation or reduction. So you measure the oxidation potential relative to ferrocene.

The correspondence to the HOMO energy is based on an interpretation of Koopmans' theorem. In short, the oxidation potential involves removing an electron from the molecule, and the lowest ionization potential should come from the HOMO.

So there should be a correlation between the oxidation potentials from electrochemistry and the orbital energies. Some people take this as fact, but it's good that you're skeptical. I see many papers that do this "conversion" without any warning that these are different things.

You asked about units - as you guessed, the conversion between potential (V) and eV (for orbitals) occurs, because in most cases, one electron is transferred, and so the charge is known. In the general case, this is certainly a cause for concern.

Maybe this might make sense if it was a one electron process, but how do I know that?

Heh. Generally, it's one. That's a good question in electrochemistry. There are multiple ways of determination. If you integrate the peaks, the area should correspond to the number of charges transferred. But usually, you don't oxidize or reduce the whole solution.

You can estimate the number of electrons based on the peak spacing, as indicated above $\frac{56.5 mV}{n}$.

You can change the scan rate and use the Randles-Sevcik equation

$$i_p = 268,600 \ n^{\frac{3}{2}} AD^{\frac{1}{2}} Cv^{\frac{1}{2}}$$

Are these peaks even the HOMO/LUMO levels at all?

They are not. There should be a correlation between oxidation and reduction potentials and HOMO and LUMO energies.

But step back and think - in one case, you have electrochemistry in the electrolyte solution at an electrode surface.

• Can the solvent change the observed redox potential? Yes.
• Can the electrode change the observed redox potential? Yes.
• Could the molecules aggregate and change the observed redox potential? Yes.
• Could the oxidized or reduced species undergo reactions that change the observed redox potential? Yes.
• Can the sweep rate change the observed redox potential? Yes.
• Okay - Thank you for your detailed answer, that seriously helps to answer most of my questions. Apart from one regarding the dimensions (sorry for the physics): I'm measuring volts [kg $m^2$ $s^−3$ $A^−1$] but without (rigorous?) justification, I'm taking these volts for energy peaks and saying they correlate to an energy [kg $m^2$ $s^-2$] in eV. I.e. I'm measuring the energy difference (between the peak and ferrocene) in mV. – Tomi Apr 6 '17 at 20:51
• @Tomi - as I now indicate above, the difference is that in most cases, one electron is transferred in the redox couple, so the conversion is "swept under the rug" so to speak. – Geoff Hutchison Apr 7 '17 at 3:01
• Actually, do you not think it would be best to measure the onset of the oxidation/reduction peak? - The HOMO according to the theory you quoted should be the "first" electron allowed into the "band", so it would make sense that we consider the onset. That would match literature "Therefore, the oxidation and reduction potentials are estimated by the onset potential, defined as the potential at which the initial injection of holes or electrons to the HOMO and LUMO..." Buzan et al. onlinelibrary.wiley.com/doi/10.1002/adma.201004554/abstract – Tomi Apr 10 '17 at 19:53
• While you can make arguments along those lines, many electrochemists prefer to take the average of the current peaks to define $E^0$ - for practical purposes. It can be tricky to define the onset, depending on the baseline and the peak. (Imagine a sloping baseline when the capacitance is changing and a small peak.) The peak position is much easier to define accurately. So I understand Bazan and Kaifer's paper, but I don't think this is widespread practice. – Geoff Hutchison Apr 11 '17 at 14:38
• 'ere we go! chemistry.stackexchange.com/q/72106/402 – Melanie Apr 16 '17 at 22:40