Units of energy in Gaussian

Question

I want to calculate the redox potential for a molecule in water using Gaussian. I found a tutorial at 1, but I'm got confused about the units at the end.

They have a result for the Gibbs Free Energy of solvation of $-532680$, but I am not sure if it is in Volts or Hartrees. The tutorial says it is all in Hartree, but at the end, they compare with a value in Volts.

1. Tutorial on Ab Initio Redox Potential Calculations

Answer 1

I don't see the value you quote in your question anywhere in the tutorial. In any event, Gibb's Free energies in Gaussian will always be reported in Hartree, while the redox potential (which you would need to calculate using these Gibb's Free energies) is typically given in Volts.

To show how this works, I'll explicitly convert their example from the last section of the tutorial. Reproducing the values here:

SCF(g)(II) : SCF Done: E(UB3LYP) = -510.439067386
SCF(solv)(II): SCF Done: E(UB3LYP) = -510.444248948
GibbsCorr (II): Thermal correction to Gibbs Free Energy= 0.134232

SCF(g)(III) : SCF Done: E(UB3LYP) = -510.170289413
SCF(solv)(III): SCF Done: E(UB3LYP) = -510.239713457
GibbsCorr (III): Thermal correction to Gibbs Free Energy= 0.132483

We want to solve for $\Delta G_{ox (sol)}$ (we will later convert this to $\Delta E_{ox (sol)}$). Using Hess's law and the thermodynamic cycle above, we can write this as $$\Delta G_{\text{ox (sol)}}=\Delta G_{\text{solv}}(\text{III})+\Delta G_{\text{ox (g)}}-\Delta G_{\text{solv}}(\text{II})$$

Evaluating this in Python and converting to volts at the end:

>>> hartree_to_Volt=-2625000.5/96500 #Numerator converts hartree to J/mol
>>> dG_g=(-510.170289413+0.132483)-(-510.439067386+0.134232)
>>> dG_II=(-510.444248948--510.439067386)
>>> dG_III=(-510.239713457--510.170289413)
>>> dG_III+dG_g-dG_II
0.20278649099998347
>>> (dG_III+dG_g-dG_II)*hartree_to_Volt
-5.516213888789659

Which gives a us a value of $E_\text{red}=5.52$ (we have to flip the sign again to give a reduction potential rather than an oxidation potential). I could have simplified the math slightly here, but note that just directly computing $\Delta G_{ox (sol)}$ from the two solvated calculations would have produced a different result, as these calculations used the gas-phase geometry and did not compute thermal corrections at the optimal geometry for the solvated species.

Answer 2

Unfortunately, not able to comment yet, but J. Phys. Chem. A 2009, 113, 6745. is a nice reference, especially if you are interested in metal complexes, which your example seems to deal with.

Some key points:

• You can profit from error cancelations by referencing against calculations for a system like Fc/Fc+.
• You usually find a systematic error for a particular DFT method. Hence, if you have known standard reduction potentials for similar systems, you could use them for a linear fit.

Answer 3

As far as I know, Gaussian outputs energy in Hartrees if other is not stated explictly.

Also the tutorial says:

The values obtained in Gaussian forthis exercise are in Hartree.

So, I think it should be in Hartrees.