How to calculate Gibbs energy (G) from a frequency output file?
This is printed (at T = 298 K) at the end of a vibrational frequency job, e.g. for H2O molecule at the HF/STO-3G level I get:
The Molecule is an Asymmetric Top
Translational Enthalpy: 0.889 kcal/mol
Rotational Enthalpy: 0.889 kcal/mol
Vibrational Enthalpy: 15.297 kcal/mol
gas constant (RT): 0.592 kcal/mol
Translational Entropy: 34.608 cal/mol.K
Rotational Entropy: 10.673 cal/mol.K
Vibrational Entropy: 0.001 cal/mol.K
Total Enthalpy: 17.667 kcal/mol
Total Entropy: 45.281 cal/mol.K
(You can tell it’s T=298 K based on the value of RT.) The value of G at T=298 K is directly computable from the values of H and S that are provided. If you’d like G at a different temperature, then you need to recompute U, H, and S based on harmonic partition functions from the vibrational frequencies that are given.
Dear jherbert,
Can you please clarify what number is Delta G in kcal/mol based on the example you provided?
I believe we need internal energy for this.
Delta G = Delta H - T*Delta S
Your answer will help me a lot.
Thank you.
To have a “Delta” you need two calculations, i.e., two different points on the potential surface. For the single point about, you have a total enthalpy (H) and a total entropy (S), each computed at T=298.15 K, so you have G at this particular point on the potential surface, at that temperature.
Thank you very much. For calculation of G, do we need to account electronic energy as follow?
G [kcal/mol] = electronic energy [kcal/mol] + total enthalpy [kcal/mol] - T * total entropy [kcal/mol]
which electronic energy comes from optimization :
Final energy is -1222.49260457338 a.u.
** OPTIMIZATION CONVERGED **
You need optimizations followed by frequencies at two different points on the potential surface to make this meaningful. The difference in total electronic energies at those two points gives you the DeltaE from the bottom of the potential surface at one local minimum or TS, to the bottom of the potential surface at the other minimum, meaning that ZPE and finite-temperature vibrational effects are not included. To obtain the latter, compute G = H - T*S at each point and take the difference, adding that to the difference in the electronic energies.
Thank you very much. The reason I asked about adding Delta E to the enthalpy is this part of Q-chem manual.
This is saying essentially the same thing that I was saying. None of it is meaningful in an absolute sense, only as a difference between two points on a potential surface.
Thank you. Since I have different result from Gaussian, I need to ask you:
Can you verify that Delta G=6.4 kcal/mol for this example?
Product
- Optimization:
Final energy is -1221.89037087261
** OPTIMIZATION CONVERGED **
- Frequency
Total Enthalpy: 294.076 kcal/mol
Total Entropy: 159.281 cal/mol.K
Reactant:
- Optimization:
Final energy is -1221.90600840095
** OPTIMIZATION CONVERGED **
- Frequency
Total Enthalpy: 294.007 kcal/mol
Total Entropy: 147.662 cal/mol.K
I appreciate your help.
This looks about the same. The DeltaU (difference in SCF energies) is
U(pdt) - U(react) = +9.8kcal/mol
Then for H-TS @ 298K, I get 246.4 kcal/mol (pdt) vs 250.0 kcal/mol (react), difference is -3.6 kcal/mol. Putting that all together, it’s Delta = 6.2 kcal/mol.