# Reproducing ZPE corrections to adsorption from literature

Background

In this paper by Lee, et al., they are looking at different functionals and dispersion corrections and how they change the predicted value of CO$$_2$$ chemisorption on an amine-functionalized metal-organic framework. In the supplemental information, they give the different computed phonon frequencies for each functional and/or dispersion correction for gaseous CO$$_2$$, the amine (m2m) on the MOF, and the final, chemisorbed amine with CO$$_2$$.

Table II on page 7 of the paper gives their computed ZPEs and thermal energy corrections for each method.

I am trying to use the data given in the SI to confirm I get the same numbers as they do for the ZPE and TE.

Problem

My understanding is that the ZPE correction for this system should simply be calculated as

$$\Delta E_{ZPE} = \frac{1}{2}(\sum_i \omega_{i,m2m+CO_2} - \sum_i \omega_{i,m2m} - \sum_i \omega_{i,CO_2})$$.

$$\omega_{i,m2m+CO_2}$$ are the phonon frequencies for the m2m + CO$$_2$$ system [section CO2-m2m of Table SIII], $$\omega_{i,m2m}$$ are the phonon frequencies for just m2m [section m2m of Table SIII], and $$\omega_{i,CO_2}$$ are the gaseous phonon frequencies for CO$$_2$$ [section CO2 of Table SII].

However, when I do the arithmetic, my numbers come out wrong. They list the ZPE to be 6.6 kJ/mol, but the above math gives me 5.6 kJ/mol. This is a small difference in the scheme of things, but since I am using their exact reported numbers, I would expect to get basically the same values.

Any help will be much appreciated.

Thank you!

• If this is what "might" fix the problem, and your answer is so short that it fits in a comment (There are 6 CO2 in the unit cell, so to calculate the binding energy and also the zero point energy per CO2, you have you do 6*E_b = E_{MOF-CO2} - (E_{MOF} + 6 * E_{CO2}). I think equation 3 is just a typo. Applying this to the ZPE might fix the discrepancy that you see) it would be best to leave a comment rather than an answer. Commented Feb 4 at 1:15