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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!

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1 Answer 1

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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.

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  • $\begingroup$ 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. $\endgroup$ Commented Feb 4 at 1:15
  • $\begingroup$ Thanks for the suggestion, @AGS. I had thought of that, but since they only compute the phonons for one of the m2m/CO2 sites (the other 5 are equivalent), that is already taken care of. I do have to use that trick to reproduce their binding energies, though. $\endgroup$ Commented Feb 4 at 23:47
  • $\begingroup$ So you have 63 modes for the bound CO2 to the diamine appended MOF, 54 modes for the diamine appended MOF without CO2, and 4 modes for gas phase CO2 (in table S2)? It looks like that’s what your original post is saying you did. $\endgroup$
    – AGS
    Commented Feb 5 at 23:03
  • $\begingroup$ Also which functional are you calculating it for? $\endgroup$
    – AGS
    Commented Feb 5 at 23:09
  • $\begingroup$ @AGS that’s correct. I can reproduce their frequencies with the correct number of eigenvalues but when I sum them up as described above, I get different numbers. I have also loaded their numbers in a spreadsheet and summed them up and still see the discrepancy. I’m doing the PBE to start. $\endgroup$ Commented Feb 5 at 23:11

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