zero-point energy

[serenity_3]

Hello,
I calculated binding energy of ammonia to a metal surface and obtained -0.98 eV using the following equation E_ad = E_surface+absorbate - E_surface - E_adsorbate. When I later calculated the zero point energy for the surface/adsorbate I got 0.99 eV. How do I interpret these results? How to report the zero-point corrected binding energy?
Thank you.

[alex]

Hello Weronika,

the ZPE correction seems to be too high, e.g., in your case 2 eV, if I got your explanation correctly (and you don't missed the sign).
If this is the case, please check the frequency analyses for convergence issues on SCF or if they went through correctly.
If you missed the sign you are on the right track, normally, these contributions have the tendendency to cancel out to a large extend.
My approach is check for the one case, where the largest influence should be expected, e.g., an H-atom is reactive, because they contribute most to ZPE, and consider the effort.

Cheers,

alex

[serenity_3]

Hi Alex,
Thanks for replying.
I thought I made a mistake but the convergence looks ok (used EDIFF = 1E-06).
Still the zero point correction seems too large.
The binding energy I have calculated is negative (-0.89 eV).
The frequencies I got are below. Summing these up and dividing by two and converting to eV gives +0.99 eV. What am I missing?

1 f = 105.521420 THz 663.010633 2PiTHz 3519.815682 cm-1 436.401329 meV
2 f = 105.498491 THz 662.866567 2PiTHz 3519.050859 cm-1 436.306503 meV
3 f = 100.978641 THz 634.467511 2PiTHz 3368.284890 cm-1 417.613914 meV
4 f = 46.234374 THz 290.499137 2PiTHz 1542.212702 cm-1 191.209919 meV
5 f = 46.204223 THz 290.309698 2PiTHz 1541.206999 cm-1 191.085228 meV
6 f = 31.902282 THz 200.447952 2PiTHz 1064.145599 cm-1 131.937180 meV
7 f = 13.333548 THz 83.777151 2PiTHz 444.759278 cm-1 55.143098 meV
8 f = 13.306780 THz 83.608964 2PiTHz 443.866401 cm-1 55.032395 meV
9 f = 8.995835 THz 56.522495 2PiTHz 300.068741 cm-1 37.203766 meV
10 f = 2.937476 THz 18.456703 2PiTHz 97.983636 cm-1 12.148417 meV
11 f = 2.119768 THz 13.318896 2PiTHz 70.707855 cm-1 8.766653 meV
12 f = 1.971149 THz 12.385095 2PiTHz 65.750456 cm-1 8.152014 meV

[alex]

Hello Weronika,

you need to correct for ZPE on _both_ sides of the equation:

M(surface) + NH3_gas --> M(surface)--NH3

in total you need three frequency calculations and 3 times ZPE correction to the total energy. Assuming, that the N--H bonds do not take part in the bonding to the surface, most of the ZPE will stay similar and the correction to the total(!) energies on both sides of the equation will be of similar size. So total effect on Delta E with proper ZPE correction is about 0 eV.

On top of that you took an additional trap if I take your ZPE correction: you need to project out rotational and translational modes from that frequency analysis _before_ you calculate the ZPE (the famous 3N-6 degrees of freedom). Phonopy should do that trick right. In case of surfaces, there is only need to get rid of the translational modes (only 3N-3 DOFs left after adsorption). However, this is _not_ the source of the + 1 eV, which is to be searched as outlined above for.

Hth,

alex

[serenity_3]

Thank you, Alex.
I appreciate your reply.