Details about ZPE and entropy of adsorbates

Question

I want to compute the ZPE and entropic terms for my platinum slab covered by a bilayer of water (network). I have performed a phonon calculation on a 3x3 q-point grid (my unit cell is ~ 4 Å long)

The calculation is finished and now I am not sure about a few things:

• I keep reading in the literature that one must calculate the ZPE/entropic terms using the adsorbate's vibration modes, the thing is that all the modes are coupled with the substrate, it is not possible to "isolate" the adsorbate's vibration.

• I am pretty sure I need to average these quantities over the q-points grid but I can't find information about that.

One of my colleagues tells me that I should compute the ZPE/entropic terms of the substrate alone and then subtract them to get the contribution of the adsorbate alone.

Could someone give more details?

Answer 1

You might be overthinking things if the system looks like what I expect it does. You can calculate all the terms for the platinum and subtract out their contribution, this is perfectly fine if you want to go this route.

In practice however, this involves a massive number of displacements with nearly no purpose. The vibrations of a water layer on platinum is unlikely to be very strongly coupled to the surface due to the relative weights of H2O and Pt. A reasonable assumption is that the surface does not move significantly in the time of a H2O vibration, leading the approximation that you fix the entire surface in its optimized position. This also has the advantage or removing Pt from the ZPE/entropy terms.

This answer assumes you are using displacements to calculate phonons. If you are using the DFPT in QE, then your original approach is probably the only way to do it.

Answer 2

Usually for an isolated species, you would just compute the vibrational modes (phonon modes) at the gamma point and sum the modes to compute the molecular ZPE $$ E^{ZP} = \frac{h}{2} \sum_{i=1}^{3N-6} \nu_i $$ You would use the same set of frequencies in your entropic corrections.

But for a periodic system, what you would want to do is compute the phonon density of states (PDOS) of the system. So, to compute the ZPE of a periodic system, you would integrate over the frequency-weighted PDOS $$ E^{ZP} = \frac{h}{2}\int_0^\infty \nu g(\nu) d\nu $$ where the PDOS $g(\nu)$ is just the number of phonon modes that exist at a specific frequency $\nu$ (across all $q$-points in your BZ). So no averaging procedure is needed, just compute the PDOS. You should be able to use the PDOS to also compute entropic corrections for the periodic system.

If you are using the ph.x code from QE to compute phonon modes, you can set the variable nat_todo (see the phonon code's documentation for details). This lets you compute the vibrational modes for a subset of atoms. Likely, you can neglect the vibrational modes of Pt since they are so much heavier than O and H. The frequencies of the Pt slab won't be very different between the isolated slab system and water bilayer system.

Alternatively, you can also use Phonopy to compute vibrational modes, and you should also be able to select subsets of atoms there as well.