Dynamic sampling of liquid metal structures for theoretical studies on catalysis

Liquid metals have recently emerged as promising catalysts that can outcompete their solid counterparts for many reactions. Although theoretical modelling is extensively used to improve solid-state catalysts, there is currently no way to capture the interactions of adsorbates with a dynamic liquid metal. We propose a new approach based on ab initio molecular dynamics sampling of an adsorbate on a liquid catalyst. Using this approach, we describe time-resolved structures for formate adsorbed on liquid Ga–In, and for all intermediates in the methanol oxidation pathway on Ga–Pt. This yields a range of accessible adsorption energies that take into account the at-temperature motion of the liquid metal. We find that a previously proposed pathway for methanol oxidation on Ga–Pt results in unstable intermediates on a dynamic liquid surface, and propose that H desorption must occur during the path. The results showcase a more accurate way to treat liquid metal catalysts in this emerging field.

4×4×1 for Ga-Pt.The projector augmented wave method was used to account for core electrons.S8,S9 Ab initio molecular dynamics (AIMD) calculations were performed within the N V T ensemble, using a 1 fs time step.The short time step was required due to the inclusion of light elements (e.g.H) in adsorbates on the liquid metal surfaces.A Verlet algorithm was used to solve the equations of motion, with the temperature controlled by coupling to a Nosé-Hover thermostat.S10

Scripts
The codes used for setting up and processing bulk VASP calculations are available on GitHub at: https://github.com/CharlieRuffman/AdsorptionSampling.git.These codes are written to work with the atomic simulation environment.See the README file for more information on how to run these scripts.
Extended sampling for the * CH 2 O + 2 H * state

Resolutions for mirror MD
To explore the effect of different resolutions for the mirror MD calculations required for the reference state, the following tests were performed on a 10 ps window within the sampling for formate adsorbing to Ga-In.The resolutions sampled here span from taking a reference state every 10 time-steps (i.e. 10 fs) to 100 time-steps.
The maximum and minimum adsorption energy peaks, as well as the average adsorption energy, all stay highly consistent at resolutions from 10 to 80 fs.It is only at a resolution of 100 fs where a narrow maximum energy peak is seen to decrease by about 0.1 eV relative to more precise resolutions.Although the resolution can be adjusted to fit the user's needs, these data suggest that a resolution of 80 fs is completely sufficient if one wishes to consider regions of high or low adsorption energy (e.g.0.5 ps wide).One may also only expect relatively small errors in the maximum/minimum energy (e.g.around 0.1 eV) going up to resolutions of 100 fs.

Mean squared displacement of metal atoms and adsorbate
From Figure S7, it can be seen that the mean square displacement of formate adsorbed on Ga-In is much larger for the adsorbate atoms themselves than the metal atoms below.This suggests that adsorbate atoms move more, and more quickly, than the structure of the metal below.

Reference states in a multi-step pathway
Figure S11 shows the energy distributions of several reference states taken from the multistep pathway for the oxidation of methanol.All of these surfaces are "clean," in that the adsorbate is not present, but the mean energies of these systems is still shown to differ.This is likely a result of the adsorbate influencing the surface structure of the liquid metal.
Therefore, to ensure a consistent reference for all reaction steps and capture possible energy differences from surface rearrangement, the energies of all reference states was translated such that the mean matches that of the "pure" clean system with no adsorbate present (Figure S11a).Note that this does not change the shape of the distribution or the sampled structures, it merely removes any systematic shift in the energy of the Ga-Pt surface due to adsorbates being present.The data involved in these translations is shown in Table S2.
Table S2: Average total energies for the adsorbed and reference states involved in the multistep path for methanol oxidation, alongside the amount by which the reference state energies need to be translated by to have the same average energy as the pure clean system.Note that the energy of the atoms in methanol (i.e.methanol in a box) is -30.21 eV.All energies shown are in eV.

System
Average E(reference)  It can be noted that in some cases (e.g. Figure S12 and S13), the adsorption energy sampling starts from a geometry with a favourable adsorption energy, but then rises in energy.This suggests the optimised structure that these runs were initiated from would not actually stably exist at-temperature.In other cases (e.g. Figure S14), the starting geometry appears to be far from the most favourable liquid metal arrangement, and the adsorption energy sampling is able to locate a more stable configuration.

Figure S1 :
Figure S1: Adsorption energy sampling plot for the * CH 2 O + 2 H * state on Ga-Pt extended from 40 ps to 100 ps.The high and low energy regions identified in the first 40 ps of sampling time are not exceeded (though are relocated) at the longer 100 ps time window.

Figure S2 :
Figure S2: 10 fs resolution.The average energy is

Figure S7 :
Figure S7: Mean squared displacement (MSD) of metal atoms in Ga-In compared to that for a formate adsorbate sampled on the surface over 40 ps.The MSD is shown calculated over different time intervals (from 0 to 16 ps) across the sampling duration in order to remove any effect of bias from the starting configuration.

Figure S8 :
Figure S8: Adsorption energy sampling plot for replicate 1 of formate adsorption on Ga-In at 450 K.

Figure S9 :
Figure S9: Adsorption energy sampling plot for replicate 2 of formate adsorption on Ga-In at 450 K.

Figure S10 :
Figure S10: Adsorption energy sampling plot for replicate 3 of formate adsorption on Ga-In at 450 K.

Figure S12 :
Figure S12: Adsorption energy sampling plot for the * CH 3 OH state on Ga-Pt.

Figure S13 :
Figure S13: Adsorption energy sampling plot for the * CH 3 O + * H state on Ga-Pt.

Figure S14 :
Figure S14: Adsorption energy sampling plot for the * CH 2 O + 2 H * state on Ga-Pt.

Figure S15 :
Figure S15: Adsorption energy sampling plot for the * CHO + 3 H * state on Ga-Pt.

Figure S18 :
Figure S18: Adsorption energy sampling plot for the * CO + 2 H * + H 2 state on Ga-Pt.