36
the same has been calculated for the 1T-MoS2 and then the same correction
has been used for the all the other materials. This is not a perfectly valid
assumption, however, a tolerance of 0.5 eV for the free energy to account
for the errors introduced due to different approximations at different levels
will likely capture the variability in the zero point and entropic corrections.
In the case of 1T-MoS2 as mentioned before the entropic corrections for the
adsorbed state has been ignored 54. The calculated zero point corrections
for the adsorbed hydrogen comes out as 0.39 eV. The zero point energy of the
hydrogen in the gas phase has been taken from the Ref. 67 and is found
to be 0.27 eV and entropy of the gaseous hydrogen has been takes as 0.40 as
mentioned in the Ref. 68. By taking the difference of the corrections in the
gas phase and the adsorbed state ZPE comes out as 0.12 eV and -TS comes
out as 0.40 eV, therefore, ZPE -TS comes out to be 0.26 eV (per hydrogen
atom). Therefore, the correction of 0.26 eV is added to the adsorption energies
for all the compounds to have an estimate of the free energy.
As mentioned before, the optimum value of the free energy for the HER is
0.0 eV, however, an energy window of 0.5 eV is taken to account for different
effects like strain, coverage and solvation 48, 69. Additionally, the estimate
of the uncertainties is obtained in the calculation with the BEEF-vdW using
the ensemble in Ref. 70. Having the uncertainties along with the energy
window of 0.5 eV helps to calculate the probability for a material to have the
free energy of the hydrogen adsorption to lie within 0.5 eV around zero. The
calculated probability helps to rank the material in order of their suitability
for the HER 71. The probabilities are calculated as:
P(|G| 0.5) = 1
p22
Z 0.5+¯E
−0.5−¯E
exp
−
E2
22
dE. (4.2)
Using the above equation, the ranking of the material meeting the criteria of
having the free energy for the HER (including the uncertainties) to lie in the
range (-0.5, 0.5) eV is shown in the Figure 4.7. The number of compounds
fulfilling these criterion in the 2H structure in the plot is 23 whereas in the 1T
structure there are 30 compounds meeting the required criterion.
The plot clearly shows that there are very few compounds which are present
in both the 2H and 1T structure indicating that the chemical properties might
differ significantly in different structures of the same compound. Additionally,
the occurence of the compounds like MoS2 and WS2 in the 1T structure
which have already been found experimentally as possible HER materials gives
credibility to our approach 50, 48.
Up to this point the stability of the compounds have been considered only