Computationally efficient determination of hydrogen isotope effects on the thermodynamic stability of metal hydrides

Although the thermodynamics of metal hydrides at low to moderate temperatures has been successfully described with density functional theory (DFT) calculations using 0 K total energies and simple harmonic models, it is unclear if this approach is valid for hydrides that are stable at high temperatures. To aid development of computationally efficient methods, this paper uses DFT to explore the predicted stabilities of ZrH${}_2$, HfH${}_2$, TiH${}_2$, LiH${}_{,}$ and NaH with four levels of theory. We also investigate isotope effects to understand if these should be accounted for in screening of deuterated or tritiated materials. We show that calculations that account for vibrational corrections to the crystal lattice are not necessary to get an accurate description of relative stabilities of metal hydrides. The shifts in dissociation temperatures due to isotope substitutions are <50 K for all materials, with larger shifts for lighter materials, as expected. We show that accounting for vibrational effects due to isotope substitution in metal hydrides is unnecessary to accurately predict the relative stabilities of metal hydrides at high temperatures.

Figure 1

Predicted lattice constants and volume thermal expansion of hcp Zr and fct ZrH${}_2$ within the quasiharmonic approximation using the volume-only (static) stress-minimization (solid curves) and full-search (dashed curves) methods: (a) lattice constant parallel to principal axis, (b) lattice constant perpendicular to principal axis, (c) volumetric thermal expansivity relative to lattice volume at 293 K.

Figure 2

The shift in the ZrH${}_2$ equilibrium unit-cell volume ($V_0$) at 0 K upon addition of the volume-dependent zero-point-energy (ZPE) correction to the DFT electronic energy ($E_0$).

Figure 3

Contribution of the explicit anharmonic free-energy term to the quasiharmonic free energies of Zr and ZrH${}_2$ determined using the methods of Wu and Wentzcovitch (Refs. 51 and 52).

Figure 4

Temperature-dependent contributions of $\Delta H$ and $\Delta (-TS)$ to $\Delta G=\Delta H+\Delta (-TS)$ for isotope-substituted Ti$X_2$ ($X$ $=$ D and T) relative to TiH${}_2$ determined using a simple harmonic model of the free energy at the zero-point-energy corrected ground-state volume: (a) TiD${}_2$ relative to TiH${}_2$ and (b) TiT${}_2$ relative to TiH${}_2$.