Anti-symmetric exchange and hydrogen evolution in titanium halide monolayers

Abstract

In order to fulfil the energy requirement of mankind through a green and sustainable source of energy, monolayers (MLs) of titanium halides (TiX₃) (X = F, Cl, Br) were studied using density functional theory, for their hydrogen evolution catalytic activity. With the R space group, the optimized structures of TiX₃ MLs attain the trigonal crystal symmetry. The computed lattice parameters for the optimized structures are a = b = 5.57 Å (TiF₃ ML), 6.15 Å (TiCl₃ ML) and 6.69 Å (TiBr₃ ML). The structural stability has been determined from the cohesive energies of −5.74 eV per atom, −4.36 eV per atom and −3.98 eV per atom, for the TiF₃ ML, TiCl₃ ML and TiBr₃ ML, respectively. The electronic properties of TiX₃ MLs are spin dependent, i.e. for the up spin and down spin of electrons, the electronic properties are varied, which suggests the presence of magnetism. The computed magnetic moments per unit cell for TiF₃, TiCl₃ and TiBr₃ MLs are 2.000 μ_B, 2.004 μ_B and 2.038 μ_B, respectively. TiF₃ MLs and TiBr₃ MLs exhibit semiconducting nature, with indirect electronic band gaps, whereas TiCl₃ MLs possess half-metal characteristics. The variation in the structural parameters, under the influence of an electric field of 0.1 eV Å⁻¹ to 1.0 eV Å⁻¹, shows the presence of Dzyaloshinsky–Moriya interaction. The anti-symmetric exchange, in all three MLs, is evocative of good magnetoelectric effects. Further, the computed Gibbs free energies are 0.01 eV, 0.13 eV and 0.14 eV, for the TiF₃ ML, TiCl₃ ML and TiBr₃ ML, respectively. From the calculated Gibbs free energy of TiF₃ MLs for intermediate hydrogen adsorption, a remarkable catalytic activity for the hydrogen evolution reaction has been determined.