**3. Hydrogen evolution reaction**

The Hydrogen evolution reaction (2H+ + 2e− → H2) is the cathodic half-cell reaction in acid-based electrolyzers. To understand the mechanism of electrocatalytic/photocatalytic processes the density functional theory has been utilized as well as to predict and design the new catalyst for water splitting [59]. Production of hydrogen in efficient manner from water-splitting is an underpinning science to realize the hydrogen economy. The Janus nanoparticles which have the two different faces each consisting of different chemistry, size, morphology, material and further one face have the hydrophilic and another face have the hydrophobic nature introduced by de Gennes in his noble lecture [60]. In 2019, Chuan Zhao et al. [61] observed the higher hydrogen evolution reaction using Janus nanoparticle catalyst with a nickel–iron oxide interface and multi-site functionality. This nanoparticles have also been compared with benchmark platinum on carbon catalyst. The structure orientation during the hydrogen evolution reaction revealed by DFT calculations that Ni–O–Fe bridge at Ni-γ-Fe2O3 interface modifies the Gibbs free energy of the adsorption of the intermediate H atoms promote the HER. Moreover, the DFT result shows that the H atom adsorb on top site of O atoms in γ-Fe2O3 (311) or in fcc site of Ni(111) with the ΔGH\* of −0.62 and −0.31 eV, respectively. The result of negative ΔGH shown to be responsible for higher HER. The study displays that the Ni(111) fcc responsible for higher rate adsorption of hydrogen as well as the good amount HER. Yong K. et al. [62] investigated the NiCoP and vanadium doped NiCoP material based on the results of crystal structure, XRD, TEM and XPS. At two different places, the Co and V were replaced by Ni and produced the most stable material. The water has allowed to interact with the surface of NiCoP. Right after the dissociation of water, the produced OH and H are placed at the surface of Ni bridge and Ni hollow sites, respectively. During the process, Vanadium was doped in NiCoP and has observed to be the increased value of adsorption energy of OH and decreased water dissociation energy by 0.05 eV on the doped system. At the same time, the adsorption energy for hydrogen on the surface observed to be lower which is advantageous to desorption for hydrogen molecule from the surface and the desorption energy observed to be decreased by 0.09 eV. The DFT results well supported and further insights to the experimental observation of lower over potential and Tafel slope of NiCoVP as lower compared to NiCoP material. Dong et al. [63] used DFT tool to understand the role of sulfur vacancies on Co9S8 and Co3S4 in dissociation of water and HER. The author used the Vienna *ab initio* simulation package (VASP) for the calculation using generalized gradient approximation (GGA) using the

*Applications of Density Functional Theory on Heavy Metal Sensor and Hydrogen Evolution… DOI: http://dx.doi.org/10.5772/intechopen.99825*

Perdew-Burke-Ernzerhof approach for the exchange−correlation term with the inclusion of correction as implemented in the method of Stephen Grimme. The adsorption energy for the H atom on Co9S8 and Co3S4 as observed to be −2.22 and −1.99 eV, respectively, investigated by Ford et al. The adsorption energy shows that both the surfaces are equally potential for the water splitting process. To understand the reaction kinetics, activation energy for H2 dissociation has been calculated using Nudged Elastic Band method on CO3S4 and CO9S8. The result shows that product of the reaction is exothermic. Moreover, the activation energy for H2 dissociation has observed to be 0.4 eV and 1.1 eV on Co3S4 and Co9S8, respectively. Also, the PDOS result shows the variation during the time of creation of the sulfur vacancy formation. From the PDOS result and low coordination of octahedral on Co9S8 surface, it can be concluded that the Co9S8 possibly act as a best catalyst for water splitting. While using Ni2Mo3N [64] as electrocatalyst for hydrogen evolution reaction, the DFT studies shown the coordination of four for N-Mo, responsible for higher adsorption energy of hydrogen and responsible for HER. The adsorption energy of hydrogen atom at Ni and Mo site of Ni2Mo3N are calculated to be −0.47 and −0.15 eV, respectively. The strong adsorption energy is expected to be the lower yield of HER. So, the active site for this surface is N rather than Ni or Mo. So, the calculated hydrogen adsorption energy was found to be in the range of −0.21 to 0.38 eV. In metal free electrocatalyst, to understand and show the interlayer electronic-coupling effect between g-C3N4 and N-graphene, the DFT calculations have been carried out particularly density of states have been computed. In the structure of C3N4@NG hybrid shows the downshifting of valence and conduction bands resulting to Fermi level crosses the conduction band of g-C3N4 responsible and significant enhancement of electrocatalytic HER. Moreover, DGH for g-C3N4 and NG were observed to be −0.54 and 0.57 eV which shows the strong and weak, respectively, adsorption of H on the surfaces. So, both the chemical surfaces are unfavorable for HER. However, while coupling both g-C3N4 and NG have yielded good and enhanced HER activity. To understand the noble-metal-free nature of catalyst on HER, recently, noble-metal-free and earth-abundant electrocatalysts as noble-metal-free core-shell catalyst, MoS2/Ni3S2 on Ni foam has been designed, synthesized and tested for HER. The synergistic effect of MoS2 and Ni3S2 combination shown to be enhanced HER. The activation energy for H2 dissociation on MoS2 has observed as without barrier and negative reaction energy of 1.36 eV. It shows the Mo is the most responsible surface for HER and have the high potential values to explore by the chemist in the near future with various synergism. In this way, in 2018 Ternary Ni-S-Se Nanorod Arrays shown to be good catalyst supported by DFT for HER. The success of this selenium doped electrocatalytic performance towards HER as Se 3d orbitals were bonded to 3d orbitals of Ni and near Fermi level of s p orbitals, and was observed to be significant electron transfer between nickel and selenium atoms. The excellent performance of the catalyst due to the synergistic effect, 3D core structure, electronic modification of Se into nickel sulfide. To understand the solvent effect [65], a single or double layer water molecules are framed around the catalyst and investigated the water splitting process through simulation. The thermodynamic barrier estimated to be 0.6 eV for the H spill-over process, and it shows that the kinetics of HER was enhanced at Ni-RGO [66] synergistic point with the new active sites for the discharge of water. In 2015, Srinivasadesikan V et al. [67] demonstrated the DFT applications to find the role of Li on Lithium decorated surface of TiO2(101) anatase surface. The results observed to be the maximum of 13 Lithium adsorbed on the surface and furthermore addition of Lithium incorporated to sub-surface of TiO2 anatase. The barrier energy for the H2 dissociation on Li adsorbed TiO2 surface has calculated to be 39.8 kcal/mol and for five Lithium decorated case, it has calculated to be 37.8 kcal/mol. The result of Lithium effect enormously reduced the barrier H2 dissociation on bare TiO2 surface which was reported [68]. Later, to understand the Ni effect on the way of doping and decorated

metal atoms on the TiO2 surface, the DFT based first principle calculation has been carried out. Nickel doping and 3Ni metal atoms decorated on TiO2 surface [69] has been investigated. Upon understanding the successful catalyst by theory, the same has been synthesized in the lab and shown good HER. With the arrival of new peak in between valence band and conduction band in density of states calculation on KSCN activation on NiO/TiO2 [70] anatase surface and upon reduction of band gap further confirms the better effect of catalyst towards HER and the same has been confirmed by experiment.

With the above discussion, one can able to understand the power of DFT on various applications. Moreover, the number of unknown science will be explored by using the density functional theory in computational chemistry. Solving the chemical problems with understanding of physics through mathematical equation will be explored for new challenges in science.
