Structural and Electronic Properties of (HfH2)n (n = 5–30) Clusters: Theoretical Investigation

https://doi.org/10.1016/j.physe.2021.114634Get rights and content

Highlights

  • Structure search method was implemented to obtain (HfH2)5-30 cluster structures.

  • Structure and electronic properties of (HfH2)5-30 clusters was investigated by Density Functional Theory.

  • Binding energy increases from (HfH2)5 through (HfH2)30 showing increased stability.

  • Orbital interaction between (HfH2)8 cluster was analyzed to obtain bonding strength.

Abstract

Metallic hydride clusters have greater importance due to its unique physicomechanical properties. For solid-state hydrogen storage, (HfH2)n clusters has been considered a promising candidate because of high hydrogen capacity, low cost and larger interacting affinity between atoms. The structural and electronic properties of (HfH2)n clusters are investigated by employing the density functional theory. From the DFT calculations, it is found that Hf atom occupies central position while H atoms tends to occupy at vertex spots. Through structural stability analysis, the calculated binding energy and second order energy difference of (HfH2)n clusters increases from (HfH2)5 through (HfH2)30. The charge density distribution and results of Bader analysis revealed ionic bonding character between Hf and H atoms and transfer of electrons is observed from Hf to H atoms. The orbital overlapping contribution of the interacting Hf and H atom is also performed.

Introduction

Energy became the fundamental part in our daily life, and with rapid rise in human living standards, currently available commercial fuels are going through energy crisis [1,2]. Which makes hydrogen a prospective energy for our eco-friendly system [3]. However due to an inefficient, expensive and insufficient hydrogen storage medium, some major bottleneck occurs to develop cost-effective storage carrier consumable for industrial applications [4]. Commercially available storage mediums including both pressurized gas and liquid at cryogenic temperature, have associated problems with safety, cost expensive and less capacity [1]. The safest proposed storage system based on last two decades is solid-state material, which offers foremost opportunity for hydrogen storage.

The transition metal Hafnium (Hf) have great importance for electronic materials because it possesses unique absorbing and structural properties [5]. Hf has ability to absorb thermal neutrons, generated due to an elastic collision of fast neutrons with H atoms, making hafnium hydride suitable and prolonged lifetime candidate in the fast reactors to be fabricated as control rods for fast neutron flux without producing Helium gas as in contrast with Boron Carbide (B4C) [6,7]. The binary hydrides of metals including Ti, Zr, Hf, Sc, and Y possesses greater stability and absorbs more hydrogen gas by implying low equilibrium hydrogen pressure, which makes hydrogen absorption irreversible even at room temperature [[8], [9], [10]]. Hafnium may favor greater hydrogen storage capacity, as it possesses larger affinity with hydrogen [11].

Several experimental and theoretical investigations on solid-state material had been developed for hydrogen storage which depicts that hydrides with transition metals are referred to be promising potential material to safely store hydrogen because of having interesting properties in both ground and excited state [12,13]. The structural and phase transforming properties of Hf based hydrides differs from their pure metals as concluded by Kulkova et al. [14]. Weaver et al. [15] reported that the binding bands of HfHx are strongly hybridized of d and sp character by studying photoelectron energy distribution curves. Thermal transport properties of HfHx and HfDx were measured by Tsuchiya et al. [6] and observed that from room temperature to 570K, thermal diffusivities for HfHx are comparatively higher than HfDx. The mechanical and electronic properties of the transition metal hydrides were discussed by Chihi et al. [12] and strong binding interaction was noticed between Hf and H atoms and he also concluded that the H–H bond orders are always negative because of brittleness. Quijano et al. [16] and Wolf and Herzig [17] calculated TiH2, ZrH2 and HfH2 electronic band structure by using LDA and GGA approximation, respectively. The metallic HfH2 electronic properties under pressure were investigated by Yunxian et al. [18] and ionic bonding nature in HfH2 was observed because the transfer of charges were mainly from Hf to H atoms. Alonso et al. [19] has studied the properties of transition metal clusters and stated that the cluster properties are not only size dependent but also non-monotonic, which enormously specify the potential interest for scientific applications. Whetten et al. [20] theoretically studied hydrogen reactivity with Fen (n < 25) and proposed that hydrogen electronic structures in the clusters are similar to those in crystals. RhH2, a binary transition metal hydride, is considered to be an ideal candidate of hydrogen storage among all known hydrides by having 163.7 g/L of high volumetric hydrogen density [21].

In this work, the electronic and structural properties of (HfH2)n clusters size ranging from 5 to 30 has been studied in detail. We believe that present study can contribute support to obtain optimal hydrogen storage material with an ideal performance. HfH2, an important binary transition metal hydride, had received great attention because of its wide applications including hydrogen storage. For theoretical calculations, energetically low lying and globally minimum cluster structures are required to obtain accurate results. For which different algorithms can be utilized to minimize hurdles in obtaining the global optimization structures including genetic algorithm (GA) [22], simulated annealing algorithm (SA) [23], and particle swarm algorithm (PSO) [24], and artificial bee colony algorithm (ABC) were studied. Among all, ABC algorithm proposed by Karaboga et al. [23] was used in this study to obtain most efficient and reliable global minimum structures.

Section snippets

Computational details

To generate the lowest energy (HfH2)n cluster structures, ABC algorithm as proposed by Zhang and Dolg. [25,26], has been implemented to optimize atomic and molecular clusters and obtained the most stable geometry of each cluster size. ABC method based on the inverted pair potential [27] was utilized for global optimization. A two-body inverted pair potential is depicted for the description of molecules vibration. The Inverted pair Potential energy was assumed to be of the following form,(r)=p0

Geometrical structures

ABC method was carried out to obtain the initial minima structures of (HfH2)n (n = 5–30). These structures with lowest energy are then re-optimized by DFT calculation, and the results are displayed in Fig. 1.

From Fig. 1, Hf5H10 cluster possesses three-dimensional configurational structure with Hf–Hf as internal pyramidal shape surrounded by H atoms cage. The Hf6H12 with C2v symmetry contains Hf atoms bipyramidally wrapped by H atoms. The Hf7H14 has C2 symmetrical bilayer structure with bicapped

Conclusions

In this paper, a detailed investigation of geometric structures and electronic properties of (HfH2)n clusters have been performed by using ABC method in combination with DFT optimization. The optimized geometries of (HfH2)n (n = 5–30) reveals that Hf atom tends to appear at central position and H encapsulates the Hf atoms. The simulated structures bonding length is in good agreement with previous researcher data through the cluster sizes studies. This result further supports our calculated

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work is supported by the National Natural Science Foundation of China (Grant No. 21776004).

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