First principles calculation of perovskite ‐ type hydrides KXH 3 (X=Al, Cu) for hydrogen storage applications

. Abstract. The primary objective of this paper is to characterize the perovskite-type hydrides KXH 3 (X=Al, Cu) and explore their potential for hydrogen storage applications using density functional theory (DFT). The study investigates various aspects such as structure, electronic and optical properties, stability, and hydrogen storage capabilities. To accomplish this, the study employs the Perdew – Burke – Ernzerhof-Generalized Gradient Approximation (PBE + GGA) functional. The KAlH 3 compound is optimized in a cubic crystal structure, yielding lattice constants of 7.55 Å. On the other hand, KCuH 3 is optimized in a tetragonal crystal structure with dimensions of a=b=11.14 Å and c=13.23 Å. These materials exhibit stability, as indicated by their negative formation energy. The electronic properties of KXH 3 (X=Al, Cu) are thoroughly investigated, including the determination of bandgap, total density of states, and partial density of states. Notably, these structures exhibit a metallic character. The optical results reveal that these novel materials demonstrate minimal energy loss and high conductivity. Regarding hydrogen storage capabilities, the gravimetric hydrogen storage values for KXH 3 (X=Al, Cu) compounds are found to be 4.38 and 2.86 wt%, respectively. These findings suggest that KAlH 3 shows promise as a potential candidate for hydrogen storage applications.


Introduction :
In recent decades, rapid developments in industries and societies have accelerated the excessive consumption of traditional fossil fuels; these sources release greenhouse gases that lead to global warming [1], [2].Hydrogen offers a clean energy solution to both transportation and stationary applications [3].It can be stored in various states, such as gaseous, liquid, or solid forms.The process of hydrogen absorption into solids has drawn considerable interest from numerous researchers because it can facilitate the development of safe, efficient, and high-hydrogen-content storing compounds suitable for transportation needs [4]- [6].Hybrid perovskites stand out as a formidable candidate for solid-state hydrogen storage materials in the future [7]; they not only boast significantly enhanced storage capabilities but also effectively tackle diverse challenges related to distribution, consumption, production, and transportation in non-conventional energy applications [8].This type of material must meet essential criteria, including appropriate gravimetric and volumetric hydrogen storage capacities, as well as high kinetics [9].When considering hydrogen storage, hydride perovskites in powder form are widely available.However, for electronic device technologies, the preference leans towards using crystalline or amorphous hydride perovskite bulk materials [10], and the gravimetric hydrogen storage densities of this type of material range between 1.2 and 6.0 wt% [11].MMgH3 (where M = Li, Na, Rb) hybrid perovskites are currently generating a lot of interest due to their cost-effectiveness, lightweight properties, and efficient hydrogen absorption [12].The familiar ABH3 structures are created in the following manners: (i) The A element comes from the group of monovalent alkali metals (such as Li, Na, K), and the B element originates from the group of divalent alkaline earth metals (like Be, Mg, Ca).(ii) The A element can be either from monovalent alkali or divalent metal groups, while the element B is a transition metal [13].In this research paper, we have investigated the structural, electronic, optical, and hydrogen storage properties of the novel ternary KXH3 (X = Al and Cu) compounds using firstprinciples calculations.It should be noted that the particular combinations of perovskite hydrides mentioned here have not been tested experimentally.Copper and aluminum are recognized as metal cations that have undergone investigation regarding their involvement in hydrogen storage.A study involving CuO/Al2O3 nanocomposites revealed that the hydrogen storage capacity exhibited an upward trend as the ratio of copper to aluminum increased [14].Our research has shown that KXH3 (where X stands for Al and Cu) is a stable combination that can store hydrogen at a rate of 4.38% and 2.86% by weight, respectively.In addition, the desorption temperature values we obtained for KXH3 are significantly higher than the hydrogen critical point (33 K), indicating that they are highly stable.

Material and Methods
In this study, we have employed first-principles calculations to evaluate various properties of KXH3 (X = Al and Cu) compounds using the Full-Potential Linearized Augmented Plane Wave method (FP-LAPW) [15] and executed in the WIEN2k package [16].We took into account the influence of exchange and correlation effects using the generalized gradient approximation (GGA) [17].To achieve full convergence of energy and charge in our computations, we utilized specific parameters.The cutoff wave (Ecut) was set at -7.00 Ry, RMT*KMAX = 7, and IMAX =10.In these parameters, Rmt represents the smallest atomic sphere radius in the muffin-tin approximation, Kmax is the largest K-vector, and Imax is the maximum angular momentum.We extended the charge density Fourier up to GMAX = 12.For the cubic structure of KAlH3, we optimized the muffin-tin radii (RMT) for the atoms K, Al, E3S Web of Conferences 469, 00067 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900067and H, which were taken as 2.5, 2.44, and 1.31 a.u, respectively.In the case of the tetragonal structure of KCuH3, the radii used were 2.50, 1.93, and 1.04 a.u for K, Cu, and H atoms, respectively.The iteration process is repeated until the total energy of the crystal calculated reaches convergence below 10 -4 Ry (Rydberg).To determine the optimal approximation for this study, we optimize the energy as a function of GGA-PBE approximation.The optimized cell parameters of these two compounds are obtained via the equation of state (EOS) using the Murnaghan equation [18].The optimized cell parameters, total energy as a function of the cell volume, and atomic positions for the cubic and tetragonal structures of KAlH3 and KCuH3 are displayed in Table 1 and Table 2, as well as Fig. 1 and Fig. 2.  The enthalpies of formation values shown in Table 1 were determined using Eq. ( 1), where    3 represents the total energy of KXH3 compounds, and E(K), E(X), and E(H) denote the ground state energies for one K atom, one X atom, and one H atom, respectively.

Results and discussion
Table 2. Optimized atomic positions of KXH3 (X = Al, Cu).The stability of compounds can be determined by their negative enthalpy of formation values, which indicate exothermic formation.Table 1 shows that all compounds mentioned are thermodynamically stable.Comparing enthalpies of formation, it can be seen that KCuH3 has a lower value than KAlH3.This indicates that KCuH3 is more likely to be synthesized experimentally due to its higher thermodynamic stability

Electronic properties:
The study investigated the total and partial densities of states (DOS) of new ternary compounds KXH3 (X = Al and Cu).The results showed that both KAlH3 and KCuH3 have  3) due to the overlapping of their valance and conduction bands near the Fermi level.This makes them highly conductive to electricity and heat, and gives them unique electronic properties.According to the PDOS analysis (Fig. 4), the valence bands of KAlH3 are primarily influenced by Al-p orbitals, while those of KCuH3 are dominated by Cu-d orbitals.In both materials, the conduction bands are mainly contributed by K-d orbitals.Additionally, the presence of high-energy states of hydrogen in the valence bands of both compounds indicates the possibility of covalent bonding interactions involving hydrogen.

Optical properties :
The investigation involved the calculation of various optical properties, such as the absorption coefficient, reflectivity (R), dielectric function (ε), electron loss function (Eloss), refractive indice (n), and optical conductivity(σ), to gain a deeper understanding of their behavior and potential applications, with a particular focus on their relevance in hydrogen storage devices.

Complex dielectric function
The complex dielectric function reveals how a material's optical properties vary with the wavelength of the incident light, and it can be characterized by: This function has two components: the real part  1 (ω), which characterizes the polarization of a medium when exposed to a light beam with energy hν, and the imaginary part  2 (ω), which represents the material's absorption.These components are determined using the Ehrenreich and Cohen formalism [19].

Absorption coefficient and reflectivity
The absorption coefficient and reflectivity were computed using the following equations, where "n" represents the refractive index, and "k" represents the extinction coefficient: The absorption coefficient ( ) quantifies the degree to which a material absorbs incident light of a specific energy (or frequency) as it passes through the material.A higher absorption coefficient indicates that the material absorbs a greater amount of incident radiation.Fig. 6 illustrates the frequency-dependent absorption for KXH3 (X = Al, Cu) hydride-perovskites concerning the incident photon energy, which ranges from 0 to 12 eV.The graph displays both increasing and decreasing absorption trends, with the maximum absorption peaks occurring at 109 × 10 4 cm −1 and 9.66 eV for KAlH3 and 114 × 10 4 cm −1 and 11.95 eV for KCuH3.In the field of hydrogen storage applications, research is focused on a material with the highest absorption coefficient.Comparing the two materials, KCuH3 exhibits a greater absorption than KAlH3, in our case it is the KCuH3 that stands out for its remarkable promises.Both of these compounds exhibit the capacity to absorb in the visible region, with KCuH3, in particular, outperforming other previously investigated compounds.[20], [21] Fig. 7.The reflectivity R (%) of KXH3 (X = Al, Cu) perovskite hydrides.
The reflectivity of a material gives its ability to bounce back the incident light.Fig. 7 shows the reflectivity R (%) of KXH3 (X = Al, Cu) compounds plotted against the varying incident light energy.The static values of reflectivity R (0%) are 11.25% and 61.5% for KAlH3 and KCuH3, respectively.The peak values of R (%) are observed as 37.31 % at 4.37 eV and 70 % at 1.29 eV for KAlH3 and KCuH3, respectively.KAlH3 shows minimum reflection from its surface as compared to the other hydride compound.

Refractive index
The refractive index was determined by calculating the dielectric function ε(ω) using the following approach: The static value of refractive index n(0) for KAlH3 and KCuH3 are 2.0 and 2.7, respectively.The peak refractive index values were found to be 3.14 at 4.25 eV for KAlH3 and 2.83 at 2.27 eV for KCuH3 (Fig. 8).Among the studied perovskites, KAlH3 exhibited the highest refractive index, indicating a significant interaction of incident radiations with valence electrons during photon transmission, leading to increased polarization in the material.
The higher refractive index of KAlH3 suggests its potential as a promising and novel hydride perovskite for hydrogen storage systems, especially in applications where photon interactions with valence electrons play a critical role.This finding highlights KAlH3 as an attractive candidate for further exploration and development in hydrogen storage-related devices.

Optical conductivity and energy loss function
The optical conductivity of a substance pertains to its capacity to conduct electric current when exposed to light.In the absence of incident light, both KXH3 (X = Al, Cu) hydrideperovskites exhibit no conductivity.However, in the low energy range, KAlH3 demonstrates the highest optical conductivity with a peak value of 6 at an energy level of 4.34 eV (fig.9), so it can be a favorable material for hydrogen storage and optoelectronic field.
The energy loss function characterizes the energy loss experienced by electrons during their transitions caused by scattering or dispersion phenomena.It is directly linked to the probabilities of scattering that occur during inner shell electron transitions [22].
The results for the energy loss function for KXH3 (X = Al, Cu) hydride-perovskites are shown in Fig. 10.The highest value of loss function is observed as 1.76 at 11.53 eV for KAlH3 and 0.77 at 11.93 eV for KCuH3.

Hydrogen storage properties :
It is essential to investigate the hydrogen storage properties, specifically the gravimetric hydrogen storage capacity and hydrogen desorption temperature, of these compounds in order to explore their potential applications in this particular field.The gravimetric hydrogen storage capacity refers to the quantity of hydrogen that can be stored per unit mass of the material.To determine this capacity, we utilized Eq.( 6) [23], considering the hydrogen-tomaterial atom ratio (H/M), the molar mass of hydrogen (MH), and the molar mass of the host material (MHost).

𝐶𝑤𝑡% = (
A critical factor to consider in the context of hydrogen storage applications is the hydrogen desorption temperature, which signifies the temperature at which stored hydrogen is released.To provide a comprehensive analysis, Table 3 includes the determined hydrogen desorption temperatures for the studied compounds.These calculated TD values are significantly good compared to the hydrogen critical point (33 K).These values were calculated using Eq. ( 7) at a pressure of 1 bar, with the formation enthalpy (ΔH) and ΔS being the entropy change of hydrogen that is 130 J/mol K [24].The compounds KAlH3 and KCuH3 exhibit intriguing gravimetric capacities compared to previously studied compounds.Specifically, KCaH3 and KSrH3 were reported to have gravimetric hydrogen storage capacities of 3.55 wt% and 2.28 wt%, respectively [25].
In certain scenarios, like fuel cell vehicles needing quick refueling, materials with low desorption temperatures could be favored (KAlH3).Conversely, in applications where maximizing hydrogen storage capacity is vital, materials with high desorption temperatures may be more appropriate (KCuH3).

Conclusion
In this study, we explore the perovskite-type hydride KXH3 (X= Al, Cu) by employing firstprinciple calculations to investigate their structural, electronic, and optical characteristics and their hydrogen storage properties.The optimized structures of these compounds demonstrate that they are thermodynamically stable and can be feasibly synthesized, specifically KCuH3, which is more likely to be synthesized experimentally than KAlH3, owing to its higher thermodynamic stability.Through the examination of their electronic properties, it has been demonstrated that both KAlH3 and KCuH3 exhibit metallic behavior due to the overlapping of valance and conduction bands near the Fermi level, endowing them with high electrical and thermal conductivities, as well as revealing unique electronic characteristics.The hydrogen storage properties of KXH3 (X= Al, Cu) were explored, revealing that KAlH3 possesses the highest gravimetric ratio of hydrogen storage capacity (4.38 wt.%), while KCuH3 exhibits the lowest value (2.86 wt.%).The desorption temperature was also investigated and it was found that KAlH3 has a lower temperature compared to the KCuH3 compound, so if the primary objective is to achieve lower desorption temperatures like fuel cell vehicles, even if it means compromising on hydrogen storage capacity, KAlH3 could be a suitable option.On the other hand, if maintaining high hydrogen storage capacity is crucial, despite the drawback of a higher desorption temperature, KCuH3 becomes a viable alternative with these considerations.These results are expected to serve as a positive motivation for scientists to conduct experimental synthesis of these compounds.

Fig. 2 .
Fig. 2. Total energy of a) cubic KAlH3 compound and b) tetragonal KCuH3 compound as a function of the cell volume.

Table 3 .
The gravimetric hydrogen storage capacity (Cwt%) and hydrogen desorption temperature (T in K) for KXH3.