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Density Functional Theory Study of the Hydrogen Evolution Reaction in Haeckelite Boron Nitride Quantum Dots

To satisfy rising energy needs and to handle the forthcoming worldwide climate transformation, major research attention has been drawn to environmentally friendly, renewable, and abundant energy resources. Hydrogen plays an ideal and significant role is such resources, due to its non-carbon-based energy and production through clean energy. In this work, we have explored the catalytic activity of a newly predicted haeckelite boron nitride quantum dot (haeck-BNQD), constructed from the infinite BN sheet, for its utilization in hydrogen production. Density functional theory calculations are employed to investigate geometry optimization, electronic and adsorption mechanism of haeck-BNQD using Gaussian16 package, employing the hybrid B3LYP and wB97XD functionals, along with 6- 31G(d,p) basis set. A number of physical quantities such as HOMO/LUMO energies, the density of states, hydrogen atom adsorption energies, Mulliken populations, Gibbs free energy, work functions, overpotentials, etc., have been computed and analyzed in the context of the catalytic performance of haeck-BNQD for the hydrogen-evolution reaction (HER). Based on our calculations, we predict that the best catalytic performance will be obtained for H adsorption on top of the squares or the octagons of haeck-BNQD. We hope that our prediction of the most active catalytic sites on haeck-BNQD for HER will be put to test in future experiments.


Introduction
Hydrogen as a clean, powerful, and efficient energy source gains sufficient attention because of climatic conditions, limitations of conventional resources, and increasing energy demands [1][2][3][4]. Hydrogen economy seems to be the best possible solution to the upcoming energy crisis and hazardous environment problems [5][6][7][8]. Presently, 96% of the hydrogen is produced through coal, oil, or natural gas, and only 4% carbon-free hydrogen production is carried out by splitting of water because of high cost [9]. Therefore, to make hydrogen a viable source of energy, we need to make its production as cost efficient as hydrocarbonbased fuels. Mass hydrogen production, purification, storage, and transportation are the factors one needs to consider for practical green hydrogen energetics [10][11][12]. In the electrochemical water splitting, a highly efficient catalyst is required to optimize the hydrogen evolution reaction (HER→ 2H + + 2e − = H2) [13][14]. Platinum (Pt) is the most promising and widely used catalyst, however due to its scarcity and high cost, one needs to replace it, and other expensive metal catalysts, with cheap, high-performance ones to make hydrogen generation cost effective [15][16][17][18][19].
The research field of nanosheets is growing exponentially because of their unique properties and wide range of applications. One of the most widely studied two-dimensional (2D) nanomaterial, graphene, and its one-dimensional counterparts carbon nanotubes, have a large number of potential applications, including hydrogen storage and splitting. After these carbon-based materials, the 2D boron nitride nanotubes and nanosheets also have a vast research literature related to hydrogen adsorption and storage because of their immense chemical and thermal stability [20][21][22][23]. In the 2D nanosheets of BN, hexagonal boron nitride (h-BN) and recently detected haeckelite boron nitride (haeck-BN) are the most studied ones analogous to the carbon structures of graphene and octagraphene [24][25][26][27][28][29][30][31]. The haeckelite (haeck-BN) nanosheets have quite different structural and electronic properties as compared to their h-BN counterpart, because of the presence of the octagon and square rings, in addition to the hexagons [30]. These differences are reflected in bond lengths, bond angles, HOMO-LUMO gaps, work function etc. The band gap in haeck-BN is higher as compared to h-BN, but the work function reduces while going from h-BN to haeck-BN [30].Interestingly, the investigations of BN in the context of hydrogen storage have also been extended to hydrogen bubbles on hexagonal BN flakes [31]. While reducing the dimensionality of nanostructures to the zero-dimensional quantum dots, it is seen that besides developing useful physical, electronic and optical properties, quantum dots are also emerging as promising candidate in energy storage and conversion sector as electrocatalysts [32][33][34]. Significant attempts have been made to analyse the catalytic properties of quantum dots (QDs) in the context of HER [35][36][37][38]. The recent works on the graphene quantum dots (GQDs) in hydrogen production have generated considerable interest in the field after successful predictions for HER. Like GQDs, further investigations are in progress to find other thermally stable, non-toxic, inert chemical catalysts. Doping GQDs with B and N enhances their catalytic activity considerably [39,40]. Considering the effect of B-N doping on the electrocatalytic activity of QDs and the significant role of B-N nanostructures for hydrogenadsorption and storage, boron nitride quantum dots (BNQDs) appear to be promising substitutes because of their tailorable properties. BNQDs display confinement and edge effects, and allow us to tune electrical, optical characteristics by varying their shapes and sizes. This unique behaviour leads to many astonishing optoelectronic, chemical, and biochemical properties and practical applications in catalysis, lighting, and bioimaging [41][42][43].In present study, a new haeckelite structure of BNQD has been predicted, showing quantum confinement effects along with its catalytic activity for HER. So far, only the haeckelite structure of the GQD has been investigated to the best of our knowledge [44].
The first-principles density functional theory (DFT) has been employed to examine the electrical and structural properties of this novel haeckelite structure of BNQD in detail.
Furthermore, the total density of states, overpotential, dipole moment, work function etc.
have been analysed thoroughly to predict H adsorption on haeck-BNQD. The HOMO-LUMO gap of haeck-BNQD has been compared with the haeck-BN structure to gain insights into its confinement effects. The results of calculations of adsorption energies and Gibbs free energies have demonstrated favourable outcomes for hydrogen adsorption, and we have also found that haeck-BNQD can be a promising electrocatalyst for HER.

Computational Methodology
All the DFT calculations including total energies, geometry optimization, and vibrational frequency analysis have been performed using the computational chemistry software Gaussian16 [45]. For the visualization of structures Gaussview6.0 [46] was utilized, while the total density of states (TDOS) plots were generated using Multiwfn [47]. Closed-shell DFT calculations are performed on the pristine and H atom absorbed structures of haeckelite BNQDs using the B3LYP and the wB97XD exchange-correlation functionals. B3LYP is a hybrid functional composed of Becke's three-parameter exchange functional with Lee, yang and Parr correlation functional containing both local and non-local terms, and wB97XD is a long-range correlation functional that includes empirical dispersion and long range correlations. B3LYP functional is effective in predicting properties related to hydrogen adsorption and storage on various materials as reported in the literature [48][49][50][51][52][53][54]. While dealing with systems involving ad-atoms, van der Waals interactions play a significant role.
To account for them, we have used the wB97XD functional that includes the London dispersion corrections arising due to long-range interactions. In the wB97XD functional, the attractive van der Waals correction term of -C6/R 6 was included by Grimme, also known as the GD2 dispersion model. Mathematically, the dispersion correction term is given by: In the first step, the geometry of the haeck-BNQD is optimized using aforementioned functionals. Next, the geometry optimization is performed with H adsorbed haeck-BNQD systems. In order to ensure the stability of the optimized structures, we computed their vibrational frequencies. Real values of the frequencies, along with converged forces, and displacements, signal stable structures. Additionally, we computed the Raman intensities for all the structures, which can be measured in future experiments.
To calculate the adsorption energies, the values of total energies of H atom ( 2 ), pristine haeck-BNQD ( ℎ − ) and all Hatom adsorbed haeck-BNQD models ( ) used are given in the Fig 1. The adsorption energy is calculated as follows: The value of adsorption energies are expected to be negative, indicating energy release during the adsorption process, leading to a lowering of the total energy, and stabilizing the system. While performing the calculations on the H-adsorbed systems, the basis-set superposition error (BSSE) arises because the same basis set is shared by both haeck-BNQD and the Hatom. The resultant extra stabilization of intermolecular interaction is taken into account by including the contribution of BSSE into the adsorption energy, leading to the modified formula: Here, is calculated using the counterpoise method [55] and is given in Table 2. The order of BSSE is relatively small in the case of B3LYP as compared to wB97XD. The BSSE highly depends on the basis set used. Larger basis sets lead to smaller BSSE, but increase the computational cost.
The catalytic activity of a system is characterized by its Gibbs free energy ( ) [56], calculated as: where ΔEads is the adsorption energy of the system. The best catalytic performance for HER is indicated by ΔG=0 [14].
Overpotential is also an important parameter to investigate the efficiency of catalyst. Low overpotential implies high catalytic activity, and vice versa. Using the value of Gibbs free energy, we have calculated the overpotential as:

Structural Properties
As stated earlier, structural properties have been studied using two different functionals, namely, B3LYP and wB97XD. Geometry optimization of pristine haeck-BNQD for both the functionals was initiated using the geometry parameters reported by Roondhe et al. [57][58]  The formation energy is another parameter to check the effectiveness of haeck-BNQD as a catalyst. The formation energy Ef is the difference between the total energy of the system and the total energy of its constituent particles can be obtained using the formula where is the total energy of the considered system, , , are the energies of the isolated boron, hydrogen, and nitrogen atoms, respectively. Also, , , , are the total number of atoms in system, and, the total number of boron, nitrogen, and hydrogen atoms, respectively. The formation energies of pristine haeck-BNQD using B3LYP and wB97XD are -6.004 eV and -6.09 eV, respectively. The of H adsorbed haeck-BNQD is presented in To get deeper insights into the vibrational properties of haeck-BNQD along with various hydrogen-adsorbed configurations, we calculated their Raman spectra, presented in Fig. 4.
There are a total of 3n-6 vibrational modes, including stretching, twisting, and bending deformations, where n represents the total number of atoms in the structure in hydrogen

Electronic Properties
To obtain deeper insights into the influence of the electrocatalytic activity on the HER performance, we have studied the electronic properties such as orbital energies of the highest The dipole moments in Table 1  The work function, which is an important property of a system related to its electronic structure, is defined as the average of the ionization potential (IP) and the electron affinity (EA): The work function values for nanostructures such as the ones considered here, broadly indicate the energy required to eject an electron from the system. From Table 1, we note that the work function values present significant changes in B3LYP functional, however, they do not display much variations for the wB97XD functional calculations on various structures.
MESP yields information about the reactivity of electrophilic and nucleophilic species from the charge density distribution. In MESP plots presented in Figs. 5 and 6, the blue and the red colours indicate the affinity of nucleophilic and electrophilic species, respectively. From Figures 5 and 6, it is obvious that the haeck-BNQD has blue colour on its boundary, but the structure with Hadsorbed on the top of the nitrogen (Fig. 6(b)) has red colour, exhibiting the electrophilic nature of the nitrogen because of its high electronegativity.
In Fig. 7(a-b), TDOS provides information about available single-particle states both below and above the Fermi level. In Fig. 8

HER
In the previous sections we discussed the electronic and structural properties of haeck-BNQD structures relevant for their catalytic activity. Next, we discuss the parameters such as adsorption energy ( ), Gibbs free energy ( ), overpotential ( ) that are relevant to the performance of haeck-BNQD in HER. In Table 2 Fig. 10, in which Gibbs free energy is plotted as a function of reaction coordinates.
The overpotentials have been calculated using the Eq. (5), and are also presented in Table 2.
From a physical point of view, the overpotential ( ) is the extra potential required to drive the electrochemical water-splitting reaction, implying that the lesser its value, the higher the electrocatalytic activity. From the calculated values of overpotential presented in Table 2

Conclusion
In the present study, a new haeckelite structure of boron nitride quantum dots has been predicted. The absence of imaginary frequencies, along with converged forces and displacements during the optimization process suggest that the structure is completely stable.
For the haeck-BNQD structure, we get the most favourable values of hydrogen adsorption and Gibbs free energy using the wB97XD functional, which are roughly the same for all the considered adsorption configurations. This, along with their similar overpotential values, suggests strong enhancement of the catalytic activity of these structures as far HER is concerned. Therefore, based upon the results of the present study, we hope that experimentalists will consider the use of haeck-BNQDas an electrocatalyst for the hydrogen evolution reaction.