Role of Functionalized Graphene Quantum Dots in Hydrogen Evolution Reaction: A Density Functional Theory Study

Density functional theory (DFT) can be quite advantageous in advancing the field of catalysis because of the microscopic insights it provides, and thus can guide experimental searches of novel catalysts. Several recent works have demonstrated that low-dimensional materials can be very efficient catalysts. Graphene quantum dots (GQDs) have gained much attention in past years due to their unique properties like low toxicity, chemical inertness, biocompatibility, crystallinity, etc. These properties of GQDs which are due to quantum confinement and edge effects facilitate their applications in various fields like sensing, photoelectronics, catalysis, and many more. Furthermore, the properties of GQDs can be enhanced by doping and functionalization. In order to understand the effects of functionalization by oxygen and boron based groups on the catalytic properties relevant to the hydrogen-evolution reaction (HER), we perform a systematic study of GQDs functionalized with the oxygen (O), borinic acid (BC$_2$O), and boronic acid (BCO$_2$ ). All calculations that included geometry optimization, electronic and adsorption mechanism, were carried out using the Gaussian16 package, employing the hybrid functional B3LYP, and the basis set 6-31G(d,p). With the variation in functionalization groups in GQDs, we observe significant changes in their electronic properties. The adsorption energy E$_{ads}$ of hydrogen over O-GQD, BC$_2$O-GQD, and BCO$_2$-GQD is -0.059 eV, -0.031 eV and -0.032 eV respectively. Accordingly, Gibbs free energy ($\Delta G$) of hydrogen adsorption is extraordinarily near the ideal value (0 eV) for all the three types of functionalized GQDs. Thus, the present work suggests pathways for experimental realization of low-cost and multifunctional GQDs based catalysts for clean and renewable hydrogen energy production.


Introduction
Continuous increase in the consumption of fossil fuels to fulfill ever-increasing energy needs of humanity has led to enormous pollution and degradation of the environment. This has prompted a worldwide effort by researchers to explore novel clean and renewable energy sources. The research has suggested hydrogen to become the first-choice fuel, with the potential to replace fossil fuels, due to its abundance in nature, high energy density, and most importantly its environmental friendliness [1][2]. Several methods have been developed for producing hydrogen of which electrochemical water splitting has demonstrated great promise because of its high hydrogen production efficiency, purity and above all absence of other greenhouse gases or pollutant production in the process [3]. The half reactions for watersplitting, the hydrogen evolution reaction (HER) is difficult to conduct unless the process is assisted by an active catalyst to effectively minimize the required overpotential which is the main concern. From past decades, electrocatalysis studies have received active attention by both experimental as well as computational groups [3] because of their possible applications in developing renewable and clean energy through energy harvesting. The economic feasibility of electrocatalytic water splitting is crucial and can be achieved by decreasing both the energetic cost (i.e., overpotential) and the material cost for the two half-reactions, the oxygen evolution reaction (OER) and the hydrogen evolution reaction (HER) [4][5][6]. Nanosized materials can be quite efficient as catalysts due to their significant advantages such as low fabrication cost and high specific surface area to reach the surface reaction area.
Generally, Pt-based materials have been regarded as the most effective catalysts for HER [7][8], however, they cannot be used widely and practically due to their scarcity and high cost.
Carbon quantum dot (CQDs) have attracted tremendous attention in the past decade due to their potential in bio-imaging [23][24], photodetectors [25], photocatalysis [26][27][28] and energy related applications [29]. Generally, CQDs including carbon nanodots [30] and graphene QDs (GQDs) [31] have multifold advantages, such as facile synthesis and excellent chemical inertness. Most importantly, GQDs are graphene fragments with desirable optical and electronic properties. Graphene has shown high electron mobility along with superior mechanical and thermal stability making it suitable for many applications, [32][33][34] but the key deficiency in graphene is its zero band gap which limits its applications in photonics and optoelectronics. Scientists have proposed many approaches by which a band gap can be opened in graphene. One of the effective and largely adopted methods is by reducing the dimensions of graphene into GQDs. The band gap of GQDs can be made to vary from 0-6 eV by: (a) adjusting their shapes and sizes, and (b) by attaching suitable functional groups or adatoms [26]. The edge chemistry, surface, and size of GQDs can be effortlessly changed in a very wide range by utilizing different synthesis approaches and subsequent treatments.
Among all methods used to the tailor electronic properties of GQDs, heteroatom doping is a very effective strategy to alter the electronic properties of nanomaterials [35]. Recently, GQDs with transition metal nanoparticles adsorbed on their surface have been used in hydrolysis for effective hydrogen evolution [36]. Introduction of various heteroatoms results in enhanced catalytic activity due to the fact that they can intensely alter the local spin or charge distribution by carrying an uneven charge distribution in the material [37]. There are several reports on various types of heteroatom doped GQDs like nitrogen (N) doping which is broadly used to tune the typical properties of GQDs as the nitrogen atom has five valence electrons with a similar atomic radius to the carbon atom. Apart from N, the boron (B) atom also has a similar atomic radius which makes it relatively easy to bond with carbon leading to negligible structural disorder. As a result, B doping of GQDs has attracted significant research interest for its novel properties [38][39][40][41][42][43]. Additionally, the fabrication method depends on the use of strong oxidizing agents which results in the unavoidable introduction of oxygen-containing functional groups attached to GQDs. These mainly include carboxyl

Computational Methodology
The geometry optimization and electronic properties calculations were performed using the density functional theory (DFT) as implemented in the Gaussian16 program package [45], along with the B3LYP hybrid exchange-correlation functional. The Gaussian-type split valence basis set 6-31G (p,d), which includes the polarization functions, was employed in the calculations. For geometry optimization, all considered systems were allowed to relax simultaneously until the gradient forces reached the set threshold value of 0.000450 Hartree/Bohr, RMS force of 0.000300 Hartree/Bohr, maximum displacement of 0.001800 Bohr, and RMS displacement of 0.001200 Bohr. The self-consistent field (SCF) convergence is set to 10 -8 Hartree. The vibrational frequencies were also evaluated to confirm the absence of imaginary frequencies, in order to ensure the stability of the optimized geometries.
Molecular orbitals (MO's) such as highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) were visualized using with GaussView [46]. The Multiwfn software was employed to generate projected density of states (PDOS) [47]. The adsorption energy was computed using the formula: The catalytic surface potential of the considered HER is calculated using the exchange current density linked to the free energy of adsorbed hydrogen (H 2 ) when the reaction is at equilibrium. The free energy of hydrogen in the adsorbed state can be computed using equation [48]: Above, denotes zero-point energy (ZPE) corrections (ranging 0.01 eV to 0.04 eV for hydrogen molecule), denotes entropy difference and is the temperature. Further, the can be written as [49] ( Here, and denote zero-point energy corrections of total energy of the systems with and hydrogen atoms adsorbed on the catalyst, respectively. represents zero-point energy of gas phase . in eq. (2) is the entropy variation among gas-phase hydrogen and adsorbed hydrogen which can be evaluated from the gas entropy [50] using the approximation Here, is the entropy of the systems with hydrogen adsorbed and is the entropy with hydrogen atoms adsorbed. is the gaseous phase entropy of hydrogen. is the vibrational entropy of the hydrogen molecule which finally leads to the value of = 0.41 eV [48]. Thus, we finally obtain the working formula: In order to develop high-quality catalyst for HER, the ideal value of should be nearly zero because a small | | shows superior HER efficacy. ∆G is one of the most significant parameters concerning HER performance of an electrocatalyst. The theory that ideal HER activity of an electrocatalyst should have a ΔG value of around zero was firstly given by Parson and later proved by others [51][52][53][54]. If the catalysts bind weakly, it will be problematic for the surface to activate them. However, if the catalysts bind too strongly, it may impede desorption of H 2 molecules by occupying all accessible surface sites, thus making the reaction ineffective. Therefore, for hydrogen evolution reaction, the optimum value of ΔG should be around zero. Additionally, the other important parameter relevant to HER is the value of , which should be in the vicinity of 0.24 eV. The overpotential (η) can be determined utilizing :

Results and Discussion
The strong motivation for the present study arises from the previous studies of oxygen and boron functionalized GQDs [55][56].      Table 1. Dipole moments not only give us information about the polarity of a given molecule, but also about its anisotropy, and reactivity as far as electrocatalysis is concerned. It is obvious from Table 1  resulting in the modification of p. It is well known that lower values of p lead to relative stability suggesting that the hydrogen adsorbed GQDs are structurally more stable as compared to the original functionalized GQDs considered here [68].

System E HOMO (eV) E LUMO (eV) E g (eV)
Dipole moment p (D) To further understand the electronic properties of the considered structures, the energies of their highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) are presented in Table 1, while the orbitals are plotted in Fig. 4. with the previously reported work [55]. An efficient electrocatalyst for HER should possess active sites for catalysis. As electrons contribute to HER process, the catalyst should have larger electronic conductivity which depends on the band gap (E g ) in a simple way: the larger the value of E g , the lower the conductivity and vice versa. From Table 1, it is obvious that H 2 -O-GQD has the smallest band gap as compared to the other two H 2 adsorbed GQDs.

ϕ (eV) d H-H (Å)
Therefore, comparatively, we expect it to have the highest electronic conductivity leading to the best electrocatalytic performance in HER [69][70][71].
The ionization potential (IP) of a system can be estimated from its HOMO energy as IP = -E HOMO , while the electron affinity can be estimated from its LUMO energy as EA= -E LUMO [73].
In above equation, 4.44 is the absolute potential value of the standard hydrogen electrode [76]. The open-circuit potential V values for all considered systems are tabulated in Table 2.
The value ranges between -0.33 V to -1.16 V following the adsorption of hydrogen molecule.
The water electrolysis device comprises anode and cathode as catalysts for HER and oxygen evolution reactions (OER) [77]. For the water-reduction reaction at the cathode, two mechanisms play important roles in the acidic media: (a) the Volmer−Heyrovsky, and (b) Volmer−Tafel mechanisms [77]. Regardless of the route acquired by HER, for both the mechanisms, of hydrogen is an essential parameter defining the catalytic activity on the surface of catalyst. According to the Sabatier principle, the free energy (ΔG) is directly proportional to the exchange current density, which in turn is a measure of catalytic efficiency [43]. Because ΔG is connected to through Eq. 5, both these quantities can be used to gauge the efficiency of the considered structures as catalysts for HER [78][79].  Because, the free-energy of adsorption of 2H* is regarded as a better descriptor of the HER activity than that of 1H* [82][83], therefore, we have calculated that quantity, and presented that in Table 2. We note that ΔG (0.181 eV) of H 2 -O-GQD is more favorable as compared to  Using eqn. 6, the overpotential (η) is evaluated and plotted in Fig. 7 for H 2 -O-GQD, H 2 -BC 2 O-GQD and H 2 -BCO 2 -GQD. Overpotential η is defined as the minimum potential difference between the two electrodes required for starting the electrochemical water-splitting reaction. The role of electrocatalysts is also to lower this η thereby enabling a highly efficient reaction. It is seen from Fig. 7 and Table 2

Conclusion
In present study, functionalized graphene quantum dots are studied using first principles calculations based on density functional theory. The ground state properties, electronic response to that we would like to state that we may not be able to achieve full quantitative agreement with the experiments due to this size difference, but, we strongly believed that our work will provide important qualitative insights and trends which will be useful for the experimentalists. Additionally, we found that the catalytic parameters of H 2 -O-GQD are quite comparable to those of Pt and Pd surfaces, which, if true, can have very far-reaching implications in the field. Therefore, we urge the experimentalists to investigate the catalytic performance of the structures considered in this work.