Rationalizing the Hydrogen and Oxygen Evolution Reaction Activity of

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Rationalizing Hydrogen and Oxygen Evolution Reaction Activity of Two-dimensional Hydrogenated Silicene and Germanene Caroline J Rupp, Sudip Chakraborty, Jonas Anversa, Rogério José Baierle, and Rajeev Ahuja ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.5b11513 • Publication Date (Web): 24 Dec 2015 Downloaded from http://pubs.acs.org on December 27, 2015

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ACS Applied Materials & Interfaces

Rationalizing Hydrogen and Oxygen Evolution Reaction Activity of Two-dimensional Hydrogenated Silicene and Germanene Caroline J. Rupp,†,‡ Sudip Chakraborty,∗,‡ Jonas Anversa,†,¶ Rogério J. Baierle,† and Rajeev Ahuja‡,§ Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil, Condensed Matter Theory Group, Department of Physics and Astronomy, Box 516, Uppsala University, S-75120 Uppsala, Sweden., Faculdade Meridional,CEP 99070-220, Passo Fundo, RS, Brazil., and Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden. E-mail: [email protected]

Abstract We have undertaken first principles electronic structure calculations to show that the chemical functionalization of two-dimensional hydrogenated silicene (silicane) and germanene (germanane) can become a powerful tool to increase the photocatalytic water To whom correspondence should be addressed Departamento de Física, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil ‡ Condensed Matter Theory Group, Department of Physics and Astronomy, Box 516, Uppsala University, S-75120 Uppsala, Sweden. ¶ Faculdade Meridional,CEP 99070-220, Passo Fundo, RS, Brazil. § Applied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden. ∗ †

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splitting activity. Spin polarized density functional theory within the GGA-PBE and HSE06 type of exchange correlation functional has been used to obtain the structural, electronic and optical properties of silicane and germanane functionalized with a series of non-metals (N, P and S), alkali metals (Li, Na and K) and alkaline earth metals (Mg and Ca). The surface-adsorbate interaction between the functionalized systems with H2 and O2 molecules have been determined that leads to envisage HER and OER activity.

Keywords: Hydrogen Evolution Reaction (HER), Oxygen Evolution Reaction (OER), Silicane, Germanane, DFT, Work-function, Free Energy, Zero Point Energy (ZPE)

Introduction In the pursuing of renewable forms of energy to substitute the fossil fuel, hydrogen as fuel has received a special attention. The possibility to use hydrogen as clean energy has attracted the interest in semiconductor catalytic material in order to use solar energy to split the water molecule and produce hydrogen and oxygen. A solar based universal energy model is based on the nature driven photosynthesis phenomenon, which generates hydrogen (H2 ) using photoelectrochemical water splitting. The asynchronizing factor of seasonal solar energy variability can be overcome by storing the energy in a form of chemical bond and consequently produce the energy carrier H2 . The efficient production of H2 is inevitable for realizing the dream of having clean fuels that drives the solar hydrogen generation research. We can afford to have enormous source of hydrogen for versatile applications by acquiring it directly from solar irradiated water splitting. Semiconducting materials emerge as the prominent media that assist water dissociated into oxygen and hydrogen with the solar influence. The active semiconductors can act as promising photocatalysts because of their efficient solar energy conversion and environment friendliness. TiO2 is the first photocatalyst 1 discovered in 1972 for water splitting by Fujishima and Honda. Hydrogenated silicene and germanene 2,3 are the possible promising candidates for light induced chemical transformations 2


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due to their unique electronic structures regarding the valence band (VB) and conduction band (CB). An electron in the valence band may be excited into the conduction band after acquiring a photon with energy hν that corresponds to the band gap energy of the semiconductor and a positive hole is created in VB. The generated electrons and holes accelerate the solar energy conversion and hydrogen production. The prime concern in this matter is the instability and recombination possibilities of electrons and holes, which can decrease the photocatalytic efficiency. During the recent years, various attempts have been made in order to improve this efficiency by forming several semiconductor based systems with different functionalizations with metal adatom. An important issue in the photocatalytic research is the band gap engineering. The reduction and oxidation abilities of semiconductor photocatalyst drive the process of water splitting using solar energy. The reducing and oxidizing powers are measured by the energy positions of the conduction band minimum (CBM) and the valence band maximum (VBM), respectively. The hydrogen and oxygen powers must lie between the CBM and VBM for a spontaneous water splitting process. It has been already predicted that the fundamental band gap of a desirable semiconductor photocatalyst should be around 2.0 eV in order to utilize the solar energy effectively. A promising semiconductor photocatalyst must satisfy the requirements of band edge alignment and the fundamental band gap simultaneously. A single layer of carbon in two-dimensional (2D) honeycomb structure was discovered in 2004 having no real band gap. 5 Since then it has become one of the most promising materials in nanoelectronics and energy harvesting due to its unique electronic properties and extremely high surface area. But, the restricted growth of graphene over large surface area and its incompatibility with the silicon-based nanotechnology pave the way of finding novel two dimensional counterpart like silicene and germanene. 6–10 Recent experimental outcomes manifest the fact that silicene can be synthesized on Ag (111), 11 ZrB2 (0001) 12 and Ir (111) 13 substrates. Honeycomb structure of germanene has been grown by dry deposition of germanium onto the Au (111) surface, 10 similarly to the formation of silicene on Ag 3



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(111). 11 Additionally, silicene and germanene buckled honeycomb structured show a zero-gap semiconductor with massless Dirac fermions, similar to graphene. 6,14 The silicene layers and ribbons present mild surface oxidation 15 in air exposition. The amazing properties of silicene like quantum spin hall effect (QSHE) and giant magneto-resistance, open up possibilities to use these nanostructures in modern electronic industry to build more efficient field effect transistors, thermoelectric devices and in valleytronics. 16–21 The rapid advancement of exfoliation and synthetic techniques has led to other single layered materials discovery of naturally abundant transition metal dichalcogenides (TMDC) with lamellar structures. TMDCs based on Titanium (Ti), Hafnium (Hf), Zirconium (Zr) are semiconducting by nature in contrast with graphene and their band gaps vary between the visible to near-infrared range. The important advantage of these TMDCs over graphene is there is no need of external perturbation like electric field or other physical entities in order to acquire a fundamental band gap and therefore no possibility of extra complexity or decreased electron mobility. Owing to the versatile chemistry that these TMDCs offer, one can certainly investigate them from fundamental and technological perspective. The micromechanical cleavage using adhesive tape applied to substrates produces single layered TMDCs peeled from their parent bulk crystals. This experimental process generates such single crystal flake, which is of high purity, clean and suitable for fundamental characterization and device fabrication. It is well known that not only the band gap value of confined systems but also the energy position of the VBM and CBM relative to the vacuum reference are different when compared to the counterpart bulk systems. The quantum confined effects can lead the VBM and CBM of nano-structured materials in the optimal region for the water splitting, as already shown by Kang et al 4 for some layers of (MoS2 ) and (WS2 ), respectively. Silicene and germanene exhibits the mixed hybridization of sp2 and sp3 lead to the nonplanar configuration with buckled geometry. The hydrogenation of silicene and germanene is a effective way to open the band gaps in silicene and germanene form more stable structures, the silicane and germanane, respectively. These structures present band gaps, which are 4


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in optical region to be used in the photocatalysis. Functionalized silicane and germanane systems with suitable guest atoms can stabilize the structures and its optical properties can be tuned. The common technique for functionalization two-dimensional nanostructures is doping by foreign atoms on the surface. In this work, using first principles calculations, we study silicane and germanane in to pristine form and when they are functionalized with atoms (N, P, S, Li, Na, K, Mg and Ca) in their surface. We focus on the energetic and electronic properties for efficient photocatalytic by studying the electronic bands position with respect to the redox potentials. In addition, we analyzed the adsorption of H2 and O2 molecules in top of foreign atoms. Modeling two-dimensional nano-materials to derive photocatalytic efficiency are yet to be done systematically, which motivates our present work. The current proposed work will also deal with the catalytic mechanism of water splitting such as hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) for the specific photocatalysts after screened through the high throughput study.

Computational Methodology The structural, electronic and optical properties of pristine and functionalized silicane and germanane have been investigated using Density Functional theory (DFT) 22,23 based electronic structure calculations implemented in the VASP (Vienna Ab-initio Simulation Package) program. 24,25 The projector augmented wave method (PAW) 26,27 is used to describe the core electrons as well as the interaction between valence electrons and the ion. The PerdewBurke-Ernzerhof (PBE) form of generalized gradient approximation (GGA) has been employed as the exchange-correlation functional 30 to obtain the optimized configurations and to determine the adsorption energies when the H2 and O2 molecules are adsorbed on the pure and functionalized silicane and germanane surfaces. It is well known that standard DFT and semi-local approximation for the exchange-correlation (like the GGA) do not describe cor-

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rectly the dispersive forces (physical interactions) and therefore a nonlocal correction term must be added. To a better description of the dispersive force, the Grimme’s dispersion 28 has been successfully implemented in the VASP-code, which we have also used while performing our electronic structure calculations. 29 The Brillouin zone has been sampled by 4x4x1 k-mesh under the Monkhorst-Pack scheme 31 to generate the special k-points. The valence electrons are described by a plane wave basis set with a energy cutoff of 500 eV. After obtaining the optimized structures 15x15x1 k-mesh has been used to determine the electronic density of states. In order to avoid the interactions between periodic images of the surface, we have used a vacuum of 15 Å perpendicular to the surface and H2 and O2 molecules are adsorbed on the top of it at an optimum distance of 3 Å. The surface-adsorbate distance has been investigated exhaustibly along with the favourable adsorption site for all the adsorption cases. The simulation cell that has been used in this study is obtained by expanding the unit cell by 3x3x1 supercell consisting of 36 atoms (18 atoms of Si or Ge and 18 atoms of H). All the structures are optimized until the Hellman-Feynman forces are smaller than 1.0 x 10−5 eV/Å. In addition to perform all the electronic structure calculations using PBE type exchange correlation functional, we have also used hybrid HSE06 functional 32,33 as implemented in the VASP code, 34,35 to obtain a better description of optical and band gap and more accurate position of VBM and CBM. The exchange part in HSE06 functional consists of 25% from Hartree-Fock (AEXX) and 75% from GGA-PBE (AGGAX) contribution. The range separation parameter (HFSCREEN) and the fraction of LDA correlation (ALDAC) in our calculations with HSE06 functional have been chosen as 0.2 and 1.0. For the calculations using HSE06 functional, we have used a k-mesh of 5x5x1 to describe the Brillouin zone. The optical absorption spectra can be determined from the frequency-dependent dielectric function ε(ω) = ε1 (ω)+iε2 (ω) and the imaginary part of the dielectric function can be derived

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from the Fermi golden rule: 36

ε2 (ω) =

4π 2 e2 1 � lim 2 2wk δ(εck − εvk − ω) Ω q→0 q c,v,k

× �µck+eα q |µvk ��µck+eβ q |µvk �∗ ,

(1)

where the indices c and v refer to conduction and valence band states, respectively, and µck represents the periodic nature of the wavefunctions at a given k-point. The real part of the ε2 (ω) can be extracted from ε2 (ω) using Kramers-Kronig relation. The absorption cross section as a function of photon energy is evaluated as � �1/2 4πe [ε21 + ε22 ]1/2 − ε1 α(E) = . hc 2

(2)

Results and discussion Crystal and Electronic Structure of Silicane and Germanane The most stable optimized geometry of both hydrogenated silicene (silicane) and germanene (germanane) are taking the chair like buckled configuration as the minimum energy structure (Figure 1). The buckling height (∆z ) are 0.717 Å and 0.729 Å in the case of silicane and germanane, respectively. The optimized lattice constants of silicane and germanane are 3.895 Å and 4.097 Å, respectively, which are in good agreement with previous work based on electronic structure calculations. 37–42 The Si-Si and Ge-Ge bond lengths are 2.361 Å and 2.475 Å, whereas the distances between Si-H and Ge-H are 1.501 Å and 1.564 Å. The electronic structure calculations for silicane and germanane have been performed using GGA-PBE and HSE06 exchange correlation functionals (Supplementary information). As evident form the band structure, silicane has a band gap of 2.195 eV (with GGA-PBE) and it’s indirect as the Valence Band Maximum (VBM) is situated at Γ point and Conduction Band Minimum (CBM) is at M point. This band gap value is in reasonable agreement 7



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(a)

(c)

(b)

(d)

Figure 1: Optimized geometries of silicane supercell [(a) top and (b) side view] and germanane supercell [(c) top and (d) side view]. The blue, red and white balls represent the silicon, germanium and hydrogen atoms, respectively. with the previous investigations. 3,38,43 This value increase to 2.728 eV while using the hybrid exchange correlation functional HSE06, which is also comparable with previous calculations. 44,45 In the case of pure germanane, we have seen an direct band gap (VBM and CBM both are localized at Γ point) with the value 0.939 eV using GGA functional, which increases to 1.612 eV using HSE06 functional. It is worth to mention that these obtained values are in good agreement with the previous theoretical and experimental findings. 37,41,44,46,47 The difference in the electronic band structure for silicane and germanane is mainly related to the corresponding d and s orbital contributions of Si and Ge atoms. In germanane, the CBM presents a small contribution from the d and s orbitals of Ge atoms, that pushes down the CBM to lower energy, leading to decreased band gap. This effect is more pronounced near Γ point than near M point, leading to the fact that germanane is a direct band gap semiconductor. For silicane, the d and s orbital contributions of the Si atoms are in higher energies and therefore their contributions for CBM is negligible. Figures 2-(a) and 3-(a) reveal the electronic density of states for pristine (before functionalization) silicane and germanane, respectively. For an efficient photocatalyst, the optimum fundamental band gap should be more than 1.23 eV providing the holes and electrons the

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energy close to the oxidation and reduction potential of water. For these requirements to be attained, the VBM and the CBM should be located in close proximity of the oxidation and reduction potential of the water. Therefore it is necessary to investigate the optical response of the specific material over a reasonable visible range in order to envisage its photocatalytic activity. The optical absorption cross sections with respect to photon energy using HSE06 hybrid functional of pure silicane and germanane are shown in Figure 4-(a) and Figure 5-(a), whereas the optical spectra using PBE type GGA functional are depicted in Figure S2 of Supplementary Information. The spectra show the consistent optical response of pure silicane and germanane in the visible range with a shift while using HSE06 in place of PBE functional, which is corresponding to the respective band gap. We can also see different behavior when the incident photons are polarized in the perpendicular (α⊥ ) or parallel (α|| ) to z direction of silicane and germanane. α⊥ more intense in the low range of energy (1.00 eV - 6.00 eV) while α|| is more intense in high range of photon energy (7.00 - 10.00 eV). We can observe in Figures 4-(a) and 5-(a), the maximum optical absorption α⊥ has occurred for silicane is around 3.70 eV, while for germanane α⊥ shows a maximum around 3.50 eV. It is worth to mention here that germanane also shows sharp picks in the visible spectrum between 1.77 and 3.50 eV.

Crystal and Electronic Structure of Functionalized Silicane and Germanane In order to tune the hydrogen and oxygen evolution reaction (HER and OER) activity by introducing external chemical species, we have functionalized silicane and germanane with foreign atoms. The functionalization process is mainly undertaken by replacing one of the hydrogen atoms that has been attached to silicane and germanane surface. We have chosen a series of foreign elements that can possibly fetch a good HER and OER activity of silicane and germanane. The series consists of eight different elements to be adsorbed, which can be classified in three different group: (a) nonmetallic atoms (X= N, P and S); (b) alkali metals 9



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(X = Li, Na and K) and (c) alkaline earth metals (X = Mg and Ca). In the optimized functionalized structures, the foreign atoms adsorbed on the threefold Si and Ge atom, which slightly move from its original position comparing to the pristine system, as can be seen in the first column of Table 1. For the adsorption of nonmetal atoms, these displacements (h) are small, while in the case of alkali metals, this displacement values are comparatively larger. From Table 1 and Table 2, we can observe that these displacements are greater in case of germanane as compared to silicane. Whereas, the Si-X bond lengths are smaller than the Ge-X bond lengths. For alkaline earth metals we observe that in the most stable configuration the foreign atom moves to a bond center position, forming new SiX-Si and Ge-X-Ge structures. The Si-X (Si-X-Si) and Ge-X (Ge-X-Ge) bond lengths (bond angle) are very similar. Table 1: Displacement (h) of the Si atom bonded with the adsorbed (X) atom from its initial position in pristine system, the bond length (Si-X) between Si and the adsorbed atom (X = N, P, S, Li, Na, K, Mg and Ca), binding energies (Eb ), band gap (Eg ) and the work function (Φ). The value of Φ of pristine Silicane is 4.97 eV. X N P S Li Na K Mg Ca

h (Å) 0.020 0.005 0.096 0.156 0.158 0.213 0.063 0.131

Si-X (Å) 1.755 2.226 2.055 2.452 2.756 3.146 2.659 2.896

Eb (eV) 3.257 2.692 3.877 2.316 2.000 2.175 1.057 1.750

Eg (eV) 1.979 1.777 — 2.646 2.584 2.582 1.449 1.044

Φ (eV) 5.438 5.409 5.238 4.736 4.646 4.469 4.501 3.855

The binding energy calculated for each individual functionalized adatoms (X = N, P, S, Li, Na, K, Mg and Ca) on silicane and germanane surface that determines how strongly the dopant binds with the surface. The calculated binding energies are shown in the fourth column of Table 1 and Table 2, which represent a trend of binding energies of functionalized atoms with silicane and germanane surface. The decreasing trend of binding energy has been observed if one goes from nonmetal to alkali metals and then alkaline metals. Both silicane and germanane surface strongly binds when sulphur is replacing the hydrogen atom of both 10


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Table 2: Displacement (h) of the Ge atom bonded with the adsorbed (X) atom from its initial position in pristine system, the bond length (Ge-X) between Si and the adsorbed atom (X = N, P, S, Li, Na, K, Mg and Ca), binding energies (Eb ), band gap (Eg ) and the work function (Φ). The value of Φ of pristine Germanane is 4.75 eV. X N P S Li Na K Mg Ca

h (Å) 0.016 0.068 0.162 0.285 0.301 0.368 0.182 0.258

Ge-X (Å) 1.886 2.304 2.149 2.463 2.769 3.160 2.681 2.899

Eb (eV) 2.683 2.428 3.497 2.336 2.039 2.276 1.036 1.769

Eg (eV) 1.349 1.347 — 1.293 1.276 1.263 0.818 0.392

Φ (eV) 5.181 5.150 4.955 4.515 4.461 4.189 4.455 3.843

the surfaces leading to the exothermic phenomena. These observations are well accord with the previous investigations. 48,49 The DOS of functionalized silicane and germanane using HSE06 hybrid functional are shown in Fig. 2 and Fig. 3. The functionalized silicane and germanane show the semiconducting nature while functionalized with the considered elements except with sulphur. In case of N and P, the spin component induces additional electronic levels inside the band gap near to CBM that leads to the band gap decrement. For silicane, the additional states are deeper (in the middle of the band gap) while for germanane due a small band gap, these states are close to CBM leading germanane as an n-type semiconductor character. In case of S, the additional electronic levels observed near VBM. The additional states from S atom are in the vicinity of the Fermi energy, leading to the metallic properties of silicane and germanane, as can be observed in Fig. 6, where we have shown the DOS with a zoom near the Fermi energy for SiH:S and GeH:S systems respectively. In this figure we can observe that the DOS for spin up and spin down components are different, which is an indication that SiH:S and GeH:S could exhibit halfmetallic characteristics. On the other hand, when silicane and germanane are functionalized with alkali metals, we do not observe any electronic levels inside the band gap, however the VBM and the CBM move towards higher energy. This shift is larger for the VBM than CBM that decreases the band gap value. For adsorbed alkaline earth metals we can notice, Fig. 2

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(h) and (i) and Fig. 3 (h) and (i), the presence of spin components states inside the band gap. The spin up states are deep in the band gap (Highest Occupied Crystalline orbital or HOCO) and their counterparts empty spin downs states (Lowest Unoccupied Crystalline orbital or LUCO) are in the vicinity of the CBM. The presence of these two states decreases the HOCO-LUCO band gap to about 50% as compared to the pristine system. From Fig. 2 (h) and (i) and Fig. 3 (h) and (i) we can also observe that there is a mix between the LUCO and the states originated from CB. 2

2

(a) SiH

DOS UP DOS DOWN

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-2 -4 2



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(e) SiH:Li

1 0 -1 -2 -4 2

-3

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0

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(h) SiH:Mg

-2 -4 2

-2 -4 2

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(c) SiH:P

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Figure 2: Total density of states of pristine (a) and functionalized silicane: (b) SiH:N, (c) SiH:P, (d) SiH:S, (e) SiH:Li, (f) SiH:Na, (g) SiH:K, (h) SiH:Mg and (i) SiH:Ca. The zero energy is set to the valence band maximum and Fermi energy is indicate by the a vertical trace red line. From the DOS we can observe that due to the presence of electronic states inside the band gap, HOCO and LUCO states exhibit strong influence induced by the functionalization. Table 1 and Table 2 have been depicted the calculated band gap (energy difference between HOCO and LUCO) for pristine and functionalized systems along with the work-function (Φ), which is defined as following: Φ = V∞ − EF ,

(3)

where V∞ is the electrostatic potential in the vacuum in the vicinity of the surface and EF 12


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2

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(a) GeH

DOS UP DOS DOWN

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(b) GeH:N

1

1

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(d) GeH:S

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(e) GeH:Li

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Figure 3: Total density of states of pristine (a) and functionalized germanane: (b) GeH:N, (c) GeH:P, (d) GeH:S, (e) GeH:Li, (f) GeH:Na, (g) GeH:K, (h) GeH:Mg and (i) GeH:Ca. The zero energy is set to the valence band maximum and Fermi energy is indicate by the a vertical trace red line. is the Fermi energy of the surface. It is known that graphene (Φ) has a small oscillatory dependence on the coverage concentration 50,51 and could be modulated by varying the concentration of foreign atoms. In this work, we do not investigate this effect but our results are useful to indicate the trend in Φ for different adsorbed atoms systematically. When silicane and germanane are functionalized with nonmetal atoms, Φ does not change much as compared to the pristine systems, while in the case of functionalization with alkali and alkaline earth metal, Φ decreases as compared to the pristine silicane and germanane. 52–54 The presence of electronic levels inside the band gap must influence the optical properties of functionalized system, as compared to the pristine. This can be verified from the optical absorption spectra for the functionalized and pristine systems. Fig. 4 and Fig. 5 are the optical absorption spectra for silicane and germanane, respectively. We have seen from the optical spectra that the functionalization with N and P does not change the prime feature of the optical response, while there is a weak absorption peak at lower photon energy can be seen for S functionalized systems. When the systems are func13



tionalized with alkali metals, we observe that α⊥ coefficient is practically similar, whereas for α|| new peaks can be observed in the energy range between 3 to 4 eV in both silicane and germanane cases. A reasonable amount of change in the optical adsorption is occurred when the both the systems are functionalized with alkaline earth metals. In these cases both α⊥ and α|| present new peaks in the visible range. The presence of these peaks are in agreement with the presence of new electronic levels inside the band gap for the functionalized systems. It is worth to mention here that these peaks in the optical absorption spectra for the visible range must increase the photocatalytic properties of silicane and germanane. 25

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Figure 4: The calculated optical absorption for pristine (a) and functionalized silicane using HSE06 functional: (b) SiH:N, (c) SiH:P, (d) SiH:S, (e) SiH:Li, (f) SiH:Na, (g) SiH:K, (h) SiH:Mg and (i) SiH:Ca. The α⊥ and α|| are the adsorption coefficients perpendicular and parallel to z-axis, respectively.

HER and OER activity of Functionalized Silicane and Germanane The HER activity of a surface can be measured by the exchange current density which can be related to the adsorption free energy of hydrogen on that surface. This adsorption free energy is defined as the free energy difference between the adsorbed hydrogen and the gas phase hydrogen at standard conditions as ∆GH ∗ = Eads + ∆EZP E - T∆S (* means adsorbed state); where, the first and second term are the adsorption energy and zero point energy difference of hydrogen in the adsorbed and gas phase state respectively. ∆EZP E value is varying from 0.01 to 0.04 eV and the third term is the entropy difference of the hydrogen molecule in the 14


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Figure 5: The calculated optical absorption for pristine (a) and functionalized germanane using HSE06 functional: (b) GeH:N, (c) GeH:P, (d) GeH:S, (e) GeH:Li, (f) GeH:Na, (g) GeH:K, (h) GeH:Mg and (i) GeH:Ca. The α⊥ and α|| are the absorption coefficients perpendicular and parallel to z-axis, respectively.

Figure 6: Zoom near to the Fermi energy in density of states for (a) SiH:S and (b) GeH:S. GeH:S. The zero energy is set to the valence band maximum and Fermi energy is indicate by the a vertical trace red line.

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adsorbed state and at gas phase having a value around 0.4 eV under experimental condition. For a good HER catalyst, ∆GH ∗ is zero and therefore the adsorption energy Eads should be in the vicinity of -0.24 eV. In case of OER, the corresponding adsorption energy plays an important role and mostly it has been hypothesised that Eads for O2 will be more for better OER catalyst because the origin should be stronger binding between surface and O2 molecule. We have calculated the adsorption energies of H2 (for HER) and O2 (for OER) considering different configuration such as bridge, hollow and top-site on both silicane and germanane surfaces. The adsorption energy can be determined using the following equation: EYads = ET [system + Y ] − ET [system] − ET [Y ].

(4)

where ET [system + Y ] is the total energy of the functionalized silicane (germanane) with the adsorbed molecule, ET [system] is the total energy of the functionalized silicane (germanane) without the adsorbed molecule and ET [Y ] is the total energy of the isolated Y (Y= H2 or O2 ) molecules. The calculated adsorption energies are shown in Table 3 for H2 and O2 adsorbed on the functionalized silicane and germanane, respectively. In this table we have shown the calculated adsorption energies with and without van der Waals corrections. We can observe that the trend of the adsorption energy is consistent with the PBE results, hence the conclusion regarding the HER and OER activity for the respective functionalized silicane and germanane is consistent and valid after incorporating the Van der Waals correction for considering dispersion effect. From Table 3, one can observe that when silicane and germanane are functionalized with alkali metals, H2 adsorption energies are in the desired energy range for appropriate HER catalyst. In both silicane and germanane, it has been found that functionalized with Li leads to the optimum HER activity. The nonmetal and alkaline earth metals are not found as suitable functionalization elements that can enhance the HER activity of silicane and germanane. In case of OER activity, alkaline earth metals are found to be more suitable as compared to non-metal and alkali metal elements. Mg func-

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tionalized silicane and germanane show the most efficient OER activity from the perspective of adsorption energy of O2 molecules with surface. Table 3: Adsorption energies (eV) of H2 and O2 molecules for silicane and germanane functionalized with non-metals (N, P and S), alkali metals (Li, Na and K) and alkaline earth metals (Mg and Ca). The values in the first bracket are the corresponding Adsorption energy with van der Waals correction Adatom N P S Li Na K Mg Ca

Silicane EH2 (eV) -0.069 (-0.101) -0.073 (-0.104) -0.074 (-0.106) -0.214 (-0.339) -0.136 (-0.217) -0.108 (-0.155) -0.072 (-0.101) -0.074 (-0.102)

Germanane EH2 (eV) -0.070 (-0.102) -0.073 (-0.104) -0.074 (-0.108) -0.222 (-0.349) -0.143 (-0.227) -0.112 (-0.162) -0.069 (-0.094) -0.072 (-0.098)

Silicane EO2 (eV) 0.008 (-0.015) 0.006 (-0.015) 0.009 (-0.015) -0.565 (-0.594) -0.319 (-0.353) -0.262 (-0.297) -2.327 (-2.358) -2.094 (-2.121)

Germanane EO2 (eV) 0.002 (-0.021) 0.001 (-0.020) 0.004 (-0.021) -0.691 (-0.723) -0.421 (-0.444) -0.345 (-0.372) -2.262 (-2.299) -2.060 (-2.084)

Conclusions In order to find the optimum photocatalytic activity of ultra-thin silicane and germanane, we have performed a systematic DFT based electronic structure calculation for a series of functionalizing adatoms (N, P, S, Li, Na, K, Mg and Ca). The density of states and optical properties of pristine and functionalized silicane and germanane have been examined in order to envisage the optical response of the individual systems to know whether they are active or not for photocatalytic water splitting. Consequently, hydrogen and oxygen evolution reaction activity have been determined from the surface-adsorbate interaction of the functionalized silicane/germanane and H2 and O2 molecules. It has been found that Li leads the series for both silicane and germane in the case HER activity,while Mg functionalized systems show he highest OER activity among all the considered systems. This study can be an intuitive way to theoretically rationalize HER and OER activity for a series of functionalized different two-dimensional systems before performing the actual experiment in the laboratory.

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Acknowledgement All calculations were performed using the computational facilities of the Cenapad/Campinas-SP, SNIC, HPC2N and UPPMAX. SC and RA would like to acknowledge Carl Tryggers Stiftelse for Vetenskaplig Forskning (CTS), Swedish Research Council (VR), Swedish Energy Agency for financial support. This work has also been supported by the Brazilian agencies CAPES and CNPq.

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(c)

(d)

ΔG=Eads+ ΔZPE - TΔS


Rationalizing the Hydrogen and Oxygen Evolution Reaction Activity of

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