Improving visible light photocatalytic activity of NaNbO₃: a DFT based investigation

Abstract

Depleting sources of fossil fuels and their adverse environmental impact drive global interest to find efficient materials for hydrogen generation through solar water splitting. Although, NaNbO₃ has several key features as an efficient photocatalyst, its large band gap restricts its photoactivity only in the UV-region of the solar spectrum. In this theoretical study, we investigate the effect of doping on the electronic structure of NaNbO₃ aiming at improving its visible light photocatalytic activity. For this purpose, we employ hybrid density functional theory (DFT), which successfully reproduces the experimental band gap of NaNbO₃. Doping with N has been found to reduce the effective band gap significantly by introducing localized acceptor states which however are known to promote the electron hole recombination rate. To overcome this, we propose codoping with W at the Nb lattice site. Interestingly this completely passivates those localized acceptor states. The band gap is found to be sufficiently reduced to enhance the visible light activity. The present strategy reduces the band gap in such a controlled way that (W, N)-NaNbO₃ satisfies the thermodynamic criteria to execute the overall decomposition of H₂O, indicated in the relative position of its band edges with respect to water redox levels. Moreover, doping of N is found to be facilitated in the presence of W due to reduction in formation energy. Additionally, spontaneous formation of charge compensated valence defects is expected to be reduced in the presence of the (W, N) pair in comparison to individual dopant elements due to maintaining the total electrical charge neutrality.

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1. Introduction

Development of efficient photocatalysts for generation of hydrogen from water using sunlight is one of the great challenges to make clean, sustainable energy sources.^1–4 In reality it is very difficult to find a single material that satisfies all the desired properties of an ideal photocatalyst. Conventionally modification is carried out on a chosen starting material to get the desired property. Perovskite materials are considered to be good starting materials due to their excellent stability, and easy to tune electronic structure. Here we choose NaNbO₃ which has been extensively studied in recent times due to nontoxicity and higher activity towards various photocatalytic processes, including water splitting, CO₂ reduction, degradation of environment pollutants etc.^5–24

However, large band gap (>3 eV) restricts applications of NaNbO₃ in presence of sunlight, which consists of nearly 55% of visible light. This opens a large area of research for band gap engineering. Khorrami et al. prepared potassium sodium niobate nanopowders, which improve the absorption property of NaNbO₃ towards visible region by a small extent.²³ The most popular way to narrow the band gap is doping with foreign elements.^21–30 However, there are few challenges for the doping strategy. Such as, the dopant may induce large structural strain that leads to significant change in the parent electronic structure. In many cases, the dopant introduces localized impurity states, thereby reducing the effective band gap. But, these strategies are well known to lead to charge carrier trapping centers and hence are not desirable for achieving good photo conversion efficiency. Another issue is the formation of charge compensating vacancy defects, which can accelerate the carrier recombination rate. So one has to choose the dopant element carefully. A significant enhancement of visible light activity has been observed in the study of Shi et al. which involves doping with N.³¹ However, photo conversion efficiency of N-doped material is largely limited by the presence of localized acceptor states in the mid gap region which promotes charge carrier recombination rate. To overcome this, we propose W as a codopant for N-doped NaNbO₃. Since the ionic radius of W is close to that of Nb (R_Nb⁵⁺ = 0.64 Å, R_W⁶⁺ = 0.60 Å),³² it can be easily doped at the Nb lattice site, without any major lattice distortion. More importantly, the energy of W 5d is closer to the energy of Nb 4d.³³ Hence the possibility of shifting the CBM in the downward direction by large extent is also less. Therefore, doping with the pair (W, N) is expected to be safe for retaining the H₂ evolution property of NaNbO₃. Here, a systematic study has been carried out for exploring the effect of this dopant pair along with their individual effect using density functional theory (DFT) as a tool. Since, the band gap calculation is severely underestimated in the conventional DFT calculation, we employed hybrid functional as prescribed by Heyd, Scuseria, and Ernzerhof (HSE)³⁴ for electronic structure calculation, although it is computationally expensive for supercell calculation. It has been reported to reproduce the experimental band gap of a wide range of semiconductor materials.^35–38

2. Computational details

All the calculations have been carried out using Vienna ab initio simulation package (VASP),³⁹ which is based on projector augmented wave (PAW) potential.⁴⁰ To model the doped structure 2 × 2 × 2 cubic NaNbO₃ supercell has been considered. We have also considered larger supercell to take care of the effect of dopant concentration on the electronic structure of NaNbO₃. All the structures have been fully optimized, i.e., relaxation of both ionic positions and cell parameters has been considered. The Brillouin zone integration has been carried out with k-point mesh of 8 × 8 × 8.⁴¹ The tolerance for energy convergence during self consistent iteration is set to 10⁻⁶ eV. The exchange correlation functional during geometry optimization is defined by Perdew–Burke–Ernzerhof (PBE) under the framework of generalized gradient approximation (GGA).⁴² However, for electronic structure calculation we have employed HSE hybrid functional. According to HSE functional the exchange energy functional is defined in terms of short range (SR) part and long range (LR) part. Here, the SR part is defined by PBE functional mixed with certain fraction of exact Hartree–Fock (HF) exchange, while the LR part is solely defined by PBE exchange. The correlation part is fully described by only PBE correlation. Thus the mathematical form for the exchange correlation energy functional is given by

E^HSE_XC = aE^SR_X(μ) + (1 − a)E^PBE,SR_X(μ) + E^PBE,LR_X(μ) + E^PBE_C (1)

here, ‘μ’ is the screening parameter, which dictates the SR and LR parts. The value of screening parameter is kept fixed at 0.2 Å⁻¹ throughout the calculation. The quantity of HF mixing is determined by the mixing coefficient ‘a’. Here, we vary the quantity of mixing from 25% to 35% and compare the calculated band gap with experimentally reported value. The band structure has been plotted along the high symmetry k-path. For density of states (DOS) we have employed the tetrahedron method with Blöchl correction.⁴³

3. Results and discussion

NaNbO₃ exists in different crystal structures at different temperatures. At room temperature, the most stable form is the orthorhombic structure. But the cubic form (Pm3̄m, space group no. 221) is reported to show best photocatalytic activity among the different forms of NaNbO₃.^17–19 So, in the present study all the calculations have been carried out using the cubic crystal structure only. As can be seen from Fig. 1, the structural framework is based on corner sharing NbO₆ octahedral units. The calculated Nb–O bond length is 2.004 Å, and the Nb–O–Nb angle is 180°. We first perform several test calculations for electronic structure employing hybrid density functional with different mixing parameter but keeping the screening parameter fixed at the standard value. As can be seen from Table 1, the calculated band gap (3.27 eV) with screening parameter 0.2 Å⁻¹ and 34% of exact HF mixing reproduces the experimental band gap (3.27 eV)²² successfully. So, all the calculations are carried out using this computational parameter. The band structure plot has been shown in Fig. 2. To analyze the nature of state at the band edge we calculate PDOS for NaNbO₃ (Fig. 2). As can be seen from Fig. 2, the VBM is composed of O 2p states and CBM is dominated by Nb 4d state. The contribution of Na related state to the band edge is negligible. This is due to ionic type bonding between Na and NbO₆ unit. We now proceed to the discussion of the effect of dopant elements on the geometry and electronic structure of NaNbO₃. For a better understanding, we will first present the scenario in presence of individual dopant elements.

Fig. 1 2 × 2 × 2 supercell of cubic crystal structure of NaNbO₃. The numbers indicate position of the dopant element.

Table 1 Variation of band gap of undoped NaNbO₃ with different computational parameters. Experiment data ‘a’ and ‘b’ are taken from ref. 20 and 22, respectively

Mixing HF exchange (%)	Screen parameter (Å^−1)	Band gap (eV)
25	0.2	2.77
30	0.2	3.05
32	0.2	3.16
34	0.2	3.27
35	0.2	3.33
Experimental		3.29^a
		3.27^b

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Fig. 2 Band structure and density of states of NaNbO₃.

3.1. N-Doped NaNbO₃

N-Doped NaNbO₃ is modeled by replacing one of the oxygen atoms in the 2 × 2 × 2 supercell of NaNbO₃, (which correspond to dopant concentration of 4.17%). The basic crystal structure is found to be nearly unchanged due to doping with N. A small increase (0.033 Å) in lattice parameter is observed only in the direction parallel to Nb–N bond. The calculated Nb–N bond distance (2.016 Å) is also close to the Nb–O distance (2.004 Å). This is due to closeness in the ionic sizes of O and N (R_O²⁻ = 1.35 Å, R_N³⁻ = 1.46 Å).³² However, the effect on the electronic structure is found to be quite significant. The band structure plot for N-doped NaNbO₃ is shown in Fig. 3a, indicates that N doping leads to introduction of occupied and unoccupied impurity states in between the VB and CB. The impurity states split the gap region in three parts (0.86 eV, 1.19 eV, and 0.84 eV), leaving the VBM and CBM almost unchanged. This is consistent with the experimental observation of enhanced visible light activity of N-doped NaNbO₃.³¹ To investigate the nature of impurity states in details we analyze DOS and PDOS for N-doped NaNbO₃ (Fig. 3a′). Both the impurity states are composed of hybridized states of O 2p and N 2p orbital. The DOS plot is unsymmetrical with respect to spin up and spin down parts due to partially occupied states. This arises because of presence of unpaired electron in the N-doped NaNbO₃, which is also evident in the calculated magnetic moment (1 μ_B per supercell). The acceptor states originate due to lesser number of electrons in the valence shell of N (2s²2p³) in comparison to O (2s²2p⁴). Although, limitation of visible light activity is greatly overcome by N doping, it fails to deliver photoconversion efficiency at the expected level. This is mainly due to strongly localized nature of the impurity states, which promote electron–hole recombination rate.^44–48 To overcome this we suggest codoping with W at the Nb lattice site, which can compensate for the electron deficiency by providing one extra electron. Let us now see the effect of W doping on the electronic structure of NaNbO₃.

Fig. 3 Band structure and density of states of N-doped NaNbO₃ (a and a′), and W-doped NaNbO₃ (b and b′).

3.2. W-Doped NaNbO₃

In the case of W doping, one of the Nb atoms in the 2 × 2 × 2 supercell is replaced by W (which corresponds to dopant concentration of 12.5%). The geometry is found to be changed by a small extent after full relaxation. The cell dimension is reduced slightly (0.105 Å) in two directions (along a and b), but is increased by 0.22 Å along ‘c’-direction. The Nb–O–W angle reduced to 168°. The average W–O bond distance is 1.872 Å, which is slightly smaller than Nb–O length (2.004 Å) in undoped NaNbO₃. The band structure and DOS plot for W-doped NaNbO₃ has been shown in Fig. 3b and b′, respectively. In contrast to the case of N doped system, occupied impurity states are introduced here close to the bottom of the CB. The Fermi level is in the CB region, indicating n-type behavior for W-doped NaNbO₃. This is due to one extra electron in the valence shell of W in comparison to that of Nb. Interestingly, the calculated band gap (2.27 eV) for W-doped NaNbO₃ is almost equal to that of N-doped NaNbO₃. The DOS plot (Fig. 3b′) is unsymmetrical with respect to spin up and spin down parts due to presence of unpaired electron, which contributes to the calculated magnetic moment of 0.87 μ_B per supercell. Analysis of PDOS indicates that the VBM is contributed by O 2p states, and the occupied impurity states at the bottom of CB are composed of hybridized states of W 5d and Nb 4d orbitals. This is due to closeness of the energy of Nb 4d orbital with W 5d orbital. This is also supported by the contribution of Nb 4d orbital (47%) and W 5d orbital (53%) to the total magnetic moment. This discussion on the effect of W on the electronic structure of NaNbO₃ indicates that codoping of W should compensate for the electron deficiency in N-doped NaNbO₃. In the following section we discuss the combined effect of both N and W.

3.3. (W, N)-codoped NaNbO₃

To model the codoped system both N and W are introduced simultaneously at the O and W lattice sites, respectively. With the advent of technology various synthetic strategies have been developed, which may deliver product with different configurations. For example, synthetic route involving solution method is known to generate product with lowest energy configuration due to equilibrium condition,⁴⁹ while processes like magnetron sputtering or supersonic cluster beam deposition, may deliver product with other configuration as major fraction.^50–52 Hence, for (W, N)-codoped NaNbO₃ two different configurations have been considered by varying the relative position of N and W. We designate these two configurations as Str. 1 and Str. 2, where N and W occupy the nearest neighboring lattice sites (Nb1, O1) and next to nearest neighboring lattice sites (Nb1, O2), respectively. Since, Str. 1 is energetically lower than Str. 2, it is likely to be formed as a major product in first type of synthetic strategy, while the second type of approach may produce Str. 2 predominantly. The structural change due to codoping in both the cases is very much similar to that of doping with only W. The calculated distances between W and N are 1.753 Å and 4.401 Å in Str. 1 and Str. 2, respectively. The band structure plot for (W, N)-codoped NaNbO₃ with two different configurations (Fig. 4a and b) are nearly same, indicating complete passivation of localized impurity states. This is due to counter balancing effect of both the dopant elements. As we have seen in the previous discussion, N doping results one electron deficiency in NaNbO₃, while doping with W leads to one excess electron. So, presence of both the dopant elements maintains the total electrical charge neutrality. Thus, in the case of (W, N)-codoped NaNbO₃, it is expected to get photoconversion efficiency at the desired level. The reduction of band gap is quite significant (0.63 eV) for the codoped system with Str. 2 configuration, while it is just 0.24 eV for Str. 1 configuration. Hence, the codoped system with Str. 2 configuration is more preferable for achieving enhancement of visible light activity by a significant extent. The codoped system no longer contains unpaired electron. This is indicated in the symmetrical nature of DOS plot with respect to spin up and spin down parts, as well as in the calculated zero magnetic moment value. Analysis of PDOS (Fig. 4a′ and b′) indicates that VBM is contributed by hybridized states of N 2p and O 2p. The mixing of N 2p and O 2p states in this case occurs in such an extent that the impurity states form continuous state with the VB. This is in favor of good charge carrier mobility. The CBM is dominated by Nb 4d state.

Fig. 4 Band structure and density of states of (W, N)-codoped NaNbO₃ with configuration Str. 1 (a and a′), Str. 2 (b and b′).

The most interesting observation is that the band gap narrowing obtained by using the present strategy is mainly controlled by shifting of VBM only (Table 2). This feature is very much desirable while modifying the band gap of hydrogen evolving photocatalyst, particularly for material like NaNbO₃, where the CBM position is close to the H⁺/H₂ level. This justifies the choice of the codoping pair for enhancing the visible light photocatalytic activity of NaNbO₃. However, there are few points we should check before reaching the final conclusion.

Table 2 Calculated band gap and band edge shifting (+: upward shifting, −: downward shifting) of (W, N)-codoped NaNbO₃ with equal and different ratio of W and N calculated using 2 × 2 × 2 supercell, 2 × 2 × 3 supercell, and 2 × 3 × 3 supercell

Dopant concentration		Configuration	(W, N)-NaNbO3
N (%)	W (%)		Gap (eV)	ΔEVBM (eV)	ΔECBM (eV)
4.17	12.5	‘Str. 1’	3.03	+0.17	−0.08
		‘Str. 2’	2.64	+0.57	−0.06
4.17	25	‘Str. 1’	2.18	+0.68	−0.41
		‘Str. 2’	1.64	+0.54	−1.09
8.33	12.5	‘Str. 1’	2.80	+0.42	−0.05
		‘Str. 2’	2.28	+0.75	−0.24
2.78	8.33	‘Str. 1’	3.11	+0.06	−0.11
		‘Str. 2’	2.46	+0.52	−0.29
2.78	16.67	‘Str. 1’	2.47	+0.47	−0.33
		‘Str. 2’	2.28	+0.73	−0.25
5.55	8.33	‘Str. 1’	3.19	+0.43	+0.35
		‘Str. 2’	2.46	+0.23	−0.51
1.85	5.55	‘Str. 1’	3.17	+0.06	−0.05
		‘Str. 2’	2.51	+0.54	−0.22
1.85	11.11	‘Str. 1’	2.36	+0.47	−0.44
		‘Str. 2’	2.43	+0.57	−0.27
3.70	5.55	‘Str. 1’	3.06	+0.31	+0.11
		‘Str. 2’	3.15	+0.23	+0.11

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3.4. Defect formation energy

The calculation of defect formation energy provides valuable information related to most favorable growth condition of material as well as relative stability. Here we have calculated the defect formation energy for (W, N)-doped NaNbO₃ and compared with that of the monodoped with W or N counterpart. The mathematical form of the defect formation energy expression is given by,^53,54

ΔH_f = E_doped − E_NaNbO3 + q∑n_Xμ_X (2)

where, E_doped and E_NaNbO3 represent the energy of the doped and undoped NaNbO₃, calculated with some supercell size, μ_X indicate the chemical potential of the element X and n_X is the number of elements added (q = −1) or replaced (q = +1) to form the doped system.

Under equilibrium condition between the reservoir of Na, Nb and O with NaNbO₃, the chemical potential of the components can be related to that of NaNbO₃ as

μ_Na + μ_Nb + 3μ_O = μ_NaNbO3(bulk) (3)

The heat of formation (Δ) for NaNbO₃ is defined as

Δ = μ_NaNbO3(bulk) − μ_Na(bulk) − μ_Nb(bulk) − 3μ_O(gas) (4)

here, Δ is negative as NaNbO₃ is a stable compound. The elemental chemical potential of the constituent elements should never cross the value in their bulk/gaseous form, i.e., μ_Na ≤ μ_Na(bulk), μ_Nb ≤ μ_Nb(bulk), and μ_O ≤ μ_O(gas). Hence, the following relations are satisfied

μ_Na(bulk) + Δ ≤ μ_Na ≤ μ_Na(bulk) (5a)

μ_Nb(bulk) + Δ ≤ μ_Nb ≤ μ_Nb(bulk) (5b)

3μ_O(gas) + Δ ≤ 3μ_O ≤ 3μ_O(gas) (5c)

Chemical potential of Na (μ_Na(bulk)) and Nb (μ_Nb(bulk)) is calculated from the energy of an atom in bulk Na and Nb, respectively. For μ_O(gas) and μ_N the energy of an oxygen or nitrogen molecule has been calculated by taking the molecule at the center of a large cubic cell of dimension 20 Å × 20 Å × 20 Å (μ_O(gas)/N = 1/2E_O2/N2).

During the growth process of NaNbO₃, some undesired compounds may be formed as competing phases. To overcome this, it is important to consider some additional constraints.^55,56 For example, to prevent the formation of Na₂O, the constraint 2μ_Na + μ_O ≤ μ_Na2O should be applied. Similarly the formation of Na₂O₂, and Nb₂O₅ can also be avoided by imposing the restrictions; 2μ_Na + 2μ_O ≤ μ_Na2O2 and 2μ_Nb + 5μ_O ≤ μ_Nb2O5. These conditions can be expressed in two dimensional space defined by μ_Na and μ_O as shown in Fig. 5a, where the shaded/filled area indicates the range of chemical potential for the stable growth of NaNbO₃. Hence, to ensure the growth of NaNbO₃ without forming the above competing phases, the chemical potential values of the components should be restricted within the filled/shaded region of Fig. 5a.

Fig. 5 Chemical potential diagram representing the stable growth of NaNbO₃ (a). The filled area is the allowed chemical domain for NaNbO₃. Variation of formation energy for N-doped NaNbO₃ (b), W-doped NaNbO₃ (c), and (W, N)-codoped NaNbO₃ with configuration ‘Str. 1’ and ‘Str. 2’ calculated using 2 × 2 × 2 supercell (d), 2 × 2 × 3 supercell (e), and 2 × 3 × 3 supercell (f).

Fig. 5b shows the variation of calculated defect formation energies for N-doped NaNbO₃ as a function of oxygen chemical potential. The formation energy is highly positive under extreme oxygen rich condition. Although, it decreases towards O-poor condition, it is still positive. This indicates that the solubility of N into the crystal structure of NaNbO₃ is not so high. On the contrary, the formation energy for W-doped NaNbO₃ is highly negative under Nb-poor condition (Fig. 5c). In case of (W, N)-codoped NaNbO₃, the formation energy profiles have been shown as a function of both oxygen chemical potential and niobium chemical potential. As can be seen from Fig. 5d, the formation of codoped system with configuration ‘Str. 1’ is more favorable than ‘Str. 2’ under equilibrium condition. This is consistent with the inference drawn in the earlier section. However, (W, N)-codoped NaNbO₃ with predominate ‘Str. 2’ configuration can also be formed by utilizing modern technologies. Fig. 5d indicates that O-rich condition is more favorable over Nb-rich condition for the growth of (W, N)-codoped NaNbO₃. The interesting observation is that the doping of N is facilitated by the presence of W, which reduces the formation energy significantly.

3.5. Concentration effect

Since the concentration of dopant we considered in the above discussion is higher than experimentally achievable limit, we increase the supercell size to investigate the effect of dopant concentration on the calculated band gap of (W, N)-codoped NaNbO₃. Here, we have considered two larger supercell 2 × 2 × 3 (dopant concentration, N: 2.78%, W: 8.33%) and 2 × 3 × 3 (dopant concentration, N: 1.85%, W: 5.55%). In both the cases two different configurations have been considered, i.e., Str. 1 and Str. 2. All the structures have been fully relaxed using same computational parameters as discussed in Section 2, except the k-point mesh, which is 6 × 6 × 4 and 6 × 4 × 4, respectively. In case of 2 × 2 × 3 supercell, the distance between the dopant elements for Str. 1 and Str. 2 are 1.753 Å, and 7.227 Å, respectively. As can be seen from Fig. 5e, the nature of plot of defect formation energy calculated by using 2 × 2 × 3 supercell looks very much similar to that calculated by using 2 × 2 × 2 supercell. This justifies the consideration of 2 × 2 × 2 supercell. The calculated band gap in the respective cases are 3.11 eV, and 2.46 eV. As can be seen from Table 2, the relative shift of the VBM and CBM for Str. 1 of 2 × 2 × 3 case is very much similar to that of 2 × 2 × 2 case. However, for Str. 2 the downward shift of CBM is relatively higher in this case, which is responsible for the difference in the calculated band gap. To investigate this in details we analyze PDOS (Fig. 6a and a′), which indicate that relative contribution of W 5d orbital to the CBM decreases with lowering of the dopant concentration. In first case, the change corresponds to only lowering the dopant concentration, while for the latter case, it is the combined effect of both lower dopant concentration and increase of dopant–dopant distance.

Fig. 6 Density of states of (W, N)-codoped NaNbO₃ calculated using 2 × 2 × 3 supercell (a, a′) 2 × 3 × 3 supercell (b, b′).

In case of 2 × 3 × 3 supercell, we keep the dopant–dopant distance same as in case of 2 × 2 × 3 supercell. The defect formation energy profiles (Fig. 5f) follow similar trend as discussed for the previous two cases. The nature of DOS (Fig. 6b and b′) remains similar to that in presence of higher dopant concentration. As can be seen from Table 2, the band gap increases slightly. This is due to lowering of the dopant concentration. The important outcome from discussion in this section is that the band gap narrowing is quite significant (Str. 2) even at lower dopant concentration. This justifies the reliability of the present strategy in practical applications.

To investigate the effect of changing concentration of one type of dopant element, while keeping other fixed, we model (W, N)-codoped NaNbO₃ with different ratio of W and N. Here we have considered three different supercells, viz., 2 × 2 × 2, 2 × 2 × 3, and 2 × 3 × 3 and introduced N and W in different proportions. All the structures have been optimized by relaxation of both ionic positions and cell parameters using the same computational method as discussed in the earlier section. To find out the most stable configuration, we have considered different lattice sites in each case. Similar to the previous discussion, the configuration with N and W directly attached to each other is designated as ‘Str. 1’, and the configuration where N and W are located far away from each other is designated as ‘Str. 2’. Electronic structure calculations have been carried out for both types of configurations. As can be seen from left column of Fig. S1–S3† that the Fermi level is located in the CB region (Fig. S1a, S1a′, S2a, S2a′, S3a, and S3a′†), similar to the case of W-doped NaNbO₃ (Fig. 3b′). This is due to the presence of excess electron in the system arising from higher proportion of W in comparison to N. On the other hand, Fig. S1b, S1b′, S2b, S2b′, S3b, and S3b′† show the presence of partially occupied impurity states. This is due to electron deficiency in the system, that arises due to higher proportion of N in comparison to that of W.

The details of the change in band gap, and relative shifting of band edges for different concentration ranges of the dopant pair have now been presented in Table 2. The calculated band gap of the codoped system with dopant concentration (N: 4.17%, W: 12.5%) are 3.03 eV and 2.64 eV for Str. 1 and Str. 2, respectively. An increase in the concentration of W to 25% keeping N concentration fixed, reduces the band gap to 2.18 eV and 1.64 eV for Str. 1 and Str. 2, respectively. The band gap changes to 2.80 eV and 2.28 eV for Str. 1 and Str. 2, respectively when the concentration of N increases to 8.35%, but W concentration is kept fixed at 12.5%. In the second set of studies, it has been shown that the band gap values for the codoped system are 3.11 eV and 2.46 eV for Str. 1 and Str. 2, respectively at dopant concentration of N: 2.78%, and W: 8.33%. The calculated band gap values are found to be equal to 2.47 eV and 2.28 eV, for Str. 1 and Str. 2, respectively on increasing the W concentration to 16.67%, keeping N concentration fixed at 2.78%. The calculated band gap values are to 3.19 eV and 2.46 eV when the N concentration is increased to 5.55%, but W concentration is kept fixed at 8.33%. In the third set of studies, we have seen similar changes in the band gap if the W concentration is varied from 5.55% to 11.11%, keeping the N concentration fixed at 1.85%, as well as by varying the N concentration with the W concentration kept fixed at 5.55% (Table 2). A critical inspection towards relative shifting of CBM and VBM with respect to that of undoped NaNbO₃ indicates that for all the dopant concentration ranges, the codoped system should show overall water splitting property, except for the case of 4.17% N and 25% W with Str. 2 configuration.

The above discussion indicates that using W and N in different ratio results into a reduction in the band gap by considerable extent in most of the cases. So, one may think of using different ratio of the dopant pair over equal ratio, as the more preferable choice for larger enhancement of visible light activity. But, it is known that improving visible light activity is only an essential condition, and it is not a sufficient one for achieving enhanced photocatalytic activity. Since unequal ratio of W and N results into the formation of charge noncompensated system, vacancy defects are formed. Thus, such systems are expected to show lower photoconversion efficiency.

Based on this analysis, it can be concluded that the dopant concentration corresponding to N: 2.78%, and W: 8.33% with Str. 2 configuration is more preferable for enhancing the photocatalytic activity of NaNbO₃ towards visible light driven water splitting process.

3.6. Band edge alignment

A material to be active for overall water splitting must satisfy the thermodynamic criteria, i.e., the CBM should be above the H⁺/H₂ level for spontaneous hydrogen evolution and the VBM should be below the H₂O/O₂ level for oxygen evolution. Hence, it is essential to determine the absolute positions of the band edges of the modified catalyst to check its applicability towards water splitting process. Here, we first calculate the absolute position of the CBM (E_CBM) of undoped material using Xu et al.,⁵⁷ viz.,

Then the absolute position of the VBM (E_VBM) can be obtained as

E_VBM = E_CBM − E_g

here, E_g indicates the band gap of NaNbO₃, and E₀ = −4.5 eV, is the scaling factor for relating the reference electrode potential with absolute vacuum scale. χ_Na, χ_Nb  and  χ_O stand for absolute electronegativity, obtained from Pearson electronegativity table. The calculated CBM for NaNbO₃ is 0.67 eV more negative than the hydrogen reduction potential and the VBM is 1.37 eV more positive than the water oxidation level. Thus, NaNbO₃ fully satisfies the thermodynamic criterion for overall water splitting, which is consistent with the experimental observation. For (W, N)-codoped NaNbO₃ the CBM and VBM values are obtained by calculating the relative shift of the band edges with respect to undoped NaNbO₃. In Fig. 7, we have shown the band edge alignment of the codoped system with ‘Str. 2’ configuration, for which band gap narrowing is significant. The VBM is 0.80 eV below the H₂O/O₂ level and the CBM is 0.61 eV above the H⁺/H₂ level, which is very close to that of the undoped NaNbO₃. Thus, the present strategy of band gap narrowing retains the overall water splitting property of NaNbO₃. More interestingly, the reducing behavior at the CB for the codoped system is expected to be similar in comparison to that of undoped NaNbO₃, which is very much crucial point while developing hydrogen evolving catalyst. We also consider the band edge alignment for the codoped systems with lower dopant concentration. As can be seen from Fig. 7, in both the cases the band edges are in appropriate positions to generate hydrogen as well as oxygen during water splitting. This justifies the codoping of (W, N) pair as an effective strategy for improving the visible light photocatalytic activity of NaNbO₃ for practical scenario.

Fig. 7 Band edge alignment of undoped and (W, N)-codoped NaNbO₃ under different dopant concentration.

4. Conclusion

In this theoretical study, we systematically investigate the effect of doping in enhancing the visible light photocatalytic activity of NaNbO₃. The computational parameters used in this calculation successfully reproduce the experimentally reported band gap of NaNbO₃. Although, doping with only N is able to reduce the band gap, localized acceptor states may suppress the photoconversion efficiency. On the other hand, W introduces donor state just below the CB, which may affect the hydrogen evolution property drastically. Interestingly, in presence of (W, N) pair, both the acceptor states and donor states are completely passivated. Formation of clean band structure for (W, N)-codoped NaNbO₃ ensures good photoconversion efficiency. The calculated band gap for (W, N)-codoped NaNbO₃ is in the desirable range to show photocatalytic activity in the visible region even at lower dopant concentration. More interestingly, the band gap narrowing in the present strategy is mainly controlled by elevation of VBM. Thus, codoping of (W, N) pair retains the overall water splitting property of NaNbO₃, which is manifested in the appropriate band edge alignment of both the VBM and CBM with respect to water redox levels. Presence of W not only facilitates introduction of N by reducing the formation energy, but also minimizes the spontaneous formation of vacancy defects by forming charge compensated system. Hence, based on the present theoretical calculation it can be predicted that codoping with N and W is one of the effective approaches to improve the visible light photocatalytic activity of NaNbO₃.

Acknowledgements

We thank the BARC Computer Centre for providing the high performance parallel computing facility. We also thank Dr B. N. Jagatap for his encouragement and support. S. K. G. is thankful to Department of Atomic Energy for the Raja Ramanna Fellowship. It is pleasure to acknowledge Dr K. Srinivasu for his valuable help and support. P. M. would like to acknowledge Dr A. U. Sonawane for his encouragement and support.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra15024a

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