Structural and electronic properties of 2D oxides orthorhombic V2O5 and MoO3 Tilak Das, Sergio Tosoni, and Gianfranco Pacchioni*
Universita’ degli Studi Milano-Bicocca, Dipartimento di Scienza dei Materiali, via R. Cozzi, 55 20125 Milano, Italy Email:
[email protected] KEYWORDS: Density functional theory, First-principles calculations, Van der Waals force, Layered oxides, Band-gap, Thermochemistry, Dielectric constant, Hubbard U, Spin-orbit, Monolayer, Bi-layer, Tri-layer.
ABSTRACT: The structural and electronic properties of the bulk, mono and few layers of layered oxides V2O5 and MoO3 are studied from the first-principles density functional theory based calculations using plane-wave and pseudo-potential to achieve the convergence of the physical properties in bulk and its two dimensional geometry. In our calculations, we have chosen Van der Waals (vdW) forces correction along with spin-polarized PBE-GGA functional and Hubbard U corrections, with careful checking of experimental geometry, band-gap, static dielectric constant and formational enthalpies of these two layered oxides. The mono-, bi- and tri-layers are cleaved along the known stable crystallographic orientation along and for V2O5 and MoO3, respectively. The different films were chopped from their respective inter-layer spacing (so called vdW spacing) and we have found that at
least three layers are needed for both layered oxides to get conversed properties like the bulk phase of these materials. Each of the thin-films retain as an indirect band-gap system in both oxides as like the bulk. Inclusion of spin-orbit has marginal impact on these predictions.
Introduction Inorganic semiconductors specially the oxides for example TiO2, ZnO, WO3, BiVO4, V2O5 and MoO3 are studied broadly for their unique catalytic, optical and electronic properties, in search for the cheap and environment friendly catalysts either active in visible or ultra-violet part of the solar light.1-3 In this current scenario of advanced and accurate experimental facilities era where the materials with lower dimensionality (for example two dimensional, 2D) has got immanence importance since it can be accurately exfoliated up to few tens of angstrom width films from their layered structure, for example transition metal dichalcogenides (TMDs) or layered oxides like vanadium pentoxide (V2O5), molybdenum trioxide (MoO3) are very much crucial as an excellent member of non-oxide and oxide family, respectively. Thus, in the post graphene discoveries, the growing interest of 2D (oxide) films exfoliation from these layered oxides can open up new domain for more suitable application of these oxide materials.4,5 For example very recent experimental research provides the possible liquid exfoliation of MoO3 nanosheets and it has been found extremely suitable for supercapacitor energy storage applications.6 Thermodynamically stable orthorhombic phase (also known as α-phase) of these two transition mental oxides with d0 orbital have been widely studied from experimental and Density Functional Theory (DFT) based tools due to their excellent opto-electronic and photo- and electro-chemical properties useful for catalysis.7,8 Recently, searching of metal-ion-battery electrodes, V2O5 is known to be very useful for the Li-ion battery (LIB) applications with theoretical capacity reached up to 294 mA h g -1, which is expected to be better than the other conventional transition metal cathode material LiMO2 (M: Cr, Mn, Ni).10 On the other hand MoO3 is also very well known for technological applications as an inorganic photochromism,12 electrochromism13 material, catalysis,14,15 and sensing16 activities.
The structural similarities of these oxides not only from their crystal symmetry type but also their unique layer arrangement connected via inter-layer weak Van der Waals interaction. The unique difference belongs in their metal-oxygen polyhedra formation, in one case (V2O5) each V atom is connected with five oxygen atoms forms a square pyramid and for the other one (MoO3) each Mo atom connected to six oxygen atoms forming an octahedra. These pyramids (octahedrons) connected via edge sharing oxygen atoms and elongated as a chain along crystallographic xyplane (xz-plane). Both of these bulk crystals have total three types of oxygen namely apex vanadyl (molybdenyl) oxygen Ov (Om), and chain oxygen Oc, and bridging oxygen between the chains, Ob. The minimum inter-layer spacing (the so called Van der Waals spacing) (d) between layers is wave-like (zigzag) formed by apeak-oxygen atoms arrangement, which is slightly lower for V2O5 (2.321Å) than MoO3 (2.644Å), in their respective experimental bulk structure. Alongside with the large number of experimental studies of electronic and optical properties of these layered oxides V2O5 and MoO3, either in bulk or thin-films geometry and their different types of oxygen vacancy models, even more numbers of DFT theoretical studies are available, to commensurate with the experimental findings. Thermodynamically the stable surface of V2O5 is (001)7 and for MoO3 it is (010)4, and in both material the vdW spacing separates each single layer on the respective crystallographic direction. To the best of our knowledge, liquid exfoliation technique is used by Rui et al. 2012, where the authors have reported for the first time V2O5 2D nanosheets of width 2.1 to 3.8nm and remarkable power density achieved using these nanosheets as a cathode material in LIBs.9 Also, many other routes for example hydrothermal, solvothermal and wet/dry exfoliation technique used for V2O5 nano structures growth are tabulated elsewhere.10 Whereas two theoretical studies available for monolayer only. In one case, authors studied using PW91-GGA+U 11 functional in periodic DFT calculations, which shows the impact of different U parameter values on V(d) and related geometry and electron localization. The other one uses QSGW calculations (over LDA ground state)30 on monolayer, and predicted a large band-gap 4 eV. Possibly, there is no study from first-principles on the layer dependent properties of this V2O5, in our knowledge. On the other side, the exfoliation of monolayer of MoO3 has been reported by Molina-Mandoza et al. 2016,4 where they have not seen any blue shift of band-gap from their experimental absorption spectra and PBE-GGA calculation of band-structure, going from monolayer to the
bulk. Whereas, the latest discovery of the Liu et al. 20184 contradicts that with their experimental preparation of micro to nano size crystals of MoO3 and optical absorption edge to predict the optical band-gap, which shows a clear blue shift (~1.5 eV) going from the 4 to 8 layers to bulk phase of MoO3. The authors also did PBE-GGA-D2 periodic DFT calculations of bulk and 4 layers models with compressive and tensile strain to explain their experimental findings. The theoretical study on the bulk, monolayer and nano-ribbons are done independently on MoO3, using PBE-GGA-D2+U DFT functional, where authors have shown a quite small increase of indirect band-gap of bulk (1.71 eV) to monolayer (1.73 eV).17 Similar to V2O5, here also we did not find any theoretical literature that overcome the current layer dependent doubts on MoO3 in the nanoscale regime. Thus, we propose here another route to better understand these layered oxides in bulk and films geometries, in broader sense. This is in fact the core point that has been discussed in this present manuscript i.e. choice of suitable theoretical tool for calculating and predicting properties of these Van der Waals oxides V2O5 and MoO3 towards a best possible matching with experimental parameters and computational cost.
Choice of Computational Methodology and Approaches The existing literatures on theoretical studies of these oxides, where most of them have used the calculated band-gap a parameter to be reproduced like experimental one in general, and some discussed the band-gap as well as lattice parameters and geometry. At least one literature have discussed the formation enthalpy from the possible redox pairs of V2O5/VO2/V2O3 and MoO3/MoO2 without any care about the geometry of the bulk phases. 28 Thus, it is probably a crucial issue to take cares all these physical parameters along with calculated static dielectric constants during the choice of the DFT functional, in a first-principles approach. Ground state search calculations were performed within density functional theory of KohnSham18 along with Perdew-Burke-Ernzerhof (PBE-GGA) formulation19 of Generalized Gradient Approximation (GGA) as implemented in the plane-wave pseudopotential code Vienna Ab-initio Simulation Package (VASP).20,21 The valence electrons are approximated with Projector
Augmented Wave (PAW) method22 with the choice of plane-wave cut-off 600 eV and core electrons fixed. Total 13 valence electrons for V(3s23p64s23d3) and 14 electrons for Mo(4s24p65s24d4) are taken in pseudopotential choice and in both cases the O atom is considered with O(2s22p4) valence configuration. All calculations were done using spin-polarization with or without spin-orbit coupling (SOC), which is considered via perturbation using scalar-relativistic wave-function of the valence states. We have seen that the ground state energy lowered by 10 (V2O5) to 100 (MoO3) meV per formula unit with inclusion of SOC. Since, the ground state DFT+SOC was not able to consider the inter-layer interaction and correct description of out-ofplane lattice parameter and vdW spacing of these oxides, we have considered the long-range dispersion energy correction in semi-empirical approach of the given formulation of 3rd generation of dispersion force correction by Grimme et al. 2010 & 2011 as implemented in VASP code i.e. the DFT-D3 method.23,24 The convergence of the total energy and HellmannFeynman forces on the atoms was con-firmed with criteria less than 1×10-8 and 3 meV/Å , respectively using a Monkhorst-Pack k-mesh grid 4×6×5 (5×4×6) for V2O5 (MoO3). The full optimized bulk crystal structure of both the oxides was used for mono or few-layers supercell model creation including vacuum length more than 20Å. It is well known the limitation of the ground state DFT functional for poor description of the strongly correlated transition metal d-orbital or oxygen p-orbital electrons and hence poorer prediction of the structural parameters and band-gap of transition metal oxides.25,26 Despite the expensive computational approach using hybrid functional or dynamical mean-field approach, the “on-site” Hubbard U correction for the correlated electrons turns out to be one suitable and cheap methodology for these oxides and their thermochemistry prediction.28 Indeed, here we have chosen the U as formulated by Dudarev et al.27 and the band-gap and formation enthalpy of these two oxides are calculated to find the optimum value of U parameter.
Calculated Fundamental Band-gap from Full Optimized Bulk Structure U parameter for bulk V2O5: The bulk crystal structure of V2O5 belongs to orthorhombic space group P mmn, an insulator with band-gap 2.35 eV,28 assigned by experimental lattice parameters a = 11.512Å, b = 3.564Å, c = 4.368Å.29 The choice of U parameter for the V(3d) is quite
extensive ranging from 2.3 to 6.6 eV to get the experimental band-gap, while the recent quasiparticle self-consistent GW calculation prediction is an insulator with 4 eV band-gap.30 The representative of the V2O5 bulk phase structure is given in Figure 1. In the panel [a] the unit cell is marked with black solid line and different optimized angles are marked along with different atoms (blue large balls are V, and red small balls are O atoms). Whereas, in panel [b], the VO5 square pyramids are shown which forms a chain along x-axis, separated by wave-like vdW inter-layer spacing marked with d. Each of this laminar is formed by VO5 is one monolayer for V2O5.
Figure 1: Full optimized bulk crystal structure of α-V2O5 from PBE-GGA-D3+SOC+U functional with effective U value 3.5 eV on V(d).
The first periodic DFT calculations on the V2O5 using U = 6.6 eV by fitting valence and conduction band edges from experimental one from Laubach et al.31 which turns out to be inappropriate as demonstrated later by Scanlon et al.32 In fact, Scanlon et al. used variable U
values depending on the reduced condition of V2O5 and hence new U values for better description of band-edges around the band-gap for the study of Li intercalation in LIBs studies. Indeed, authors did not mention clearly even for the pristine bulk phase the choice of U value, which gives the suitable experimental band-gap 2.26 eV compared to 2.35 eV. But, in our point it is not enough since the c lattice was overestimated by nearly 10% and thus ruled out. A similar recent studies by Jovanović et al.33 found that a U= 6 eV for better understanding of the transition metal ion doping in V2O5, since in the pristine bulk phase calculated band-gap (2.3 eV) was excellent and c parameter was only 4% higher than the experimental one. But, such large U value effects on the other physical properties like formation enthalpy or dielectric function for the pristine phase has not been pointed out. The Mg ion intercalation in different phases of V2O5 is considered using GGA+U method with U = 3.1 eV without any hints on the bulk geometry after full optimization of the structures.34 Here, we took help of calculated formation enthalpy of the V2O5 and MoO3, as well as dielectric constant and thus fix the U value along with the reasonable band-gap and pristine bulk geometry in our PBE-GGA-D3+SOC+U approach an finally, in V2O5 bulk phase we have chosen the effective value of U= 3.5 eV for V(d). We tabulated the calculated structural parameters and band-gap values in the upper panel of Table 1, compared to experimental data for V2O5. The dispersion energy correction via vdW-D3 formalism is quite crucial, since the vdW spacing is corrected by 0.3Å compared to ground state PBE-GGA calculated value, and the out-of-plane lattice parameter is well described compared to experimental data.
Figure 2: Full optimized bulk crystal structure of α-MoO3 from PBE-GGA-D3+SOC+U functional from applied effective U value 5 eV on O(p)
U parameter for bulk MoO3: Similar, ambiguity about the choice of the U parameter is observed for the MoO3 bulk phase study. The U value was applied on the 4d of the Mo, which varies from 4.3 to 8.6 eV from studies to studies. The crystal structure of α-MoO3 is as similar to V2O5 is centro-symmetric with orthorhombic symmetry and space group in Pbnm. It is an wide gap insulator (2.0-3.0 eV) affined with lattice parameters a = 3.963Å , b = 13.860Å and c = 3.697Å.39,40 The representative of the MoO3 bulk phase structure is given in Figure 2. In the panel [a] the unit cell as marked with black solid line and different optimized angles are marked along with different atoms (grey large balls are Mo, and red small balls are O atoms), whereas, in panel [b], the MoO6 octahedrons are shown forming a chain along z-axis, separated by zigzag vdW spacing d.
The first DFT+U (= 6.3 eV) calculation by Coquet and Willock35 on MoO3 without any dispersion energy correction surprisingly led to quit good lattice parameter for the bulk phase, with calculated band-gap 2.1 eV. Whereas, from the formation enthalpy based calculations using GGA+U method by Lutfalla et al.27 on MoO3 redox pairs, predicts a largest value of the U= 8.6 eV parameter for Mo(d) where, the c-parameter was extremely overestimated (4.5Å) larger). Recently, Akande et al.36 has calculated the lattice parameters of α-MoO3 using U= 4.3 and 6.3 eV on Mo(d), and an excellent agreement is achieved, whereas the band-gap shows almost no changes than the GGA one which remain around 2 eV even with larger U values. Thus, they have used periodic hybrid functional calculation using HSE0637,38 functional (over GGA ground state) and reached to closer band-gap value 3.1 eV, as like the experimental one 3.0 eV.39 Finally, Inzani et al.41 have checked many possible Van der Waals density functional theory (vdW-DF), along with U correction on Mo(d). They have concluded that even though the geometry was better described with vdW-DF2 functional and almost no effect on the band-gap using U values from 2 to 8 eV on Mo(d). What is quite surprise is that the effect of U on Mo(d) very much negligible as we see in all previous studies and this is possibly due to the fact that Mo being in lower in periodic table row, the d electron correlation becomes lower. Thus, consideration of correlation effect on the O(p) of MoO3 could be necessary, maintaining the O2 molecule’s binding energy. In fact, we have done series of U parameter check from 5 to15 eV for MoO3 either over Mo(d) or O(p), separately or combined using PBE-GGA-D3+U or functional (details are in supporting data Section S1) and reached to a conclusion that maintaining the O2 dissociation energy, a reasonable indirect bulk phase band-gap, formation enthalpy of bulk MoO3, better lattice geometry and good static dielectric constant can be reproduced for MoO3 at U= 5 eV on O(p). More details discussion is given in the next subsections. We have tabulated the calculated geometry and band-gap values in the lower panel of Table 1, and compared with experimental data for MoO3. In this case, the vdW-D3 correction is stronger than V2O5, which improves the vdW spacing by nearly 0.8Å, and out-of-plane lattice parameter is best described.
Table 1: Calculated full optimized bulk structure parameters of V2O5 and MoO3 from PBE-GGA and PBE-GGA-D3+SOC+U functional and compared to experimental data. In the parentheses the % changes of the values w.r.t. experimental.
Orthorhombic α-V2O5 (Pmmn) Parameters
PBE-GGA
PBE-GGA-D3+SOC+U
a(Å)
11.551
11.628 (+1.0%)
11.512
b(Å)
3.567
3.615 (+1.5%)
3.564
c(Å)
4.716
4.359 (-0.3%)
4.368
vdW Spacing, d (Å)
2.637
2.280 (-1.8%)
2.321
V-Ov (Å)
1.591
1.602
1.585
V-Ob (Å)
2×1.789
2×1.798
2×1.780
V-Oc (Å)
2×1.889
2×1.902
2×1.878
1×2.044
1×2.034
1×2.021
◦
149.3 (+0.7%)
141.7
◦
1.98
