First-Principles Calculation of MoO2 and MoO3 Electronic and Optical Properties Compared with Experimental Data

MoO3 and MoO2 systems have attracted particular attention for many widespread applications thanks to their electronic and optical peculiarities; from the crystallographic point of view, MoO3 adopts a thermodynamically stable orthorhombic phase (α-MoO3) belonging to the space group Pbmn, while MoO2 assumes a monoclinic arrangement characterized by space group P21/c. In the present paper, we investigated the electronic and optical properties of both MoO3 and MoO2 by using Density Functional Theory calculations, in particular, the Meta Generalized Gradient Approximation (MGGA) SCAN functional together with the PseudoDojo pseudopotential, which were used for the first time to obtain a deeper insight into the nature of different Mo–O bonds in these materials. The calculated density of states, the band gap, and the band structure were confirmed and validated by comparison with already available experimental results, while the optical properties were validated by recording optical spectra. Furthermore, the calculated band-gap energy value for the orthorhombic MoO3 showed the best match to the experimental value reported in the literature. All these findings suggest that the newly proposed theoretical techniques reproduce the experimental evidence of both MoO2 and MoO3 systems with high accuracy.


Introduction
The molybdenum oxides family includes compounds characterized by different Mo:O stoichiometries and polymorphs. Among them, the most common are MoO 3 and MoO 2 , which differ in their chemical structure as well as in their electronic and optical properties [1,2]. Molybdenum oxides are widely used as redox-active catalysts in organic chemistry; for example, they act as catalysts in the oxidation reaction of methane or propane [3,4]. Moreover, the ability of the metal center to be involved in the redox process, together with the numerous oxidation states, and the four, five, or six coordination modes of molybdenum have attracted particular attention even for many other widespread applications such as sensors [5] and solar cells [6].
As for WO 3 [7], MoO 3 is also well known to have pronounced chromism-it is able to undergo color change under proper stimulations. Molybdenum oxide coloration can be determined by applying a potential (electrochromism) [8], by optical irradiation (photochromism) [9], and by changing the temperature (thermochromism) [10].
The doping of MoO 3 with different elements and the creation of an oxygen vacancy inside the crystal lattice have enhanced the applicability of this material to electronic and optical devices. As a matter of fact, doping with special substituents allows for the controlling and tuning of the carrier concentration and band structure peculiarities [11,12]. verify the reliability of the chosen method, the electronic properties of MoO 2 and MoO 3 were also calculated using the Generalized Gradient Approximation (GGA) PBEsol and hybrid HSE06 functionals. Both these methods are known to be very accurate for solid state oxide systems. In fact, both these materials have been already studied by the theoretical model with different methodologies. Authors such as Chen et al. [33], Rozzi et al. [34], and Eyert and coworkers [35,36] used the ab initio DFT based on local density approximation (LDA); Coquet and Willock [37] used the generalized gradient approximation (GGA) with the Hubbard correction term to understand the effect of oxygen vacancies while remarking on the importance of such a methodology for complex electronic systems. Scanlon et al. [2] used the generalized gradient approximation (GGA) with PBE in the plane wave basis set to study both MoO 3 and MoO 2 . More recently, Gulomov et al. [38] used and compared two DFT approaches, namely, PBE and HSE06 functionals, calculating in both cases the band gap energy of MoO 3 that was found to be, in the best case from HSE06 calculation, 3.027 eV.
The results obtained were confirmed and validated by comparison with literature data and our recorded experimental findings. In particular, the calculated density of the electronic state (DOS) was in good agreement with that in the literature, and the frontier orbitals detection, in terms of Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbitals (LUMO), confirmed the dielectric-to-conductor transition moving from MoO 3 to MoO 2 . Moreover, the calculated optical spectra were compared with experimental findings, showing very good agreement; finally, the band-gap energy calculated for the dielectric α-MoO 3 best matched the one reported experimentally rather than the other theoretical DFT-based studies. The use of our proposed computational method on Mo-based materials could clarify the interesting change in the properties of the systems, better describing the nature of each Mo-O bond in MoO 2 and MoO 3 .

Theoretical Modeling and DFT Calculation
The Quantum Atomistic Toolkit (ATK) atomic-scale modeling platform was used to model all polymorphs and to perform all calculations [39]. The monoclinic MoO 2 (P2 1 /c) and the orthorhombic MoO 3 (Pbmn) polymorphs were modelled starting from the Materials Project database [40] and optimized. The electron basis was expanded in linear combination using the atomic orbital (LCAO) method for Mo and O entities resembling the SIESTA formalism [41]. In comparison with other basis sets, the whole electron LCAO calculations describe accurately electronic distributions both in the valence and the core region with a limited number of basis functions. All simulations were carried out using the MGGA density functional called SCAN for the electron exchange-correlation energy [42]. It is described as follows (1): where n is the electron density, ∇n(r) is its gradient, while t (r) is the positive orbital kinetic energy density. This latter term is the additional one to the canonical GGA approach, and it is determined by (2): where ϕ i (r) are the Kohn-Sham orbitals. For each atom, the ionic cores were represented by norm-conserving (NC) PDj pseudopotentials [30]. To model the systems, the periodic boundary conditions (PBCs) were used along all axes; in this way, it was possible to avoid problems with boundary effects caused by the finite size and to reduce the calculation time while maintaining high accuracy. The energy cut-off was fixed at 1200 eV, and the Brillouin-zone integration was performed over a 15 × 15 × 15 k-points grid. The optical properties of the MoO x structures were determined by two components of the dielectric function ε(ω) = ε r (ω) + iε i (ω).
The imaginary part ε i (ω) of the dielectric constant was determined from Equation (3) [43]: where HOMO, LUMO, ω, Ω, W k , ρ ij were the valence band, conduction band, photon frequency, volume of the lattice, weight of the k-point, and elements of the dipole transition matrix, respectively. The real part of the dielectric constant was obtained with Equation (4): Finally, the refractive index (n) and extinction coefficient (k) of MoO x systems were calculated as follows using Equations (5) and (6): Finally, with the aim of comparing the simulated results between them and then to validate the computational approach, the electronic properties of MoO 2 and MoO 3 were calculated again using Generalized Gradient Approximation (GGA) PBEsol and hybrid HSE06 functionals, maintaining the same approach in relation to the basis sets and pseudopotentials adopted.

Experimental Section
Amorphous MoO 3 and MoO 2 thin films were deposited at room temperature by e-beam evaporation using MoO 3 and MoO 2 pellets (Pi-KEM 99.99% purity) in a Leybold SYRUS pro 710 on n-type silicon (100). The n-type Si (100) wafers were cleaned before the deposition using a standard RCA cleaning procedure. The nominal thickness of these MoO 3 and MoO 2 films targeted was 150 nm. After the deposition, MoO 3 and MoO 2 were annealed in N 2 at 400 • C for 30 min in order to fully crystallize them.
Spectroscopic ellipsometry [44][45][46] was performed on the 150 nm-thick MoO 2 film and on the 150 nm-thick MoO 3 deposited on n-type silicon (100). The measurements were performed at a 70-degree incidence using a Woollam M2000 ellipsometer in the UV-VIS-NIR spectral range. The collected ellipsometry data were analyzed considering a four-layer optical model, i.e., air/MoO 3 /interfacial oxide/silicon, and for this purpose Woollam's CompletEASE software was used.

Geometrical and Lattice Parameters
In Figure 1 are reported the structures of both MoO 3 and MoO 2 from xy, yz, and xz planes, while in Table 1 are listed the values obtained after the geometry optimization for both the examined molybdenum oxides in terms of crystallographic lattice constant (the coordinate files of the optimized geometries are reported in the Supplementary Material). After the optimization of the geometry, the lattice constants of α-MoO 3 were (a) 3.909 Å, (b) 13.855 Å, and (c) 3.681 Å, and α = β = γ = 90 • . MoO 2 adopted a monoclinic crystallographic arrangement characterized by space group P2 1 /c, with the lattice constant of (a) 5.625 Å, (b) 4.872 Å, and (c) 5.645 Å, and α = γ = 90 • , and β = 120.5 • . These values were in good agreement with the previous literature [2,[47][48][49], confirming the ability of our methodology to reproduce both MoO x systems.        Figure 3B). These results perfectly match what was observed by other authors previously [35,36].  With the aim of testing the effective reliability of the SCAN functional, the MoO structure was calculated again using the GGA PBEsol and the hybrid HSE06 funct (Figure 4). The results were compared with the those obtained with the MGGA app The indirect bandgap detected with PBEsol was 2.61 eV, which means that the Ge  Figure 3C), and, to the best of our knowledge, this value is the one that best matches the experimental one of 3.2 eV [12], also considering other theoretical studies [2], where a band gap of 3.027 eV was found with the HSE06 method [38]. Similarly to the MoO 2 , even for MoO 3 the PDOS calculation showed that the valence band derived from the oxygen 2 p states with a small contribution of the d state of Mo. Above the Fermi level, in the conduction portion, the Mo 6 d states determined the principal trend with a minor involvement of the O states ( Figure 3D). These results are in line with previous literature reports [2].
With the aim of testing the effective reliability of the SCAN functional, the MoO 3 band structure was calculated again using the GGA PBEsol and the hybrid HSE06 functionals (Figure 4). The results were compared with the those obtained with the MGGA approach. The indirect bandgap detected with PBEsol was 2.61 eV, which means that the Generalized Gradient Approximation tended to underestimate the energy gap between valence and conduction bands. Using HSE06, the incorporation of a portion of the exact exchange from Hartree-Fock theory allowed us to obtain an indirect bandgap value of 3.03 eV, which is also in line with other previously conducted studies [38]. In any case, the SCAN functional was found to be the most accurate for the prediction of electrical properties of Mo-O-based systems, and for this reason, all the next calculations reported were performed using this MGGA approach. With the aim of testing the effective reliability of the SCAN functional, the MoO3 band structure was calculated again using the GGA PBEsol and the hybrid HSE06 functionals (Figure 4). The results were compared with the those obtained with the MGGA approach. The indirect bandgap detected with PBEsol was 2.61 eV, which means that the Generalized Gradient Approximation tended to underestimate the energy gap between valence and conduction bands. Using HSE06, the incorporation of a portion of the exact exchange from Hartree-Fock theory allowed us to obtain an indirect bandgap value of 3.03 eV, which is also in line with other previously conducted studies [38]. In any case, the SCAN functional was found to be the most accurate for the prediction of electrical properties of Mo-O-based systems, and for this reason, all the next calculations reported were performed using this MGGA approach.  The HOMO-LUMO visualization of both MoO x materials was also reported to better indicate the metallic and dielectric behaviors of MoO 2 and MoO 3 , respectively. Starting with the first one, LUMO was evidently present in correspondence of the Mo atoms, even if it was possible to easily identify it also on the O atoms in a symmetrical manner by following the space group of the unit cell ( Figure 5A). This confirmed that the largest contribution in the bands beyond the Fermi level came from the 4 d electrons of Mo, and only a small contribution was associated with the 2 p electrons of O. In a parallel way, HOMO followed a symmetric trend showing a higher localization on O atoms and moving again with a lower contribution on Mo entities. This behavior is in perfect agreement with the DOS plot, since the highest contribution in the bands below the Fermi level arose from the 2 p electrons of O, and only a very small participation was attributed to the 4 d electrons of Mo ( Figure 5B). In any case, HOMO and LUMO clouds complemented each other in the MoO 2 structure, confirming the metallic behavior and the bonding homology between Mo and O entities. with a lower contribution on Mo entities. This behavior is in perfect agreement with the DOS plot, since the highest contribution in the bands below the Fermi level arose from the 2 p electrons of O, and only a very small participation was attributed to the 4 d electrons of Mo ( Figure 5B). In any case, HOMO and LUMO clouds complemented each other in the MoO2 structure, confirming the metallic behavior and the bonding homology between Mo and O entities. Focusing on MoO3, peculiar characteristics were detected. In this case, LUMO was again predominantly localized on Mo entities, but only axial O atoms showed a small contribution ( Figure 5C). This means that the Mo-O connections exhibited both ionic (the charge transfer from 2 p orbital of oxygen to molybdenum) and covalent (charge accumulation in the region of Mo-O) components, and the MoO3 bonds were not equal. Furthermore, HOMO was particularly localized on the O atoms in an asymmetric way ( Figure  5D). This means that the valence band came from the 2 p electrons of O and only in a small part from 4 d electrons of Mo, while the opposite was observed for the conduction bands.

Experimental and Theoretical Optical Spectra
In order to confirm the ability of the DFT methodology proposed herein to describe the peculiarities of both MoO2 and MoO3, the experimentally recorded optical spectra were compared to the simulated ones. The evaluation regarded (i) the refractive index, Focusing on MoO 3 , peculiar characteristics were detected. In this case, LUMO was again predominantly localized on Mo entities, but only axial O atoms showed a small contribution ( Figure 5C). This means that the Mo-O connections exhibited both ionic (the charge transfer from 2 p orbital of oxygen to molybdenum) and covalent (charge accumulation in the region of Mo-O) components, and the MoO 3 bonds were not equal. Furthermore, HOMO was particularly localized on the O atoms in an asymmetric way ( Figure 5D). This means that the valence band came from the 2 p electrons of O and only in a small part from 4 d electrons of Mo, while the opposite was observed for the conduction bands.

Experimental and Theoretical Optical Spectra
In order to confirm the ability of the DFT methodology proposed herein to describe the peculiarities of both MoO 2 and MoO 3 , the experimentally recorded optical spectra were compared to the simulated ones. The evaluation regarded (i) the refractive index, which is useful to understand the ability of the matter to bend or refract the light that passes through the material itself; (ii) the extinction coefficient, which represents the capability of the matter to absorb the light; (iii) the real part (ε r ) of the dielectric function, which describes the ability of the matter to interact with an electric field without absorbing energy; and (iv) the imaginary part (ε i ) of the dielectric function, which describes the ability of the matter to permanently absorb energy from a time-varying electric field; the spectra were reported in the function of the energy of the applied (and simulated) electric field expressed in eV. The MoO 2 optical spectra, simulated and recorded experimentally, are reported in Figure 6. From the comparison between the theoretical curve (in red) and the experimental (black) it is possible to notice good agreement in all four reported cases, with a small overestimation in the calculated spectra in terms of the extinction coefficient and the imaginary part of the dielectric constant. The reason for the small discrepancies between calculated and experimental evidence may be due to some small differences in the three-dimensional systems. In fact, MoO 2 and MoO 3 were considered in simulations as single crystals, while polycrystalline structures can be obtained during fabrication. These differences in microstructures of the materials were reflected in the optical properties observed and plotted together. Overall, good agreement was observed in the position of most critical points in the optical constants spectra. Moreover, when a disorder occurred, a change in the magnitude of the optical properties was expected.
pability of the matter to absorb the light; (iii) the real part (εr) of the dielectric function, which describes the ability of the matter to interact with an electric field without absorbing energy; and (iv) the imaginary part (εi) of the dielectric function, which describes the ability of the matter to permanently absorb energy from a time-varying electric field; the spectra were reported in the function of the energy of the applied (and simulated) electric field expressed in eV.
The MoO2 optical spectra, simulated and recorded experimentally, are reported in Figure 6. From the comparison between the theoretical curve (in red) and the experimental (black) it is possible to notice good agreement in all four reported cases, with a small overestimation in the calculated spectra in terms of the extinction coefficient and the imaginary part of the dielectric constant. The reason for the small discrepancies between calculated and experimental evidence may be due to some small differences in the three-dimensional systems. In fact, MoO2 and MoO3 were considered in simulations as single crystals, while polycrystalline structures can be obtained during fabrication. These differences in microstructures of the materials were reflected in the optical properties observed and plotted together. Overall, good agreement was observed in the position of most critical points in the optical constants spectra. Moreover, when a disorder occurred, a change in the magnitude of the optical properties was expected. Similarly, Figure 7 reported the optical spectra of MoO3. In this case, agreement between the experimental obtained and the estimated by the theoretical method was more evident, demonstrating the capability of the MGGA-SCAN proposed methodology to predict and verify the experimental findings. Similarly, Figure 7 reported the optical spectra of MoO 3 . In this case, agreement between the experimental obtained and the estimated by the theoretical method was more evident, demonstrating the capability of the MGGA-SCAN proposed methodology to predict and verify the experimental findings.
The slight increase in discrepancy between experimental and simulated data for MoO 2 can be attributed to the metallic character of the material, since this behavior is more difficult to reproduce with first-principle methods during optical properties calculations. Nevertheless, the SCAN functional seems to satisfactorily approach the experimental evidence.  The slight increase in discrepancy between experimental and simulated data for MoO2 can be attributed to the metallic character of the material, since this behavior is more difficult to reproduce with first-principle methods during optical properties calculations. Nevertheless, the SCAN functional seems to satisfactorily approach the experimental evidence.

Conclusions
In the present study, the properties of the well-known MoO3 and MoO2 systems were investigated. These compounds have attracted the attention of the scientific community thanks to their electronic and optical properties. MoO3 assumes an orthorhombic phase, named α-MoO3 that belongs to the space group Pbmn; MoO2 adopts a monoclinic crystallographic disposition described by space group P21/c. The electronic and optical properties of both MoO3 and MoO2 were investigated using the MGGA-SCAN functional and the PseudoDojo pseudopotential, and then our calculated results were compared with previously reported experimental data and our recorded optical spectra. The results obtained confirmed that the chosen theoretical modeling methodology is highly accurate and able to reproduce the experimental findings of both MoO3 and MoO2. Moreover, it is important to underline that the band structure and the respective band gap calculated for MoO3 is the one that best matches the experimental one. Even by repeating the calculation with other known and widely used functionals, it was not possible to obtain the optimal bandgap, thus indicating the high sensitivity of the chosen method. The HOMO-LUMO descriptions of both MoO2 and MoO3 better clarified the peculiarities of these materials, shedding light on the role of different Mo-O bonds on the basis of metallic-dielectric behavior. Additionally, the recorded optical spectra in terms of refractive index, extinction coefficient, and the real and imaginary parts of the dielectric constant were in very good agreement with the corresponding calculated values by means of our ab initio methodology. The adopted first-principles study verified the experimental data available, identified the effects of one more O atom in the Mo-based structure, and provided a reasonable prediction of the physical-chemical properties of both systems, allowing us to clarify in detail the properties of these materials at the nanoscale.

Conclusions
In the present study, the properties of the well-known MoO 3 and MoO 2 systems were investigated. These compounds have attracted the attention of the scientific community thanks to their electronic and optical properties. MoO 3 assumes an orthorhombic phase, named α-MoO 3 that belongs to the space group Pbmn; MoO 2 adopts a monoclinic crystallographic disposition described by space group P2 1 /c. The electronic and optical properties of both MoO 3 and MoO 2 were investigated using the MGGA-SCAN functional and the PseudoDojo pseudopotential, and then our calculated results were compared with previously reported experimental data and our recorded optical spectra. The results obtained confirmed that the chosen theoretical modeling methodology is highly accurate and able to reproduce the experimental findings of both MoO 3 and MoO 2 . Moreover, it is important to underline that the band structure and the respective band gap calculated for MoO 3 is the one that best matches the experimental one. Even by repeating the calculation with other known and widely used functionals, it was not possible to obtain the optimal bandgap, thus indicating the high sensitivity of the chosen method. The HOMO-LUMO descriptions of both MoO 2 and MoO 3 better clarified the peculiarities of these materials, shedding light on the role of different Mo-O bonds on the basis of metallic-dielectric behavior. Additionally, the recorded optical spectra in terms of refractive index, extinction coefficient, and the real and imaginary parts of the dielectric constant were in very good agreement with the corresponding calculated values by means of our ab initio methodology. The adopted first-principles study verified the experimental data available, identified the effects of one more O atom in the Mo-based structure, and provided a reasonable prediction of the physical-chemical properties of both systems, allowing us to clarify in detail the properties of these materials at the nanoscale.