Electronic properties and Compton scattering studies of monoclinic tungsten dioxide

Radiation Physics and Chemistry 106 (2015) 33–39

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Electronic properties and Compton scattering studies of monoclinic tungsten dioxide N.L. Heda a,n, Ushma Ahuja b a b

Department of Pure and Applied Physics, University of Kota, Kota 324010, India Faculty of Engineering, University College of Science, M.L. Sukhadia University, Udaipur 313001, India

H I G H L I G H T S








Presented first-ever Compton profile (CP) measurements on WO2. Analyzed CP data in terms of LCAO–DFT calculations. Discussed energy band, DOS and Mulliken's population. Discussed equally scaled CPs and bonding of isoelectronic WO2, WS2 and WSe2. Reported metallic character and Fermi surface topology of WO2.

art ic l e i nf o

a b s t r a c t

Article history: Received 26 December 2013 Accepted 14 June 2014 Available online 21 June 2014

We present the first ever Compton profile measurement of WO2 using a 20 Ci 137Cs γ-ray source. The experimental data have been used to test different approximations of density functional theory in linear combination of atomic orbitals (LCAO) scheme. It is found that theoretical Compton profile deduced using generalized gradient approximation (GGA) gives a better agreement than local density approximation and second order GGA. The computed energy bands, density of states and Mulliken's populations (MP) data confirm a metal-like behavior of WO2. The electronic properties calculated using LCAO approach are also compared with those obtained using full potential linearized augmented plane wave method. The nature of bonding in WO2 is also compared with isoelectronic WX2 (X ¼S, Se) compounds in terms of equal-valence-electron-density profiles and MP data, which suggest an increase in ionic character in the order WSe2-WS2-WO2. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Compton scattering Band structure calculations Density functional theory

1. Introduction Tungsten dioxide (WO2) is an interesting material due to its high melting point which makes it suitable for high temperature applications. It exhibits great potential for industrial interests, relevance for solar energy technology, catalytic applications, etc. Among earlier studies, Ben-Dor and Shimony (1974) have presented the x-ray diffraction (XRD) analysis of pure and doped WO2 while the x-ray photoelectron spectroscopy (XPS) study of several oxidation states of tungsten oxide was reported by De Angelis and Schiavello (1977). The monoclinic structural parameters of WO2 were refined using powder neutron diffraction data at room temperature by Palmer and Dickens (1979) and in framework of the Rietveld method by Bolzan et al. (1995). Gulino et al. (1996) have checked the influence of metal–metal bonds in WO2 by

n

Corresponding author. E-mail address: [email protected] (N.L. Heda).

http://dx.doi.org/10.1016/j.radphyschem.2014.06.013 0969-806X/& 2014 Elsevier Ltd. All rights reserved.

measuring the photoemission and electron energy loss spectra. The photoemission spectra of WO2 was reported by Jones et al. (1997) for the surface structure and spectroscopy, while Bigey et al. (1998) have correlated the catalytic activity in the surfaces and bulk tungsten oxides using XRD, XPS and x-ray absorption spectroscopy. Further, an experimental study of low-lying electronic states of WO2 was undertaken by Davico et al. (1999). Regarding earlier theoretical data on WO2, plane-wave pseudopotential (PP) calculations using local density approximation (LDA) have been reported by Dewhurst and Lowther (2001). Jiang and Spence (2004) have discussed WO2 in terms of experimental high-energy transmission electron energy-loss absorption spectra and density of states (DOS) of both the oxygen atoms. The ab-initio structural, energy bands and DOS of monoclinic (room temperature stable state) and orthorhombic (high temperature metastable state) phases of WO2 have been presented by Shaposhnikov et al. (2011). Since the last three decades, the Compton scattering technique has been recognized as a versatile and unique tool to estimate the ground state electronic properties of materials (Cooper et al., 2004;

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N.L. Heda, U. Ahuja / Radiation Physics and Chemistry 106 (2015) 33–39

Heda and Ahuja, 2010). In this technique, the measured quantity so called Compton profile (CP) J(pz) is the projection of the electron momentum density n(p) along the scattering vector direction (usually taken along the z-axis). In fact, the J(pz) is experimentally deduced from the measured double differential scattering cross2 section ðd σ =dΩdω2 Þ. Mathematically, ! 2 1 d σ Jðpz Þ ¼ : ð1Þ Cðω1 ; ω2 ; θ; pz Þ dΩdω2 The conversion function Cðω1 ; ω2 ; θ; pz Þ depends upon ω1 and ω2 (incident and scattered energies of the γ-ray) and the scattering angle θ. It may be noted that n(p) is a square modulus of the momentum space wave function, χ i ðpÞ; which is basically the Fourier transformation of the real space wave function, ψ i ðrÞ, as given below, Z occ 3 ð2Þ nðpÞ ¼ ∑ jχ i ðpÞ ¼ M ψ i ðrÞeip:r d rj2 : i

In Eq. (2), M is the normalization factor (Cooper et al., 2004). To the best of our knowledge, CP measurements on monoclinic WO2 have not been reported yet. To shed some more light on the electronic properties using momentum densities, we present the first ever experimental CP of WO2 using 20 Ci 137Cs Compton spectrometer (Ahuja et al., 2006). It may be noted that in case of Compton profile measurement of materials involving high-Z elements (like 5d transition metals), a high energy γ-emitting source like 137Cs is preferred (due to impulse approximation criteria) than low-energy 241Am source as used by Raykar et al. (2013) for the measurement of CPs of CdTe. The theoretical CPs, energy bands, DOS and Mulliken's population (MP) analysis have also been reported for the first time using linear combination of atomic orbitals (LCAO) scheme as embodied in the CRYSTAL09 code (Dovesi et al., 2009). In addition, the energy bands, partial and total DOS and Fermi surfaces have also been computed using the full potential linearized augmented plane wave (FP-LAPW) method (Blaha et al., 2011). Further, relative nature of bonding among isoelectronic W-compounds namely WO2, WS2 and WSe2 has been studied on the basis of equal-valence-electron-density (EVED) profiles and MP analysis.

2. Methodologies 2.1. Experiment The isotropic CP of monoclinic WO2 was measured by employing 20 Ci 137Cs Compton spectrometer (Ahuja et al., 2006) with a resolution of 0.34 a.u. (Gaussian full width at half maximum). A pellet of 17 mm diameter and 3.3 mm thickness was prepared under argon environment using high purity polycrystalline WO2 sample. The pellet was sealed in a perspex ampoule using thin Mylar sheets on both sides. The incident photons of energy 661.65 keV were scattered by the sample, which was held

vertically in the scattering chamber. The scattered photons were detected by a high purity Ge detector (Canberra, USA) in which the cross-sectional area and thickness of the Ge crystal were 500 mm2 and 10 mm, respectively. An integrated Compton intensity of 2.02  107 photons was accumulated during the exposure of about 150 h. Throughout the measurement, the electronic drift was checked from time to time using weak 57Co and 133Ba calibration sources and was found to be negligible. To extract the true CP, raw Compton data were corrected for background, detector response (limited to stripping-off the low energy tail), sample absorption, Compton cross-section and multiple (up to triple) scattering (Timms, 1989; Felsteiner et al., 1974). Finally, the CP was normalized to free atom (FA) Compton profile area of 34.97e  in the momentum (pz) range from 0 to þ7 a.u. (Biggs et al., 1975). Due to the non-availability of the large sized single crystals (15 mm diameter and 2 mm thickness) of WO2 and to explore the relative nature of bonding in isoelectronic WO2, WS2 and WSe2 compounds on EVED scale, we have only measured the isotropic CP of WO2. 2.2. Theory 2.2.1. LCAO method To compute the directional and isotropic J(pz), energy bands, DOS and MP data, we have employed LCAO-PP scheme (Dovesi et al., 2009) in the framework of density functional theory (DFT) within LDA and generalized gradient approximation (GGA) along with the hybridization of Hartree–Fock (HF) and DFT (the so called B3LYP) scheme. For the second order GGA (SOGGA) (Zhao and Truhlar, 2008) exchange enhancement factor is taken as equal (50% each) mixing of Perdew–Becke–Ernzerhof (PBE) (Perdew et al., 1996) and revised PBE (Hammer et al., 1999) exchange functionals. It is worth mentioning that the SOGGA is claimed to be an advanced GGA functional as it mends the gradient expansion for both exchange and correlation through second order. In case of B3LYP, the standard exchange of Becke (1988) and Lee–Yang–Parr (LYP) (Lee et al., 1988) correlation energies along with 20% mixing of the HF exchange has been used. The exchange and correlation potentials used in the present computations are compiled in Table 1. In the present effective core pseudopotential (ECP) calculations, we have taken a large core PP for W and all-electron Gaussian basis sets for oxygen (O) ions. The basis sets were energy optimized for WO2 environment using BILLY software (Dovesi et al., 2009). Further, self consistent field (SCF) calculations have been performed using 205k points in the irreducible Brillouin zone (IBZ) and the absolute isotropic CPs were calculated by adding the FA core CP contribution (Biggs et al., 1975) to the normalized valence CPs. 2.2.2. FP-LAPW method In addition to the LCAO scheme, we have also computed energy bands, partial and total DOS and Fermi surfaces of monoclinic WO2 using the FP-LAPW method in the framework of DFT–GGA (Blaha et al., 2011) using the formulation of Wu and Cohen (2006). It is

Table 1 Exchange and correlation energies within the LCAO-PP approach (Dovesi et al., 2009), as used in the present work. Scheme

Exchange energies

Correlations energies

Nomenclature used in the text

DFT with LDA DFT with GGA DFT with GGA

Dirac-Slater (Dovesi et al., 2009) Wu and Cohen (2006) Second order GGA (Zhao and Truhlar, 2008) Becke (1988)

Perdew and Zunger (1981) Perdew and Wang (1992) Perdew–Becke–Ernzerhof (Perdew et al., 1996) Lee–Yang–Parr Lee et al. (1988)

DFT–LDA-PZ DFT–WCGGA DFT–SOGGA

Hybridization of Hartree-Fock and DFT (B3LYP)

B3LYP

N.L. Heda, U. Ahuja / Radiation Physics and Chemistry 106 (2015) 33–39

35

kz

Y

Γ

ky

C

Z

B D

kx

Fig. 1. (a) Structural sketch of WO2 and (b) labeled standard Brillouin zone of monoclinic structure.

DFT-LDA-PZ DFT-SOGGA

0.10 0.05 0.00

DFT-WCGGA B3LYP

-0.05 -0.10 0.10

ΔJ(e/a.u.)

worth mentioning that in the FP-LAPW approach, the crystal potential is considered within the muffin-tin (MT) atomic spheres and depends upon the spherical harmonics, while outside the MT it is represented by plane waves. The MT radii (RMT) for W and O atoms were taken to be 1.88 and 1.66 Å, respectively. The SCF convergence was achieved using 260k points in the IBZ. The value of RMTKmax (Kmax being the magnitude of largest reciprocal vector k in the combined basis sets) and lmax were set to 7 and 10, respectively. In both the first-principles computations, the monoclinic structure (space group P21/c) consisting of 12 atoms (4 W and 8 O atoms) in the unit cell was considered. The lattice parameters were taken as a¼ 5.563 Å, b¼ 4.896 Å, c¼ 5.563 Å and β ¼120.471 (Shaposhnikov et al., 2011). The structure of monoclinic WO2, sketched using visualization software of Kokalj (2003) and the Brillouin zone corresponding to the monoclinic structure are shown in Fig. 1(a and b).

0.05 0.00 -0.05 -0.10 0.10 0.05 0.00

3. Results and discussion

-0.05 -0.10

3.1. Compton profiles and bonding 0

In Fig. 2, we have shown the anisotropies between the pairs of unconvoluted Compton profiles namely (a) J110–J100 (b) J001–J100 and (c) J001–J110 using LCAO based DFT–LDA-PZ, DFT–SOGGA, DFT– WCGGA and B3LYP approaches. The small differences in the anisotropies in the high momentum side (pz Z3 a.u.) are understandable because this region is dominated by core electrons whose contributions cancel while taking the directional differences. In the low momentum region the anisotropies in the momentum densities show many oscillations of small amplitudes which depict small anisotropic nature of electron density. In Table 2, the numerical values of the unconvoluted isotropic CPs using DFT–LDA-PZ, DFT–SOGGA, DFT–WCGGA and B3LYP schemes along with the experimental data have been reported. In the low momentum region, different approximations of DFT theory show different amplitudes of deviations (Table 2) which are understandable in terms of underlying assumptions of exchange and correlation energies. Before comparing the experimental CPs with the theoretical data, the theoretical profiles have been convoluted with the Gaussian instrumental resolution of the experiment (0.34 a.u. fwhm). The differences between the convoluted theoretical and experimental Compton profiles have been plotted in Fig. 3. The differences between the theoretical and experimental

1

2

3

4

5

6

7

pz (a.u.) Fig. 2. Anisotropies in the unconvoluted theoretical LCAO based Compton profiles of monoclinic WO2 corresponding to (a) J110–J100 (b) J001–J100 and (c) J001–J110 using DFT–LDA-PZ, DFT–SOGGA, DFT–WCGGA and B3LYP schemes. The solid lines are drawn only to guide the eyes.

momentum densities in the pz r5 a.u. are understandable due to non-inclusion of relativistic effects and Lam–Platzman (LP) correlation correction (Cooper et al., 2004). On the basis of the χ2 fitting (which decides goodness of fitting), it is found that the LCAO–DFT– WCGGA scheme gives a better agreement than DFT–LDA-PZ, DFT– SOGGA and B3LYP schemes. The B3LYP based CP depicts a closeness to DFT–WCGGA data, which shows an overall small role of HF in hybridization of HF and DFT. Also, a better reconciliation of DFT– WCGGA based CP with experiment than that due to DFT–LDA-PZ shows a superiority of GGA over the LDA. Now we discuss, the ionicity in WO2 on the basis of EVED profiles. This approach was found to be very successful in our earlier studies (Heda et al., 2008; Sharma et al., 2010; Bhamu et al., 2012). Closeness in EVED profiles of isoelectronic materials suggests that

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Table 2 Unconvoluted isotropic CPs of monoclinic WO2 computed using the LCAO-PP scheme using various exchange and correlation potentials as mentioned in the text along with the experimental CP. The statistical error ( 7 σ) is shown at a few points.

Expt. DFT–SOGGA

DFT–WCGGA

B3LYP

14.538 14.514 14.324 14.136 13.795 13.382 12.868 12.251 11.777 10.413 8.975 7.663 6.588 5.824 5.287 3.949 3.126 2.410 1.849 1.432

14.536 14.513 14.323 14.137 13.797 13.385 12.873 12.257 11.784 10.419 8.980 7.665 6.587 5.821 5.283 3.948 3.125 2.409 1.849 1.432

14.519 14.495 14.307 14.121 13.782 13.372 12.861 12.246 11.776 10.417 8.983 7.672 6.596 5.830 5.291 3.950 3.126 2.410 1.849 1.432

14.502 14.480 14.298 14.123 13.796 13.388 12.870 12.247 11.774 10.418 8.980 7.669 6.596 5.830 5.291 3.950 3.126 2.410 1.849 1.432

ΔJ (Theory-Expt.) (e/a.u.)

0.3

14.2747 0.037 14.200 14.053 13.834 13.540 13.175 12.747 12.267 11.736 10.559 7 0.029 9.308 8.092 7.039 6.208 5.563 70.018 3.836 70.013 3.0127 0.011 2.362 70.009 1.834 7 0.007 1.454 7 0.006

DFT-LDA-PZ DFT-SOGGA DFT-WCGGA B3LYP Ι Error

0.2 0.1 0.0 -0.1 -0.2 -0.3

0

1

1.8

2.4

3.0 10

8

WSe 2

DFT–LDA-PZ

-0.4

1.2

WS 2

J(pz) (e/a.u.) Theory

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 6.0 7.0

0.6

WO 2

8

2

3

4

5

6

7

pz (a.u.) Fig. 3. Difference between isotropic convoluted theoretical (DFT–LDA-PZ, DFT– SOGGA, DFT–WCGGA and B3LYP) and experimental profiles. The solid lines are drawn only to guide the eyes.

wave functions for the bonding electrons may be identical if expressed in terms of r/b (b being the lattice parameter). Since covalent bonding arises from localization of charge in the direction of bonding, the materials with covalent bonding show sharpness in the CPs. In Fig. 4, we have plotted the valence experimental and theoretical EVED profiles of isoelectronic WX2 (X¼O, S and Se). Since theoretical DFT–WCGGA based CP data on WS2 and WSe2 are not available, we have chosen B3LYP based profiles of WO2 for the sake of similarity with the available data (Arora et al., 2009). The Fermi momentum (pF) for WO2 is taken to be 0.864 a.u. It is seen from Fig. 4 (a and b) that the experimental EVED J(pz ¼0) for WS2 and WSe2 are 23.44% and 28.95% higher than those for WO2, while in case of B3LYP scheme the respective values are 30.87% and 40.11%. Therefore, the present data unambiguously show more localization of charge along direction of bonding which reduces in

J(pz)*pF (e)

pz (a.u.)

0.0

10

6

6

4

4

2

2

0 0.0

0.6

1.2

1.8

2.4

3.0

0

pz/pF Fig. 4. Equal-valence-electron-density (EVED) profiles (i.e., on pz/pF scale) of WO2 along with the isoelectronic compounds WS2 and WSe2 (Arora et al., 2009) using (a) experiment and (b) B3LYP scheme. The experimental error is within the size of symbols used and the solid lines are to guide the eyes.

the order WSe2-WS2-WO2. This trend of covalent character is also in the accordance with the MP data as discussed below. The MP based charge transfer data in monoclinic WO2 using LCAO–DFT–LDA-PZ, DFT–SOGGA, DFT–WCGGA and B3LYP schemes show that W plays the role of donor atom while both O atoms (marked as O1 and O2 in Fig. 1a) play the role of acceptor. In DFT– WCGGA scheme, it is noted that the amount of charge donated by W atom (2.46e  ) is unequally distributed between O1 (1.29e  ) and O2 (1.17e  ) atoms. The numerical value of the charge transfer from W-O1 and O2 within DFT–LDA-PZ, DFT–SOGGA, DFT–WCGGA and B3LYP schemes are 2.48, 2.44, 2.46 and 2.66e  , respectively. In case of our earlier work on WO3 (Heda and Ahuja, 2013) using the similar DFT–WCGGA, where two WO3 molecules are combined together to form W2O6, such an unequal distributions of charge from W1 (1.54e  ) and W2 (1.53e  ) to O1 (1.18e  ), O2 (1.13e  ), O3(0.26e  ), O4 (0.20e  ), O5 (0.16e  ) and O6 (0.14e  ) were also observed. Further, Arora et al. (2009) have also reported the MP based charge transfer data in isoelectronic WS2 and WSe2, being 0.21 (0.14) e  in WS2 and 0.06 (0.01) e  in WSe2 within LCAO–DFT– LDA-PZ (B3LYP). The MP data from both (DFT–LDA-PZ and B3LYP) schemes show the highest value of charge reorganization in WO2 and which further decreases in the order WS2-WSe2. Therefore, a systematic trend of charge transfer between W and O/S/Se, shows a decreasing trend of ionicity or increasing trend of covalent bonding from WO2-WS2-WSe2. Since, the basis sets in the present computations on WO2 and earlier data on WS2 and WSe2 (Arora et al., 2009) involve sufficient diffuse external atomic orbitals, therefore the MP analysis is expected to be quite reliable. 3.2. Energy bands and Fermi surface topology In Fig. 5, we have shown the E v/s k relation (with EF shifted to zero reference level) of monoclinic WO2 along with the highsymmetry directions of BZ (Fig. 1b) using FP-LAPW–WCGGA scheme. Except some fine structures and energy values, the overall shape of bands are in tune with those reported by Shaposhnikov et al. (2011). The cross-overs of Fermi level (EF) by the energy bands in several branches of BZ show a metal-like character of the compound. To analyze the energy bands, in Fig. 6 (a–c), we have shown DOS (total and projected) corresponding to s, p, d, egðdx2 y2 þ dz2 Þ and t2g(dxy þ dxz þ dyz) states of W, O1 and O2. The total and partial DOS are in agreement with the limited data

N.L. Heda, U. Ahuja / Radiation Physics and Chemistry 106 (2015) 33–39

37

reported by Jiang and Spence (2004) and Shaposhnikov et al. (2011). The non-zero value of DOS at EF also confirms the metallic character of WO2. The energy bands (upper side) and total DOS (lower side) using LCAO–DFT–WCGGA scheme shown in Fig. 7 are also in agreement with those obtained from FP-LAPW scheme (Figs. 5–6). Separately, we have seen a similar topology of the energy bands and DOS using LCAO–DFT–LDA-PZ, DFT– SOGGA and B3LYP schemes, hence the energy bands and DOS using these schemes are not shown here. Moreover, due to similarity (except some fine structures) of the energy bands and

WO2

DOS (states/eV)

300

200

100

0 -10

-6

-4

-2

0

2

4

-6

-4

-2

6

-8

-6

-4

-2

0

2

4

6

4

6

8

8

s p d 1.5 eg

W O1 O2

8

2

Fig. 7. (a) Energy bands and (b) total DOS of monoclinic WO2 using LCAO–DFT– WCGGA scheme. The positions of vertices are mentioned in Fig. 5.

WO2

12

0

Energy (eV)

Fig. 5. Energy bands of monoclinic WO2 using the FP-LAPW–WCGGA method. The positions of Γ, Y, B, Γ, Z, C, D and Z vertices corresponds to (0,0,0), (0,1/2,0), (  1/ 2,0,0), (0,0,0), (0,0,1/2), (0,1/2,1/2), (  1/2,0,1/2) and (0,0,1/2), respectively.

-10 -8

-8

t2g 1.0

DOS (states/ev)

4

0.5

0.0

0

s p

1.5

s p

1.5

1.0

1.0

0.5

0.5

0.0 -10

0.0 -8

-6

-4

-2

0

2

4

6

-8

-6

-4

-2

0

2

4

6

8

Energy (eV) Fig. 6. The FP-LAPW–WCGGA scheme based (a) density of states (DOS) of WO2, W, O1 and O2 (b) partial DOS of W showing the contribution of s, p, d, eg ðdx2 y2 þ dz2 Þand t2g (dxy þ dxz þdyz) states (c) partial DOS of O1 showing the contribution of s and p states and (d) partial DOS of O2 for the s and p states.

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N.L. Heda, U. Ahuja / Radiation Physics and Chemistry 106 (2015) 33–39

Fig. 8. The FP-LAPW–WCGGA based Fermi surfaces of WO2 arising from (a) 79th band (b) 80th band (c) 81st band and (d) total mapping (a þ bþ c).

DOS deduced from various approximations of FP-LAPW, we have limited our discussion on energy bands and DOS deduced using FP-LAPW–WCGGA scheme only. The energy bands and DOS (Figs. 5–6) can be divided into five major parts: (a) The first part (not shown here) is found around  20 eV which arises from the O 2s and W 5d states. (b) The bands in the second part (  10.57 to  3.96 eV) are formed mainly due to overlapping between t2g and eg states of W and 2p states of O1 and O2. (c) The third part between  2.41 eV and EF level, mainly consists of the t2g and eg states of W with a small admixture of the 2p states of O1 and O2. The cross-overs of EF level by energy bands corresponding to t2g and eg states of W and 2p states of O1 and O2 lead to metallic nature. (d) The fourth part ranging between EF to 3.16 eV is dominated by 5d (t2g and eg) states of W with overlapping of 2p states of O1 and O2. (e) The fifth part (3.20 eV and above) mainly corresponds to unoccupied 5d states of W and 2sp states of O1 and O2. Further, from Fig. 6 (c and d), we have calculated the integrated DOS (IDOS, which provides the number of electrons) for the valence electrons in the energy range  2.41 eV to EF. It is found that IDOS is higher for O1 (0.85e  ) than that for O2 (0.54e  ) which shows unequal distribution of charge between outer valence states of O1 and O2. Such an unequal distribution is also in the tune with the DOS of individual oxygen atoms as reported

by Jiang and Spence (2004) and present MP data. The FP-LAPW– WCGGA based Fermi surfaces (FSs) of monoclinic WO2 (metallic like) have been depicted in Fig. 8 (a–d). It is seen that the reported FSs mainly originate from 79th to 81st bands. Peculiar Fermi shapes as shown in Fig. 8 (a and b) are due to the 79th and 80th bands respectively, while the FS in Fig. 8(c) corresponds to the 81st band.

4. Conclusions The Compton profile measurement of monoclinic WO2 has been reported for the first time using 661.65 keV photons. It is found that theoretical Compton profiles based on LCAO–DFT–GGA with Wu–Cohen exchange and Perdew–Wang correlation energies gives a better agreement with the experimental profile than other approximations like DFT–LDA, DFT–SOGGA. In addition, the energy bands, partial and total density of states have also been reported using LCAO and FP-LAPW schemes. The energy bands and density of states from both the first-principles calculations confirm a metal-like behavior of WO2. Integrated density of states and Mulliken's population data show an unequal distribution of charge between two oxygen atoms as transferred from W-O1 or O2. A decreasing trend in the ionic character while going from WO2WS2-WSe2 is established unambiguously by Mulliken's data and Compton profiles scaled on equal-valence-electron-density.

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