Theoretical and Experimental Study of the Electronic Structures of ...

4638 J. Phys. Chem. C, Vol. 114, No. 10, 2010 Scanlon et al.behavior of these materials and also accounting for the drivingforce for distortion in terms of stabilization of two electronsper metal pair in a metal-metal bond. By contrast, in the d 2oxide MoO 2 the one extra electron per metal cation partiallypopulates the higher t ⊥ bands. MoO 2 therefore displays bothmetallic conductivity and metal-metal bonding. A refinementof the Goodenough model takes account of the possibility ofπ-type overlap between pairs of t ⊥ orbitals. 45,46MoO 2 is less important in technological applications thanMoO 3 , but it has been used as a catalyst for alkane isomerization47–51 or oxidation 52 reactions and as a gas sensor. 53 It is alsoa promising anode material for Li ion batteries. 54–57There have been several previous studies of MoO 2 by X-rayphotoelectron spectroscopy. 2,45,47–49,51,52,58,59 Valence level spectrashow that a band of Mo 4d states around 3 eV wide lies abovean O 2p band whose width is about 6 eV. However, the energyresolution in this previous work has in general been too poorto properly reveal the expected splitting of the Mo 4d bandspredicted by the Goodenough model. The splitting has howeverbeen observed in ultraviolet photoemission spectra. 45,52,58 Inaddition, XAS has been used to explore the unoccupied O 2pstates and has found three distinct peaks 0.4, 3.1, and 4.6 eVabove the Fermi energy. 46 Optical reflectivity measurementshave been used to infer that the lowest unfilled Mo 4d levelsare situated ∼2.5 eV above the top of the O 2p bands. 60–62Theoretically MoO 2 has received less attention than MoO 3 ,with only a handful of studies in the literature. 42,46,63–67 Thesehave included tight binding 42 and cluster calculations. 42,63–66Recently, two studies by Eyert and co-workers used LDA withinthe augmented spherical wave (ASW) method to study thePeierls-like instability in MoO 2 and investigated the Fermisurface of MoO 2 in comparison with angle-resolved photoemissionspectroscopy and de Haas-van Alphen measurements. 46,67This work identified three Fermi surface sheets with electroneffective masses of 0.85 m 0 , 1.87 m 0 , and 2.85 m 0 , where m 0 isthe electron rest mass.In the present study we used GGA density functional theorycalculations to study the geometry and electronic structure ofMoO 2 and MoO 3 . The theoretical results are compared withhigh-resolution X-ray photoemission data. We find excellentagreement between experimental X-ray valence band photoemissionspectra and the calculated cross-section weighteddensity of states. At the same time it is shown that the complexcore level structure noted previously for MoO 2 and attributed47–49,51,52to complex and ill-defined “surface phases” such as Mo 2 O 5is intrinsic to the material and arises from final state metallicscreening.2. Theoretical MethodsThe periodic DFT code VASP 68,69 was employed for all ourcalculations. This uses a plane wave basis set to describe thevalence electronic states. The Perdew-Burke-Ernzerhof 70(PBE) gradient-corrected functional was used to treat theexchange and correlation. Interactions between the cores (Mo:[Kr] and O:[He]) and the valence electrons were described usingthe projector-augmented wave 71 (PAW) method.Structural optimizations of bulk MoO 2 were performed at aseries of volumes in order to calculate the equilibrium latticeparameters. In each case the atomic positions, lattice vectors,and cell angles were allowed to relax, while the total volumewas held constant. The resulting energy volume curves werefitted to the Murnaghan 72 equation of state to obtain theequilibrium bulk cell volume. This approach avoids the problemsof Pulay stress and changes in basis set which can accompanyvolume changes in plane wave calculations. Convergence withrespect to k-point sampling and plane wave energy cut off waschecked, with a cutoff of 500 eV and a k-point sampling of 4× 6 × 4 found to be sufficient. Structural optimizations weredeemed to be converged when the force on every ion was lessthan 0.005 eV Å -1 .As MoO 3 is a layered structure, with the interlayer distancedetermined by noncovalent interlayer forces, a simple relaxationas outlined above is not sufficient. DFT methods have long beenknown to be unable to describe van der Waals forcescorrectly, 29,73–78 and as expected, attempting to minimize thestructure using the system above resulted in the absence of aminimum in the b vector. Indeed, relaxing the stress tensor atan elevated cutoff of 1000 eV gave a b lattice parameter of16.539 Å, which far exceeds the experimentally reported valueof 13.855 Å. Thus, we used the method proposed by Coquetand Willock, 29 which involved holding the b lattice parameterat the experimental value of 13.855 Å and optimizing the aand c lattice constants by allowing the atomic coordinates torelax at a series of fixed volumes around the experimentallyreported lattice parameters. A cutoff of 500 eV and a k-pointsampling of 6 × 2 × 6 were found to be sufficient, and structuraloptimizations were deemed to be converged when the force onevery ion was less than 0.005 eV Å -1 , consistent with the MoO 2calculations above.3. Experimental SectionSingle-crystal MoO 3 was prepared by a flux method. 79 Thesample selected for study by photoemission had a plate-likemorphology with dimensions of around 8 mm × 4mm× 1mm and came from a batch of crystals previously used inconductivity measurements. 80 The large flat face had (010)orientation. A second crystal from the batch was ground to apowder, and it was confirmed that the powder X-ray diffractionpattern matched that described in the literature and wasconsistent with orthorhombic space group Pbnm with a ) 3.962Å, b ) 13.855 Å, and c ) 3.696 Å. 4,5,81 MoO 2 was prepared byreduction of MoO 3 in a flowing H 2 /H 2 O/Ar mixture as describedelsewhere. 58 The H 2 /H 2 O atmosphere was set with p H2 ) 25.8Torr, p H2O ) 2.4 Torr, and with a balance of Ar around 730Torr, and reduction was carried out at 547 °C over a period of4 days. The effective oxygen partial pressure under theseconditions is estimated to be about 10 -11 mbar, and theseconditions render MoO 2 the thermodynamically favored product.The O/Mo ratio in the product was established to be 2.000 (0.002 by a volumetric procedure involving oxidation byK 3 Fe(CN) 6 . 82 The powder sample was pressed between tungstencarbide dies to give a ceramic disk which was then sintered invacuo in a sealed quartz tube at 900 °C to give mechanicalstrength. The final pelletized sample gave a monoclinic X-raypowder diffraction pattern in agreement with that publishedpreviously and consistent with space group P21c with a ) 561pm, b ) 486 pm, c ) 563 pm, and β ) 121°. 39,42,81High-resolution X-ray photoemission spectra were measuredin a Scienta ESCA 300 spectrometer. This incorporates a rotatinganode Al KR (hν ) 1486.6 eV) X-ray source, a 7-crystal X-raymonochromator, and a 300 mm mean radius spherical sectorelectron energy analyzer with a parallel electron detectionsystem. The X-ray source was run with 200 mA emission currentand 14 kV anode bias, while the analyzer operated at 150 eVpass energy. Gaussian convolution of the analyzer resolutionwith a line width of 260 meV for the X-ray source gives aneffective instrument resolution of 400 meV. Binding energiesare referenced to the Fermi energy of a silver sample regularly