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Periodic density functional study on V2O5 bulk and (001) surface
Applied Surface Science 130–132 Ž1998. 539–544
Periodic density functional study on V2 O5 bulk and ž001 / surface Xilin Yin, Adil Fahmi 1, Akira Endou, Ryuji Miura, Isao Gunji, Ryo Yamauchi, Momoji Kubo, Abhijit Chatterjee, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba-ku, Sendai 980-77, Japan Received 30 September 1997; accepted 11 December 1997
Abstract Density functional calculations on periodic models are performed to investigate the structural and electronic properties of both V2 O5 bulk and Ž001. surface. Full geometry optimizations of both V2 O5 bulk and Ž001. surface are presented. For the bulk, the optimized structure is very close to the experimental one, the calculated band gap and binding energy are in very good agreement with experimental values, from population analysis it is observed that vanadyl oxygens are least ionic ŽOy0.37 ., doubly coordinated oxygens are ionic ŽOy0.56 ., while triply coordinated oxygens become the most ionic ŽOy0.68 .. The structural and electronic properties of the surface are very close to those of the bulk. The interlayer interaction is mainly electrostatic and is found to be 4 kcalrmol. Surface acidic and basic properties are described in terms of projected density of states analysis. q 1998 Elsevier Science B.V. All rights reserved. Keywords: V2 O5 ; Ž001. Surface; Density functional calculations
1. Introduction Vanadium pentoxide has been subject of many experimental studies w1–7x. The catalytic properties of V2 O5-based catalysts depend strongly on their ability to provide lattice oxygen as a reactant in oxidation of hydrocarbons. Therefore the investigation of V2 O5 lattice oxygens is crucial. There are three kinds of oxygen atoms: O 1 singly coordinated which is the vanadyl oxygen; O 2 doubly coordinated; and O 3 triply coordinated. A recent atomic force microscopy ŽAFM. study of V2 O5 Ž001. surface w1x has shown that the O 2 oxygen )
Corresponding author. Fax: q81-22-217-7235; e-mail: [email protected]. 1 Present address: Fritz-Haber-Institut, Faradayweg 4-6, D-14 195 Berlin-Dahlem, Germany.
is more negatively charged than O 3 and proposed O 2 as the surface active site. On the other hand, electronic spin resonance spectroscopy ŽESR. and infrared spectroscopy ŽIR. studies have indicated that CO, SO 2 and C 2 H 4 adsorb at the O 1 oxygen w2x or at O 3 oxygen centers w3x. The various experimental results concerning the active site and the oxidation process are still controversial. In contrast to the numerous experimental studies devoted to V2 O5 bulk and surfaces, very few theoretical works have been undertaken. Moreover, different active sites of V2 O5 w3,8,9x have been proposed theoretically. Periodic Hartree–Fock ŽHF. calculations of V2 O5 crystal by Kempf et al. w10x have shown that the oxide is essentially ionic, though the vanadyl bond appears to be rather covalent. Atomic charges Ž Q . on the different oxygen atoms decrease in the order: QŽO 3 . ) QŽO 2 . ) QŽO 1 .. However, as
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 1 - 1
540
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
it is common in Hartree–Fock methods, the band gap was over estimated. Using a DFT method and cluster models for the Ž001. surface of V2 O5 , Michalak et al. w11x reported the same trend for the charges of surface oxygens as the previous HF study. So far no first principles calculations using a slab model for the Ž001. surface of V2 O5 to study various adsorptions were reported. In the present communication we present periodic DFT calculations of V2 O5 bulk and Ž001. surface. We optimize the geometries and determine the electronic properties. In the future, we will present the adsorption and dissociation of water on the Ž001. surface. We will discuss the localization of the proton on the surface and describe the topology of surface hydroxyl groups.
2. Method of calculation We have used two programs to perform our calculations, they both use the density functional formalism: CASTEP and BAND. CASTEP Žfrom MSI. uses a conjugated gradient technique in a direct minimization of the Kohn–Sham energy functional w12x and employs pseudopotentials to represent core electrons. Basis sets are plane-wave functions. In this approach, Hellmann–Feynman forces on ions can be easily evaluated, and therefore geometry optimizations can be performed to get stable structures. Exchange and correlation effects were included within both the Ceperley–Alder local density approximation ŽLDA. w13x and the generalized gradient approximation ŽGGA.. Gradient-corrected energies were computed self-consistently. We used a plane-wave cutoff energy of 650 eV, for which vanadium and oxygen pseudopotentials are well converged. BAND program w14x uses a matrix diagonalization technique to solve Kohn–Sham equations w15,16x. It employs a numerical Gaussian integration scheme w17x for the Hamiltonian matrix elements, and a quadratic tetrahedron method for the k-space integration w18x. We have used a basis set of double-zeta plus polarization ŽDZP. quality. It consists of Herman–Skillman numerical atomic orbitals ŽNAOs. and Slater-type orbitals ŽSTOs.. For vanadium, with a 3d 34s 2 ground state, the 1s–3p shells were frozen, the valence electrons are described by 3d and 4s NAOs, augmented with 3d, 4s and 4p STOs. For
oxygen, the 1s orbital was kept frozen and valence electrons were described with 2s and 2p NAO and STOs plus a 3d polarization function. For each atom a special set of s, p, d, f and g STOs was used to fit the deformation of the density w19x, these functions are required for the calculation of the Coulomb potential at the integration points and the gradient of the electron density. The Perdew–Wang nonlocal correction is implemented in a perturbative manner and is not computed self-consistently, therefore the LDA density is used as an input for nonlocal corrections. This approximation has minor effects on bond energies. In contrast to CASTEP, BAND provides Mulliken population analysis. Therefore it is possible to calculate atomic charges, overlap populations and projected density of states ŽPDOS.. Our methodology is the following: we have performed structural optimizations with CASTEP at the GGA level, and next, we used BAND to recalculate the optimized structures at the same level and perform population analysis.
3. Bulk structure We performed geometry optimizations of both lattice parameters and atomic coordinates at LDA and GGA levels using CASTEP program. A set of six special k-points was used. The unit cell contains 14 atoms, four vanadium and 10 oxygen atoms ŽFig. 1a.. The lattice parameters obtained using GGA are
Fig. 1. The optimized V–O bond lengths in Ža. V2 O5 bulk Žthe corresponding experimental values are shown in the brackets., and Žb. V2 O5 Ž001. surface Žthe corresponding optimized bulk values are in the brackets..
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544 Table 1 Optimized and experimental w20x lattice parameters and fractional coordinates of V2 O5 bulk Exp. w20x
GGA
LDA
˚. a ŽA ˚. b ŽA
11.519
11.535
3.564
3.603
3.670
˚. c ŽA V
4.373 0.149 0.000 0.105 0.149 0.000 0.458 0.320 0.000 0.000 0.000 0.000 0.000
4.422 0.149 0.000 0.102 0.148 0.000 0.465 0.320 0.000 0.001 0.000 0.000 y0.002
4.481 0.150 0.000 0.102 0.148 0.000 0.466 0.320 0.000 0.001 0.000 0.000 y0.003
O1
O2
O3
x y z x y z x y z x y z
11.557
closer to experimental values w20x than those using LDA ŽTable 1.. Therefore, we used the GGA technique in the rest of the work. The V–O bond lengths are well reproduced ŽFig. . 1a , the deviation from the experimental values w20x ˚ except the vanadyl oxygen V5O is less than 0.01 A ˚ Moreover, the for which the deviation is 0.07 A. ˚ is close to calculated interlayer distance of 2.83 A ˚ w x the experimental value of 2.82 A 20 . To be precise, our DFT lattice parameters appear better than those obtained by a periodic HF method w10x. Mulliken analysis by BAND Žsee Table 2. gives results in agreement with previous DFT study with cluster models w11x. Charges on oxygen atoms decrease in the order: QŽO 3 . ) QŽO 2 . ) QŽO1 .. Therefore the highest coordinated oxygen atom bears the largest charge. Mulliken overlap populations ŽOP. of V–O bonds give a measure of the coordination of oxygens: O 3 ) O 2 ) O 1. The V–O 1 ŽOP s 0.47. bond is stronger than a V–O 2 Žtwo bonds of OP s
541
0.24 each. or a V–O 3 Žtwo bonds of OP s 0.39 and one of OP s 0.15.. Therefore V–O 1 is more covalent than the other possible V–O bonds. In contrast to earlier HF calculations w10x which gave a band gap of ; 12 eV, our calculated band gap between the top of the valence and bottom of the conduction band is about 2.0 eV, which is close to the experimental value of ; 2.3 eV w4x. It shows that the calculated V2 O5 may act as a semiconductor. The ‘experimental’ binding energy of V2 O5 can be roughly estimated from the standard heat of formation and from the heat of atomization w21x, neglecting the zero point motion and specific heat contributions, one finds y2.91 a.u. Žper cell.. Our calculated binding energy is y3.29 a.u. which is in good agreement with the experimental one and also better than HF study w10x.
4. The (001) surface The stacking of the Ž001. layers seems to be due mainly to electrostatic forces. It is so weak that V2 O5 cleaves easily along the Ž001. plane. Since only van der Waals bonds are broken, it is assumed that the remaining bonds are not modified such that the Ž001. surface remains identical to a parallel bulk plane w5x. Ab initio DFT and semi-empirical SINDO methods w22x show no influence of a second layer on the surface properties. In our calculations we used only one vanadium layer ŽFig. 1b. as a model for the surface. In CASTEP calculations successive slabs along the c direction are separated by a vacuum region. The shortest distance between atoms belonging to ˚ interlayer interacsuccessive slabs is larger than 6 A; tion is not significant at such a distance. The energy difference between the bulk and the Ž001. surface is only 4 kcalrmol which is an estimation of the weak
Table 2 Mulliken charges and total overlap populations of the various V–O bonds of V2 O5 bulk and Ž001. surface Charges Overlap population
Atoms
V
O1
O2
O3
bulk Ž001. surface bulk Ž001. surface
q1.34 q1.33 1.64 1.62
y0.37 y0.33 0.47 0.45
y0.56 y0.60 0.24 = 2 0.25 = 2
y0.68 y0.71 0.15r0.39 = 2 0.16r0.38 = 2
542
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
Fig. 2. PDOS pictures of Ža. vanadium atom of both V2 O5 bulk and Ž001. surface, and Žb. oxygen atoms ŽO1 , O 2 and O 3 . of Ž001. surface. The origin of the energy scale is taken at the Fermi levels Žthe Fermi levels of bulk and surface are y0.205 a.u. and y0.367 a.u., respectively..
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
interlayer electrostatic interaction. The optimized Ža and b. surface lattice parameters remain very close to the corresponding bulk values. However, V–O 2 ˚ and and V–O 3 bonds show expansions of 0.04 A ˚ respectively, and the vanadyl V–O1 bond 0.01 A, ˚ ŽFig. 1b.. shows a small contraction of 0.01 A When going from surface to bulk, the charges of O 3 and O 2 decrease whereas that of O 1 increases. This is related to redistribution of electron density within each layer rather than interlayer electron transfer. Zhang and Henrich w6x found that the surface band structure of the UHV-cleaved V2 O5 Ž001. surface is similar to that of the bulk, and Goschke et al. w7x reported a band gap of 2.3 eV for the surface. We calculated a band gap of 2.1 eV and binding energy of y3.29 a.u. which are very close to the calculated bulk values, 2.0 eV and y3.29 a.u., respectively. These results confirm again the similarity between the bulk and the Ž001. surface.
5. Density of states of bulk and (001) surface The PDOS on vanadium orbitals are presented in Fig. 2a for both V2 O5 bulk and Ž001. surface. For surface vanadium, DOS are shifted down in energy. Then surface empty orbitals situated above the Fermi level Žequivalent to lowest unoccupied molecular orbitals, LUMOs. are closer to the Fermi level than bulk empty orbitals. This is an indication of the increase of the acidity of vanadium atom. These empty orbitals are available to interact with Lewis bases such as H 2 O Žin preparation. or NH 3 Žwork in progress.. PDOS on oxygen orbitals presented in Fig. 2b show two sets of peaks. The peaks at low energy correspond to 2s orbitals, and those close to the Fermi level correspond to 2p orbitals. The latter peaks are more broadened and cover a wide energy region because of the overlap with vanadium 3d orbitals. The stability of oxygen 2s orbitals decreases in the order: O 3 ) O 2 ) O 1. From Fig. 2b we also see that the centers of the 2p-DOS have globally the same order as 2s-DOS. Therefore O 1 occupied orbitals Žequivalent to highest occupied molecular orbitals, HOMOs. are closer to the Fermi level. This means that acidic species such as a proton will interact with O 1 rather than O 2 or O 3 . Therefore the
543
basicity of the surface should decrease in the order: O 1 ) O 2 ) O 3 . In contrast, the order of atomic charges suggest the opposite trend since O 3 has the largest charge. Our preliminary results concerning water dissociation and atomic hydrogen adsorption on Ž001. surface correlate with the trend of DOS and we find that the proton is more stable on O 1 site rather than on O 3 site. This suggests that the index for the surface reactivity is the density of states rather than the atomic charges.
6. Conclusions In this work we have presented periodic density functional calculations of V2 O5 bulk and Ž001. surface. The optimized geometries at GGA level are in good agreement with experimental values, and the calculated band gap and binding energy are very close to experimental ones. Interaction between V2 O5 layers is mainly electrostatic and is found to be 4 kcalrmol. For the Ž001. surface, the structural and electronic properties are very close to those of the bulk. The systems are mostly ionic. However, the vanadyl bond V–O 1 seems to be mostly covalent. The atomic charges on oxygen atoms decrease in the order: O 3 ) O 2 ) O 1 for both V2 O5 bulk and Ž001. surface, which may suggest a large reactivity for O 3 . The PDOS show that O 1 occupied levels are closer to the Fermi level than those of O 2 or O 3 . Therefore a large reactivity can be expected for O 1 site. References w1x A.D. Costa, C. Mathieu, Y. Baxbaux, H. Poelman, G. Dalmai-Vennik, L. Fiermans, Surf. Sci. 370 Ž1997. 339. w2x K. Tarama, S. Yoshida, S. Ishida, H. Kakioka, Bull. Chem. Soc. Jpn. 41 Ž1968. 2840. w3x R. Ramirez, B. casal, L. Utrera, E. Ruiz-Hitzky, J. Phys. Chem. 94 Ž1990. 8960. w4x V.G. Mokerov, V.L. Makarov, V.B. Tulvinskii, A.R. Begishev, Opt. Spectrosc. 40 Ž1976. 58. w5x H. Poelman, J. Vennik, G. Dalmai, J. Electron Spectrosc. Relat. Phenom. 44 Ž1987. 251. w6x Z. Zhang, V.E. Henrich, Surf. Sci. 321 Ž1994. 133. w7x R.A. Goschke, K. Vey, M. Maier, U. Walter, E. Goering, M. Klemm, S. Horn, Surf. Sci. 348 Ž1996. 305. w8x A. Andersson, J. Solid State Chem. 42 Ž1982. 263. w9x J. Sambeth, A. Juan, L. Gambaro, H. Thomas, J. Mol. Catal. A 118 Ž1997. 283.
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w10x J.Y. Kempf, B. Silvi, A. Dietrich, C.R.A. Catlow, B. Maigret, Chem. Mater. 5 Ž1993. 641. w11x A. Michalak, M. Witko, K. Hermann, Surf. Sci. 375 Ž1997. 385. w12x M.P. Teter, M.C. Payne, D.C. Allan, Phys. Rev. B 40 Ž1989. 12255. w13x J.P. Perdew, A. Zunger, Phys. Rev. B 23 Ž1981. 5048. w14x G. te Velde, E.J. Baerends, Phys. Rev. B 44 Ž1991. 7888. w15x P. Hohenberg, W. Kohn, Phys. Rev. B 136 Ž1964. 864. w16x W. Kohn, L.J. Sham, Phys. Rev. A 140 Ž1965. 1133. w17x G. te Velde, E.J. Baerends, J. Comput. Phys. 99 Ž1992. 84. w18x G. Wiesenekker, G. te Velde, E.J. Baerends, J. Phys. C 21 Ž1988. 4263.
w19x G. te Velde, E.J. Baerends, Phys. Rev. B 44 Ž1991. 7888. w20x R.W.G. Wyckoff, Crystal Structures, 2nd edn., Robert E. Krieger Publishing, FL, 1982, p. 184. w21x D.D. Wagman, W.H. Evans, V.B. Parker, R.H. Schumm, I. Halow, S.M. Bailey, K.L. Churney, R.L. Nuttall, ‘The NBS tables of chemical thermodynamic properties’, wJ. Phys. Chem. Ref. Data, 11 Ž1982., Suppl. 2x, American Chemical Society and American Institute of Physics for National Bureau of Standards Ž1982.. w22x M. Witko, K. Hermann, R. Tokarz, A. Michalak, Book of Abstracts of 213th ACS National Meeting, PETR 074, San Francisco, 1997.
Periodic density functional study on V2 O5 bulk and ž001 / surface Xilin Yin, Adil Fahmi 1, Akira Endou, Ryuji Miura, Isao Gunji, Ryo Yamauchi, Momoji Kubo, Abhijit Chatterjee, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba-ku, Sendai 980-77, Japan Received 30 September 1997; accepted 11 December 1997
Abstract Density functional calculations on periodic models are performed to investigate the structural and electronic properties of both V2 O5 bulk and Ž001. surface. Full geometry optimizations of both V2 O5 bulk and Ž001. surface are presented. For the bulk, the optimized structure is very close to the experimental one, the calculated band gap and binding energy are in very good agreement with experimental values, from population analysis it is observed that vanadyl oxygens are least ionic ŽOy0.37 ., doubly coordinated oxygens are ionic ŽOy0.56 ., while triply coordinated oxygens become the most ionic ŽOy0.68 .. The structural and electronic properties of the surface are very close to those of the bulk. The interlayer interaction is mainly electrostatic and is found to be 4 kcalrmol. Surface acidic and basic properties are described in terms of projected density of states analysis. q 1998 Elsevier Science B.V. All rights reserved. Keywords: V2 O5 ; Ž001. Surface; Density functional calculations
1. Introduction Vanadium pentoxide has been subject of many experimental studies w1–7x. The catalytic properties of V2 O5-based catalysts depend strongly on their ability to provide lattice oxygen as a reactant in oxidation of hydrocarbons. Therefore the investigation of V2 O5 lattice oxygens is crucial. There are three kinds of oxygen atoms: O 1 singly coordinated which is the vanadyl oxygen; O 2 doubly coordinated; and O 3 triply coordinated. A recent atomic force microscopy ŽAFM. study of V2 O5 Ž001. surface w1x has shown that the O 2 oxygen )
Corresponding author. Fax: q81-22-217-7235; e-mail: [email protected]. 1 Present address: Fritz-Haber-Institut, Faradayweg 4-6, D-14 195 Berlin-Dahlem, Germany.
is more negatively charged than O 3 and proposed O 2 as the surface active site. On the other hand, electronic spin resonance spectroscopy ŽESR. and infrared spectroscopy ŽIR. studies have indicated that CO, SO 2 and C 2 H 4 adsorb at the O 1 oxygen w2x or at O 3 oxygen centers w3x. The various experimental results concerning the active site and the oxidation process are still controversial. In contrast to the numerous experimental studies devoted to V2 O5 bulk and surfaces, very few theoretical works have been undertaken. Moreover, different active sites of V2 O5 w3,8,9x have been proposed theoretically. Periodic Hartree–Fock ŽHF. calculations of V2 O5 crystal by Kempf et al. w10x have shown that the oxide is essentially ionic, though the vanadyl bond appears to be rather covalent. Atomic charges Ž Q . on the different oxygen atoms decrease in the order: QŽO 3 . ) QŽO 2 . ) QŽO 1 .. However, as
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 1 - 1
540
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
it is common in Hartree–Fock methods, the band gap was over estimated. Using a DFT method and cluster models for the Ž001. surface of V2 O5 , Michalak et al. w11x reported the same trend for the charges of surface oxygens as the previous HF study. So far no first principles calculations using a slab model for the Ž001. surface of V2 O5 to study various adsorptions were reported. In the present communication we present periodic DFT calculations of V2 O5 bulk and Ž001. surface. We optimize the geometries and determine the electronic properties. In the future, we will present the adsorption and dissociation of water on the Ž001. surface. We will discuss the localization of the proton on the surface and describe the topology of surface hydroxyl groups.
2. Method of calculation We have used two programs to perform our calculations, they both use the density functional formalism: CASTEP and BAND. CASTEP Žfrom MSI. uses a conjugated gradient technique in a direct minimization of the Kohn–Sham energy functional w12x and employs pseudopotentials to represent core electrons. Basis sets are plane-wave functions. In this approach, Hellmann–Feynman forces on ions can be easily evaluated, and therefore geometry optimizations can be performed to get stable structures. Exchange and correlation effects were included within both the Ceperley–Alder local density approximation ŽLDA. w13x and the generalized gradient approximation ŽGGA.. Gradient-corrected energies were computed self-consistently. We used a plane-wave cutoff energy of 650 eV, for which vanadium and oxygen pseudopotentials are well converged. BAND program w14x uses a matrix diagonalization technique to solve Kohn–Sham equations w15,16x. It employs a numerical Gaussian integration scheme w17x for the Hamiltonian matrix elements, and a quadratic tetrahedron method for the k-space integration w18x. We have used a basis set of double-zeta plus polarization ŽDZP. quality. It consists of Herman–Skillman numerical atomic orbitals ŽNAOs. and Slater-type orbitals ŽSTOs.. For vanadium, with a 3d 34s 2 ground state, the 1s–3p shells were frozen, the valence electrons are described by 3d and 4s NAOs, augmented with 3d, 4s and 4p STOs. For
oxygen, the 1s orbital was kept frozen and valence electrons were described with 2s and 2p NAO and STOs plus a 3d polarization function. For each atom a special set of s, p, d, f and g STOs was used to fit the deformation of the density w19x, these functions are required for the calculation of the Coulomb potential at the integration points and the gradient of the electron density. The Perdew–Wang nonlocal correction is implemented in a perturbative manner and is not computed self-consistently, therefore the LDA density is used as an input for nonlocal corrections. This approximation has minor effects on bond energies. In contrast to CASTEP, BAND provides Mulliken population analysis. Therefore it is possible to calculate atomic charges, overlap populations and projected density of states ŽPDOS.. Our methodology is the following: we have performed structural optimizations with CASTEP at the GGA level, and next, we used BAND to recalculate the optimized structures at the same level and perform population analysis.
3. Bulk structure We performed geometry optimizations of both lattice parameters and atomic coordinates at LDA and GGA levels using CASTEP program. A set of six special k-points was used. The unit cell contains 14 atoms, four vanadium and 10 oxygen atoms ŽFig. 1a.. The lattice parameters obtained using GGA are
Fig. 1. The optimized V–O bond lengths in Ža. V2 O5 bulk Žthe corresponding experimental values are shown in the brackets., and Žb. V2 O5 Ž001. surface Žthe corresponding optimized bulk values are in the brackets..
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544 Table 1 Optimized and experimental w20x lattice parameters and fractional coordinates of V2 O5 bulk Exp. w20x
GGA
LDA
˚. a ŽA ˚. b ŽA
11.519
11.535
3.564
3.603
3.670
˚. c ŽA V
4.373 0.149 0.000 0.105 0.149 0.000 0.458 0.320 0.000 0.000 0.000 0.000 0.000
4.422 0.149 0.000 0.102 0.148 0.000 0.465 0.320 0.000 0.001 0.000 0.000 y0.002
4.481 0.150 0.000 0.102 0.148 0.000 0.466 0.320 0.000 0.001 0.000 0.000 y0.003
O1
O2
O3
x y z x y z x y z x y z
11.557
closer to experimental values w20x than those using LDA ŽTable 1.. Therefore, we used the GGA technique in the rest of the work. The V–O bond lengths are well reproduced ŽFig. . 1a , the deviation from the experimental values w20x ˚ except the vanadyl oxygen V5O is less than 0.01 A ˚ Moreover, the for which the deviation is 0.07 A. ˚ is close to calculated interlayer distance of 2.83 A ˚ w x the experimental value of 2.82 A 20 . To be precise, our DFT lattice parameters appear better than those obtained by a periodic HF method w10x. Mulliken analysis by BAND Žsee Table 2. gives results in agreement with previous DFT study with cluster models w11x. Charges on oxygen atoms decrease in the order: QŽO 3 . ) QŽO 2 . ) QŽO1 .. Therefore the highest coordinated oxygen atom bears the largest charge. Mulliken overlap populations ŽOP. of V–O bonds give a measure of the coordination of oxygens: O 3 ) O 2 ) O 1. The V–O 1 ŽOP s 0.47. bond is stronger than a V–O 2 Žtwo bonds of OP s
541
0.24 each. or a V–O 3 Žtwo bonds of OP s 0.39 and one of OP s 0.15.. Therefore V–O 1 is more covalent than the other possible V–O bonds. In contrast to earlier HF calculations w10x which gave a band gap of ; 12 eV, our calculated band gap between the top of the valence and bottom of the conduction band is about 2.0 eV, which is close to the experimental value of ; 2.3 eV w4x. It shows that the calculated V2 O5 may act as a semiconductor. The ‘experimental’ binding energy of V2 O5 can be roughly estimated from the standard heat of formation and from the heat of atomization w21x, neglecting the zero point motion and specific heat contributions, one finds y2.91 a.u. Žper cell.. Our calculated binding energy is y3.29 a.u. which is in good agreement with the experimental one and also better than HF study w10x.
4. The (001) surface The stacking of the Ž001. layers seems to be due mainly to electrostatic forces. It is so weak that V2 O5 cleaves easily along the Ž001. plane. Since only van der Waals bonds are broken, it is assumed that the remaining bonds are not modified such that the Ž001. surface remains identical to a parallel bulk plane w5x. Ab initio DFT and semi-empirical SINDO methods w22x show no influence of a second layer on the surface properties. In our calculations we used only one vanadium layer ŽFig. 1b. as a model for the surface. In CASTEP calculations successive slabs along the c direction are separated by a vacuum region. The shortest distance between atoms belonging to ˚ interlayer interacsuccessive slabs is larger than 6 A; tion is not significant at such a distance. The energy difference between the bulk and the Ž001. surface is only 4 kcalrmol which is an estimation of the weak
Table 2 Mulliken charges and total overlap populations of the various V–O bonds of V2 O5 bulk and Ž001. surface Charges Overlap population
Atoms
V
O1
O2
O3
bulk Ž001. surface bulk Ž001. surface
q1.34 q1.33 1.64 1.62
y0.37 y0.33 0.47 0.45
y0.56 y0.60 0.24 = 2 0.25 = 2
y0.68 y0.71 0.15r0.39 = 2 0.16r0.38 = 2
542
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
Fig. 2. PDOS pictures of Ža. vanadium atom of both V2 O5 bulk and Ž001. surface, and Žb. oxygen atoms ŽO1 , O 2 and O 3 . of Ž001. surface. The origin of the energy scale is taken at the Fermi levels Žthe Fermi levels of bulk and surface are y0.205 a.u. and y0.367 a.u., respectively..
X. Yin et al.r Applied Surface Science 130–132 (1998) 539–544
interlayer electrostatic interaction. The optimized Ža and b. surface lattice parameters remain very close to the corresponding bulk values. However, V–O 2 ˚ and and V–O 3 bonds show expansions of 0.04 A ˚ respectively, and the vanadyl V–O1 bond 0.01 A, ˚ ŽFig. 1b.. shows a small contraction of 0.01 A When going from surface to bulk, the charges of O 3 and O 2 decrease whereas that of O 1 increases. This is related to redistribution of electron density within each layer rather than interlayer electron transfer. Zhang and Henrich w6x found that the surface band structure of the UHV-cleaved V2 O5 Ž001. surface is similar to that of the bulk, and Goschke et al. w7x reported a band gap of 2.3 eV for the surface. We calculated a band gap of 2.1 eV and binding energy of y3.29 a.u. which are very close to the calculated bulk values, 2.0 eV and y3.29 a.u., respectively. These results confirm again the similarity between the bulk and the Ž001. surface.
5. Density of states of bulk and (001) surface The PDOS on vanadium orbitals are presented in Fig. 2a for both V2 O5 bulk and Ž001. surface. For surface vanadium, DOS are shifted down in energy. Then surface empty orbitals situated above the Fermi level Žequivalent to lowest unoccupied molecular orbitals, LUMOs. are closer to the Fermi level than bulk empty orbitals. This is an indication of the increase of the acidity of vanadium atom. These empty orbitals are available to interact with Lewis bases such as H 2 O Žin preparation. or NH 3 Žwork in progress.. PDOS on oxygen orbitals presented in Fig. 2b show two sets of peaks. The peaks at low energy correspond to 2s orbitals, and those close to the Fermi level correspond to 2p orbitals. The latter peaks are more broadened and cover a wide energy region because of the overlap with vanadium 3d orbitals. The stability of oxygen 2s orbitals decreases in the order: O 3 ) O 2 ) O 1. From Fig. 2b we also see that the centers of the 2p-DOS have globally the same order as 2s-DOS. Therefore O 1 occupied orbitals Žequivalent to highest occupied molecular orbitals, HOMOs. are closer to the Fermi level. This means that acidic species such as a proton will interact with O 1 rather than O 2 or O 3 . Therefore the
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basicity of the surface should decrease in the order: O 1 ) O 2 ) O 3 . In contrast, the order of atomic charges suggest the opposite trend since O 3 has the largest charge. Our preliminary results concerning water dissociation and atomic hydrogen adsorption on Ž001. surface correlate with the trend of DOS and we find that the proton is more stable on O 1 site rather than on O 3 site. This suggests that the index for the surface reactivity is the density of states rather than the atomic charges.
6. Conclusions In this work we have presented periodic density functional calculations of V2 O5 bulk and Ž001. surface. The optimized geometries at GGA level are in good agreement with experimental values, and the calculated band gap and binding energy are very close to experimental ones. Interaction between V2 O5 layers is mainly electrostatic and is found to be 4 kcalrmol. For the Ž001. surface, the structural and electronic properties are very close to those of the bulk. The systems are mostly ionic. However, the vanadyl bond V–O 1 seems to be mostly covalent. The atomic charges on oxygen atoms decrease in the order: O 3 ) O 2 ) O 1 for both V2 O5 bulk and Ž001. surface, which may suggest a large reactivity for O 3 . The PDOS show that O 1 occupied levels are closer to the Fermi level than those of O 2 or O 3 . Therefore a large reactivity can be expected for O 1 site. References w1x A.D. Costa, C. Mathieu, Y. Baxbaux, H. Poelman, G. Dalmai-Vennik, L. Fiermans, Surf. Sci. 370 Ž1997. 339. w2x K. Tarama, S. Yoshida, S. Ishida, H. Kakioka, Bull. Chem. Soc. Jpn. 41 Ž1968. 2840. w3x R. Ramirez, B. casal, L. Utrera, E. Ruiz-Hitzky, J. Phys. Chem. 94 Ž1990. 8960. w4x V.G. Mokerov, V.L. Makarov, V.B. Tulvinskii, A.R. Begishev, Opt. Spectrosc. 40 Ž1976. 58. w5x H. Poelman, J. Vennik, G. Dalmai, J. Electron Spectrosc. Relat. Phenom. 44 Ž1987. 251. w6x Z. Zhang, V.E. Henrich, Surf. Sci. 321 Ž1994. 133. w7x R.A. Goschke, K. Vey, M. Maier, U. Walter, E. Goering, M. Klemm, S. Horn, Surf. Sci. 348 Ž1996. 305. w8x A. Andersson, J. Solid State Chem. 42 Ž1982. 263. w9x J. Sambeth, A. Juan, L. Gambaro, H. Thomas, J. Mol. Catal. A 118 Ž1997. 283.
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