ARTICLE pubs.acs.org/JPCC
DFT Study of the Electronic Properties of LaOCl Surfaces Steeve Chretien and Horia Metiu* Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
bS Supporting Information ABSTRACT: We use density functional theory to study the properties of low index flat faces (i.e., not having steps) of lanthanum oxychloride LaOCl. We calculate the surface energies and the energies to make oxygen and chlorine vacancies on the surface by producing 1/2O2 or 1/2Cl2 in the gas phase. We find that the electrons left behind when the vacancies are formed are localized at the vacancy site, making these sites very reactive with electrophiles. It is also possible to make Cl vacancies by a spillover process (a Cl atom leaves its lattice site to move onto the surface) but these vacancies are not chemically active. We show that p-doping, with dopants having lower valence than La, will facilitate oxygen or chlorine vacancy formation.
1. INTRODUCTION Lanthanum oxychloride, LaOCl, is involved in the catalytic oxychlorination of methane to CH3Cl,13 in the low temperature, catalytic destruction of chlorinated methane derivatives and in the dehydrochlorination of halogenated ethane to vinyl chloride.49 The chlorination of methane is a possible route for methane activation and conversion to high value chemicals. Current methods for disposing of unwanted chlorinated hydrocarbons involve burning at very high temperature and a low temperature route is therefore desirable. Vinyl chloride is the monomer for polyvinyl chloride, the polymer produced in largest amounts after polyethylene. In the papers mentioned above, the catalyst surface is exposed to chlorine source (HCl or a halogenated alkane) and oxygen. The presence of the chlorine source provides the driving force to convert La2O3 to LaOCl and then to LaCl3. The presence of the oxygen provides the driving force for converting LaCl3 to LaOCl and subsequently into La2O3. When the surface is exposed simultaneously to a halogen source and oxygen, it will reach a steady state in which the surface composition will consist of a mixture of Cl and O atom (and, of course, La). The O to Cl ratio will depend on the partial pressure of the oxygen and chlorine source and the temperature. The catalyst in the above processes is a LaOxCly surface layer. In this paper, we use density functional theory to examine some of the chemical properties of lanthanum oxychloride (LaOCl) surfaces, which we consider to be an idealized model of a halogenated catalyst surface. The methodology used in the calculations is described in section 2. Previous calculations3,6,8 examined only the (001) face, which is the largest face in the crystallite. We examine the (001), (101), (100), (111) and (110) faces because their structure is different and therefore they may have different reactivity. In Section 3, we give the calculated surface energies of these faces. Section 4.1 presents the energy to remove a Cl atom from the surface to make 1/2Cl2 in gas phase and a chlorine vacancy. r 2011 American Chemical Society
In section 4.2 we calculate the energy to pull a Cl atom from the surface and adsorb it on another surface site. We call this a spillover effect. Section 5 presents similar results for oxygen. In addition, we examine the energy of oxygen vacancy formation by desorption of OCl from the surface or by the reaction of an adsorbed oxygen atom with a surface oxygen atom to form an O2 molecule in gas. We show that these processes require too much energy to be observed in experiments. It is however probable, on one of the faces, that the oxygen and chlorine atoms on the surface exchange places. Section 6 examines the projected density of states (PDOS) of various faces of LaOCl with or without defects (vacancies or spillover). The PDOS when an Cl or an O vacancy is present on LaOCl surfaces are shown in sections 6.2 and 6.3. Making a Cl vacancy leaves behind an unpaired electron, which used to be engaged in the bond of the removed atom with the surface. We find that for all faces, except (111), this electron occupies an orbital that is localized at the vacancy site and whose energy is in the band gap. When a Cl vacancy is made on the (111) face, the unpaired electron ends up at the bottom of the conduction band. Making an oxygen vacancy leaves behind two unpaired electrons occupying orbitals localized around the vacancy and with the energy in the band gap. In this case too, the (111) face is different and the two unpaired electrons are in the conduction band. The analysis of the density of states shows that the Cl vacancy formed by a Cl spillover is very different from the one formed by removing Cl from the surface. In the case of the spillover, there is no unpaired electron in the vacancy; the electron is used by the Cl atom to form its bond with the surface. The vacancy formed by
Received: August 1, 2011 Revised: December 9, 2011 Published: December 15, 2011 681
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removing Cl will react with electrophilic compounds, while the one formed by spillover will not. Section 8 examines the energy of Cl and O vacancy formation in the case when the solid has an additional electron or it misses an electron. This simulates the effect of dopants that are charge donors or acceptors.1012 We find that the presence of a hole greatly decreases the energy of vacancy formation, while the presence of an extra electron has a minor effect. This suggests that dopants that create an electron deficit in the system (e.g., Mg, Zn, Na) will lower substantially the energy of vacancy formation. We found this to be true13 for doped La2O3 and it is very likely to be true for LaOCl.
2. COMPUTATIONAL DETAILS 2.1. The DFT Method. The density functional theory (DFT) calculations have been performed with the VASP program1417 with the Perdew, Burke, and Ernzerhof (PBE) functional.18 The ionic cores were described by projected augmented wave (PAW) pseudopotentials.19,20 allowing 11, 6, and 7 valence electrons for La, O, and Cl atoms, respectively. The energy cutoff for the plane wave expansion was 409 eV. Relativistic effects were partially taken into account through relativistic scalar pseudopotentials. The effect of spinorbit coupling was ignored. The number of unpaired electrons (Ns) was fixed during geometry optimization. We used Ns equal to zero or two when the number of electrons was even and Ns equal to one or three otherwise. We have performed spin-restricted calculations when Ns is zero, and performed spin-polarized calculations otherwise. We report here only the results for those values of Ns that give the lowest energy. 2.2. Determination of the LaOCl Bulk Crystal Structure. The LaOCl crystal structure was determined by performing an automatic relaxation of the cell shape and volume. The positions of the atoms were varied, by using quasi-Newton optimization, until all components of the forces acting on the atoms were smaller than 0.01 eV/Å. No symmetry was imposed during the optimization procedure. The Brillouin zone was sampled using an automatically generated 9 9 5 MonkhorstPack mesh21 giving a total of 203 irreducible k-points. The convergence criterion was 105 eV for the self-consistent electronic minimization. Fractional occupancies of the bands were allowed using a window of 0.05 eV and the Gaussian smearing method. The LaOCl crystal belongs to the tetragonal space group P4/nmm. The unit cell (see Figure 1a) contains two LaOCl units. La, Cl, and O occupy sites 2(c), 2(c), and 2(a) located at (1/4,1/4, zLa), (1/4, 1/4, zCl), and (3/4, 1/4, 0), respectively. The structure of LaOCl consists of a LaO layer sandwiched between two Cl layers. A comparison between the calculated and measured22,23 structural parameters is provided in Table 1 in the Supporting Information. The unit cell dimensions obtained with PBE (a = 4.110 Å and c = 6.897 Å) are within 0.3% of the experimental values. Differences less than 0.03% are observed between the calculated and measured z-component of the fractional coordinates of the La and Cl atoms (zLa and zCl). The largest difference between experiments and theory for the bond lengths is 0.2%. The structure of the LaOCl crystal is well reproduced by DFT calculations. 2.3. Characterization of the LaOCl Surfaces. LaOCl surfaces were studied using a slab consisting of periodically repeated supercells, which are shown in Figures 26. An empty space of
Figure 1. (a) Unit cell of the LaOCl crystal structure. (b and c) Schematic representation of an LaOCl crystal showing the location of the crystallographic planes considered here. (b) Top view along the [001] direction. (c) Side view along the [100] direction.
15 Å is inserted between the slab and its periodic replica in direction perpendicular to the surface. The electrostatic interaction between the slab and its periodic images in the direction perpendicular to the surface was canceled by applying monopole, dipole and quadrupole corrections to the energy, using a modified version of the method proposed by Makov and Payne.24 We included a HarrisFoulkes correction when we calculated forces. The KohnSham matrix was diagonalized iteratively using a Davidson block iteration scheme. The convergence criterion was 104 eV for the self-consistent electronic minimization. Structural optimization was stopped when all components of the atomic forces were smaller than 0.02 eV/Å. Fractional occupancies of the bands were allowed using a window of 0.05 eV and the Gaussian smearing method. Different kmeshes were used depending on the surface and on the calculated properties. The surface energy (Es) is obtained using: Es ¼ ðEslab nEbulk Þ=SA
ð1Þ
Here, Eslab is the total energy of a completely relaxed [1 1] slab, n is the number of La2O2Cl2 units in the slab, and Ebulk is the total energy of the bulk having one unit cell (i.e., one La2O2Cl2 unit). SA is the area of the two faces of the supercell taken to be planar. This definition is good for flat surfaces but it underestimates the real area of the corrugated (101), (011), and (111) faces. 682
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Table 1. Surface Energies (Es in J/m2) of Clean and Stoichiometric LaOCl Surfacesa K-mesh
Es
(001)
9 9 1(41)
0.099
(101) and (011) (100) and (010)
5 7 1(18) 5 7 1(18)
0.516 0.598
(111)
5 7 1(18)
0.694
(110)
7 5 1(18)
0.819
surface
a
K-mesh indicates the number of subdivisions of the Brillouin zone along each lattice vectors for automatic generation of the Monkhorst Pack meshes.21 The total number of irreducible k-points for each mesh is indicated between parentheses. The results were obtained with the PBE functional and the PAW pseudopotential using one unit cell along the ^x and ^y directions and slabs composed of 9 stoichiometric layers. All the structures are singlets (Ns = 0). The surfaces are shown in Figures 26.
relaxed LaOCl surface having one O or Cl vacancy per supercell and one O or one Cl atom adsorbed at the surface site where it has the highest binding energy.
3. THE SURFACE ENERGY OF THE CLEAN STOICHIOMETRIC SURFACES We impose two conditions on the slab used for calculating the surface energies of various crystal faces. 1) The slab must contain an integer number of La2O2Cl2 units, to have the same stoichiometry as the crystal, and 2) the two surfaces of the slab must have the same structure so that the slab is not polar. These conditions leave only one way of cutting the bulk to form the crystal faces considered here. We have restricted ourselves to the planes with low indices. We have studied the crystal faces shown in Figures 26. Because of the symmetry along the [100] and [010] directions (see Figure 1a), the (010) face is identical with (100), and the (011) face is identical with (101). The manner in which these faces will appear in a crystallite is shown in parts b and c of Figure 1. The (110) and the (100) surfaces were not observed in experiments.22 The surface energies Es obtained for slabs composed of 9 stoichiometric layers are given in Table 1. Tests were performed to ensure that the values of Es are converged with respect to the number of stoichiometric layers and the number of k-points. The values of Es reported in Table 1 are converged within 0.002 J/m2 for all surfaces. Increasing the number of k-points and number of layers causes a variation of less than 2%. We find large differences between the values of Es of various faces. The (001) face has the lowest energy (Es= 0.099 J/m2) and the (110) the largest (Es = 0.819 J/m2). The surface energy increases in the following order: (001) < (101) = (011) < (100) = (010) < (111) < (110). We do not know experimental values for surface energy but we can use the calculated surface energies and the GibbsWulff construction25,26 to determine the shape of a LaOCl crystal and compare it to the measured shape.22 The LaOCl crystallite described by Maslen et al.22 has two (001), four (101) and eight (111) faces whose centers are located, respectively, at 3.6, 12.5, 12.5, and 16.2 μ from the center of the crystallite. According to the GibbsWulff theorem, these distances imply that the surface energy of various faces increase in the following order: (001) < (101) = (011) < (111). This is in agreement with the trend found in our calculations. However, this correlation may be fortuitous.
Figure 2. (a) Top view of the LaOCl(001) surface showing a [3 3] supercell. The unit cell is defined by the region contained within the black dashed lines. The x-, y-, and z-axes are aligned along the [100], [010], and [001] directions, respectively. (b) Side view of the LaOCl(001) surface along the [100] direction showing a slab composed of two stoichiometric layers. We show only two stoichiometric layers (more layers were used in the calculations). The atoms in the bottom stoichiometric layer (BL) are colored differently from the ones in the top stoichiometric layer.
The vacancy formation energy (Evf[X]) is the energy needed for removing one atom (X is either O or Cl) from the surface to form 1/2X2 in the gas-phase. Evf[X] is calculated with: 1 Evf ½X ¼ E½LaOClðDÞ þ E½X2 E½LaOClðSÞ 2
ð2Þ
Here, X stands for O or Cl, E[X2] is the total energy of O2 or Cl2 in gas-phase, E[LaOCl(S)] is the total energy of the stoichiometric slab, and E[LaOCl(D)] is the total energy of a relaxed, defective LaOCl slab having one O-vacancy or one Cl-vacancy in the surface of the supercell. The spillover energy (Espill) corresponds to the energy needed for removing one atom from its equilibrium position in the top surface layer of the stoichiometric slab (creating a vacancy) and putting it on the surface site for which the atom has the largest binding energy. The spillover energy is similar to the vacancy formation energy except that the removed atom is bound to the surface instead of desorbing from it as half a diatomic molecule. Espill[X] is calculated using: Espill ½X ¼ E½X=LaOClðDÞ E½LaOClðSÞ
ð3Þ
Here, X stands for O or Cl, E[LaOCl(S)] is the total energy of the stoichiometric surface, E[X/LaOCl(D)] is the total energy of a 683
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Figure 4. (a) Top view of the LaOCl(101) surface showing a [2 3] supercell. The unit cell is defined by the region contained within the black dashed lines. The y-axis is aligned along the [010] direction. (b) Side view of the LaOCl(101) surface along the [010] direction. (c) Side view along the x-axis. We show only two stoichiometric layers (more layers were used in the calculations). The atoms in the bottom stoichiometric layer (BL) are colored differently from the ones in the top stoichiometric layer.
Figure 3. (a) Top view of the LaOCl(100) surface showing a [2 3] supercell. The unit cell is defined by the region contained within the black dashed lines. The x- and y-axes are aligned along the [001] and [010] directions, respectively. (b) Side view of the LaOCl(100) surface along the [010] direction. (c) Side view along the [001] direction. We show only two stoichiometric layers (more layers were used in the calculations). The atoms in the bottom stoichiometric layer (BL) are colored differently from the ones in the top stoichiometric layer.
which the halogen that goes into CH3Cl originates from the surface; the role of HCl is to replenish the halogen removed from the surface by the desorption of CH3Cl. Making a halogen vacancy is therefore an important step in the reaction mechanism. This means that the energy of halogen-vacancy formation is a descriptor of the reactivity, for oxyhalogenation, of different faces of LaOCl. A face from which it is easier to remove a Cl atom (to form 1/2Cl2 in gas) is more active for oxychlorination. Because of the large size of the supercell needed for calculating the energy of vacancy formation, the Brillouin zone was sampled at the Γ point only. Increasing the number of irreducible k-points to two, by using a 2 2 1 Monkhorst-Pack mesh,21 affects the vacancy formation energies by less than 0.05 eV (less than 1%), which we consider negligible. The distances between a vacancy site and its periodic images are 12.33 Å on the (001), (100), and (101) surfaces, 11.63 Å on the (110) surface, and 16.06 Å on the (111) surface. These large distances should minimize the vacancy vacancy interaction. For the LaOCl(001) surface, increasing the size of the supercell from a [3 3] to a [4 4] supercell changes the Cl and O vacancy formation energy by 0.05 eV at most. The lowest energy structures of the slabs with a Cl vacancy have one unpaired electron (Ns = 1). Except for the (110) surface, two kinds of Cl atom are present in the top stoichiometric layer (see Figures 2b, 3b, 4b, 5b, and 6b). We refer to them as the upper and the lower Cl, meaning closer or further from the vacuum, respectively. Removing one Cl atom in the top stoichiometric layer of the surfaces shown in Figures 26 results in the following Cl vacancy
The experiments measured the shape of crystallites exposed to atmosphere and it is very likely that their surface was contaminated. This contamination and the presence of steps and defects (e.g., Cl or O vacancies) affect surface energy and the measured crystallite shape in a way that we cannot determine. Such effects are not included in our calculations. It has been the tendency in surface science to study the properties of the face that has the lowest surface energy, in the belief that because this has the largest area it is likely to be the most important in catalysis. It is not clear that this reasoning is correct. If catalytic activity is structure dependent, then different faces should have different reactivities. It is possible that a high surface energy indicates a high reactivity, and such a face contribute more to product formation than a less active face that has a bigger area. A dramatic example of this situation is provided by the MoS2 crystallites whose face with largest area is inactive.27
4. THE FORMATION OF CHLORINE VACANCIES 4.1. Chlorine Vacancy Formation by Desorbing Cl2 from the Surface. Lercher and co-workers2,3,28 have studied the
oxychlorination reaction 2CH4 + 2HCl + 1/2O2 = 2CH3Cl + H2O catalyzed by either LaCl3 or LaOCl or LaO3. These materials have the same catalytic activity, if they are given time to reach steady state under reaction conditions. The reaction takes place through a Marsvan Krevelen like mechanism, in 684
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Figure 5. (a) Top view of the LaOCl(110) surface showing a [2 2] supercell. The unit cell is defined by the region contained within the black dashed lines. The x-axis is aligned along the [001] direction. (b) Side view along the y-axis of the LaOCl(110) surface. (c) Side view along the [001] direction. We show only two stoichiometric layers (more layers were used in the calculations). The atoms in the bottom stoichiometric layer (BL) are colored differently from the ones in the top stoichiometric layer.
coverage: 0.11 monolayer (ML) for the (001) surface, 0.17 ML for the (100), (101), and (111) surfaces, and 0.25 ML for the (110) surface. Here, a monolayer refers to the total number of Cl atoms in the layer from which the atom was removed. For example, there are nine upper Cl atoms in the top stoichiometric layer of the unit cell for the (001) surface (see Figure 2(b)]. Removing one of these Cl atoms corresponds to a vacancy concentration of 1/9 = 0.11 ML. The lower Cl vacancy on the (001) surface cannot be seen in the top view of the surface (see Figure 2a) and it is not accessible to a gas phase molecule. This is not the case for the (100), (101), and (111) surfaces (see the top view of the surfaces shown in Figures 3a, 4a, and 6a). The (111) surface is more open than the (100) surface and the lower Cl atom in the (111) face is more accessible to a gas phase molecule. For some oxides the calculated vacancy formation energies depend on the slab thickness. A dramatic example is the rutile TiO2(110) surface2933 for which the energy to form an oxygen vacancy at the surface varies with the number of layers used in the calculations and the number of layers allowed to relax. In the worse case this variation is as large as 0.84 eV (corresponding to a 30% deviation).29,30 Because of this we have tested how the Clvacancy formation energy depends on the slab thickness and the number of oxichloride layers that are allowed to relax (i.e., they are not kept in the bulk-positions). The results of these tests are given in Table S2 in the Supporting Information. Using four stoichiometric layers and allowing three of them to relax lead to converged results (the change in the vacancy formation energy when adding one extra layer is small). The only exception is the
Figure 6. (a) Top view of the LaOCl(111) surface showing a [3 2] supercell. The unit cell is defined by the region contained within the black dashed lines. (b) Side view along the x-axis of the LaOCl(111) surface. (c) Side view along the y-axis. We show only two stoichiometric layers (more layers were used in the calculations). The atoms in the bottom stoichiometric layer (BL) are colored differently from the ones in the top stoichiometric layer.
(111) surface where the change between the best calculation (four layers with three layers relaxing) and the next best calculation is fairly substantial (i.e., 0.28 eV or 9.2%). Adding a fifth stoichiometric layer to test whether the 2.76 eV value for the (111) surface is converged exceeds the scope of this paper. The problem observed for the LaOCl(111) surface is not corrected by the inclusion of the on-site correction34 by using the PBE + U functional or by the inclusion of 25% of the exact DFT exchange by using an hybrid functional. The upper and lower Cl vacancy formation energies obtained for a [3 2] supercell and a the slab composed of two stoichiometric layers decrease by less than 0.08 eV when the on-site correction is applied to the 5d electrons of the La atoms (we used the values of the parameter Ueff ranging from 0.5 to 9.5 eV in increments of 1 eV). The Cl vacancy formation energies increase by about 0.2 eV when the hybrid-PBE functional (HSE06)3537 is used. We speculate that the larger difference observed with the HSE06 functional is related to the smaller supercell used (a [2 2]instead of a [3 2]). The converged results (see above) for the energy of Clvacancy formation are given in Table 2. It is curious that for all 685
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Table 2. Energies Evf[Cl] of Vacancy Formation by Removal of One Chlorine Atom To Form 1/2Cl2 in the Gas and the Energy Espill[Cl] To Form a Vacancy by Chlorine Spillover (in eV)a Evf
Evf
Espill
Espill
surface
[Cl(upper)]
[Cl(lower)]
[Cl(upper)]
[Cl(lower)]
LaOCl(001)
4.21
3.92
2.04
2.03
LaOCl(100) LaOCl(101)
4.23 4.21
3.86 3.99
0.24 0.54
0.08 0.66
LaOCl(110)
3.86
LaOCl(111)
2.94
2.76
0.10 0.73
Table 3. Energies Evf[O] of Vacancy Formation by Removal of One Oxygen Atom To Form 1/2O2 in the Gas and the Energy Eex To Exchange the Position of a Cl and O Atom in the Surfacea Evf[O]
Eex
LaOCl(001)
6.38 (Ns = 0)
3.68
LaOCl(100)
6.53 (Ns = 0)
1.32
LaOCl(101) LaOCl(110)
6.35 (Ns = 0) 5.63 (Ns = 0)
1.06 0.40
LaOCl(111)
4.94 (Ns = 2)
1.40
surface
a
Ns is the number of unpaired spins in the reduced structure. The results were obtained with the PBE functional, the PAW pseudopotential. See Figures 26 for the supercells used in calculations.
0.58
a
The structures formed by Cl spillover are singlets (Ns = 0) and those formed by desorption of 1/2Cl2 are doublets (Ns = 1). The results were obtained with the PBE functional and the PAW pseudopotential.
in an oxidation reaction with a Marsvan Krevelen mechanism. The smaller the energy to form an oxygen vacancy on an oxide surface the better oxidant the surface is.3840 It is for this reason that we are interested in the energy of oxygen vacancy formation on the oxychloride surface. Table 3 gives the energy of oxygenvacancy formation for the faces of the LaOCl crystal shown in Figures 26. We consider only the removal of the oxygen atoms from the oxygen layer closest to the vacuum. The dependence of these energies on the number of layers in the slab and the number of layers with fixed geometry is given in Table S3 of the Supporting Information. We report here results for four stoichiometric layers with the atoms in the bottom layer fixed in the positions they have in the bulk oxychloride. The lowest energy structures of the (001), (100), and (101) faces that have an oxygen vacancy on them, are singlets (Ns = 0), while the lowest energy of the (111) face having an oxygen vacancy on it, is a triplet (Ns = 2). The spin state preferred by the defective (110) surface depends on the number of fixed layer during geometry optimization (see Table S3 in the Supporting Information). The singlet is more stable when the maximum number of layers are allowed to relax. However the difference between the energies of singlet and the triplet is 0.06 eV, which is less than the error of the DFT method. Evf[O] increases in the following order: 4.9 eV (111) < 5.6 eV (110) < 6.4 eV [(001) and (101)] < 6.5 eV (100). This trend is similar to that reported for the creation of the upper Cl vacancy. The energy required to form O-vacancies is higher than that needed for forming Cl-vacancies by about ∼2 eV. We conjecture that, when involved in a Marsvan Krevelen process, the (111) surface is the best oxidant and the best chlorination agent, and (100) is the least active. The fact that it is easier to make Cl vacancies than oxygen vacancies is consistent with experiments performed in Lercher’s group2,3,28 regarding the reaction CH4 + HCl + 1/2 O2 = CH3Cl + H2O. The Cl atom in CH3Cl originates from the surface, while the O atom in water originates from the gas phase oxygen. 5.2. The Energy To Exchange a Surface Oxygen Atom with a Surface Chlorine Atom. Our calculations show that oxygen spillover is unlikely to occur because it requires very large energies. We have found however that it is possible to exchange the position of an oxygen atom with that of a chlorine atom. The energies of this process obtained using a slab composed of two stoichiometric layers are given in Table 3. Note the substantial dependence on the face: 3.68 eV for (001) and 0.40 eV for (110). At the temperatures where the oxychlorination is performed we
faces it takes less energy to make a lower vacancy than an upper vacancy. There is no correlation between the surface energy and the energy of Cl vacancy formation in either the upper or the lower chlorine layer. Table 2 shows that Evf[Cl(upper)] increases in the following order: 2.9 eV for the (111) face
