J. Phys. Chem. B 2006, 110, 8959-8964
8959
Electronic and Geometric Properties of ETS-10: QM/MM Studies of Cluster Models Anne Marie Zimmerman and Douglas J. Doren* Department of Chemistry and Biochemistry, UniVersity of Delaware, Newark, Delaware 19716
Raul F. Lobo Department of Chemical Engineering, UniVersity of Delaware, Newark, Delaware 19716 ReceiVed: February 10, 2006; In Final Form: March 15, 2006
Hybrid DFT/MM methods have been used to investigate the electronic and geometric properties of the microporous titanosilicate ETS-10. A comparison of finite length and periodic models demonstrates that band gap energies for ETS-10 can be well represented with relatively small cluster models. Optimization of finite clusters leads to different local geometries for bulk and end sites, where the local bulk TiO6 geometry is in good agreement with recent experimental results. Geometry optimizations reveal that any asymmetry within the axial O-Ti-O chain is negligible. The band gap in the optimized model corresponds to a O(2p) f Tibulk(3d) transition. The results suggest that the three Ti atom, single chain, symmetric, finite cluster is an effective model for the geometric and electronic properties of bulk and end TiO6 groups in ETS-10.
1. Introduction ETS-10 is a microporous titanosilicate containing O-Ti-O chains that are embedded in a SiO2 framework. The chains of O-Ti-O behave as one-dimensional semiconducting wires insulated by a SiO2 shell.1,2 ETS-10 has been shown to photodegrade various organic pollutants,3-6 and due to its porous nature, can selectively photodegrade substrates based on size or shape.7,8 Recent studies have shown that the photocatalytic activity of ETS-10 can be enhanced by the use of dopants5,9-11 and/or increasing the defect concentration.8 In addition, ETS10 has attracted attention for its high ion exchange capacity.12-15 The unit cell composition of ETS-10 is [Na+/K+]2[Si5Ti1O13]2-.16,17 The unit cells can be stacked in two different sequences along the [001] direction to form zigzag (polymorph A) or diagonal (polymorph B) channels. In the real ETS-10 system, an intergrowth of both polymorphs occurs, creating numerous stacking faults and line defects.18,19 Anderson et al.16,19 first proposed the structure of ETS-10 using a combination of electron microscopy, X-ray diffraction data, NMR, and molecular modeling techniques. Their findings were later confirmed by Wang and Jacobson using single-crystal diffraction.17 The structure of ETS-10 is built from TiO6 octahedra which share axial vertexes to form zigzag O-Ti-O wires running in two perpendicular directions. The equatorial oxygens in the octahedra are bonded to an extended SiO2 framework with large SiO2 pores (8 Å × 5 Å),16 separating O-Ti-O chains. The Ti atoms are in a tetravalent state requiring two cations (Na+/K+) per TiO62group. Five unique cation sites have been identified: four along the O-Ti-O chain and one at the edge of the large SiO2 pore.20 Similar to TiO2, the optical band gap transition in ETS-10 is a O(2p) f Ti(3d) transition.21,22 The experimental band gap energy of ETS-10 is ∼4.03 eV,1,2 which is blue-shifted from that of TiO2 (anatase: 3.2 eV). This blue-shift has been attributed to quantum confinement in the radial direction of the O-Ti-O wire in ETS-10.1,2 Interestingly, the optical properties * Address correspondence to this author. Phone: 302-831-1070. Fax: 302-831-6335. E-mail:
[email protected].
of the O-Ti-O wire are not significantly affected by the extended structure1,2 due to the highly insulating SiO2 framework, which makes the potential outside the O-Ti-O chain very large. For this reason, the local geometric and electronic structure of the O-Ti-O wire dominate the optical properties of this material. Previous experimental17,23-25 and theoretical24,26 research has confirmed a distorted octahedral coordination for Ti4+, with equatorial Ti-O distances of ∼2.02 Å. There remains some uncertainty, however, regarding the geometry along the O-Ti-O chain. Initially, the entire extended X-ray absorption fine structure (EXAFS) spectrum was modeled with a large asymmetry within the O-Ti-O chain: one short (1.71 Å) and one long (2.11 Å) Ti-O axial bond length for each Ti4+.24 These findings have been contradicted by recent studies, which have identified two equivalent Ti-O axial bond lengths of ∼1.88 Å.25,26 In addition, the extent of nonlinearity in the O-Ti-O chain is unclear. In the asymmetric chain model proposed by Sankar et al.24 the Ti-O-Ti angle is 165°. In model structures with a more symmetric O-Ti-O chain, such as that proposed by Wang et al.17 based on single-crystal data, or the periodic ab initio model calculated by Damin et al.,26 more obtuse angles of 177.9° and 172.6°, respectively, have been reported. The model recently suggested by Prestipino et al.,25 based upon a fit to EXAFS data, has a completely linear chain, ∠Ti-O-Ti ) 180°. In this paper we describe a computational model that can be fully optimized to investigate the optimal local geometry of the O-Ti-O chain. Previous theoretical research has investigated the local geometric and electronic structure of bulk states within ETS-10 with use of periodic models.26,27 Due to the fact that redox reactions take place at Ti-OH sites generally found on the surface and/or defect sites of ETS-10, it would be advantageous to develop a finite system that allows for the modeling of both bulk and surface TiO6 states. To model the constraints imposed by the framework, we have adopted an embedded cluster method, which has been successfully applied to cluster models of similar microporous titanosilicate systems.28-31
10.1021/jp0608877 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/14/2006
8960 J. Phys. Chem. B, Vol. 110, No. 18, 2006
Figure 1. Model structures for studies of chain length effects: (a) 3Ti model and (b) 5Ti model. Color key: O-Ti-O chains highlighted in blue for clarity; Ti in teal; Si in gray; O in red; Na in purple; and H in white.
We have divided this investigation into two parts. In the first, three unoptimized models of varying length have been used to investigate the effects of chain length on the optical properties of ETS-10. The results of this study have been used to develop finite models that represent the bulk and surface sites in the O-Ti-O chain of ETS-10, while minimizing computational demands. In the second part of the study these cluster models have been used to investigate the Ti4+ bulk and end-site effects on the geometric and electronic structure of ETS-10. We have optimized these clusters using a hybrid QM/MM embedded cluster method, which allows for full optimization of the cluster by placing mild forces at the boundary regions. 2. Computational Methods All models contain a single TiO2 chain encapsulated in the supporting SiO2 framework, with the geometry being derived
Zimmerman et al. from the coordinates reported by Anderson et al.16 The optimal cation sites reported by Grillo and Carrazza32 were used for initial placement of Na+ counterions. All models have been terminated with hydroxyl groups. Terminating H’s were placed at the same bond angles and dihedral angles as the appropriate Si or Ti atom in the extended structure reported by Anderson et al.16 A bond distance of 0.96 Å has been used for all terminating O-H bonds. Figure 1 illustrates two of the models used for the chain length investigation. These consist of small finite cluster models containing three Ti (3Ti) and five Ti (5Ti) atoms within the O-Ti-O chain. A one-dimensional periodic model has also been considered, which includes four Ti atoms in the unit cell (pTi). Cutting these systems from their three-dimensional hosts creates boundary regions that do not have realistic forces, making it difficult to carry out full optimizations. For this part of the study, we are interested in the differences of the electronic properties of varying chain length models and are not concerned with the exact geometric structure. Therefore, no optimizations have been carried out on these models. Using the Gaussian 03 computer code33 all three models (3Ti, 5Ti, pTi) have been calculated using density functional theory (DFT). The 1996 functional of Perdew, Burke, and Ernzerhof34 has been employed with a CEP-121G* basis set on Na, O, Si and a CEP-121G basis set on Ti, H.35 In the second part of this study, we have employed the embedded cluster ONIOM method, developed by Morokuma and co-workers36,37 as implemented in Gaussian 0333 for the optimization of an asymmetric (3Ti-opt-A; Figure 2a) and a Ci symmetric (3Ti-opt-S; Figure 2b) model of a three-Ti cluster. This method enables us to apply forces at the cluster boundaries without significantly increasing the computational costs. The clusters have been optimized by using density functional theory (DFT), using the same PBE/CEP-121G* (Na, Si, O) or PBE/ CEP-121G (Ti, H) model chemistry as described above. Initial cluster geometries were taken directly from the 3Ti model with slight accommodations made in the symmetric case to allow for an inversion center. These clusters were embedded into an extended SiO2 framework,38 which has been described by using the molecular mechanics (MM) Universal Force Field (UFF) method.39 For 3Ti-opt-A, the MM layer was formed by the
Figure 2. Front and side views of the (a) asymmetric (3Ti-opt-A) and (b) Ci symmetric (3Ti-opt-S) ONIOM models used for optimization. The DFT layer is shown in the ball-and-stick form, the MM layer is shown in stick form. Color key: Ti in teal; Si in gray; O in red; Na in purple; and H in white.
Electronic and Geometric Properties of ETS-10
J. Phys. Chem. B, Vol. 110, No. 18, 2006 8961
Figure 3. Highest occupied molecular orbitals for (a) 3Ti, (b) 5Ti, and (c) periodic models. For all models the state at the top of the valence band is clearly due to the occupation of O(2p) orbitals delocalized along the axial O within the O-Ti-O chain. The periodic model shows two unit cells along the axial direction and was created with the Cubist program [ref 48].
Figure 5. Delocalized Ti(3d) states for (a) 3Ti, (b) 5Ti, and (c) periodic models. The Ti(3d) states shown here are located near the bottom of the conduction band and are preceded by the unoccupied edge states depicted in Figure 4. The periodic model shows two unit cells along the axial direction and was created with the Cubist program [ref 48].
depends on the “g factor” defined by
g)
Figure 4. Lowest unoccupied molecular orbitals for the (a) 3Ti, (b) 5Ti, and (c) periodic models showing examples of the types of edge states observed. The periodic model shows two unit cells along the axial direction and was created with the Cubist program [ref 48].
surrounding SiO2 pores on either side of the TiO2 chain. The low layer of 3Ti-opt-S includes not only these SiO2 pores but also regions at the ends of the TiO2 chain. This extension of the low layer in 3Ti-opt-S was done to make the forces at the end of the cluster more representative of an extended chain. In all geometry optimizations the MM region has been fixed, while the DFT region has been allowed to relax. This allows us to fully optimize the DFT cluster while still placing some mild forces at the boundaries. The extrapolated energy for the two-layer ONIOM system, E(ONIOM), is defined as follows:
E(ONIOM) ) EC,DFT + EX,MM - EC,MM
(1)
where EX,MM is the energy of the entire model (X, extended system) calculated with molecular mechanics (MM), and EC,DFT and EC,MM are energies of the cluster system (C) calculated with DFT and MM, respectively. In our model the outer region of the cluster system was terminated with O atoms, with H used as link atoms to cap the dangling bonds and create terminating O-H groups for the cluster. Placement of the H link atoms
d(BDFT-L) d(BDFT-BMM)
(2)
where d(BDFT-L) is the distance between the DFT boundary atom (B) and the link atom (L), and d(BDFT-BMM) is the distance between the boundary atoms of the DFT and MM layers. Assuming a value of ODFT-H ) 0.96 Å, we have calculated g values using average BDFT-BMM distances from preliminary optimizations. With use of this method, optimal g values of 0.5878 and 0.5078 for the ODFT-SiMM and ODFTTiMM regions, respectively, have been chosen. Although the 3Ti, 5Ti, 3Ti-opt-A, and 3Ti-opt-S models used in the present work are finite clusters with discrete states, for simplicity, we refer to the HOMO f LUMO transition as the “band gap”. In addition, we refer to the HOMOs and LUMOs of the finite cluster models as the top of the valence band and bottom of the conduction band, respectively. For all models optical transition energies have been calculated by taking the difference in energy between the appropriate LUMO and HOMO.
Eg ) E(LUMO) - E(HOMO)
(3)
To test the accuracy of this method, we have also applied time-dependent DFT40-42 (TDDFT) to the 3Ti-opt-A and 3Tiopt-S systems, as a more accurate method of calculating excitation energies. It is well-known that DFT systematically underestimates the band gap of semiconductors, with typical errors ∼40%.43,44 These errors are generally corrected by using a scissors operator, which rigidly shifts the conduction band upward.45 We are primarily interested in the differences among models, so all values will be reported “as calculated” with no shift assumed. 3. Results and Discussion 3.1. Chain-Length Effects: 3Ti, 5Ti, and pTi. For the unoptimized 3Ti, 5Ti, and pTi models (Figure 1), similar orbital contributions are found for the top of the valence band and bottom of the conduction band. As expected,21,22 the primary atomic orbital contributions to the top of the valence band (Figure 3) arise from occupation of the O(2p) orbitals of the
8962 J. Phys. Chem. B, Vol. 110, No. 18, 2006
Zimmerman et al.
TABLE 1: Predicted Optical Band Gap Energies Calculated from Orbital Energy Differences and TDDFT Methods in Comparison with the Experimental Band Gap of 4.03 eV [ref 1] model
3Ti
5Ti
periodic
3Ti-opt-A
3Ti-opt-S
LUMO-HOMO TDDFT
3.14a
3.01a
2.94a
3.09 3.10
3.09 3.10
a
Assumes that the unoccupied edge states can be ignored (see text).
axial O (within the O-Ti-O chain). The LUMOs, which are concentrated at the edge of the cluster, appear to be artifacts of the model (Figure 4). They are not consistent with expectations from previous work where the bottom of the conduction band is dominated by Ti(3d) character.21,22 The geometry for all three models was cut directly from an empirically determined threedimensional periodic system and has not been optimized. Consequently, the edges do not represent realistic surface geometries. For all three models the series of unoccupied edge states are followed by a delocalized Ti(3d) state (Figure 5). Under the assumption that the unoccupied edge states are artifacts, we have disregarded them in determining band gap energies, Eg. Instead, we calculated energies based upon an O(2p) f Ti(3d) transition.21,22 Table 1 compares the relative band gap energies for the 3Ti, 5Ti, and periodic systems calculated with eq 3, which shows that there is little variation in the O(2p) f Ti(3d) transition energy as we increase chain length. Thus, even the smallest 3Ti model gives an estimate of the band gap comparable to the one-dimensional periodic model, once edge states are accounted for. These findings are consistent with our expectations from the quantum confinement model of the ETS-10 chain modeled as a quantum well wire of TiO2 surrounded by a highly insulating medium,1,2,46,47
∆Eg )
h2 h2 + 2 4µD 8µL2
(4)
Here, ∆Eg is the change in the band gap relative to bulk TiO2, h is Plank’s constant, µ is the reduced effective mass of the electron-hole pair, and D and L are the diameter and length of
Figure 6. DFT cluster region for ONIOM models. Some atoms are not shown as spheres to facilitate visualization of the structure. The numbering scheme shown here has been used to identify geometric parameters in Table 2.
the quantum wire, respectively. The first and second terms on the right-hand side of eq 4 represent the radial (∆EgR) and axial (∆EgA) quantum confinement effects, respectively. There is significant quantum confinement in the radial direction of ETS10, leading to a blue-shift of ∆EgR ≈ 0.85 eV compared to anatase.1,2 Using this experimental band gap shift, Lamberti2 has calculated µXY values for the reduced effective mass of the electron-hole pair perpendicular to the axis of the wire to be ∼1.97me, where me is the free electron mass. Assuming a similar value of µz for the reduced effective mass of the electron-hole pair along the wire, we can approximate the band gap shift due to a finite chain length, ∆EgA. For the 3Ti model with an oxygen-to-oxygen length of L ) 1.12 nm and assuming µz ) 1.97me, ∆Eg ) 0.15 eV. This is consistent with the results of our DFT calculations showing that the band gap energy differences between a finite O-Ti-O chain containing three Ti atoms and an infinitely long O-Ti-O chain are small. 3.2. Optimized Structures: 3Ti-opt-A and 3Ti-opt-S. 3.2.1. Geometric Structure. Optimized geometric parameters for the asymmetric (3Ti-opt-A) and Ci symmetric (3Ti-opt-S) ONIOM ETS-10 models are reported in Table 2, using the atom labeling in Figure 6. The optimized structures for both systems are quite similar, with respect to the local chain geometry and the SiO2
TABLE 2: Predicted Geometric Parametersa for the Local O-Ti-O Chain Geometry in the Optimized ETS-10 ONIOM Model and Comparisons to Literature Values (Atom Labels Are Defined in Figure 6) present work 3Ti-opt-A 3Ti-opt-S Ti1-Ti2 Ti1-O1 Ti1-O2 Ti2-O1 Ti2-O3 Ti3-O2 Ti3-O4 Ti1-O5 Ti2-O6 Ti3-O7 Ti1-O8 Ti1-O6 Ti1-O9 Ti2-Si1 Ti1-Na1 O5-Si1 Ti1-O1-Ti2 Ti1-O2-Ti3 Ti1-O5-Si1 a
3.74 1.89 1.97 1.94 1.96 1.86 2.07 1.99-2.02 1.92-2.09 1.91-2.13 3.53-3.56 3.84-4.42 3.92-4.54 3.20-3.31 3.07-3.14 1.64-1.65 157.7 152.6 122.4-128.8
Distances in Å and angles in deg.
3.71 1.88 1.88 1.89 1.92 1.89 1.92 2.03 1.92-2.11 1.92-2.11 3.56 4.16-4.40 3.92-4.40 3.27-3.32 3.06 1.65 157.6 157.6 124.8-128.4
EXAFS25
EXAFS24
periodic ab initio26
XRD17
3.73 1.87(1) 1.87(1)
3.76 1.71 2.02
3.743 1.872(1) 1.872(1)
3.759 1.883 1.883
2.05(1)
2.02
1.99(1)
2
3.78(2) 4.10(3) 4.22(3) 3.32 3.05(2) 1.60(2) 180(5) ( 30
3.31 3.07 1.63 165
3.74 4.17 4.23-4.25 3.27 3.15-3.20 1.61 177.9
3.5 4.05-4.15 4.18-4.33 3.26-3.27 2.976 1.61-1.62 172.6
132(5) ( 15
130
130.2
128.6-129.8
Electronic and Geometric Properties of ETS-10
J. Phys. Chem. B, Vol. 110, No. 18, 2006 8963
Figure 7. Frontier orbitals for the Ci symmetric ONIOM optimized structure. Similar orbitals are found for the asymmetric model. At the top of the valence band O(2p) states are delocalized along the axial O, while the bottom of the conduction band is formed by a series of Ti(3d) states, one delocalized along the Tibulk atom and two delocalized over all Ti atoms (surface and bulk). Vertical positions of the orbitals represent their relative energies.
framework in the high layer cluster. This demonstrates that the inclusion of the extended MM region along the O-Ti-O chain in the 3Ti-opt-S model does not make the TiO6 end site geometry identical to that of a bulk site. Consistent with previous experimental17,23-25 and theoretical reports,24,26 both the end and central Ti atoms in our ONIOM models show a distorted TiO6 octahedron where the TiO(equatorial) bond lengths are longer than the Ti-O(axial) bond lengths. In the 3Ti-opt-A model a difference of
