Atomic Structures of CH3NH3PbI3 (001) Surfaces Limin She,†,§ Meizhuang Liu,†,§ and Dingyong Zhong*,†,‡ †
State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, and ‡Micro & Nano Physics and Mechanics Research Laboratory, School of Physics and Engineering, Sun Yat-sen University, 510275 Guangzhou, China ABSTRACT: We report on the atomic structures of methylammonium (MA) lead iodide (CH3NH3PbI3) perovskite surfaces, based on a combined scanning tunneling microscopy and density functional theory calculation study. A reconstructed surface phase with iodine dimers, coexisting with the pristine zigzag phase, was found at the MA−iodineterminated (001) surfaces of the orthorhombic perovskite films grown on Au(111) surfaces. The reorientation of surface MA dipoles, which strengthens the interactions with surface iodine anions, resulting in a slight energy reduction of 34 meV per unit cell, is responsible for the surface iodine dimerization. According to our calculation, the surface MA dipoles weaken the surface polarity and are therefore considered to be stabilizing the surface structures. KEYWORDS: organic−inorganic hybrid perovskites, surface structures, scanning tunneling microscopy, density functional theory
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reconstruction on the polar surfaces provides a compensatory depolarization field to stabilize the surfaces and at the same time alter the surface electronic structures.17,18 For instance, intricately mixed phases have been found coexisting at the SrTiO3(110) reconstruction surfaces, depending on the surface metal concentration, annealing, and oxidizing conditions.17−19 The corresponding electron redistributions on the terminations of various reconstructions suppress the perpendicular component of the dipole moment and therefore reduce the surface energy. In contrast, the SrTiO3(100) surface with weak polarity is more stable than the (110) and (111) surfaces.17,18 Compared with inorganic perovskites, how the organic cations in hybrid perovskites affect the surface structures is unknown. Here, we report on the surface structures of atomically smooth MAPbI3 films by scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. Orthorhombic MAPbI3 thin films were obtained on Au(111) surfaces. Two types of surface structures, the zigzag phase and the dimer phase, were found at the methylammonium iodine (MA−I)-terminated (001) surfaces by STM: The former basically follows the original structure of the (001) planes in the bulk, while the latter exhibits iodine dimer rows with a shortened I−I distance in each dimer. We revealed that the reorientation of MA cations is responsible for the iodine dimerization. Furthermore, the net charge distributions and the effect of MA reorientation on surface polarization have been
rganic−inorganic hybrid perovskites, consisting of organic cations intercalated in the metal−halogen octahedron frameworks, have attracted much interest due to their promising applications in electronics and optoelectronics.1−7 In the past few years, their crystallographic structures and electronic properties have been intensively investigated experimentally and theoretically.8−14 The organic cations in hybrid perovskites are considered to stabilize the metal−halogen octahedron frameworks and play a key role in bulk structure transitions, although they are believed to make a negligible contribution to the electronic states near the Fermi energy (EF).9,10 For example, three types of bulk phases were found for methylammonium lead iodide (CH3NH3PbI3, MAPbI3) crystals at various temperatures from 100 to 358 K, and the corresponding phase transitions are ascribed to the possible dynamics of PbI6 octahedrons and methylammonium (MA) cations.8 Furthermore, the organic cations in hybrid perovskites affect the ferroelectric behaviors in the case of carrying intrinsic dipole moments.12,13 In general, the asymmetry of the organic cations in hybrid perovskites causes the absence of an inversion center and results in spontaneous electric polarization, which may affect the charge carrier transport in optoelectronic devices.12,15 Although the bulk structures of hybrid perovskites have been intensively studied, the information about the surface and interface structures, which are of importance for device performances,16 has been very rare so far. In the case of metal oxide perovskites, the surface structures exhibit rich phase diagrams due to the inherent instability originating from the perpendicular macroscopic polarization at the surfaces. The © XXXX American Chemical Society
Received: October 13, 2015 Accepted: December 8, 2015
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Figure 1. STM images of MAPbI3 films deposited on Au(111). (a) Large-scale image with atomically flat terraces (300 × 300 nm2; U = 2.5 V; I = 30 pA). (b) Height profile along the dashed line in (a), showing the 6.3 Å high step edge of the MAPbI3 film as well as the 2.4 Å high step edge from the Au(111) substrate. (c,d) High-resolution images of the zigzag and dimer structures (4.3 × 4.3 nm2; 2.5 V; 50 pA). The unit cells are denoted by dashed rectangles. A zigzag row is denoted by dashed line in (c), and an iodine dimer is denoted by a dashed ellipse in (d). (e) STM image of the two phases coexisting at the same region (5.6 × 5.6 nm2; U = 2.5 V; I = 50 pA). The inset is the height profile along the dashed line. (f) Model of the orthorhombic MAPbI3 structure.
stacking of two PbI6 octahedrons along the c-axis. The thickness of the topmost uncompleted layer observed by STM is one-half of the lattice constant in the c-axis, corresponding to one PbI6 octahedron layer (one MA−I layer and one Pb−I layer). According to the bulk structure (Figure 1f), the (001) surface of the orthorhombic MAPbI3 films are terminated either by MA−I or by Pb−I layers. As shown in Figure 2, we observed occasionally that the zigzag and dimer phases converted into each other, induced by tunneling current during STM tip scanning. Based on the observation of reversible transformation between the zigzag and dimer phases, assigning the two surface phases to different terminated layers (MA−I or Pb−I) is ruled out. Furthermore, our STM images of PbI2 films (not shown) indicate that both iodine and lead are visible under similar tunneling conditions. There would be four bright protrusions per unit cell for the Pb−I layer-terminated surface with a Pb−I distance of ∼3.2 Å. Therefore, based on the above analysis, we believe that the observed (001) surfaces are MA−I-terminated and the bright protrusions in our STM images are assigned to iodine anions, considering the negligible contribution of electronic states near EF from MA anions.10 The identification of a MA−I-terminated surface is further verified by our simulated STM images discussed below. Figure 3 shows the dI/dV curves obtained from different sites of the two surface phases. On both the zigzag and dimer structures, a band gap of 1.7 eV was observed between the valence and conduction bands. All of them exhibit a conduction
discussed. Our results not only elucidate the origin of CH3NH3PbI3 surface structures and the nature of phase transitions between the two surface structures but also unveil the polarized feature of the surfaces.
RESULTS AND DISCUSSION Figure 1a shows a large-scale STM image of the MAPbI3 films with atomically smooth terraces and step edges. Besides the step edges with a height of 2.4 Å originating from the Au(111) substrate, those with a height of 6.3 Å correspond to the uncompleted topmost perovskite layer, as indicated by the height profile in Figure 1b. High-resolution STM images revealed two types of surface structures coexisting at the MAPbI3 surfaces, as shown in Figure 1c,d: the zigzag phase and the dimer phase. Both structures exhibit a quasi-square unit cell containing two bright protrusions per unit cell. In the zigzag phase, the position of the bright protrusion inside the unit cell (green rectangles) is slightly deviated from the center, closer to two corners of the unit cell, resulting in zigzag rows (Figure 1c). In the dimer phase, the bright protrusion is shifted toward one corner of the unit cell with the formation of dimer (Figure 1d). Figure 1e shows the STM image of the two surface phases coexisting at the same region, indicating a height difference less than 10 pm between them (inset of Figure 1e). The measured lattice constants of a = 8.8 ± 0.2 Å and b = 8.5 ± 0.2 Å are consistent with the (001) plane of the orthorhombic structure analyzed by X-ray diffraction reported elsewhere.8 As shown in Figure 1f, the orthorhombic structure exhibits a periodic B
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MA−I units were fixed, while the MA−I-terminated surface and underlying Pb−I layer were further relaxed. The top view and side view of the relaxed MAPbI3 surface are presented in Figure 4a,b. The relaxed structure with angular distortions of the PbI6 octahedrons indicates that the neighboring MA cations are interlaced with each other, consistent with previous works.9,10 Compared with the bulk structure, the surface MA cations are 29.9 and 37.3° tilted with respect to the (001) plane. Figure 4c shows the simulated STM image by integrating the density of states from 0 to 2.5 eV of the MA−I-terminated (001) surface, in which the iodine anions appear bright while the MA cations are invisible. The simulated STM image resembles our experimental result (Figure 1c), verifying the MA−I-terminated surface of the investigated MAPbI3 films. To understand the formation mechanism of the dimer phase, we first referred to the possibility of covalent interaction between the surface iodines. Although MAPbI3 is considered an ionic material showing very weak covalence,21 it has been reported recently that both the Pb cations and I anions exhibit strong covalency, forming Pb dimers and I trimers with strong covalent bonds at some of the intrinsic defects.22 We intentionally shortened the distance between the neighboring surface iodine anions as the starting point for our calculation. In this case, the surface iodine anions moved back to the configuration of the zigzag phase during geometrical relaxation, implying repulsive interactions between the surface iodines. We further referred to the effect of surface MA orientation. The initial model was constructed by rearranging the orientation of the surface MA cations. A stable configuration was found, in which the MA cations follow a head-to-head (or tail-to-tail) fashion along the y-axis and an alternative orientation along the x-axis, as shown in Figure 4d,e. Compared with the zigzag phase, the surface MA cations are tilted with larger angles (36.1 and 58.4°) with respect to the (001) plane, and meanwhile, one of them is ∼90° rotated in the x−y plane, resulting in a total energy decrease of ∼34 meV per unit cell. Importantly, the position of the surface I anions along y-axis is accordingly rearranged, resulting in I dimer formation with a I− I distance of ∼5.3 Å, which is 0.8 Å shorter than the bulk
Figure 2. Sequential STM images acquired at the same region showing the reversible transition between the dimer and zigzag structures (4.2 × 12.8 nm2; U = 2.0, 0.85, and −1.25 V; I = 30 pA). A point defect is denoted by the short arrows in (a−c). Phase boundaries are denoted by dotted lines. Iodine zigzag rows and dimers are denoted by dashed lines and ellipses, respectively.
band minimum ∼0.7 eV above the EF and the valence band maximum ∼1.0 eV below the EF, agreeing with the results from photoelectron spectroscopy reported elsewhere.20 DFT calculations have been conducted to understand the formation mechanism of the observed surface structures. We first optimized the orthorhombic structure of the MAPbI3 crystal, using the initial lattice constants, the orientation of MA cations and atomic coordinates from the X-ray diffraction results.8 The optimized lattice constants are a = 9.0 Å, b = 8.4 Å, and c = 12.8 Å, consistent with our STM measurement. Based on the optimized crystal structure, we constructed a MAPbI3 slab consisting of three Pb−I/MA−I repeated units in the c-axis with a vacuum layer of 20 Å. The two bottom Pb−I/
Figure 3. dI/dV spectra acquired from different sites of the two surface structures: (a) zigzag structure; (b) dimer structure. The sites are denoted in the inset. The curves are vertically shifted for clarity, and their intensities are normalized with an identical value at a bias of −1.4 V. The conduction band minimum and valence band maximum are 0.7 eV above and 1.0 eV below the EF, respectively, resulting in an energy gap of 1.7 eV. C
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Figure 4. Geometrical structures of MA−I-terminated MAPbI3 (001) surfaces optimized by DFT calculations. (a−c) Side view, top view, and simulated STM image of the zigzag phase. (d−f) Dimer phase. The simulated STM images were acquired by integrating the density of states from 0 to 2.5 eV.
Figure 5. Deformation charge density of MA−I-terminated MAPbI3 (001) surfaces. (a) Zigzag structure. (b) Dimer structure. The isosurfaces of positive and negative values (±0.02e/Å3) are shown in blue and green colors, respectively. The dipole direction of MA cations is denoted by brown arrows.
structure. Figure 4f shows the simulated STM image of the dimer phase, agreeing well with our STM result. On the basis of the calculations, the energy barrier of the phase transition between the two surface structures is 0.18 eV per unit cell. In the transition state, the orientation of the surface MA cations is almost perpendicular to the (001) plane. Our result is comparable with the rotational barrier of the MA cation (∼50 meV) in the tetragonal CH3NH3PbI3 crystal, and such relatively low-energy barriers explain the surface phase transition observed in our experiments and bulk phase transition reported in the literature.12,13,23−26
Our atomic charge analysis indicates that the surface MA cations are, on average, +0.723e charged in both the zigzag and dimer phases. Such positive charge is mainly contributed from the ammonium H atoms, which exhibit an average +0.468e (+0.471e) charge in the zigzag (dimer) phase. Meanwhile, the surface I anions are, on average, −0.590e (−0.598e) charged in the zigzag (dimer) phase. Compared with the zigzag phase, the slightly larger amount of charge on the surface ammonium H and I in the dimer phase indicates relatively stronger electrostatic interactions. Especially, the head-to-head fashion of the surface MA cations in the dimer phase strengthens the interactions with the nearest neighboring iodine anions. Figure D
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were decoupled with the metal substrate. The codeposited films were characterized by STM in constant current mode at 78 K. Scanning tunneling spectroscopy has been carried out on the MAPbI3 surface to investigate the local density of states. The lock-in technique was used with a sinusoidal modulation signal (30 mVrms, 553 Hz). Computational Model. Density functional theory calculations were conducted with the Vienna Ab Initio Simulation Package (VASP), using the Perdew−Burke−Ernzerhof exchange-correlation functional. The plane-wave energy cutoff used for all calculations is 500 eV. The van der Waals interactions were considered by using the Becke−Jonson damping DFT-D3 method.29 The convergence criterion for the forces of all structure relaxations is 0.01 eV/Å. The energy barrier of the phase transition between the two surface structures was calculated by using the climbing image nudged elastic band method with six images, and the forces were relaxed to 0.06 eV/ Å.30,31 The Berry phase method within the modern theory of polarization was employed for the calculation of the macroscopic electric polarization.12,32
5a,b shows the deformation charge density distributions of the topmost MA−I layer in the zigzag and dimer phases, respectively. The deformation density was obtained by subtracting the charge density of neutral atoms from the charge density of the calculated system.27 It is found that the negative charge density of the I anions is redistributed at the regions between the I anions and the NH3 group of the MA cations. Based on the above analysis, we believe that the “attractive” interaction between the surface iodine anions is mediated by the MA cations. According to our calculation, the net charges on the MA−I and Pb−I layers are alternatively positive and negative, implying a macroscopic polarization in the film.28 The calculated net charge on the topmost MA−I layer is +0.267e (+0.249e) for the zigzag (dimer) phase, which is about 0.05e (0.1e) smaller than that on the underlying MA−I layer. The nonuniform distribution, originating from the diversities of the chemical compositions between the surface region and their bulk counterparts, is a typical characteristic of the surface with perpendicular macroscopic polarization, according to previous studies on the ferroelectricity of MAPbI3.11−14,28 Moreover, the surface MA cations, which are tilted at an angle with respect to the c-axis, may result in ferroelectric order with their polar direction opposite to the macroscopic polarization.12−14 Consequently, the overall surface polarization is reduced, facilitating the stabilization of the surface structures.17,18 The calculated macroscopic electric polarization of bulk CH3NH3PbI3 (orthorhombic) crystal along the c-axis is 38.5 μC/cm2, very close to the previous work,12 while the values of the slabs with zigzag and dimer phases are 34.5 and 36.7 μC/ cm2, respectively. Compared with the polarity compensation at the surface of oxide perovskite materials by charge transfer, surface reconstruction, adsorption of charged foreign species, and so on, the MA cations as rotatable dipoles at MAPbI3 surfaces not only reduce the surface polarization but also play a crucial role for the surface reconstruction and phase transition.17,18
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Author Contributions §
L.S. and M.L. contributed to the work equally.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work was financially supported by NSFC (Project 11374374, 11574403) and the computation part of the work was supported by National Supercomputer Center in Guangzhou. REFERENCES (1) Kagan, C. R.; Mitzi, D. B.; Dimitrakopoulos, C. D. OrganicInorganic Hybridmaterials as Semiconducting Channels in Thin-Film Field-Effect Transistors. Science 1999, 286, 945−947. (2) Hodes, G. Perovskite-Based Solar Cells. Science 2013, 342, 317− 318. (3) Snaith, H. J. Perovskites: the Emergence of a New Era for LowCost, High-Efficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623− 2630. (4) Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.; Grätzel, M. Sequential Deposition as A Route to High-Performance Perovskite-Sensitized Solar Cells. Nature 2013, 499, 316−319. (5) Liu, M.; Johnston, M. B.; Snaith, H. J. Efficient Planar Heterojunction Perovskite Solar Cells by Vapour Deposition. Nature 2013, 501, 395−398. (6) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050−6051. (7) Heo, J. H.; Im, S. H.; Noh, J. H.; Mandal, T. N.; Lim, C.-S.; Chang, J.; Ah; Lee, Y. H.; Kim, H.-J.; Sarkar, A.; Nazeeruddin, M. K.; et al. Efficient Inorganic-Organic Hybrid Heterojunction Solar Cells Containing Perovskite Compound and Polymeric Hole Conductors. Nat. Photonics 2013, 7, 486−491. (8) Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-State Sensitised Solar Cell Applications. J. Mater. Chem. A 2013, 1, 5628− 5641. (9) Yin, W.-J.; Yang, J. H.; Kang, J.; Yan, Y.; Wei, S.-H. Halide Perovskite Materials for Solar Cells: A Theoretical Review. J. Mater. Chem. A 2015, 3, 8926−8942. (10) Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H. M.; Yang, H. G.; Yao, X. D.; Zhao, H. J. Density Functional Theory Analysis of
CONCLUSIONS In summary, we have studied the atomic structure of MAPbI3 (001) surfaces. Two surface phases, the zigzag and dimer phases, have been observed on the MA−I layer-terminated surfaces by scanning tunneling microscopy. Based on DFT calculations, the surface MA cations as rotatable dipoles are considered to play a crucial role in the surface reconstruction and phase transition. The “attractive” effect of surface I anions, which result in the formation of I dimers, are attributed to the electrostatic interactions with the reoriented MA cations. At the same time, the reoriented surface MA dipoles weaken the surface polarity and take part in stabilizing the surface structures. METHODS Experimental Details. Experiments were carried out under ultrahigh vacuum with a base pressure of 1 × 10−10 mbar. Single crystalline Au(111) surfaces were cleaned by several cycles of Ar+ sputtering and annealing. After the methylammonium iodide and lead iodide were purified above the required deposition temperature (CH3NH3I, 378 K; PbI2, 563 K), the films were prepared by codeposition of CH3NH3I and PbI2 with a molar ratio of 1:3 on Au(111) at 110−130 K for 8 min, followed by annealing to 373 K. The nominal thickness is ∼10.8 atomic layers (MA−I or Pb−I layers), including a four atomic layer thick buffer layer initially formed on the Au(111) surface. The CH3NH3PbI3 films grown on the buffer layers E
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ACS Nano Structural and Electronic Properties of Orthorhombic Perovskite CH3NH3PbI3. Phys. Chem. Chem. Phys. 2014, 16, 1424−1429. (11) Kutes, Y.; Ye, L.; Zhou, Y. Y.; Pang, S.; Huey, B. D.; Padture, N. P. Direct Observation of Ferroelectric Domains in Solution-Processed CH3NH3PbI3 Perovskite Thin Films. J. Phys. Chem. Lett. 2014, 5, 3335−3339. (12) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584− 2590. (13) Leguy, A. M. A.; Frost, J. M.; McMahon, A. P.; Sakai, V. G.; Kochelmann, W.; Law, C. H.; Li, X.; Foglia, F.; Walsh, A.; O’Regan, B. C.; Nelson, J.; et al. The Dynamics of Methylammonium Ions in Hybrid Organic−Inorganic Perovskite Solar Cells. Nat. Commun. 2015, 6, 7124. (14) Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells. APL Mater. 2014, 2, 081506. (15) Liu, S.; Zheng, F.; Koocher, N. Z.; Takenaka, H.; Wang, F. G.; Rappe, A. M. Ferroelectric Domain Wall Induced Band Gap Reduction and Charge Separation in Organometal Halide Perovskites. J. Phys. Chem. Lett. 2015, 6, 693−699. (16) Zhou, H. P.; Chen, Q.; Li, G.; Song, T. B.; Duan, H. S.; Hong, Z.; You, J. B.; Liu, Y. S.; Yang, Y. Interface Engineering of Highly Efficient Perovskite Solar Cells. Science 2014, 345, 542−546. (17) Noguera, C. Polar Oxide Surfaces. J. Phys.: Condens. Matter 2000, 12, R367−R410. (18) Goniakowski, J.; Finocchi, F.; Noguera, C. Polarity of Oxide Surfaces and Nanostructures. Rep. Prog. Phys. 2008, 71, 016501. (19) Li, F. M.; Wang, Z. M.; Meng, S.; Sun, Y. B.; Yang, J. L.; Guo, Q. L.; Guo, J. D. Reversible Transition between Thermodynamically Stable Phases with Low Density of Oxygen Vacancies on the SrTiO3(110) Surface. Phys. Rev. Lett. 2011, 107, 036103. (20) Liu, X. L.; Wang, C. Q.; Lyu, L.; Wang, C. C.; Xiao, Z. G.; Bi, C.; Huang, J. S.; Gao, Y. L. Electronic Structures at the Interface between Au and CH3NH3PbI3. Phys. Chem. Chem. Phys. 2015, 17, 896−920. (21) Yin, W. J.; Shi, T.; Yan, Y. Unusual Defect Physics in CH3NH3PbI3 Perovskite Solar Cell Absorber. Appl. Phys. Lett. 2014, 104, 063903. (22) Agiorgousis, M. L.; Sun, Y. Y.; Zeng, H.; Zhang, S. B. Strong Covalency-Induced Recombination Centers in Perovskite Solar Cell Material CH3NH3PbI3. J. Am. Chem. Soc. 2014, 136, 14570−14575. (23) Onoda-Yamamuro, N.; Matsuo, T.; Suga, H. Dielectric Study of CH3NH3PbX3 (X = Cl, Br, I). J. Phys. Chem. Solids 1992, 53, 935−939. (24) Wasylishen, R. E.; Knop, O.; Macdonald, J. B. Cation Rotation in Methylammonium Lead Halides. Solid State Commun. 1985, 56, 581−582. (25) Mosconi, E.; Quarti, C.; Ivanovska, T.; Ruani, G.; De Angelis, F. Structural and Electronic Properties of Organo-Halide Lead Perovskites: A Combined IR-Spectroscopy and ab initio Molecular Dynamics Investigation. Phys. Chem. Chem. Phys. 2014, 16, 16137− 16144. (26) Arrighi, V.; Higgins, J. S.; Burgess, A. N.; Howells, W. S. Rotation of Methyl Side Groups in Polymers: A Fourier Transform Approach to Quasielastic Neutron Scattering. 1. Homopolymers. Macromolecules 1995, 28, 2745−2753. (27) Fonseca Guerra, C.; Handgraaf, J. W.; Baerends, E. J.; Bickelhaupt, F. M. Voronoi Deformation Density (VDD) Charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD Methods for Charge Analysis. J. Comput. Chem. 2004, 25, 189−210. (28) Bottin, F.; Finocchi, F.; Noguera, C. Stability and Electronic Structure of the (1 × 1) SrTiO3(110) Polar Surfaces by FirstPrinciples Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 035418. (29) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104.
(30) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901. (31) Henkelman, G.; Jónsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978. (32) Resta, R. Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Rev. Mod. Phys. 1994, 66, 899.
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