Hubbard and van der Waals Corrections v - ACS Publications

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Benchmarking Density Functional Theory Based Methods To Model NiOOH Material Properties: Hubbard and van der Waals Corrections vs Hybrid Functionals Jeremie Zaffran and Maytal Caspary Toroker* Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel S Supporting Information *

ABSTRACT: NiOOH has recently been used to catalyze water oxidation by way of electrochemical water splitting. Few experimental data are available to rationalize the successful catalytic capability of NiOOH. Thus, theory has a distinctive role for studying its properties. However, the unique layered structure of NiOOH is associated with the presence of essential dispersion forces within the lattice. Hence, the choice of an appropriate exchangecorrelation functional within Density Functional Theory (DFT) is not straightforward. In this work, we will show that standard DFT is sufficient to evaluate the geometry, but DFT+U and hybrid functionals are required to calculate the oxidation states. Notably, the benefit of DFT with van der Waals correction is marginal. Furthermore, only hybrid functionals succeed in opening a bandgap, and such methods are necessary to study NiOOH electronic structure. In this work, we expect to give guidelines to theoreticians dealing with this material and to present a rational approach in the choice of the DFT method of calculation.

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INTRODUCTION Photoelectrochemical cells constitute an attractive solution to address the environmental issues facing modern society.1 Such devices use solar energy to produce hydrogen fuel by splitting water molecules. Although the hydrogen is obtained without major difficulties at the cathode, the anode, where the Oxygen Evolution Reaction (OER) occurs, is the major limitation of this technology.2 To date, only a few materials based on noble metals are known to be efficient catalysts for the OER; however, such materials are not economically viable.3 Recently, a new class of materials based on metal hydroxides has been considered for the OER.3 Among them, nickel oxyhydroxide (NiOOH) has outstanding photoelectrochemical properties,4 especially when doped with Fe impurities.5 Density Functional Theory (DFT) is well-known for its good performance in modeling catalysis and photocatalysis.6 For this reason, many authors have used this computational method to investigate the physical and chemical properties of NiOOH.5a,7 However, several discrepancies in the techniques used by the various research groups can be discerned. For example, when the Hubbard parameter8 is used, the (UJ) value that is chosen for Ni has not been consistent between different research groups (e.g., 4 eV for Toroker and coworker,9 5.5 eV for Selloni and co-workers,7b and 6.6 eV for Nørskov and co-workers5a). These high (U-J) values are required to fit the experimental data.10 However, several ab initio calculations related to NiO recommend the use of a low (U-J) value that ranges between 3.8 and 5 eV.11 Moreover, because H bonds and dispersion forces are intrinsic to NiOOH, the use of van der Waals (vdW) corrections (sometimes © 2016 American Chemical Society

coupled with hybrid functionals) has been proposed to improve the description of its structure.7a Finally, because DFT+U fails to predict a band gap for NiOOH, previous works have already shown the importance of hybrid functionals in predicting the bandgap.7a,c,12 To this end, a variety of methods and exchange-correlation (XC) functionals are available in the literature that can be used to study NiOOH. Hence, in the current paper we will present a comprehensive analysis of several basic NiOOH bulk properties. For this task, we will consider a set of several popular XCfunctionals, including hybrids methods and other DFT corrections of first importance for oxide and hydroxide materials, namely Hubbard and van der Waal (vdW) corrections. We will assess advantages and limitations of each calculation method and determine if they are equally efficient regarding the main NiOOH bulk properties. We first consider the performance of DFT in predicting the NiOOH structure and investigate its oxidation states. We then focus on its electronic structure and corresponding bandgap.

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COMPUTATIONAL METHODS AND MATERIALS All calculations were performed using the VASP software package.13 We considered a set of 11 XC functionals, including standard DFT, DFT with the Hubbard correction (DFT+U),8 DFT with van der Waals (vdW) corrections,14 and hybrid calculations.15 In the framework of standard DFT, we used the Received: July 14, 2016 Published: July 15, 2016 3807

DOI: 10.1021/acs.jctc.6b00657 J. Chem. Theory Comput. 2016, 12, 3807−3812

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Journal of Chemical Theory and Computation

structure compared with the γ phase and is therefore an excellent starting point for systematic investigations. For all of the calculations, we relaxed the unit cell using a convergence criterion of 10−5 eV for electronic iterations and 0.05 eV/Å for ionic iterations. The same pseudopotentials were used for each XC-functional in the Projected Augmented Waves (PAW) formalism to model electron−ion interactions.24 For all of the XC-functionals excluding the hybrid functionals, we used a k-mesh of 5 × 5 × 3 in the Monkhorst−Pack scheme25 and an energy cutoff of 700 eV for the plane-wave basis set. We found that such parameters were able to reach an accuracy of 1 meV/atom. Regarding the hybrid functionals, we lowered the k-grid to 3 × 3 × 3 and the energy cutoff to 600 eV to minimize the computational cost, which gave an energy per atom convergence of 5 meV/atom. We systematically performed a Bader charge analysis (see Table S1 in the S.I.) after each relaxation using the tools provided in ref 26. Oxidation states were inferred from atomic magnetic moments, which were verified to correlate with the Bader charges.

Perdew−Burke−Ernzerhof (PBE) XC functional.16 Regarding DFT+U, we considered PBE with three different (U-J) values (i.e., 5.5, 6, and 3.8 eV) using the approach of Dudarev et al.17 High (U-J) values such as 5.5 and 6 eV are derived from linear response theory and are often reported to fit well with experiment for NiOOH materials,5a,7b whereas the relatively low (U-J) value of 3.8 eV originates from Hartree−Fock calculations.11b Two different hybrid functionals were used: PBE015a and HSE06,15b which are known for their good predictive behavior of solid state materials.15b Finally, we tested two different corrections for vdW interactions. Both corrections are in the standard DFT framework, that is, without the Hubbard correction. The first correction is vdW-DF,18 which includes three different functionals known to model H bonds and dimerization energies fairly well: optPBE,19 optB86,19 and optB88,19 which will subsequently be termed “opt-X″ when these three functionals are discussed together. The second vdW correction is the D2 correction, which is related to the theory proposed by Grimme.20 This correction has been added to the PBE0 and HSE06 functionals. The Grimme correction consists of including a term related to dispersion forces involving a 1/R6 dependence in the expression for the XC-functional, where R is the internuclear distance between two atoms. To sum up, the complete list of XC functionals investigated in the present work includes the following: PBE, PBE+U(3.8), PBE+U(5.5), PBE +U(6), optPBE, optB86, optB88, PBE0, HSE06, PBE0-D2, HSE06-D2. NiOOH material is known to present the following two stable phases: β-NiOOH and γ-NiOOH.4,5b,21 Both phases are comprised of stacked layers that are dominated by H bonds and dispersion forces.21b Water molecules and various electrolytes are inserted between the layers of the γ-NiOOH phase,4,5,21b whereas β-NiOOH consists of alternating stacks of NiO2 or Ni(OH)2 stabilized by H bonds, as recently suggested by a genetic algorithm approach (see Figure 1).7a Because of the

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RESULTS AND DISCUSSION In this section, we will show that the XC-functionals are not equally accurate to evaluate various properties of bulk NiOOH. While standard PBE-DFT is excellent to address geometries, PBE+U is necessary to model the oxidation states. Concerning the bandgap and the electronic structure calculations, we will demonstrate that only hybrid functionals are able to reliably reproduce the correct experimental features. 1. Structure. We begin by comparing the various NiOOH structures obtained from our set of XC functionals to experimental data. We first considered the a, b, and c lattice constants in Figure 2 and then focused on the α, β, and γ angles

Figure 1. NiOOH unit cell lattice model and corresponding notation for the lattice parameters. Red: O, gray: Ni, white: H.

Figure 2. DFT-estimated lattice distances vs experiment (in %) for various XC functionals for the NiOOH unit cell. Errors are defined as 100 × (DFT value-experimental value)/experimental value.

experimental uncertainties on the positions of the H atoms, other structures have also been proposed with different H distributions between the layers.7c However, such configurations are not considered in the current paper except one that is provided in the Supporting Information (S.I.).7b,21b In the following, we will mainly consider the β-NiOOH phase (hereafter denoted simply as “NiOOH”) because this phase is often considered to be the most active one regarding the OER process for undoped NiOOH,22 although recent experiments have shown that the γ-NiOOH phase is the one active when doped with Fe.5b,23 Moreover, the β phase has a simpler

in Figure 3. The corresponding data are presented in Table S3 in the S.I. We reported the error percentage of the DFT estimates vs experimental data in those graphics, as follows:27 a = 4.88 Å, b = 2.92 Å, c = 9.24 Å, α = 90°, β = 88.80°, γ = 90°, as denoted in Figure 1. As shown in Figure 2, the a parameter is consistently overestimated by 4−6% regardless of which XC functional is used. This relative error corresponds to an absolute error of ∼0.20−0.30 Å. Although the maximum error is obtained with the PBE functional, the improvement is not dramatic with either the hybrid functionals or vdW-corrections, which 3808


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the calculated structure and why the standard PBE-DFT functional is sufficiently accurate. Instead of using several XC-functionals, other authors were able to improve agreement between experiment and DFT by considering different structural models.7c In particular, the impact of the distribution of H atoms on the c-axis was evaluated.7c Consequently, aside from the performance of the computational methods, it is also important to consider the major lack of experimental data on the NiOOH geometry. Moreover, some experimental works even not accord themselves regarding the c-axis values,27a,b,28 hence attesting about the uncertainty of H atoms position. All those varieties of geometries are stable and close to each other on the energetic point of view.7c As shown in Figure 2 and Figure 3 and also in Table S5 of the S.I. for a different structure, all of the computational methods are essentially equivalent with respect to calculating the NiOOH geometry. 2. Oxidation States. The oxidation states of the Ni atoms are strongly dependent on the calculation method. Indeed, while the average oxidation state of Ni is always close to 3, the relative proportion of Ni(II), Ni(III), and Ni(IV) is different according to the XC functional used, as shown in Figure 4 (and Table S2 in the S.I.). Those results are consistent with experimental observations, obtained by XPS measurements29 and various electrochemical techniques of analytical chemistry.30 We note that we also provide in the S.I. a complete analysis on the magnetic state of NiOOH as calculated with

Figure 3. DFT-estimated lattice angles vs experiment (in %) for various XC functionals for the NiOOH unit cell. Errors are defined as 100 × (DFT value-experimental value)/experimental value.

decrease the absolute error by only 0.10 Å. Regarding the b parameter, the error is generally much small than that for a (0.24−2.05% or 0.01−0.06 Å). In addition, the value is always underestimated, except for the PBE functional, which leads to the lowest error. Notably, regarding the b axis, the errors relative to the c axis are of low magnitude for all functionals (0.00−1.62% or 0.00−0.15 Å). Regarding PBE+U, we see that the error increases when high (U-J) values are used. Indeed, the maximum error is observed for (U-J) = 6 eV, whereas an error of just 0.65% (0.06 Å) is obtained for the standard PBE-DFT functional. Moreover, while the hybrid functionals (i.e., PBE0 and HSE06) produce no error for the c axis relative to experiment, both D2-corrected hybrid functionals underestimate the axis by 1.08%. Finally, the three vdW-corrected functionals (termed opt-X) tend to overestimate the c axis. Despite the relatively small size of these errors (lower than ∼1% or 0.10 Å), it is worth noting that except for optB86, which gives an error of 0.32%, both optPBE and optB88 give an error that is higher than that for standard PBE-DFT (1.05 and 0.74%, respectively, vs 0.65% for PBE). Hence, the errors are all very low, and the differences between the functionals are generally lower than 0.05 Å. In some ways, such results are counterintuitive because we would expect that the vdW correction improves the description of the c axis. However, the enhancements included in the opt-X functionals or the D2 corrections for the NiOOH geometry are only marginal. Similar conclusions can be made for our assessment of the angles, especially the β angle (Figure 3). This angle is consistently overestimated by every functional investigated and has the highest error (∼15% or ∼15°). However, the β angle could be related to the interlayer distance (see Figure 1). Hence, any change in this angle suggests a sliding motion between the NiO2 and Ni(OH)2 layers, which is directly impacted by the strength of the H bonds and dispersion forces. Further, despite the nature of such forces, vdW-corrected functionals are not able to provide a correct estimate of the β parameter. Previous observations suggest that dispersive forces are not predominant in NiOOH relative to covalent and coordination bonding. Additionally, the H bonds that are present between the layers, which ensure bulk cohesion, are significantly stabilizing and lead to strong layer stacking. This is why the vdW-corrected functionals are not able to significantly improve

Figure 4. Ni oxidation states in NiOOH according to several XCfunctionals. Blue: Ni (II); green: Ni (III); orange: Ni (IV). 3809


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correction tends to delocalize electrons and thus favors metallic states, which manifests as a lowering of the bandgap. As in any chemical reaction, the electronic states present at the band edges are of major importance to the water splitting process for reactivity. That is why it is necessary to observe a bandgap in order to look for the relevant electronic states at the band edges. Hence, we only considered hybrid calculations to analyze the DOS and PDOS. As shown in Figure 5, Ni(II)

different XC functionals, albeit no experimental data is available for comparison. Standard PBE-DFT calculations and those with low (U-J) values provide three Ni(III) for one Ni(IV), with the highest oxidized Ni being localized in the NiO2 layer (see top panel of Figure 4). However, this result is not fully consistent with chemical intuition, because we would expect the Ni(II) states to be in the Ni(OH)2 layer. Similar results are obtained using the vdW corrections. Alternatively, functionals with high (U-J) values (e.g., 5.5 and 6 eV, see intermediate panel in Figure 4) lead to the Ni(OH)2 layer being fully occupied with Ni(II) states, and the NiO2 layer contains Ni(III) and Ni(IV). Finally, with hybrid functionals or those coupled with D2 corrections (lower panel in Figure 4) we observe one Ni(II) in the Ni(OH)2 layer. It is clear that XC-functionals that localize electrons on specific atomic sites, such as high (U-J) values in DFT+U, have the tendency to favor low oxidized states of Ni (e.g., Ni(II)). This observation is caused by the overstabilization of high spin states induced by such functionals, as already reported in the literature.8b,31 Indeed, the electronic configuration of Ni(II) is [Ar]3d84s0, leading to a total magnetization of 2 μB. However, for Ni(III) and Ni(IV) the electronic configurations are [Ar]3d74s0 and [Ar]3d64s0, respectively, corresponding to 1 μB and 0 μB, respectively. Hence, standard PBE-DFT is not able to reproduce the electronic properties of NiOOH accurately, even with vdW corrections. For this reason, only DFT+U or hybrid functionals are capable of reproducing such properties. 3. Band Gap and Electronic Structure. In order to fully grasp electronic features of any material, it is necessary to consider the bandgap, as well as the density of states (DOS) and the projected density of states (PDOS) on specific atom sites. Experimentally, debate exists regarding the value of the NiOOH band gap, which varies according to the growth technique that is employed. Some authors have reported a value of 1.7−1.8 eV,32 whereas others have reported a much higher value of 3.75 eV.33 The source of the discrepancy between the experiments may result from not fully hydroxylating NiO, which has a much larger band gap. Concerning the band gap calculations, Table 1 shows that all of the methods fail to open

Figure 5. NiOOH projected density of states (PDOS) calculated with HSE06. Red: O p-states; blue: Ni (II) d-states; green: Ni (III) d-states; orange: Ni (IV) d-states.

states are prevalent (blue line) close to the valence band (VB) edge. However, at the conduction band edge (CB), the Ni(III) and Ni (IV) states are predominant. Such features fit well with our estimated photoelectrochemical process of the NiOOH material. Indeed, following light excitation, an electron is ejected from the VB toward the CB. This electron can be taken only from Ni(II) (present in the Ni(OH)2 layer, Figure 4), which is oxidized to Ni(III). While the remaining hole is located in the VB, the electron can be hosted in the CB by Ni(III) and Ni(IV) species (present in the NiO2 layer, Figure 4). Thus, electron transfers and exciton separation in NiOOH proceed between two different layers. An important requirement for photoactive materials is to present electronic states at the CB edge that can favorably capture excited electrons. Therefore, a reliable computational method must be able to identify the chemical character of CB and VB edges. The result presented in Figure 5 was obtained with the HSE06 functional. However, we observed similar features at the band edges using PBE0 and with adding the D2 correction. Accordingly, any XC-functional that can open a bandgap is able to reproduce the electronic properties at the band edges reasonably well. It is worth noting that the performance of DFT on electronic structure calculations is dependent on the distribution of H atoms. Indeed, for different NiOOH geometries (see the S.I.), we found that PBE+U(6) is sufficient to open a band gap of 0.26 eV. Moreover, only the Ni(III) oxidation state is observed and is present at both the VB and CB edges for the structure reported in the S.I. We were able to demonstrate that for electronic properties, hybrid methods are generally required to reproduce bandgap and relevant electronic states at the band edges.

Table 1. DFT-Estimated Bandgap for NiOOH with Different XC-Functionals XC-functional

bandgap (eV)

PBE PBE+U(3.8) PBE+U(5.5) PBE+U(6) optPBE optB86 optB88 PBE0 HSE06 PBE0-D2 HSE06-D2

0.01 0.06 0.00 0.19 0.04 0.01 0.01 2.47 1.73 2.20 1.47

a bandgap for NiOOH except the hybrid XC functionals. The PBE0 calculation provides a high bandgap value (2.60 eV), which becomes lower with HSE06 (1.86 eV). This behavior of PBE0 to overestimate the bandgap relative to HSE06 has already been reported in the literature.34 We note that PBE0D2 and HSE0-D2 slightly decrease the bandgap (to 2.40 and 1.67 eV, respectively). Regarding dispersion forces, the D2

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CONCLUSION We tested the performance of several XC-functionals to assess various bulk properties of NiOOH, including its geometry, 3810


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(3) Fabbri, E.; Habereder, A.; Waltar, K.; Kötz, R.; Schmidt, T. J. Developments and perspectives of oxide-based catalysts for the oxygen evolution reaction. Catal. Sci. Technol. 2014, 4, 3800−3821. (4) Gao, M.; Sheng, W.; Zhuang, Z.; Fang, Q.; Gu, S.; Jiang, J.; Yan, Y. Efficient water oxidation using nanostructured alpha-nickelhydroxide as an electrocatalyst. J. Am. Chem. Soc. 2014, 136, 7077−84. (5) (a) Friebel, D.; Louie, M. W.; Bajdich, M.; Sanwald, K. E.; Cai, Y.; Wise, A. M.; Cheng, M. J.; Sokaras, D.; Weng, T. C.; Alonso-Mori, R.; Davis, R. C.; Bargar, J. R.; Norskov, J. K.; Nilsson, A.; Bell, A. T. Identification of highly active Fe sites in (Ni,Fe)OOH for electrocatalytic water splitting. J. Am. Chem. Soc. 2015, 137, 1305−13. (b) Klaus, S.; Cai, Y.; Louie, M. W.; Trotochaud, L.; Bell, A. T. Effects of Fe Electrolyte Impurities on Ni(OH)2/NiOOH Structure and Oxygen Evolution Activity. J. Phys. Chem. C 2015, 119, 7243−7254. (c) Butera, V.; Caspary Toroker, M. Electronic Properties of Pure and Fe-Doped β-Ni(OH)2: New Insights Using Density Functional Theory with a Cluster Approach. J. Phys. Chem. C 2016, 120, 12344−12350. (6) (a) Liao, P.; Keith, J. A.; Carter, E. A. Water oxidation on pure and doped hematite (0001) surfaces: prediction of Co and Ni as effective dopants for electrocatalysis. J. Am. Chem. Soc. 2012, 134, 13296−309. (b) Neufeld, O.; Toroker, M. C. Platinum-Doped αFe2O3for Enhanced Water Splitting Efficiency: A DFT+UStudy. J. Phys. Chem. C 2015, 119, 5836−5847. (c) Mavros, M. G.; Tsuchimochi, T.; Kowalczyk, T.; McIsaac, A.; Wang, L. P.; Voorhis, T. V. What can density functional theory tell us about artificial catalytic water splitting? Inorg. Chem. 2014, 53, 6386−97. (7) (a) Li, Y.-F.; Selloni, A. Mosaic Texture and Doublec-Axis Periodicity of β-NiOOH: Insights from First-Principles and Genetic Algorithm Calculations. J. Phys. Chem. Lett. 2014, 5, 3981−3985. (b) Li, Y.-F.; Selloni, A. Mechanism and Activity of Water Oxidation on Selected Surfaces of Pure and Fe-Doped NiOx. ACS Catal. 2014, 4, 1148−1153. (c) Tkalych, A. J.; Yu, K.; Carter, E. A. Structural and Electronic Features of β-Ni(OH)2and β-NiOOH from First Principles. J. Phys. Chem. C 2015, 119, 24315−24322. (8) (a) Cococcioni, M.; de Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035105. (b) Himmetoglu, B.; Floris, A.; de Gironcoli, S.; Cococcioni, M. Hubbard-Corrected DFT Energy Functionals: The LDA + U Description of Correlated Systems. Int. J. Quantum Chem. 2014, 114, 14−49. (9) Zaffran, J.; Caspary Toroker, M. Metal-Oxygen Bond Ionicity as an Efficient Descriptor for Doped NiOOH Photocatalytic Activity. ChemPhysChem 2016, 17, 1630. (10) Zaffran, J.; Caspary Toroker, M. Designing efficient doped NiOOH catalysts for water splitting with first principles calculations. ChemistrySelect 2016, 1, 911. (11) (a) Alidoust, N.; Toroker, M. C.; Carter, E. A. Revisiting Photoemission and Inverse Photoemission Spectra of Nickel Oxide from First Principles: Implications for Solar Energy Conversion. J. Phys. Chem. B 2014, 118, 7963−7971. (b) Alidoust, N.; Toroker, M. C.; Keith, J. A.; Carter, E. A. Significant Reduction in NiO Band Gap Upon Formation of LixNi1−xO alloys: Applications To Solar Energy Conversion. ChemSusChem 2014, 7, 195−201. (c) Bengone, O.; Alouani, M.; Blöchl, P.; Hugel, J. Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of NiO. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, 16392−16401. (12) (a) Fidelsky, V.; Caspary Toroker, M. Engineering Band Edge Positions of Nickel Oxyhydroxide through Facet Selection. J. Phys. Chem. C 2016, 120, 8104−8108. (b) Fidelsky, V.; Butera, V.; Zaffran, J.; Toroker, M. C. Three fundamental questions on one of our best water oxidation catalysts: a critical perspective. Theor. Chem. Acc. 2016, 135, 135. (13) (a) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15−50. (b) Kresse, G.; Hafner, J. Ab

oxidation state, bandgap, and electronic structure. We were able to show that hybrid calculations are not necessary to model the material structure and that standard PBE-DFT or DFT+U functionals are sufficient for that task, hence saving a significant computational time. Notably, the benefit of DFT-vdW and DFT-D2 for calculating an accurate geometry is marginal. Although DFT+U is superior to standard PBE-DFT for calculating oxidation states, hybrid functionals are required for the electronic structure calculations, especially when calculating the chemical character of the band edges. Indeed, only hybrid functionals can be used to successfully open the bandgap. As a result, hybrid methods should be used for electronic properties when a bandgap must be observed in the band structure. However, for all other structural and redox properties, we recommend to use DFT+U that leads to satisfying results with low cost calculations. We anticipate that such conclusions established for NiOOH may be valid also for other oxyhydroxide materials with a layered structure.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.6b00657. NiOOH structure coordinates relaxed using various XCfunctionals; structure presented in the current article and another structure often reported in the literature: for both structures an analysis of the Bader charges, the magnetization and spin orientation, the geometrical parameters, the oxidation states, and the electronic properties (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +972 4 8294298. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Morantz Energy Research Fund, the Nancy and Stephen Grand Technion Energy Program, the I-CORE Program of the Planning and Budgeting Committee, and the Israel Science Foundation (grant no. 152/ 11). The COST Action (IC1208) is acknowledged for funding travel that promoted this research. This work was supported by the post Link-SCEEM-2 project, funded by the European Commission under the seventh Framework Program through the Capacities Research Infrastructure, INFRA-2010-1.2.3 Virtual Research Communities, Combination of Collaborative Project and Coordination and Support Actions (CP-CSA) under grant no. RI-261600. J.Z. acknowledges a fellowship from the Israel Ministry of Aliyah and Immigrant Absorption.

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REFERENCES

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