Ferroelectric Oxides with Strong Visible-Light ... - ACS Publications

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Ferroelectric Oxides with Strong Visible-Light Absorption from Charge Ordering Jiangang He,†,‡ Cesare Franchini,‡ and James M. Rondinelli*,†,§ †

Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States Faculty of Physics and Center for Computational Materials Science, University of Vienna, Vienna, Austria § Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States ‡

S Supporting Information *

ABSTRACT: The applications of transition metal oxides as photovoltaic and photocatalytic materials are mainly impeded by their poor visible light absorption, low photogenerated carrier mobility, and low valence band position, which originate from the generally large band gap (≥3 eV), narrow transition metal d states, and deep oxygen 2p states. Here, we conceive a design strategy to realize small band gap polar oxides with high carrier mobilities by combining small radii A cations with Bi3+/Bi5+ charge disproportion. We show that these cation sizes and chemical features shift the valence band edge to higher energies and therefore reduce the band gap, promoting the formation of highly dispersive Bi 6s states near the Fermi level as a byproduct. By means of advanced many-electron-based first-principles calculations, we predict a new family of thermodynamically stable/ metastable polar oxides ABiO3 (A = Ca, Cd, Zn, and Mg), which adopt the Ni3TeO6-type (space group R3) structure and exhibit optical band gaps of ∼2.0 eV, as promising single phase photovoltaic and photocatalytic materials operating in the visible light spectrum.

O

fundamental band gap, and the BPVE allows the PCE to exceed the Shockley−Queisser limit formulated for p-n junctions7−11 by taking advantage of the intrinsic built-in electric field found within the ferroelectric material. In addition, oxides are chemically and thermally stable, abundant, cost-effective, and environmentally benign. However, low solar energy conversion efficiencies in TMO ferroelectrics have significantly impeded their commercial applications as PV and PC materials. The main factors for the low energy conversion efficiency of ferroelectric oxides are due to the large band gaps they exhibit (BaTiO3, 3.2 eV; PbTiO3, 3.5 eV), which hinders efficient visible light adsorption in the 1.65 to 3.1 eV range (the main portion of solar radiation impinging on the earth), and the transition metal d bands are highly localized near the Fermi level, which increases the opportunity for electron−hole recombination during carrier

wing to limited fossil fuel resources and growing environmental challenges, the search for clean and more efficient energy harvesting materials, i.e., photovoltaic (PV) and photocatalysis (PC) platforms, is of paramount importance in today’s evolving clean energy ecosystem. Contemporary PV research has been largely influenced by the discovery of PV solar cells that utilize hybrid halide perovskites such as CH3NH3PbI3 (MAPbI3), owing to their high power conversion efficiency (PCE) of approximately 20%.1,2 Such excellent performance stems mainly from a suitable band gap (∼1.6 eV),3 large visible light absorption coefficient, high carrier mobility (small effective mass), and a long carrier diffusion length (small electron−hole binding energy and long recombination lifetime). However, the toxicity of lead and the poor environmental stability of MAPbI3 continue to hamper practical applications.4 An alternative materials family for efficient solar energy conversion is transition metal oxide (TMO) ferroelectrics by virtue of the bulk photovoltaic effect (BPVE),5,6 which facilitates the separation of the photogenerated electron and hole pairs in a single phase material (without requiring a p-n junction). It also provides higher open-circuit voltages than the © 2016 American Chemical Society

Special Issue: Computational Design of Functional Materials Received: August 23, 2016 Revised: October 26, 2016 Published: October 26, 2016 2445

DOI: 10.1021/acs.chemmater.6b03486 Chem. Mater. 2017, 29, 2445−2451

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Chemistry of Materials

increasing temperature (T),39 P21/c → C2/m → R3̅ → Fm3m ̅ (see Figure S1 in the Supporting Information), which can be understood by using representation theory of the symmetric groups and inspecting the phonon dispersion relationships (see Figures S2 and S3): The low-T P21/c phase is obtained by a simultaneous stabilization of the main phonon instabilities present in the high-T Fm3̅m structure (see Figure 1), namely,

transport from the bulk to surface of the material. Indeed, recent experiments have verified that the PCE of polar Bi2FeCrO6 increases from 0.5% to 8% by optimizing its band gap, layer thickness, and domain and electrode interfaces.12,13 Although designing smaller band gap ferroelectric oxides is highly desired, the task is conceptually challenging. One route for designing ferroelectric ABO3 oxides involves selecting cations that yield a small Goldschmidt tolerance factor, τ = (RA−O)/(√2RB−O),14 where RA−O and RB−O are the corresponding A−O and B−O bond lengths.15,16 ABO3 compounds with τ < 0.85 commonly adopt the polar LiNbO3-type (R3c) structure, which exhibits a ferroelectric polarization, or the centrosymmetric ilmenite (R3̅) structure, which can be transformed to the LiNbO3-type structure under hydrostatic pressure.17 For example, LiNbO3-type PbNiO3 (τ = 0.84), ZnSnO3 (τ = 0.814), ZnPbO3 (τ = 0.764), CdPbO3 (τ = 0.828), and LiOsO3 (τ = 0.820) have been synthesized utilizing high-pressure methods and were found to exhibit large electric polarizations. 18−24 On the other hand, several distinct approaches have been applied to reduce the band gap of TMOs: chemical substitution or doping,25,26 epitaxial strain,27 replacing d0 with d10 cations,16 and by tuning rotations of octahedra.16,28 The shallow energy level induced by dopant/ defect always acts as the electron−hole recombination center, which reduces the photogenerated carriers and therefore current density. The other methods cannot guarantee the ferroelectric phase is most stable.29−31 Here we propose a strategy to design small band gap ferroelectric oxides by combining small A-site cations such as Mg2+, Zn2+, Cd2+, and Ca2+ with B cations prone to charge ordering, specifically disproportionation of Bi4+ into Bi3+/Bi5+. This approach offers the advantage of having small τ ferroelectric ABO3 compounds with the band edges formed by the 6s-like states derived from the Bi3+ and Bi5+ cations. Second, the excitation gaps that open from charge ordering are expected to be smaller than TMOs with d0 electronic configurations and comparable to those of Mott insulators; hence, such compounds are better light absorbers. Third, the spatially extended 6s orbitals of Bi3+ and Bi5+ cations should guarantee high photogenerated carrier mobility as observed in a recent work.32 Last, the band gap reduction is mainly due to the stereochemically active lone pair of Bi3+ 6s shifting the top of the valence band to higher energy, which does not affect H+ reduction processes during PC.33 Following this prescription combined with a crystal-structure search based on density functional theory, lattice dynamics, and representation theory, we identify four novel (thermo)dynamically stable/metastable polar-chiral ferroelectric ABiO3 oxides (A = Mg, Zn, Cd, and Ca) with band gaps around 2 eV and large spontaneous polarizations ranging from 56 to 74 μC/ cm2. Quasiparticle band structures and optical properties were computed within the many-body GW method34 and by solving the Bethe−Salpeter equation (BSE), respectively. Our results indicate that these bismuthate oxides are promising photovoltaic and photocatalytic materials. We start by inferring the stability of Bi-based perovskites through the analysis of the lattice dynamics. The most studied bismuthates are based on semiconducting BaBiO3, which exhibits an indirect bandgap of 0.84 eV35 and a direct band gap ≈2 eV36 associated with a charge-ordered state triggered by Bi−O hybridization and charge disproportionation at the Bi sites.37,38 Earlier experimental studies have reported that BaBiO3 undergoes three continuous structural transitions with

Figure 1. Crystal structures of A2Bi3+Bi5+O6 (A = Ca, Cd, Zn, and Mg) in the highest symmetry (Fm3̅m) phase (a) and the Ni3TeO6-type ground state phase (b). (c−f) Main unstable phonon modes of CaBiO3 in Fm3̅m phase, (c) Γ+4 , (d) X+3 , (e) Γ−4 , and (f) X+5 . Large (green) and small (red) spheres indicate the A cation and oxide ion, respectively, whereas the middle-sized blue and purple spheres refer to the Bi3+ and Bi5+ ions. Arrows indicate the relative atomic displacement size and direction.

the BiO6 titling mode Γ+4 (in the language of representation theory) and the in-phase BiO6 rotation mode X+3 . These two modes are very common lattice instabilities observed in ABO3 perovskites with τ ≪ 1.39,40 The same stabilization path is commonly observed in B-site ordered double perovskites A2BCO6 as well.41 Moreover, this phase transition is expected because the ideal cubic (Ba,Sr)BiO3 (Pm3̅m) perovskite should be considered as a double perovskite when including the Bi valence difference, i.e., (Ba,Sr)2Bi3+Bi5+O6(Fm3̅m), from the Bi3+/Bi5+ disproportionation as discussed in our previous work.42 On the basis of the above analysis, we next select small divalent A-site cation chemistries needed to obtain the desired Ni3TeO6-type ferroelectric ground state and charge-ordered bismuthates by hypothesizing that our pool of initial candidates 2446


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favors B-site ordering and charge disproportionation.43 Indeed, after fully relaxing the ABiO3 (A = Ca, Cd, Zn, and Mg) crystal structures in the cubic Fm3̅m symmetry, we find that the frequency of the unstable modes Γ+4 and X+3 (see Figure 1) become more negative with decreasing τ (see Figure S3), consistent with previous observations in other perovskites.15,16 We now search for the ground state crystal structures constrained to the ABiO3 composition (A = Ca, Cd, Zn, and Mg) using the unstable phonon modes, following the procedure adopted in our previous works.16,30 All density functional theory (DFT) calculations were based on projector augmented wave (PAW) pseudopotentials,44,45 a plane wave basis set with energy cutoff of 520 eV, and the PBEsol exchange-correlation functional46 as implemented in the Vienna Ab intio Simulation Package (VASP).47,48 A 12 × 12 × 12 Monkhorst−Pack k-point grid was used to sample the Brillouin zone for the cubic structure, and the same dense k-points grid was used for all the other structures. The reliability of our method was validated by comparing the relaxed structure with experimental crystal structures of Sr 2 Bi 3+ Bi 5+ O 6 and Ba2Bi3+Bi5+O6, as collected in Table 1. All parameters agree with the experimental data within 1% error. Phonon dispersion curves of reference phase (cubic, Fm3̅ m) and the ground state phase (rhombohedral, R3) were calculated by using the finite displacement method as implemented in the PHONOPY package,49 where a 2 × 2 × 2 supercell was used for both structures. The subgroup structures were generated by condensing one, two, and three of the most unstable modes simultaneously. All structures were fully relaxed until the Hellmann−Feynman force on each atom is less than 10 meV/ Å. The low energy structures are identified by inspecting the total energy gain with respect to the high-T (Fm3̅m) phase, as shown in Figure 2 using BaBiO3 and CaBiO3 as examples. The condensation of the unstable Γ+4 and X+3 phonons associated with the rotation and tilting of the BiO6 octahedra are energetically more favorable than the other modes, which is typical for perovskites with τ < 1.0. However, for the smaller τ perovskites considered in our study, i.e., CaBiO3, a finite mode

ABiO3 (A = Ca, Cd, Zn, and Mg) would adopt a high-T Fm3m ̅ phase with rock-salt ordered Bi3+/Bi5+ sites, in analogy with the prototype bismuthates Ba2Bi3+Bi5+O6. This is corroborated by noting that the smaller volume of ABO3, prompted by a smaller size of the A-site cation, decreases the tolerance factor τ (from BaBiO3, τ = 0.936, to MgBiO6, τ = 0.708; see Table 1), which increases the electrostatic repulsion between B-site cations and Table 1. Structure and Properties for ABiO3 (A = Ba, Sr, Ca, Cd, Zn, and Mg) Compounds: Space Group (SG), Tolerance Factors (τ, See SI for Details), Lattice Parameters, the Distance from Convex Hull (ΔHs in meV/Atom, Negative/Stable; Positive/Unstable), Indirect Band Gap (Eig, eV), Direct Band Gap (Edg , eV), Optical Band Gap (Eopt g , eV), Effective Mass (Electron, m*e ; hole, m*h ), and Electric Polarization (P, μC/cm2)a BaBiO3

SrBiO3

τ

0.936

0.882

SG

P21/c (14)

P21/c (14)

PBEsol a (Å) b (Å) c (Å) β ΔHs Eg

HSE06

6.177 6.156 8.688 90.27 −72 0.00

0.52

Exp.b

PBEsol

6.174 6.125 8.652 90.27

6.124 5.932 8.478 90.06 −80 0.432

0.2c 0.84d 0.5e

CaBiO3 τ

0.850

SG

R3 (146) PBEsol

a (Å) c (Å) ΔHs Eig Edg Eopt g m*e m*h P

5.8114 15.2259 −138 0.80

HSE06

1.58

1.03

R3 (146) GW0@ HSE06

1.89 2.41 2.09 0.45 1.16

PBEsol

HSE06

5.833 15.386 −87 0.82

5.760 15.135 1.60

GW0@ HSE06

1.80 2.15 1.92 0.52 1.08

52

τ

0.711

SG

R3 (146) PBEsol

60

6.095 5.948 8.485 90.06

0.841

56

5.509 14.653 48 0.86

Exp.b

CdBiO3

ZnBiO3

a (Å) c (Å) ΔHs Eig Edg Eopt g m*e m*h P

HSE06

HSE06

1.80

MgBiO3 0.708 R3 (146) GW0@ HSE06

2.07 2.32 1.97 0.63 1.01

PBEsol

HSE06

5.475 14.597 27 0.94

1.94

GW0@ HSE06

2.33 2.47 2.06 1.55 1.11

Figure 2. Energy gain (ΔE) with respect to the ideal Fm3̅m phase by condensing the atomic displacements obtained from the calculated soft phonons for BaBiO3 (left) and CaBiO3 (right). The amplitudes (Q) of all modes are normalized by the size of the unit cell for each subgroup realized from each phonon. The dashed lines are fits to the computed DFT total energy using an even homogeneous polynomial expansion in the mode amplitude.

74

a

The band gap reduction from Zn to Cd and from Mg to Ca can be understood as arising from the reduced bond strength (larger lattice constant) across the series. bRef 39. cRef 63. dRef 35. eRef 64. 2447


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Chemistry of Materials amplitude of the remaining Γ−4 , Γ+5 , X+5 , and X−5 soft modes yields an appreciable energy gain (Figure 2), indicating that other dynamical instabilities could cooperate with the primary unstable modes Γ+4 and X+3 in driving further symmetry lowering transitions and a considerable energy gain. We therefore examined and searched for other more stable polymorphs of these compounds by considering all meaningful combinations of the unstable modes and fully relaxing the resulting crystal structures. In addition, we included in our pool of structures 15 prototype crystal structures with chemical formulas A2BCO6 and ABO3 that either do not adopt the perovskite structure or are not directly linked by a group− subgroup relationship with the cubic Fm3̅m phase. We found that the polar R3 phase (Ni3TeO6-type, see Figure 1b), resulting from the simultaneous condensation of the octahedral rotation (Γ+4 ) and polar (Γ−4 ) modes, is the lowest energy structure for all considered ABO3 chemistries (see Tables S1, S2, and S3). The R3 structure is similar to that adopted by LiNbO 3 -type oxides, such as ZnPbO 3 , ZnSnO 3 , and NiPbO3,18−20 although it does not contain a glide operation along the trigonal axis. In the Ni3TeO6-type structure, the A-site cation is 6- rather than nominally 12-fold coordinated with the oxide anions in perovskite because of its smaller radius. This is consistent with the phonon analysis that the A cations contribute the largest component to the phonon eigendisplacement vector. The edge-shared AO 6 and Bi 3+O 6 octahedra stack alternatively with AO6 and Bi5+O6 octahedra along the [001] direction; see Figure 1b. We further verified that all of the R3-structured ABiO3 (A = Ca, Cd, Zn, and Mg) oxides are dynamically stable by means of DFT phonon calculations (Figure S4). We also calculated each material’s thermodynamic stability by constructing the convex hull formation-energy diagram using the formation energies of the competing phases included in the Open Quantum Material Database (OQMD).50 Our results show that CaBiO3 and CdBiO 3 are on the convex hull and therefore are thermodynamically stable, whereas ZnBiO3 and MgBiO3 are metastable with formation energies less than 50 meV/atom above the convex hull (see Figure S5), indicating that these phases should be able to be synthesized with proper experimental conditions, i.e., temperature and pressure, or soft chemistry methods; see Table S4. The small tolerance factor ABO3 compounds, such as LiNbO3-type and Ni3TeO6type oxides, usually are synthesized at high-pressure (3−12 GPa) and high-temperature (1000−1500K) conditions.51−53 After ascertaining that the ground state structure for all ABiO3 (A = Ca, Cd, Zn, and Mg) compounds is R3, we then examined the electronic structures, optical absorption properties, and spontaneous polarizations. The electronic structures of ABiO3 were explored by using partially self-consistent GW (GW0, ref 34) calculations based on Heyd−Scuseria−Ernzerhof (HSE06, ref 56) orbitals including electron−hole ladder diagrams and local field effects, namely, the GWTC−TC @HSE 0 method, where TC refers to test-charge, which significantly improves the agreement of the calculated band gap with experiment.30,57 The accuracy of this method for similar systems has been demonstrated in our previous works; for example,16,37,58 the calculated band gaps for BaBiO3 are 1.15 eV (indirect) and 2.39 eV (direct), which are slightly larger than the experimental values of 0.8 and 2.0 eV. The band dispersion of the highest valence band and the lowest conduction band, and the corresponding density of state (DOS) of CaBiO3 are shown in Figure 3 and are representative

Figure 3. Quasiparticle band dispersion (left, blue curves) of the highest valence band and the lowest conduction band interpolated from GW eigenvalues (red circles) by using the VASP2WANNIER90 interface54 and Wannier90 code55 (a) and the density of states (DOS, right) (b) of CaBiO3 calculated at the GW0@HSE06 level.

of the family. The overall features are very similar to the prototype Bi-based perovskite BaBiO3 (ref 37), indicating that the Bi chemistry dictates the electronic structures of the ABiO3 compounds. CaBiO3 is an indirect band gap semiconductor with a quasiparticle (QP) band gap of 1.89 eV and an optical band gap of 2.09 eV; see Table 1. Although an indirect band gap is not optimally functional for light absorption, it reduces substantially the probability of photogenerated electron−hole radiative recombination and could result in longer carrier lifetime (τ) and therefore longer carrier diffusion length; the net consequence being higher photogenerated currents as conjectured for hybrid halide perovskites.59,60 The band gap separates states created from hybridized Bi3+6s/O2−-2p orbitals (valence band) and Bi 5+-6s/O 2−-2p (conduction band) states. This character is different from the electronic structure of conventional TMOs with d0 configurations, where intermixed B-d/O-2p states typically form the valence and conduction bands. Here, the low-energy band structure originates from chemical back-bonding effects, hybridization of the antibonding Bi3+-6p/O2−-2p states with the antibonding Bi3+-6s orbitals, an effect due to the 6s lone pair electron of Bi3+ (see Figure S6).38,61 Consequently, the bismuth−oxygen hybridization shifts the valence band to higher energy and considerably improves the valence band mismatch for water splitting, as observed in the widely used photocatalysis BiVO4.62 As already anticipated, Bi-based oxides like the ones considered here exhibit broadly dispersive s bands near the Fermi energy (conducive to small effective masses m*), which should improve the carrier mobility (μ) because μ ∝ 1/m*. The calculated effective masses of these compounds are tabulated in Table 1. The electron (m*e ) and hole effective mass (m*h ) are smaller than the well studied BPVE material BiFeO3 (me* = 0.691 m0 and mh* = 3.171 m0) and KNbO3 (me* = 1.559 m0 and m*h = 2.743 m0), and comparable with the tetragonal BaTiO3 (m*e = 0.482 m0 and m*h = 1.082 m0). The other three considered compounds, CdBiO3, ZnBiO3, and MgBiO3, share qualitatively similar QP band dispersions but with slightly smaller optical band gaps and narrower 6s bands as shown in Figure S7 and Table 1. The frequency dependent dielectric response was simulated by solving the Bethe−Salpeter equation (BSE, ref.65) on top of 2448


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cell) are considerable: 56, 52, 60, and 74 μC/cm2 for CaBiO3, CdBiO3, ZnBiO3, and MgBiO3, respectively, coinciding with the size of the A-site cation radius. It is worth noting that more than 50% of the polarization originates from A-site cation polar displacements, similar to LiNbO3-type oxides.16 This also explains why the polarization is strongly correlated to the radius of the A-site cation. This polarization generates a large dipole moment along the pseudocubic [111] direction, similar to the prototypical BPVE material BiFeO3,68 which is known to aid in the separation of photogenerated electron−hole pairs and reduce carrier recombination. In conclusion, we proposed a novel strategy to design polar oxides for PV and PC applications by taking advantage of Bi3+/ Bi5+ charge disproportionation and small radii A-site cations in ABiO3 compounds. Our design principles were examined within four, as-yet reported, oxides CaBiO3, CdBiO3, ZnBiO3, and MgBiO3 based on first-principles calculations. Our results show that the oxides exhibit small band gaps, strong visible-light absorption, small carrier effective masses, and large electric polarizations. Moreover, these materials were also found to be thermodynamically and dynamically (meta)stable and therefore are likely to be synthesized using high pressure or soft chemistry methods. More importantly, our strategy is general and could be extended to other small divalent A-site cations and charge disproportionating B cations such as Ni2+ (0.69 Å) and Cu2+ (0.73 Å) with Sb3+/Sb5+ as long as the 3d states of the A-site cation do not appear at the band edge (which would alter the band gap and effective mass). For example, Ni3TeO6-type oxides with Mn2+ at the A-site, such as Mn2FeMO6 (M = Mo and W) and Mn2ScSbO6, have been synthesized; and the DFT calculations show that Mn 3d orbitals have no contribution to the top of the valence band and the bottom of conduction bands of Mn2FeWO6.52,69 We hope this work leads to detailed experimental investigations into this family of compounds.

the GWTC−TC @HSE quasiparticle structures. The absorption 0 coefficient was calculated as 2ω α(ω) =

ϵ12(ω) + ϵ22(ω) − ϵ1(ω) 2

c

where ϵ1 and ϵ2 are the real and imaginary parts of the dielectric function, respectively, ω is the photon frequency, and c is the speed of light. As shown in Figure 4, remarkably, all these

Figure 4. Optical absorption coefficients for ABiO3 (A = Ca, Cd, Zn, and Mg) obtained from the dielectric function calculated at the BSE level. The background shadow represents the solar spectrum. As a comparison, we also display the absorption spectra of MAPbI3 and Bi2FeCrO6 taken from refs 67 and 12, respectively.

compounds show strong optical absorption in the visible-light region, owing to the strong intersite transition between Bi3+ 6s and Bi5+ 6s states, which is similar to the metal-to-metal charge transfer mechanism observed in CaCu3Ti4O12.66 The restrictions imposed by dipole selection rules are alleviated by the strong hybridization and broken inversion symmetry, which should improve the PCE. The visible light absorption spectra of these compounds are superior to MAPbI3 and Ba2FeCrO6.12,67 The red-shift of the absorption spectrum from CaBiO3 to ZnBiO3 in Figure 4 mainly arises from the decrease in the optical band gap and the increase of the excitonic effect. The situation for these ABiO3 compounds is very different from what is usually observed in the typical TMOs such as SrTiO3, where the lowest energy absorption originates from optical transitions from the occupied O-2p to unoccupied TM-d orbitals and also occurs typically at higher photon energies due to the large electronegativity difference between the cation and anion. Last, we obtained the ferroelectric properties of the ABiO3 family by computing the spontaneous electric polarization e Pα = Ω ∑k , β Zk*, αβuk , β , from the Born effective charges (Z*) and atom displacements (u) of the polar structure with respect to the reference phase R3̅ (Ω and e are the volume of the unit cell and the elementary electron charge, respectively). As shown in Figure S1, the R3̅ phase is obtained by condensing Γ+4 mode along the [111] direction (see Figure 1a), and it was also found to be a high-T phases of BaBiO3.39 Therefore, R3̅ likely represents the lowest energy nonpolar parent phase of R3. These two phases are also connected through a single polar mode, Γ−1 , with the [001] order parameter direction. The calculated polarizations along the [0001] direction of the crystallographic unit cell (or [111] direction of the primitive

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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.chemmater.6b03486. Description of the theoretical methods, calculation of the absorption coefficient, complete structure search results, phase stability assessment, and additional tables and figures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

Work at the University of Vienna was sponsored by the FWFSFB project VICOM (Grant No. F41). J.M.R. was supported by the U.S. DOE, Office of Basic Energy Sciences, under grant no. DE-AC02-06CH11357 and a 3M Non-Tenured Faculty Award. All calculations were performed on the Vienna Scientific Cluster (VSC). 2449


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