- freely available
Crystals 2013, 3(3), 431-442; doi:10.3390/cryst3030431
Abstract: Two barium phosphide halides, Ba2P7Br and Ba2P7I, were synthesized and structurally characterized by single crystal X-ray diffraction. Both compounds crystallize in the monoclinic space group P21/m (No. 11) and are isostructural to Ba2P7Cl. The crystal structures of Ba2P7X (X = Cl, Br, I) feature the presence of heptaphosphanortricyclane P73− clusters along with halogen anions and barium cations. According to the Zintl concept, Ba2P7X compounds are electron-balanced semiconductors. Quantum-chemical calculations together with UV-Visible spectroscopy confirm the title compounds are wide bandgap semiconductors. The bonding in the P73− clusters was analyzed by means of electron localization function. The elemental compositions were confirmed using energy dispersive X-ray spectroscopy.
Polyphosphides are known to form a variety of crystal structures with different elements [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. From three-dimensional frameworks to isolated cages, phosphorous backbones form a wide range of stable structures. The P73− cluster, heptaphosphanortricyclane, heptaphosphatricyclo[22.214.171.124(2,6)]heptane, is a commonly present phosphorus fragment which is able to form binary and ternary compounds with different counter-cations, like A3P7 (A = alkali metal) or Ba3P14 [1,2,3,4,5]. The P73− clusters are quite stable and have been found in both solution and solid phases [1,2,3,4,5,15]. Heavier analogs of such clusters with As and Sb are also known [16,17,18].
Similar to other intermetallics, the electronic structures of polyphosphides can be rationalized by application of the Zintl concept [19,20]. Zintl theory implies the valence electrons of electropositive atoms are donated to more electronegative atoms. The latter realize their electron octet by forming 2c–2e chemical bonds and by having electron lone pairs. In A3P7, one electron is donated from each A atom to allow for the formation of the P73− cage . In Ba3P14, three Ba atoms donate two electrons each to allow for the formation of two P73− cages . An interesting example of a compound combining the P73− Zintl anion with a classical chloride anion was reported by von Schnering and Menge in 1981 . In the Ba2P7Cl Zintl salt, the total charge of two Ba2+ cations is compensated by a combination of Cl− and P73− anions. In this work, we expand the family of P73− structures to include the isostructural Ba2P7Br and Ba2P7I. We report the synthesis, characterization, and chemical bonding of three Ba2P7X (X = Cl, Br, I) compounds.
2. Results and Discussion
2.1. Crystal Structure
Originally, Ba2P7I was discovered accidentally during attempts to grow large single crystals of BaP3 utilizing I2 as a transport reagent. After the crystal structure and composition were established, a sample of Ba2P7I was synthesized by the reaction of stoichiometric amounts of the elements at 1073 K. The bromine-containing analog was synthesized from barium, red phosphorus, and barium bromide at the same temperature. A summary of pertinent information related to single crystal X-ray diffraction unit cell parameters, data collection, and refinements is provided in Table 1. Energy-dispersive X-ray spectroscopy (EDS) investigations of the selected single crystals confirmed the presence of only the expected Ba, P, and X halogen elements.
|Space Group||P21/m (No. 11)|
|λ [Å]||Mo K α, 0.71073|
|ρ [g cm−3]||3.485||3.742||3.912|
|θ [deg.]||3.23 < θ < 30.66||3.25 < θ < 30.57||3.22 < θ < 30.58|
|R1 (I > 2 σ(I))||0.028||0.012||0.019|
|wR2 (I > 2 σ(I))||0.047||0.025||0.037|
|Δ ρmax and Δρmin, e/Å3||1.36 and −1.14||0.50 and −0.73||1.22 and −0.92|
* More information can be obtained from Fachinformations-Zentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany, by quoting the depository CSD (Crystal Structure Database) numbers given above.
The new compounds, Ba2P7Br and Ba2P7I, are isostructural to the previously reported Ba2P7Cl (Figure 1) . The crystal structure of Ba2P7X can be described as consisting of two distinct ionic layers, [Ba2X2]2+ and [Ba2(P7)2]2− stacked along the  direction (Figure 2a). According to the Zintl concept [19,20], the Ba2P7X compounds are electron balanced. The barium and halogen atoms realize their electron octet by donating and accepting two and one electrons, respectively. Phosphorous atoms bonded to three other phosphorus atoms should be P0, realizing their electron octet by maintaining an electron lone pair. Phosphorous atoms bonded to two other phosphorus atoms should be P1−, realizing their electron octet by maintaining two electron lone pairs. The P73− clusters contain four three-bonded phosphorus atoms (P1, P2, P5) and three two-bonded P atoms (P3, P4) (Figure 3a). Thus, the total charge per cluster is −3, (3b-P0)4(2b-P1−)3, and the charge-balanced formula is (Ba2+)2(P73−)(X−). In accordance with this formulation, the halogen atoms of Ba2P7X are surrounded by barium atoms in the first coordination sphere, while the phosphorus atoms are situated further apart. The P73− units are surrounded by barium atoms coordinating to the faces, edges, and corners of the cluster (Figure 3b). The Ba–P separations for all Ba2P7X are in the range of 3.3–3.6 Å. The shortest P–X interatomic separations are longer than 3.6 Å.
An interesting feature of the Ba2P7X crystal structure is the relative arrangement of its P73− fragments. All fragments are arranged parallel to each other in a head-to-head fashion. To the best of our knowledge, no other structures composed of the P73− anions are known to form with such straight linear arrangements of P73− anions. For example, in Ba3P14, the heptaphosphanortricyclane clusters are rotated with respect to each other (Figure 2b) . Apparently, the presence of [Ba2X2]2+ layers fixes the orientation of the P73− clusters, probably due to the repulsion between negatively charged species. The lack of halogen atoms in Ba3P14 allows for more structural flexibility, and the P73− clusters are free to face different directions.
In Ba2P7X, the P73− cluster is made up of only five symmetrically unique phosphorous atoms. Bond lengths and angles, and a general view of the P73− clusters are presented in Table 2 and Figure 3, respectively. The heptaphosphanortricyclane of Ba2P7X has Cs local symmetry with a mirror plane containing the P1, P2, and P3 atoms. In Ba3P14, A3M7 (A = alkali metal), and ammonia solvates of alkali metal phosphides, the P73− heptaphosphanortricyclane clusters have C1 local symmetry [3,4,15].
|Atoms||Distances (Å)||Angle Type||Angle (θ)|
The P73− clusters of Ba2P7X contain phosphorus atoms P1 and P5 in strained geometries, with angles in the basal triangle close to 60°. Other angles are significantly larger and closer to the typical tetrahedral angles found in most polyphosphide anions. In the P73− clusters of Ba3P14 and Li3P7, the P–P distances in the basal triangle are similar, 2.23–2.29 Å [3,4]. In Ba2P7X, the P–P bond perpendicular to the mirror plane is significantly elongated compared to the other two basal triangle bonds: d(P5–P5) = 2.34 Å, d(P1–P5) = 2.23 Å. The other bond lengths and angles in the Ba2P7X P73− clusters appear to be similar to those found in the crystal structures of Ba3P14 and Li3P7.
The local coordination of the barium and halogen atoms is shown in Figure 4. Five barium atoms form the first coordination sphere of the halogen atoms. Each barium atom is surrounded by 11 neighbors. Four halogen atoms and seven phosphorus atoms form irregular polyhedra around Ba1, while the Ba2 atoms are surrounded by 10 phosphorus atoms and only one halogen atom. As expected, with an increase of the halogen size from chlorine to iodine, the unit cell volume increases (Table 1). The P73− unit remains nearly the same in all three Ba2P7X compounds (Table 2). The shortest Ba–P distance also exhibits a minor variation upon a change in the halogen atom, with the shortest Ba2–P distance remaining the same in all compounds: 3.30–3.31 Å. An increase of the unit cell occurs mainly due to the increase in the shortest Ba–X distances from 3.14 Å (Cl) to 3.32 Å (Br) to 3.47 Å (I).
2.2. Electronic Structure
The electron balanced Zintl salts, Ba2P7X, are expected to exhibit semiconducting and diamagnetic properties. Band structure calculations were performed to verify this description (Figure 5). According to the calculations, the Ba2P7X compounds are wide band-gap semiconductors with indirect bandgaps Eg = 1.71 eV (X = Cl), 1.86 eV (X = Br), 1.91 eV (X = I). The results of calculations were verified with UV-Vis spectroscopy (vide infra). In the electronic structure of Ba2P7X, the top of the valence band is dominated by the contribution of phosphorus 3p orbitals, with both halogen and barium orbitals also contributing to the states near the Fermi level. The contribution of the halogen orbitals to the states near the Fermi level increases in the Cl–Br–I series. The bottom of the conduction band is comprised of phosphorus and barium orbitals with negligible contributions from halogen orbitals. The main contribution of halogen p-orbitals to the valence band is located between −1 and −3 eV.
To clarify the bonding in the P73− phosphorus clusters, we applied Electron Localization Function (ELF) analysis [22,23,24,25] to the Ba2P7I compound (Figure 6). According to the Zintl concept, single covalent 2e–2c bonds are expected to be present at short P–P interatomic separations. Additionally, one and two electron lone pairs are expected to be located on the two- and three-bonded phosphorus atoms, respectively. The ELF analysis indicates the presence of the expected number of electron lone pairs (Figure 6a). The two bonded phosphorus atoms, P4 and P3, have two electron lone pairs, while the three-bonded P1, P2, and P5 have only one electron lone pair. These results are similar to the results of ELF calculations for less symmetric P73− clusters .
Localization domains corresponding to the covalent two centered P–P interactions were found for all of the short interatomic separations (Figure 6b–e). The ELF maxima of the P1–P5 bonds were shifted from the lines connecting the P1 and P5 atoms. The ELF domain for the P5–P5 bond exhibited lower values of ELF (Figure 6c). This localization domain is also shifted from the line connecting the P5 atoms and it is not well separated from the domains corresponding to the electron lone pairs on the P5 atoms (Figure 6c–e). The P1–P5–P5 basal triangle, with a topology close to that of cyclopropane, is the most strained face of the P73− cluster. Angles of ~60° hamper the direct overlap of phosphorus orbitals. This explains the displacement of the bonding maxima from the lines connecting the atoms.
In ELF studies performed for the P73− clusters of the ammonia solvates of alkali metal phosphides, the heptaphosphanortricyclane units are less symmetric, with point group C1 . These units have almost identical bonds, 2.26–2.30 Å, between phosphorus atoms forming a strained basal triangle. Three well-separated and similar localization domains were found displaced from the line connecting phosphorus atoms . Heptaphosphanortricyclane units in Ba2P7X have a different geometry (Table 2) with shorter P1–P5 distances (2.23 Å) and longer P5–P5 distance (2.34 Å) than those distances present in ammonia solvate compounds . This difference is probably due to the presence of a Ba atom coordinated to the P4–P5–P5–P4 square (Figure 3b) . This is reflected in the bonding picture: the localization domains for P1–P5 bonds are well pronounced and remain separated from the lone pair domains, while the localization domain for the P5–P5 bond is less pronounced and is not separated from the domains corresponding to the lone pairs located on the P5 atoms (Figure 6e).
No ELF maxima were detected near the shortest Ba–X separations, which are indicated by the dashed lines in Figure 1, Figure 4. Presumably, all Ba–X interactions are electrostatic cation-anion interactions.
2.3. UV-Vis Spectroscopy
Ba2P7Cl, Ba2P7Br, and Ba2P7I are red, orange, and yellow-orange, respectively. Solid state UV-Visible spectroscopy was employed for experimental bandgap determinations.
According to the calculated Tauc plots [26,27], Ba2P7Cl has indirect optical transitions corresponding to a bandgap of 1.83(2) eV (Figure 7, Table 3). The calculated bandgap for this compound, 1.71 eV, is in reasonable agreement with the experimental data. Calculations predict the increase of the bandgaps in the Cl–Br–I series (Figure 5). This increase was observed experimentally and is consistent with the visual color change of the Ba2P7X analogs from red to yellow. The experimental indirect bandgaps of the bromine and iodine analogs, 1.92(4) eV and 1.89(2) eV, respectively, are approximately 0.1 eV larger than the Ba2P7Cl bandgap. In our UV-Vis experiments we were not able to detect the small predicted difference between the indirect bandgap values for Ba2P7Br and Ba2P7I, when estimated standard deviations are taken into account. A combination of the spectroscopic and calculation approaches indicates the compounds obtained are wide bandgap semiconductors.
|Direct Bandgap (eV)||2.16(3)||2.20(4)||2.19(4)|
|Indirect Bandgap (eV)||1.83(2)||1.92(2)||1.89(2)|
|Calculated Bandgap (eV)||1.71||1.86||1.91|
3. Experimental Section
All samples of Ba2P7Cl, Ba2P7Br, and Ba2P7I were prepared via solid-state reactions in evacuated and sealed silica ampoules. The samples were prepared in an Argon-filled glovebox with p(O2) and p(H2O) < 1 ppm. The starting materials: metallic barium (Sigma Aldrich, St. Louis, MO, USA, 99.9%), iodine (Alfa Aesar, Ward Hill, MA, USA, 99.9985%), and red phosphorous (Alfa Aesar, Ward Hill, MA, USA, 99%) were used as received. Barium bromide and barium chloride (Alfa Aesar, Ward Hill, MA, USA, 99.998% and 99%, respectively) were heated at 573 K overnight under an inert atmosphere to remove traces of water.
A single phase sample of Ba2P7I was synthesized by annealing stoichiometric amounts of the elements at 1073 K for 140 h. Samples of Ba2P7Cl and Ba2P7Br were prepared using metallic barium, phosphorous, and barium chloride or barium bromide in a 3:14:1 ratio under similar annealing conditions. In agreement with the previous report , Ba2P7Cl crystals have a red color. Ba2P7Br and Ba2P7I crystals exhibit orange and orange-yellow colors, respectively. The color of all Ba2P7X lightened upon grinding. Similar to other compounds containing the P73− phosphorus cluster, Ba2P7X degrades in air over time, and appears to quickly decompose in water, so samples were stored in an Argon-filled glovebox.
The samples were characterized by X-ray powder diffraction (XRD) using a Bruker D8 Advance diffractometer employing Cu Kα radiation. Elemental analysis of the selected single crystals was carried out on a Hitachi S4100T scanning electron microscope (SEM) with energy-dispersive X-ray (EDX) microanalysis (Oxford INCA energy). Sample analysis confirmed the presence of only Ba, P, and X (X = Cl, Br, I). Solid-state UV-Visible spectroscopy (Thermo Scientific Evolution 220 Spectrometer) was employed for experimental bandgap determinations. For UV-Vis measurements, solid samples were ground into powders and gently pressed onto rough filter paper to form a thick layer of sample. Attempts to dissolve samples of Ba2P7X for solution-based UV-Vis measurements were unsuccessful. Samples of Ba2P7X were water sensitive, turning to amorphous yellow material when immersed. No visible color change was observed for immersion in ethanol, but as samples dried they turned brown.
Single crystal X-ray diffraction experiments were carried out at 90 K using a Bruker AXS SMART diffractometer with an APEX-II CCD detector and Mo Kα radiation. The data sets were recorded as ω-scans at a 0.3° stepwidth and integrated with the Bruker SAINT software package . A multiscan absorption correction was applied. The solution and refinement of crystal structures were carried out using the SHELX suite of programs . The structures were solved in the P21/m space group and the final refinement was performed using anisotropic atomic displacement parameters for all atoms.
Density functional band structure calculations and bonding analyses were carried out using the tight binding—linear muffin tin orbitals—atomic sphere approximation (TB–LMTO–ASA) program package . The Barth–Hedin exchange potential was employed for the local density approximation (LDA) calculations . The radial scalar-relativistic Dirac equation was solved to obtain partial waves. A basis set containing Ba(6s,5d,4f), P(3s,3p), Cl(3p), Br(4p), and I(5p) orbitals was employed for a self-consistent calculation, with Ba(6p), P(3d), Cl(4s,3d), Br(5s,4d), and I(6s,5d,4f) functions being downfolded. The ELF (η) was evaluated with modules implemented within the TB–LMTO–ASA program package [22,23,24]. The ParaView program was used for visualization of ELF isosurfaces [32,33].
Two new compounds, Ba2P7Br and Ba2P7I, have been synthesized and their crystal structures have been determined by means of single crystal X-ray diffraction. In the crystal structure of Ba2P7X (X = Cl, Br, I) negatively charged layers of heptaphosphanortricyclane P73− clusters surrounded by barium cations are stacked along the  direction, alternating with positively charged Ba2X2 layers. According to the Zintl count and quantum-chemical calculations, Ba2P7X are electron-balanced semiconductors with wide bandgaps. UV-Vis spectroscopy confirms the semiconducting nature of Ba2P7X compounds. Analysis of the chemical bonding in P73− clusters by means of electron localization function indicates their bonding generally follows the Zintl counting scheme. However, for the basal triangle of phosphorus atoms, the ELF localization domains are displaced from the shortest interatomic separations.
The authors would like to thank J. Zhao and J. Wang for their assistance with the UV-Vis measurements. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008931.
Conflicts of Interest
The authors declare no conflict of interest.
- Pöttgen, R.; Hönle, W.; von Schnering, H.G. Phosphides: Solid State Chemistry. In Encyclopedia of Inorganic Chemistry, 2nd ed.; King, R.B., Ed.; Wiley: Chichester, UK, 2005; volume 8, pp. 4255–4308. [Google Scholar]
- Von Schnering, H.G.; Hoenle, W. Bridging chasms with polyphosphides. Chem. Rev. 1988, 88, 243–273. [Google Scholar] [CrossRef]
- Dahlmann, W.; von Schnering, H.G. Die Polyphosphide SrP3 und Ba3P14. Naturwissenschaften 1973, 60, 429–429. [Google Scholar] [CrossRef]
- Manriquez, V.; Hönle, W.; von Schnering, H.G. Trilithiumheptaphosphid Li3P7: Darstellung, Struktur und Eigenschaften. Z. Anorg. Allg. Chem. 1986, 539, 95–109. [Google Scholar] [CrossRef]
- Scharfe, S.; Kraus, F.; Stegmaier, S.; Schier, A.; Fässler, T.F. Zintl ions, cage compounds, and intermetalloid clusters of group 14 and group 15 elements. Angew. Chem. Int. Ed. 2011, 50, 3630–3670. [Google Scholar] [CrossRef]
- Shatruk, M.M.; Kovnir, K.A.; Shevelkov, A.V.; Popovkin, B.A. Ag3SnP7: A polyphosphide with a unique (P7) chain and a novel Ag3Sn heterocluster. Angew. Chem. Int. Ed. 2000, 39, 2508–2509. [Google Scholar] [CrossRef]
- Lange, S.; Sebastian, C.P.; Zhang, L.; Eckert, H.; Nilges, T. Ag3SnCuP10: [Ag3Sn] tetrahedra embedded between adamantane-type [P10] cages. Inorg. Chem. 2006, 45, 5878–5885. [Google Scholar] [CrossRef]
- Lange, S.; Bawohl, M.; Weihrich, R.; Nilges, T. Mineralization routes to polyphosphides: Cu2P20 and Cu5InP16. Angew. Chem. Int. Ed. 2008, 47, 5654–5657. [Google Scholar] [CrossRef]
- Dewalsky, M.V.; Jeitschko, W.; Wortmann, U. The metallic polyphosphide titanium nickel phosphide (Ti2NiP5). Chem. Mater. 1991, 3, 316–319. [Google Scholar] [CrossRef]
- Eisenmann, B.; Rößler, U. Ein Erdalkalimetallpolyphosphid ungewöhnlicher Zusammensetzung: Die Kristallstruktur von Ba5P9. Z. Anorg. Allg. Chem. 2003, 629, 459–462. [Google Scholar] [CrossRef]
- Chen, X.; Zhu, L.; Yamanaka, S. High-pressure synthesis and structural characterization of three new polyphosphides, α-SrP3, BaP8, and LaP5. J. Solid State Chem. 2003, 173, 449–455. [Google Scholar] [CrossRef]
- Eschen, M.; Jeitschko, W. Au2PbP2, Au2TlP2, and Au2HgP2: Ternary gold polyphosphides with lead, thallium, and mercury in the oxidation state zero. J. Solid State Chem. 2002, 165, 238–246. [Google Scholar] [CrossRef]
- Kovnir, K.; Stockert, U.; Budnyk, S.; Prots, Y.; Baitinger, M.; Paschen, S.; Shevelkov, A.V.; Grin, Y. Introducing a magnetic guest to a tetrel-free clathrate: Synthesis, structure, and properties of EuxBa8−xCu16P30 (0 ≤ x ≤ 1.5). Inorg. Chem. 2011, 50, 10387–10396. [Google Scholar] [CrossRef]
- Fulmer, J.; Kaseman, D.C.; Dolyniuk, J.; Lee, K.; Sen, S.; Kovnir, K. BaAu2P4: Layered Zintl Polyphosphide with Infinite Chains. Inorg. Chem. 2013, 52, 7061–7067. [Google Scholar] [CrossRef]
- Kraus, F.; Korber, N. The Chemical Bond in Polyphosphides: Crystal Structures, the Electron Localization Function, and a New View of Aromaticity in P42− and P5−. Chem. A Eur. J. 2005, 11, 5945–5959. [Google Scholar] [CrossRef]
- He, H.; Tyson, C.; Bobev, S. New compounds with [As7]3− clusters: Synthesis and crystal structures of the Zintl phases Cs2NaAs7, Cs4ZnAs14 and Cs4CdAs14. Crystals 2011, 1, 87–98. [Google Scholar] [CrossRef]
- Knapp, C.M.; Large, J.S.; Rees, N.H.; Goicoechea, J.M. A versatile salt-metathesis route to heteroatomic clusters derived from phosphorus and arsenic Zintl anions. Dalton Trans. 2011, 40, 735–745. [Google Scholar] [CrossRef]
- Hirschle, C.; Röhr, C. Darstellung und Kristallstruktur der Bekannten Zintl-Phasen Cs3Sb7 und Cs4Sb2. Z. Anorg. Allg. Chem. 2000, 626, 1992–1998. [Google Scholar] [CrossRef]
- Kauzlarich, S.M. Chemistry, Structure, and Bonding of Zintl Phases and Ion; John Wiley and Sons Ltd.: New York, NY, USA, 1996. [Google Scholar]
- Miller, G.J.; Schmidt, M.W.; Wang, F.; You, T.S. Quantitative advances in the Zintl-Klemm formalism. Struct. Bond. 2011, 139, 1–55. [Google Scholar]
- Von Schnering, H.G.; Menge, G. Dibariumheptaphosphidchlorid Ba2P7Cl, eine Verbindung mit dem polycyclischen Anion P73−. Z. Anorg. Allg. Chem. 1981, 481, 33–40. [Google Scholar] [CrossRef]
- Becke, A.D.; Edgecombe, K.E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 1990, 92, 5397–5403. [Google Scholar] [CrossRef]
- Savin, A.; Jepsen, O.; Flad, J.; Anderson, O.K.; Preuß, H.; von Schnering, H.G. Electron localization in solid-state structures of the elements: The diamond structure. Angew. Chem. Int. Ed. 1992, 31, 187–188. [Google Scholar] [CrossRef]
- Savin, A.; Nesper, R.; Wengert, S.; Fässler, T.F. ELF: The electron localization function. Angew. Chem. Int. Ed. 1997, 36, 1808–1832. [Google Scholar] [CrossRef]
- Kovnir, K.; Kolen’ko, Y.V.; Baranov, A.I.; Neira, I.S.; Sobolev, A.V.; Yoshimura, M.; Presniakov, I.A.; Shevelkov, A.V. Sn4As3 revisited: Solvothermal synthesis and crystal and electronic structure. J. Solid State Chem. 2009, 182, 630–639. [Google Scholar] [CrossRef]
- Morales, A.; Mora, E.; Pal, U. Use of diffuse reflectance spectroscopy for optical characterization of un-supported nanostructures. Rev. Mex. Fis. S. 2007, 53, 18–22. [Google Scholar]
- Nobbs, J.H. Kubelka—Munk theory and the prediction of reflectance. Rev. Prog. Color. Relat. Top. 1985, 15, 66–75. [Google Scholar] [CrossRef]
- SMART and SAINT. Bruker AXS Inc. Madison, WI, USA, 2007.
- Sheldrick, G. A short history of SHELX. Acta Crystallogr. A 2008, 64, 112–122. [Google Scholar] [CrossRef]
- Jepsen, O.; Burkhardt, A.; Andersen, O.K. The Program TB-LMTO-ASA, Version 4.7; Max-Planck-Institut für Festkörperforschung: Stuttgart, Germany, 1999. [Google Scholar]
- Barth, U.V.; Hedin, L. A local exchange-correlation potential for the spin polarized case. J. Phys. C Solid State Phys. 1972, 5. [Google Scholar] [CrossRef]
- Paraview: Parallel visualization application, version 3.8.1 64 bit. Available online: http://paraview.org.
- Baranov, A.I. Visualization Plug-in for ParaView, Version 3.4.11; Springer: Dresden, Germany, 2012. [Google Scholar]
© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).