Octahedral vs. Trigonal-Prismatic Coordination and Clustering in Trans - PDF document

J. Am. Chem. SOC. 1984, 106, 3453-3460 Octahedral vs. Trigonal-Prismatic Coordination and Clustering in Transition-Metal Dichalcogenides 3453 the Department University, Ithaca. band calculations, the metals to enter octahedral then as the electron count increases, finds again octahedral albeit distorted transition-metal chalcogenides, two layers close-packed chalcogenide atoms sand- one metal layer between der Waals contacts ta 4 1 found in one fundamental transition series. two chalcogenide layers forming slab can be stacked directly making trigonal prismatic stagger, forming octahedral The 4B 3 all have octahedral structures. For octahedral structures some have 6B the true. In group octahedral structures, albeit distorted this variation preferred solid-state geometry? deformations alluded Chemistry of Layer-type Phases"; 0002-786318411506-3453$01.50/0 4 such a to form approximate infinite one-dimensional chains. Is reason for a semiconductor is suggestive in most 5B dichalcogenides instabilities tied work. In structures and total layers, trigonal-prismatic Le., we different compounds across average band necessarily not individual compounds a more favorably the other hand, the model is, shall see, In the second part of ~~~ ~ Acta Chem. Scand. these has been described recently: Marolikas, (3) (a) are isostructural 1971, 24, 73-81. another, more dense Theory of Solids"; Oxford University Press: 108. (b) (6) (a) (d) Ingelsfield, (7) (a) See: Whangbo, M.-H.; Hoffmann, R. J. Am. Chem. SOC. 1978, 100,6093-98. (b) Hoffmann, R. H.; Shaik, S.; Scott, J. C.; Whangbo, M.-H. Foshee, M. J. J. Solid State Chem. 1980, 34, 263-269. 144 1-1 477. 1984 American Chemical Society 3454 J. Am. Chem. SOC., Vol. 106, No. 12, 1984 Kertesz and Hoffmann a trigonal prismaticgb configuration. not very sensitive to the rigid band model. interested in difference between and the trigonal-prismatic band some differences due to the different packing, octahedral case trigonal-prismatic case. following Brillouin MX2 Transition-Metal Dichalcogenide Layers (X trigonal-prismatic octahedral compd cla compd cla do ZrS, 1.59 TiSe, 1.70 NbSz 1.80 WSe, 1.98 d3 ReSe2c 1.92 typical and selected from more polytypes have (1.849), 3R (1.861), Trigonal-Prismatic vs. Octahedral Structures as a Function of the Electron Count d-electron count changes going across no bonding these di- contrast to trichalcogenides such safely assign X, reaching the metals be taken count variation must enter. The size cavities for depend on A simple to measure to compare In the ideal close-packed trigonal-prism c/a = 1.633 c/o = 2.0 5 deviations from ideal ratios bonding, among other factors. choice between seen in choose between must be based on on a plot radius ratios metal-chalcogen bond. Packing considerations have for some time. electronic factors. In studying differences between energy band two different trigonal prismatic. In order to most clearly, case alternative two-dimensional layers an octahedral (8) Gamble, F. R. J. Solid Store Chem. 1974, 9, 358-367. 6 zone is enclosed special points point in will be reserved high-symmetry edge point. occupied bands Brillouin zone,I0 high symmetry points special concern since these In discussing main features focus on interactions, because these to the differences between AA and two two-dimensional shown in D 7 0 The dark and the in both cases, but it different one double layer, discussion is nearest interlayer one unit but between two and three be such layer (“out layer (“in plane”). expect two the “undistorted” octahedral ReSel ex erimental’ geometry layers, with the trigonal-prismatic model was be most close the octahedral one: all distances within layers were kept fixed, Mechanics”; Pergamon: London, Transition- Metal Dichalcogenides At the same (four, altogether) be pushed up because 1 with to the atomic orbital the famous a single its Brillouin This can overlap population 1, 1 combination overlap population, each antibonding, with “bond each contribution changes is lower; interplane interactions. This splitting gives rise to the trigonal prismatic case for the octahedral their splittings interlayer separations general features two chalcogen layers’ scheme for these high symmetry points, trigonal-prismatic case. AB AA 9 10 2 (numbering weakly bonding. in-plane orbital, this orbital. Then pair may be bonding or antibonding across two layers, small splitting. interacting strongly nonbonding separation between chalcogens, 11 But the out-of-plane interactions. illustrated schematically 13 12 14 that the due to inter-unit-cell interactions intracell interactions is similar-it is one for the AA case where larger along point is quite different. Now, due to theorem,lob a is associated 2?r/3) for one each other. As a consequence, degeneracies present the AB lifted in illustrate this case through 1s 16 r K 17 r K 18 computed band is shown in necessary avoided crossings occur along route from precisely those discussed above. to the filling every AB layer with a transition metal every second trigonal-prismatic hole Re, and band structures these band p bands AA or AB lie between -10.5 -16.5 eV. resonance with levels, placed -12.66 eV, Thus, there interaction, splitting into other expected consequence a three-below-two pattern. This octahedral case also for A similar, well-known degeneracy occurs at K. of the these graphite orbitals graphite intercalation compounds have discussed recently “Intercalated Graphites”; Dresselhaus, Elsevier: Amsterdam, 3456 J. Am. Chem. SOC., Vol. 106, No. 12, 1984 Kertesz and Hoffmann E (eV) -10 octahedral t I E(eV) -10 c 1 trigonal prismatic 7 K Energy band with octahedral packing) and oc. t a h edr a I E (eV) r r Energy band coordination around band structures bands, largely region between level in will be in Jellinek, F. Transition-Metal Dichalcogenides J. Am. Chem. Soc.. Vol. 106, No. 12, 1984 3451 OCTAHEDRON la OCTAHEDRON 1 C TRIGONAL PRISM -15' E (ev) total L c 'total for an The dashed c) orbitals, ........ ................ .....A -5 1 ........ .... ....... � ................................. c::--4 ....... .......................................................... ;;; I .................................... E(eV) ........... ..... -15 -. ...... E -zol ---__ ............ ............ I ........... ............... Re-Re Se-ss Crystal orbital trigonal prismatic bonds become strongly antibonding the layer projection spreads much broader energy range than strongly with ligand orbitals than the spread out metal-metal interactions. peaks in -13 eV have a contribution but orbitals. These characteristics not fully in accord usual simplified picture based crystal field for electron d3, according to other (pyrites, marcasites) structures observed for compare the with those three-dimensional is worth looking population curves displayed in trigonal prismatic is very negative peak for all these M-X), indicating the structure, as such, although electrons. Also M-X bonds up to some antibonding the d eV). The significant antibonding contribution from eV, a in-plane bands metal free bands (cf. Figure orbitals around for all many interesting features structure and these dichalcogenides, in on prime interest to a do-electron count, bands energy between and octahedral bands differ. on bands a preference significant differences prism relative the octa- the center from interacting with a d 19 200 20b its energy down. trigonal prismatic can interact traced to same symmetry- factor that bilayer produced a up, relative to the an important role in the same symmetry-lowering factor bilayer produced a substantial splitting these bands, first become relatively more stable, effect reaches its maximum around starts, and the ~~ ~~ R. R. 3458 J. Am. Chem. Soc., Vol. 106, No. 12, 1984 Kertesz and Hoffmann I 4E = Et.p.-Eoct. sV/MX, OCTAHEDRAL MORE STABLE r K' Ax' I / :.\ I I a' Y3 4 n TRIGONAL PRISMATIC MORE STABLE Relative stabilities octahedral and trigonal-prismatic extended Hiickel energy band three different series corresponds parameter sets: and Se parameters, experimental geometry. Connecting lines more stable, to the upward shift energy differences as a calculation for TiSe2 as trend: for do the octahedral more stable; then starts to For still larger d-electron octahedral geometry more stable. two effects is in Most notable this correlation count from the actual atomic parameters electronic effect a consequence symmetry-controlled band perimental results and HaeringI3 Li intercalation indicate transformation layers from trigonal prismatic charge transfer from Li outlined above. The Clustering Distortion in ReSe2 the actual structure2 can be as a distorted ideal layer compound. distortion leads arrays, as 21 valence electrons filling M K' \ I 2x - r K' M K back folded derived from ReSe2 band structure. The cell (Re,Se,) than that 22 primed high-symmetry to the zone while inequivalent in old zone mapped to A number degeneracies occur special points. because after distortion takes new bands be pieced slowly but systematically, from mappings indicated in such piecing-together electrons have particular importance around are the degenerate bands (originating from doubly degenerate (originating from through 41. (37 and originating from and the Transition- Metal Dichalcogenides I J. Am. Chem. Soc., Vol. 106, No. 12, 1984 3459 E (eV) r‘ K’ E (eV) distortion coordinate, the undistorted and the experimental from bands Figure 2a These d orbitals a layer will be strongly affected in which metal-metal overlaps it another way, these in-plane bands substantial band these bands 39 is perturbed upward indicated schematically a distortion will be energetically favorable. expect a situation such E I/ K 23 24 have chosen linearly between octahedral ReSez structure and observed one. Figure 7 a Walsh diagram for two points, Brillouin zone. several avoided crossings (37 and pushed down orbital 40, is moved As a result, around occupied levels move distort. How strong this electronic distortion force? whole Brillouin a varying our calculations, per Re4Ses large number levels in close d-Electron Count d” do d’ d2 d3 d4 d6 AE -0.97 0.26 1.15 3.45 1.10 -8.84 -I5P E (eV) !- -*Ob each other, their strongly along calculated total experimentally observed and the structure as a function electron count incides with the fact distortion observed is energetically this distortion band This can be most seen in given in the mutual orbitals around discussed in lies close to the experimental (optical) calculated direct a Peierls-Distorted Structure? above discussion a Jahn-Teller small distortion values large enough to level, whose for the is in contrast to other, quite familiar, in quasi-one- -two-dimensional systems or several d’ transition-metal Peierls distortion and For these Fermi surface, often not the lattice. These instabilities most easily visualized surface separated a single (14) (a) Application of the Mooser-Pearson rule (see: Solid Stare Chem. to the Stare Chem. (15) See: Schaad, L. J.; Hess, B. A,; Ewig, C. S. J. Am. Chem. Soc. 1979, 16 1-214. 101, 2281-2283. 3460 J. Am. Chem. SOC., Vol. 106, No. 12, 1984 Kertesz and Hoffmann 7 overlap population, p” t 0.21 I empty circles splitting their energy strongly. Thus, an and the periodic lattice distortion, this picture to further into it is the Fermi surface its energy this semiconductor. particular deformation? Since three d-type bands, Thus, the regions should this to unit cell may sufficient. However, system with contacts cannot derived from system where this On the other hand, for four fulfilled with diamond shaped clusters ReSez structure. In any extended system overlap populations for a from the crystal case a molecular Jahn-Teller system 41n13 1 2 25 from the degenerate orbitals they depend within the degenerate two slightest distortion populations from these orbitals, not depend strongly calculation for metal-metal bonds in distortion. For technical reasons, have chosen summarizes some these overlap particularly suitable for all bonds overlap populations; those which does not deformation, in analogy small deformation actual deformation. fully developed metal-metal bonding may conclude posed in Overlap Populations Electron Count, and Deformation €=3% €= 100% c = 1% d3 d3 ~~~~ intrachain 2,3 27 40 31 13 -18 21 193 1,3 26 37 36 10 -18 13 143 1,2 26 37 36 10 -18 12 140 1,4’ 26 36 36 10 -19 11 89 interchain 33 33 -0.4 -22 34 34 analogous systems: X-ray and electron diffraction experiments16 revealed also slip a close-packed chains like is very close to three here to chains Their structure the MoSz but these essentially 3-dimensional compounds, metals coordinate to eight which belong to one to the next above systems, a model for M a formal formal count for those would be to argue network toward experimentally found a Jahn-Teller distortion discussed in this paper. grateful to Sunil Wijeyesekera for to John Corbett for bringing our attention, to research was generously supported the National Science Foundation through the Materials Cornell University. on leave from the Appendix energy band program originally written and Ch. convergency with respect to the been checked, 24 point of only points could therefore the orbital given for total energy changes justified a atomic parameters 2.44, ((4p) 1.5, (l(3d) 1.44, with coefficients 2.4, ((6p) Numbering according to ReSe2, 12038-64-1; ____ ~~~~ (16) Deblieck, R.; Wiegens, G. A,; Bronsema, K. D.; Van Dyck, D.; Van Tendelov, G.; Van Landuzt, J.; Amelinckx, S. In “Solid State Chemistry 1982, Proceedings of the 2nd European Conference”; Metselaar, R., Heijligers, H. J. M., Schoonman, R., Eds.; Elsevier: Amsterdam, 1983; pp 671-75. (17) (a) van den Berg, J. M. Inorg. Chim. Acta 1968, 2,216. (b) Guillevic, J.; Le Marouille, J.-Y.; Grandjean, D. Acta Crystallogr., Sect. 8 1974, 830, 11 1. (c) Chevrel, R.; Sergent, M.; Meury, J. L.; Quan, D. T.; Colin, Y. J. Solid State Chem. 1974, 10, 260.