PAPER Thinking about metal-metal quadruple bonding in extended www.rsc.org/njc NJC structures: a hypothetical A2M6E8 network Musiri M. Balakrishnarajan,a Peter Kroll,b Michael J. Bucknuma and Roald Hoffmann*a a Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853-1301, USA. E-mail: [email protected] b Institut fu¨r Anorganische Chemie, Rheinisch-Westfa¨lische Technische Hochschule Aachen, Professor-Pirlet-Strasse 1, 52056, Aachen, Germany Received (in Montpellier, France) 13th September 2003, Accepted 25th November 2003 First published as an Advance Article on the web 19th January 2004 The electronic and structural possibilities of a recently conceived, as-yet unsynthesized, AM6E8 (or A2M6E8) structural type are explored. With A an alkaline earth metal, M a transition metal, and E a main group element, a range of geometries containing M–M pairs with very short separations is feasible. Density functional theory geometry optimizations and an extended Hu¨ckel analysis of the bonding in a representative Ca2W6O8 realization support the qualitative picture of quadruple metal-metal bonding in these hypothetical phases. The MM pairs interact moderately (metallic behavior is anticipated) through linking atoms. Geometry optimizations of a wide range of hypothetical compounds show that the M–M separation in these will be in the range of realistic quadruple metal-metal bonding, 2.20–2.30 A˚ . The working out of the idea of metal-metal quadruple bonding Another connection may be made to the Cr3Si type (A15 in by F. A. Cotton is certainly one of the prettiest chapters of Strukturberichte). The A2M6 (=M3A=Cr3Si) framework is modern chemistry.1 Can one realize such bonding in extended stuffed with eight E atoms that fill trigonal bypyramidal holes. structures? There are a number of compounds in which short The superconducting Nb3Ge and Nb3Sn phases belong to this metal-metal separations are observed and which reach formal structural family too.9a Our particular choice of atoms A, M, bond orders of three—for instance, RE2ReO5 (RE ¼ rare and E can be thought of as causing bond localization within 2 2 3 4 earth), RE3Re2O9 , Li6Ca2Mn2N6 , Ca6Cr2N6H, NaNb3- the chains formed by the M atoms of the above-mentioned 5a 5b 5c 5d 9b O5F, Ca0.75Nb3O6 , Ca0.95NbO6 , Na0.74Ta3O6 and structures. 6 some others. Here we propose a hypothetical three-dimen- The A2M6E8 structure may also be related to the fluorite sional network that, while apparently not yet made, seems structure type (CaF2). In CaF2 , Ca atoms are arranged in attainable and that should allow moderately localized MM a cubic closest packing (ccp) arrangement, forming a face- quadruple bonds. centered cell with Ca atoms at the origin as well as on the faces of the cube. F atoms occupy all tetrahedral holes. The coordi- nation of Ca is eight, that of F is four. The octahedral intersti- The structure tial sites (in the center of the cell as well as on the edges) are empty. The composition of the conventional cubic unit cell One of us (MJB) recently proposed a new AM6E8 network, of CaF is Ca F .AM E can be derived from CaF in the 7 2 4 8 2 6 8 2 space group Pm3. The network is shown in Fig. 1. The atoms following way: the Ca at the origin is replaced by an A atom. are located as follows: A: 1(a) (0, 0, 0); M: 6(f) Æ (x, 0, 1/2); Then we split every Ca on the faces into an M–M dimer and E: 8(i) Æ (y, y, y). This net may also exist as a centered exchange all F by E atoms. Finally, we fill the octahedral site A2M6E8 variant, with an additional A atom at (1/2, 1/2, 1/2). in the center of the cube with one A. There are several possibilities to relate the proposed A2M6E8 We present these relations to known structural types structure to well-known structural types in solid state chemis- because of their potential utility in the design of a manifold try. The closest connection is to the known Pt3O4 structure and of structures containing dimer pairs. the Pt bronzes and their chalcogenide analogs.8 In these the Pt–Pt bonding is weak (and interesting) and linearly extended, Design, potential realizations, and sample which, as we will see, is a point of contrast to the structures we propose. calculations Putting A ¼ an alkaline earth metal (a lanthanide, actinide or alkali metal would fit as well), M, a transition metal, and E, a main group element from group 15, 16, or 17, we found a large range of viable structures. Viable is in the sense of A–E, A–M falling in the range of normal ionic separations, M–E a typical coordinate covalent distance, and M–M short, in the range of MM multiple bonds. The environment of the MM unit in 2À AM6E8 is clearly approximately that of Re2Cl8 , as Fig. 1 shows. A further exploration began with three representative d4–d4 10.1039/b311231d compounds: Ca2W6O8 , CaNb6Cl8 , and La2Re6N8 . When DOI: Fig. 1 The proposed A2M6E8 structure. computed within the extended Hu¨ckel (eH) method, the first This journal is Q The Royal Society of Chemistry and the New. J. Chem., 2004, 28, 185–190 185 Centre National de la Recherche Scientifique 2004 of these had a reasonable gap between three flattish d bonding parameters produced a reasonable correspondence between bands and three d* antibonding ones. The other two com- the eH and DFT band structures of Ca2W6O8 . With the new pounds were metallic as a result of greater dispersion due to parameters, the Ca2W6O8system is metallic in eH. A–E and M–E interactions. When Ca W O was calculated with the Vienna Ab initio 2 6 8 Metal-metal bonding in molecules and the extended structures Simulation Package (VASP) density functional theory (DFT) suite of programs (see details in the Theoretical methods Though the W–W distances computed in our systems are cer- section), permitting complete optimization of all structural tainly short, is there in fact WW quadruple bonding in these parameters (atomic positions and the lattice constant), there structures? Let us look first at a model d4–d4 molecular system, ˚ 12À resulted a short W–W distance of 2.27 A. The distance is W2O8 , computed in the geometry that a dimer unit has in similar to WW quadruple bond separations in molecular Ca2W6O8 . Fig. 2 shows a construction of such a molecule, ˚ ˚ 6À solids, for example, 2.165 A in W2(O2CR)4 and 2.26 A in from two WO4 units. Nothing surprising here—we see the 10 1 Li4W2(CH3)xCl8 À xÁTHF and Li4W2(CH3)8 . expected pattern of s, p, d, d*, p*, s* levels as one goes up There is an important difference between the eH and DFT in energy, perturbed only by an inversion in the order of the results for Ca2W6O8 . In the latter there was substantive den- p* and s* levels. sity of states (DOS) and band crossing at the Fermi level Fig. 3 compares local s, p, and d contributions to the W–W 4À region. The disagreement led us in two directions: (a) explora- crystal orbital overlap population (COOP) in W6O8 and tion with the more reliable DFT code of a wider range of com- Ca2W6O8 . Each was calculated within the eH method, using pounds and (b) a readjustment of the eH parameters, so as to DFT optimized geometries and the adjusted eH parameters potentially match the DFT results. mentioned. s, p and d refer to all combinations that contribute Table 1 shows the compounds we studied, in each case opti- to the COOP, so for instance p is not only dxz(1) À dxz(2) but 4 mizing all structural parameters. Most are d systems (88 elec- also includes dxz(1) þ px(2) and px(1) þ px(2) contributions trons in the formula unit), but we also included a range of (where z is the internuclear axis; obviously the analysis is 2.67 compounds with formal electron counts ranging from d restricted to one of the three equivalent W2 sets). 4.67 4À to d . Clearly atom substitutions can be used to tune the W6O8 has a band gap, Ca2W6O8 does not. We see in both electron count and to study its influence on the structure, in compounds well-defined s, p, d, d*, p*, s* regions, though not 4À particular the W–W bond distance. What is remarkable is necessarily in that order. The Fermi level for W6O8 comes how stable the short W–W distance is in these compounds. exactly at the crossing of the W–W COOP from bonding to ˚ ˚ It is down to 2.08 A in one case, up to 2.37 A in another, antibonding, and not far from that crossing in Ca2W6O8 .In but mostly stays in the quadruple bond range of 2.20–2.30 A˚ . the latter compound there is some electron transfer from the 4 4 4À 2þ The shortest WW bond is obtained for 88 electrons, the d –d W6O8 sublattice to the Ca sublattice; this moves the Fermi system. There is no correlation of WW distances with the lat- level into the d region of the metal oxide sublattice. A crystal tice constant. We take the computed geometries as an indica- orbital Hamilton population (COHP) analysis of the DFT tion that these systems should be stable. All systems turn out calculation on Ca2W6O8 leads to the same conclusion. 4À to be metallic in the DFT calculations, except W6E8 , E ¼ O, S, and W O F (no A atom in these cases).