Position‐Space Bonding Indicators for Hexaborides of Alkali, Alkaline‐Earth, and Rare‐Earth Metals in Comparison to the Molecular Crystal K₂[B₆H₆]

Abstract

The crystal structure of the hexaborides MB 6 of alkali, alkaline-earth, and rare-earth metals displays a network of interconnected B 6 octahedra, while isolated B 6 H 6 units occur in the molecular crystal K 2 [B 6 H 6 ]. For the case of a total charge transfer of two electrons from the metal atoms, the B 6 units serve as classical examples of electron deficient clusters. QTAIM and ELI-D analyses of chemical bonding based on solid state DFT/APW+lo quantum chemical calculations were performed. Consistent with Wade's rules, a number of about seven endohedral bonds for the octahedral units is recovered from the 2013 delocalization index (DI). Detailed analyses of two-and three-center delocalization indices yield a clear two-center character of the exohedral B-B bonds and a mixed two-and three-center character of the endohedral B-B bonds. The picture obtained by topological analysis of ELI-D is in agreement with the DI results. With changing effective electron transfer from the metal atoms, electronic saturation of the intra-cluster bonding is found, which leads to the notion of generally two-valent rare-earth atoms in MB 6 hexaborides. 2014The partitioning of position space into basins of ELI-D offers the possibility to determine regions of different bonding characteristics. The projection of the orbital contributions to the total ELI-D (partial ELI-D) [15] reveals the possibility to compare the results for the molecule [B 6 H 6 ] 2-, a molecular crystal K 2 [B 6 H 6 ], and finally for crystalline hexaborides. Results and DiscussionThe optimized structures of the hexaborides are in good agreement with numerous previous studies: [11,12,17] the exohedral B-B distance is significantly shorter than the endohedral distance. The lattices are characterized by a linear relationship between the metal-octahedral face distance and the volume of the unit cell (Figure 2, top). Figure 2. Optimized MB 6 structures, black experimentally observed and red hypothetical MB 6 representatives. Top: metal-octahedral face distance vs. unit cell volume. Bottom: endohedral (diamonds) and exohedral (circles) B-B distances vs. unit cell volume.Notably, a limiting volume range for the experimentally observed MB 6 representatives is evident. It is found between 67 Å 3 and 77 Å 3 , which correlates with a small window for realizable metal-octahedral face distances between 2.5 and

Atomic Charges and Chemical Bonding in Y-Ga Compounds

“…These findings are additionally supported with the bond delocalization ratio G(A,B) characterizing the three-center character of a two-center interaction A-B. This tool was developed during the bonding study on metal hexaborides [14], and subsequently applied to intermetallic diborides [46]. For the classical three center bonding in H 3 + it amounts to 1, for the two-center bond it is close to zero.…”

“…For the classical three center bonding in H 3 + it amounts to 1, for the two-center bond it is close to zero. For the Ga-Ga bond in YGa 2 , G(Ga,Ga) = 0.45, which is already at the upper limit of observed bond delocalization ratios in classical valence compounds, i.e., for Ge bond delocalization ratios G(Ge,Ge') = 0.32, while G(B,B') ≈ 1 for endohedral B-B bonds in B 6 octahedra for CaB 6 and YB 6 [14]. For YGa, the calculated delocalization index Ga−Ga' equals 0.60, and G(Ga,Ga') = 0.74, which clearly shows the trend of decreasing effective covalent bond order Ga-Ga corresponds with an increasing delocalization of the Ga−Ga bonding.…”

“…For the DFT/PBE [37] calculation the atomic Y(4s 2 p 6 d 1 5s 2 ) and Ga(3s 2 p 6 d 10 4s 2 p 1 ) states were treated as semi-core and valence states; the remaining atomic states of lower energy were treated as core states. The resulting wavefunction was analyzed and two-center delocalization indices were calculated with the DGrid-4.7 program [38], the subsequent calculation of three-center delocalization indices and bond delocalization ratios G [14] was effectuated with the DISij program [39].…”

Hierarchical and chemical space partitioning in new intermetallic borides MNi21B20(M = In, Sn)

“…ELI-D/QTAIM intersection reveals them to represent effectively (1 Sn + 1 Ni3)-diatomic polar bonds, with 0.14 e belonging to QTAIM Sn and 1.76 Å) observed also for the deltahedral bonds in hexaborides. 41 Decomposition of G(B1, B2) into a sum of all three- center contributions reveals that four similar 3c-DIs of type δ(B1, B2, Ni) play the dominant role. The four Ni atoms involved are just those 2Ni2 and 2Ni3 atoms already identified above with the ELID/QTAIM basin intersection method.…”

Ab Initio and Molecular Dynamics-Based Pair Potentials for Lanthanum Hexaboride

“…7,19 Electron donation from the metal stabilizes the electron-deficient boron framework, 20 ideally requiring 2 electrons to fill the valence orbitals of the octahedra. 21 Barium, calcium, strontium, and most lanthanoids have been found to form hexaboride structures, producing systems which exhibit various magnetic and super-, semi-, and electrically-conductive properties dependent on the cation types. 11 …”