Article pubs.acs.org/IC
Molecular and Electronic Structures of M2O7 (M = Mn, Tc, Re) Keith V. Lawler,†,‡ Bradley C. Childs,† Daniel S. Mast,†,‡ Kenneth R. Czerwinski,† Alfred P. Sattelberger,†,§ Frederic Poineau,† and Paul M. Forster*,†,‡ †
Department of Chemistry and Biochemistry, ‡High Pressure Science and Engineering Center, University of Nevada Las Vegas, Las Vegas, Nevada 89154, United States § Office of the Director, Argonne National Laboratory, Lemont, Illinois 60439, United States S Supporting Information *
ABSTRACT: The molecular and electronic structures of the group 7 heptoxides were investigated by computational methods as both isolated molecules and in the solidstate. The metal−oxygen−metal bending angle of the single molecule increased with increasing atomic number, with Re2O7 preferring a linear structure. Natural bond orbital and localized orbital bonding analyses indicate that there is a three-center covalent bond between the metal atoms and the bridging oxygen, and the increasing ionic character of the bonds favors larger bond angles. The calculations accurately reproduce the experimental crystal structures within a few percent. Analysis of the band structures and density of states shows similar bonding for all of the solid-state heptoxides, including the presence of the three-center covalent bond. DFT+U simulations show that PBE-D3 underpredicts the band gap by ∼0.2 eV due to an undercorrelation of the metal d conducting states. Homologue and compression studies show that Re2O7 adopts a polymeric structure because the Re-oxide tetrahedra are easily distorted by packing stresses to form additional three-center covalent bonds.
1. INTRODUCTION
cial utility, although its importance in the nuclear fuel cycle is still under investigation. Technetium and rhenium heptoxides have been experimentally investigated by several techniques, including electron and X-ray diffraction,11 Raman spectroscopy,12 17O-NMR,13 and mass spectrometry.3 Concerning theoretical methods, the solidstate structure of Tc2O7 and its compression up to 10 GPa have been recently investigated.14 The solid-state structures of Mn2O7 and Re2O7 are less well-characterized from a simulation standpoint. Most work on species containing Mn2O7 has been done on manganites and layered manganites with a composition of (R, A)n+1MnnO3n+1, where R and A are trivalent rare-earth and divalent alkaline ions, because of their high magnetoresistance and frustrated magnetic phase changes.15−17 The interest in Re-oxo compounds as catalysts has led to more research into the electronic structure and optical properties of Re2O7, but mainly as surface-supported species.18−22 Amado et al. performed a thorough simulation study of neutral, dianionic, and quadrianionic single molecule heptoxides.23 Their study is among the most comprehensive to date comparing the different possible symmetries to understand trends in bonding in the heptoxides. In our previous investigation of Tc2O7, we replicated the study of Fang et al., but we compared against a higher-quality crystal structure refined at 100 K.3 We were able to show that, despite preferring a bent structure similar to Mn2O7 as a single
Transition metal heptoxides with the stochiometry M2O7 (M = Mn, Tc, Re) present an interesting problem for solid-state chemistry. The group 7 heptoxides are unique not only because of their unusually high formal oxidation state but also because the structures adopted by Mn and Tc are among the few known solid binary molecular oxides. While similar behavior is anticipated based on periodic trends, each of the Group 7 heptoxides crystallizes differently in the solid-state. Mn2O7 produces monoclinic P21/c crystals with a = 6.796 Å, b = 16.687 Å, c = 9.454 Å, β = 100.2°, V = 1055.1 Å3, and Z = 8 (Figure 1).1 The solid-state Mn2O7 molecules prefer a C2v(syn) molecular geometry with the bridging oxygen bent in the same direction as a terminal oxygen on the eclipsed tetrahedra. Tc2O7 produces Pbca crystals with a = 7.312 Å, b = 5.562 Å, c = 13.707 Å, V = 557.5 Å3, and Z = 4 (Figure 1).2,3 The solid-state Tc2O7 molecules prefer a linear D3d molecular geometry with staggered tetrahedra in a herringbone packing. Re 2 O 7 crystallizes as P212121 with lattice parameters of a = 12.508 Å, b = 15.196 Å, c = 5.448 Å, V = 1035.5 Å3, and Z = 8 (Figure 1). This structure is polymeric with both tetrahedral and octahedral metal sites and no easily discernible single molecular substructure.4 Owing to their high volatility (explosively so for Mn), the group 7 heptoxides have found limited applications, including utilization of their highly oxidizing nature in catalysis,5−7 as lubricants,8 nanomaterial synthesis,9 and using microdetonations of Mn2O7 for graphene oxide surface preparation.10 The radioactivity of 99-Tc negates its commer© XXXX American Chemical Society
Received: October 14, 2016
A
DOI: 10.1021/acs.inorgchem.6b02503 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
Figure 1. Experimental crystal structures for Mn2O7 (left), Tc2O7 (center), and Re2O7 (right). To show scale, the longest crystallographic axis has been shown vertically and the second longest has been shown horizontally. The origins of Mn2O7 and Tc2O7 have been shifted to show connectivity and packing. (EOS)37 from a series of constant volume conjugate-gradient optimizations of the cell shape and atomic positions that spanned ±16% of the experimentally determined unit cell volumes. To minimize the effect of Pulay stress, the constant volume optimizations were performed in three parts: two sequential optimizations and a final single point energy evaluation.38−41 The energy convergence criterion for a single SCF cycle was 10−5 eV. An energy convergence criterion of 10−4 eV was used to stop the geometry optimizations, which led to forces of 16 meV/Å or less for Tc2O7 and Re2O7 and 25 meV/Å or less for Mn2O7 after optimization. The Brillouin zone was integrated using the tetrahedron method with Blöchl corrections.42 A single molecule was extracted from the optimized unit cells and placed into an empty 20 Å cubic box; then, a single point calculation was run to compute the cohesive energies. To minimize the interaction with periodic images of the molecule, the empirical dispersion corrections were cut off at 7 Å for the single molecule piece of the cohesive energy calculations. The hybrid PBE0 functional, which contains 25% exact exchange at all length scales,43,44 and the Hubbard-U method were used to investigate the error in the PBE-D3 band gaps. PBE+U simulations were performed using the formalism of Dudarev et al.,45,46 where the U and J parameters are combined into one effective parameter Ueff = U − J. Owing to the large cell size of Re2O7, the exact exchange contribution of PBE0 was computed only at the Γ point, whereas the rest of the functional was evaluated on the same k-point mesh described above. The PBE0 and DFT+U simulations used the PBE-D3 charge density and wave functions as an initial guess. All band structures and density of states are shifted so that they are relative to the Fermi energy.
molecule, solid-state Tc2O7 prefers a linear structure owing to the preferable compression of the linear structure and a larger cohesive energy from the optimal packing of the linear structure.3 The dearth of information on the electronic structure and bonding in these species in the literature motivated this work, which analyzes trends in the structure and bonding across the group 7 heptoxides. Here, we demonstrate why these transition metals adopt such dramatically different heptoxide structures in the solid-state.
2. METHODS Single molecule simulations were performed with the Q-Chem 4.0 package24 using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE)25 with Grimme’s D326 semiempirical dispersion correction. The simulations employed the def2-TZVP triple-ζ valence with polarization basis set with small core effective core potentials (ECPs) for the second and third row transition metals that account for scalar relativistic effects.27,28 The exchange-correlation functional was evaluated on an Euler−Maclaurin−Lebedev quadrature grid with 75 angular points and 302 radial points per atom. The energy convergence tolerance was 10−9 Hartree (2.7 × 10−8 eV) with an integral cutoff of 10−14 Hartree. Structures were optimized without symmetry considerations with a convergence criterion of a maximum gradient component of 10−4 Hartree/Å and a maximum atomic displacement of 10−4 Å. The initial guesses for the structures were taken from our experimental crystal structure and manually made to have broken symmetry. Analysis of the bonding interactions were performed with both natural bonding orbital (NBO)29,30 analysis using the NBO 5.0 package and localized orbital bonding analysis (LOBA)31 based off of the Pipek−Mezey32 localized orbitals. Vibrational frequencies were evaluated by numeric higher order derivatives using the analytic gradient. The solid-state was modeled with plane-wave density functional theory (PW-DFT)33,34 with the Vienna ab initio simulation package (VASP), version 5.4.1, also using the PBE-D3 functional. The projector augmented wave (PAW)35 pseudopotentials formulated for PBE GW calculations were used to represent the ionic cores, and the valence configurations were 4s24p65s25d5 for Tc and 2s22p4 for O.36 An automatically generated Γ-centered k-point mesh of size 2 × 2 × 2 tested for convergence (see the Supporting Information) spanned the first Brillouin zone. The plane waves were cut off at 600 eV. The Kohn−Sham34 equations were solved using the RMM-DIIS algorithm. Cell volumes were obtained through a fit to the Vinet equation of state
3. RESULTS AND DISCUSSION 3.1. Molecular Structure. Several M2O7 structures of different symmetries with one bridging oxygen can be constructed,23 and Figure 2 shows the computed potential energy pathways connecting the highest symmetry structures. Each structure along the pathway was optimized unconstrained regarding molecular or electronic symmetry, with the only constraints being the molecular degree of freedom being mapped (the M−O−M bending angle at the bridging oxygen or the dihedral angle between the tetrahedra) and a minimal number of dihedral angles between the tetrahedra to retain the desired molecular point group. The potential energy surfaces are relative to their respective D3d conformer. The D3d conformers are either saddle points or maxima along each B
DOI: 10.1021/acs.inorgchem.6b02503 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
Figure 3. Geometry of the lowest energy M2O7 structures: C2v(syn) Mn top, C1 Tc middle, and D3h Re bottom. The average M−OBri bond length, M−OTer bond length, and M−OBri−M bond angle are displayed. Cartesian coordinates are included in the Supporting Information.
Figure 2. Potential energy surfaces connecting the high symmetry conformers of M2O7 (red M = Mn, black M = Tc, and blue M = Re).
potential energy surface and the highest energy stable conformer. Mn2O7 is the only composition with a strong energetic preference for a particular conformer; the lowest energy point simulated for Mn2O7 in Figure 2 closely matches the experimental structure. On the other hand, Tc2O7 and Re2O7 have exceptionally flat potential energy surfaces. The lowest energy structures for Tc2O7 and Re2O7 are only about 1 and 5 meV more stable than the least stable D3d conformer, respectively (zoomed-in figure in the Supporting Information). The low energy barriers along the potential energy surfaces for Tc2O7 and Re2O7 imply that, at ambient temperatures, all of the conformations should be accessible. For Mn2O7, the very high energy barrier from C2v(syn) to D3d strongly favors a C2v(syn) geometry. Figure 2 also indicates that each of the molecules prefers eclipsed tetrahedra, with each potential becoming quite repulsive beyond the optimal bending angle. The repulsion comes from the steric interaction of terminal oxygen atoms on the opposite tetrahedra. The preference for eclipsed is in contrast to the staggered conformation in solid-state Tc2O7, which Tc2O7 adopts to maximize the cohesive energy between molecular units.3 In each of the optimized structures calculated to produce Figure 2, the tetrahedra retained virtually identical internal geometries. The bond lengths for the terminal oxygen atoms closest to being in-plane with the bend of the bridging oxygen decreased slightly (
