15586
J. Phys. Chem. C 2008, 112, 15586–15594
Electronic Structure of Ternary Ruthenium-Based Hydrides Emilio Orgaz* Departamento de Fisica y Quı´mica Teo´rica, Facultad de Quı´mica, UniVersidad Nacional Auto´noma de Me´xico, CP 04510, Coyoaca´n, Me´xico, D.F. Me´xico, and Departamento de Quı´mica, CINVESTAV, AVenida Polite´cnico Nacional 2508, A.P. 14740, CP 07000, Me´xico, D.F. Me´xico
Andrea Aburto Departamento de Fı´sica, Facultad de Ciencias, UniVersidad Nacional Auto´noma de Me´xico CP 04510, Me´xico, D.F. Me´xico ReceiVed: April 23, 2008; ReVised Manuscript ReceiVed: June 23, 2008
We have investigated the electronic structure and bonding characteristics of a series of ternary hydrides composed of transition metals (iron, ruthenium, osmium) and different alkaline-earth elements. Using firstprinciple methods to compute the electronic structure, the systematic investigation of this isostructural series of compounds allows us to establish chemical trends on different properties. We extend our investigation to the case of low-symmetry, low-hydrogen-coordination ruthenium-based hydrides. We were able to systematize the computed properties in terms of transition-metal-hydrogen and interlattice interactions. We found that the charge state of the transition metal correlates with the hydrogen site energy, indicating the importance of the charge redistribution in the molecular anions. The H site energy exhibits an interesting correlation with the hydride formation enthalpy. The formation enthalpy, from the elements, shows a correlation with the interlattice interaction energy, indicating the importance of the alkaline-earth sublattice. 1. Introduction In the last two decades, a large number of ternary hydrides based on transition metals and alkali or alkaline-earth elements have been synthesized.1 These compounds have been systematically characterized by neutron diffraction and, in some cases, their physical properties have been investigated. The most important feature of this class of compounds is their ability to show a large variety of crystal structures, including several hydrogen coordinations around the transition-metal atom. This is particularly evident in the case of ruthenium-based ternary hydrides.2-8 Ternary ruthenium hydrides are generally formed by direct exposure of the transition metals to hydrogen and a hydride of the alkali or alkaline-earth element. The structure exhibits ordered RuHx molecular anions compensated by a counterions sublattice. From an extreme viewpoint, the formal oxidation state of the transition metal can be assigned by taking the H atom in the hydrido form and the alkali or alkaline-earth element in the fully cationic state. Although this approach is frequently successful, it cannot be used in all cases and does not explain the role of the cationic sublattice in stabilizing the different coordinations, local symmetries, and crystal structures. The stabilizing effect of the cationic sublattice has been suggested by Miller, Deng, and Hoffmann9 in the particular case of Mg-Ru hydrides. This has been also recently discussed in the case of the Na(K)2Pd(Pt)H4 hydrides.10 It is important to note that these systems has been classified as mixed ionocovalent bonding compounds. We found a variety of electronic as well as magnetic behaviors, from insulators to conductors and diamagnetic to magnetically ordered systems. For these reasons, a deeper investigation of electronic structure of these systems is frequently necessary. In Table 1, we summarize a * Author to whom correspondence should be addressed. Fax: 52-5-6223776, ext. 107. E-mail:
[email protected].
TABLE 1: Structural Parameters for Different Types of Complex Ternary Ruthenium Hydridesa hydride
reference
space group
symmetry
Li(Na)4RuH6 Mg2RuH6 Mg3RuH6 Mg2RuH4 Mg3RuH3
Kritkos et al.7 Huang et al.3 Bronger et al.4 Bonhomme et al.5 Bonhomme et al.6
R3jc Fm3m Cmcm Cmcm P42/mnm
D3h Oh C4V C2V C2V
BaRuMg2H8
Huang et al.8
P42/mmc
Oh
a
T-H units RuH6 RuH6 RuH5 RuH4 dimeric [RuH3]2 RuH6
The approximate local symmetry of the RuHx units is indicated.
selection of representative ruthenium hydrides. We indicate the local symmetry, hydrogen coordination, and some crystal properties. As it can be observed, this family of compounds exhibit a wide range of H coordinations and symmetries. The Mg2RuH6 hydride belongs to a large family of diamagnetic insulator hydrides of K2PtCl6 structure (space group Fm3m). We have also considered the related Fe- and Os-derived hydrides with a cation sublattice formed by Mg, Ca, Sr, and Ba. This family offers a singular opportunity to investigate the role of the alkaline-earth element in an isostructural series of ternary hydrides. The electronic and phonon structure of the A2TH6 (where A) Mg, Ca, Sr, Ba and T ) Fe, Ru, Os) hydrides have been largely investigated.11-17 A semiquantitative approach to the electronic structure has been provided by Miller et al.9 and discussed by King18 and Yvon.1 Although the general aspects of the T-H bonding are well established, theirs is not a systematic investigation of the full series within a first-principles approach. In this report, we focus on the description of the electronic properties of the A2TH6 hydrides looking for trends on different properties as a function of the A sublattice and hydrogen-bonding interaction. In a second part, we investigated
10.1021/jp8035605 CCC: $40.75 2008 American Chemical Society Published on Web 09/10/2008
Electronic Structure of Ternary Ru-Based Hydrides the low-symmetry Mg-Ru hydrides, in particular, the Mg2RuH4, Mg3RuH6, and Mg3RuH3 systems. We conclude this paper by summarizing our most important findings.
J. Phys. Chem. C, Vol. 112, No. 39, 2008 15587 TABLE 2: Structural Parameters for the A2TH6 (where A ) Mg, Ca, Sr, Ba; T ) Fe, Ru, Os)a Bond distance, Lattice Shift from d (Å) Parameter (Å) Experimental Datab (%)
2. Methodology The electronic structure of all the compounds investigated in this paper has been obtained by means of a density functional theory (DFT) approach. Two methods have been used; first, a pseudo-potential scheme and, in a second instance, an allelectron energy band method. In both cases, we used the generalized gradient approximation (GGA)19 to the exchange and correlation energy. Geometry optimizations of the crystal structures were then obtained using the projected-augmented plane wave method (PAW; VASP code).20 The full structure relaxation was conducted until a value of 10-3 eV/Å in the local forces was attained. Sampling of the Brillouin zone was performed by selecting special k-points with the Monkhorst-Pack method.21 Ab-initio calculations of the electronic structure of the investigated hydrides were conducted using the all-electron full potential-linear augmented plane waves (LAPW; WIEN2K code) method.22 The RKmax parameter, which controls the plane wave expansion, was selected to obtain a converged total energy of up to 10-4 eV (usually, RKmax ) 6). The sampling of the Brillouin zone was performed by a grid of at least 100 k-points. The total density of states (DOS) and partial density of states (PDOS) were computed from the energy bands obtained with the LAPW method, using a tetrahedra integration scheme. The analysis of the wave function coefficients at high symmetry points of the Brillouin zone allows us to identify the atomic orbital contributions to each energy band. We performed integrations of the density charge, following the Bader’s criteria (AIM), to compute the charge state of the atoms in the solids.23 Additional molecular cluster calculations were performed on the anionic subunits THx and alkali or alkaline-earth atoms and their cations, using a density functional approach (Gaussian code).19,24 In these computations, besides the standard Mu¨lliken population analysis (MPA), we computed the Bader’s charges, as well as the natural bond order (NBO) analysis. It is important to indicate that all the molecular cluster computations were performed at the transition-metal-hydrogen distances and symmetry dictated by the crystallographic data. 3. The Electronic Structure of the A2TH6 Hydrides (A ) Mg, Ca, Sr, Ba; T ) Fe, Ru, Os) We investigated the electronic structure of this series of isostructural compounds. We performed full geometry optimizations of the crystal structure using a pseudo-potential scheme. In Table 2, we summarize the resulting crystal data and we compare the information with the reported experimental values. As it can be appreciated, differences between experiment and theory are generally
