Effects of strain, d-band filling, and oxidation state on the bulk electronic structure of cubic 3d perovskites
Sneha A. Akhade and John R. Kitchin, “Effects of strain, d-band filling, and oxidation state on the bulk electronic structure of cubic 3d perovskites”, The Journal of Chemical Physics 135(10), 104702 (2011). https://doi.org/10.1063/1.3631948
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Question
For metal surfaces, simple models connect composition, strain and ligand effects to reactivity through d-band descriptors, and these models have guided catalyst design. No comparable framework existed for oxides, whose electronic structure is complicated by metal-oxygen hybridization, mixed ionic and covalent bonding and electron correlation. Strain had been studied for a few perovskites relevant to solid oxide fuel cells, but a general picture of how strain, d-band filling and oxidation state shape the electronic structure was missing. As a first step toward understanding perovskite surface reactivity, this paper asks how these three factors control the d band of the B cation in bulk cubic perovskites, and whether metal-derived models (a tight-binding matrix element for the d-band width and a rectangular band model linking width and center) carry over (Akhade 2011).
Approach
The authors studied cubic (Pm3m) LaBO3 and SrBO3 with B = Sc, Ti, V, Cr, Mn, Fe, Co, Ni and Cu, so the B cation is formally +3 in the La series and +4 in the Sr series. Calculations used the DACAPO plane-wave code with the PW91 GGA functional, Vanderbilt ultrasoft pseudopotentials, a 400 eV cutoff, a 6 x 6 x 6 Monkhorst-Pack grid and a five-atom cubic cell. All calculations were non-spin-polarized for consistency, and no Hubbard U was used; the authors cite prior evidence that U changes specific values but leaves trends across the 3d series largely intact, and note that the transferability of U to strained states is unclear. Equilibrium lattice constants came from a Murnaghan fit, and strains of -5, -2.5, 0, +2.5 and +5% were then applied. The d-band center was taken as the first moment of the B-projected d density of states relative to the Fermi level and the width as the square root of the second moment about the d-band center (a slight change from their earlier definition about the Fermi level, chosen to better reflect band width for nearly full or nearly empty bands). Because the B d states hybridize with O s,p states, the authors defined “the d band” by expanding each lattice up to 50% tensile strain and by computing the projected states of the structure with all O removed, which let them draw a boundary between the localized d band and the O s,p region that contains hybridized d states.
Key findings
DFT lattice constants agreed with experiment with a mean absolute error of 0.08 Å, which the authors judge irrelevant to strain trends. In LaTiO3, compressive strain broadened both the d band and the O s,p band and widened the gap between them, while tensile strain did the opposite. Even at very large tensile strain the d states remained visibly hybridized, which the authors suggest may be an artifact of GGA delocalization, implying that functional errors could depend on strain as well as on the oxide. For higher d filling the two bands overlap, which is why the deconvolution procedure was needed.
Across all 18 compounds, tensile strain narrowed and compressive strain broadened the B d band, through reduced or increased B-O orbital overlap, with a slightly nonlinear dependence that was stronger for Ti than for Cu. Using Harrison’s solid state table, the width was modeled as proportional to the d-orbital radius to the 3/2 power divided by the B-O distance to the 7/2 power. The width was linear in the inverse 7/2 power of distance for every compound, and the slope raised to the 2/3 power was linear in the tabulated d-orbital radius, so the larger the B atom the more strain-sensitive its band (LaTiO3 more than LaCuO3). The La and Sr trend lines nearly coincided, with small deviations at low filling, so the oxidation state (set by the A cation) acts mainly through the lattice constant.
The d-band filling was practically constant under strain, and the d-band width and center were linearly correlated for each compound, in qualitative agreement with a rectangular band model: positive slopes for early and negative slopes for late transition metals. The model places the sign change at a fractional filling of 0.5, but it occurred near 0.8, possibly because of limits in counting electrons from projected densities of states. Similar correlations held for the s,p band.
Significance
The work shows that the constant-filling, rectangular-band picture and the matrix-element model of band width, developed for metals, describe the bulk B-site d band of 3d perovskites once hybridized states are separated out. It establishes the d-band definition and strain trends used in the companion surface study, and suggests strain as a predictable handle on perovskite electronic structure and hence surface reactivity (Akhade 2011).