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* Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA *Corresponding author, Email: jkitchin@andrew.cmu.edu Supporting Information Available: 1. Comparison of DFT calculated lattice constants to experimental values. 2. Example of bulk electronic structure convergence with computational parameters. 3. Strain dependence of fractional band filling of bulk LaBO3 and SrBO3 systems (where B = Sc, Ti, V, Cr, Mn, Fe, Co, Ni and Cu). 4. Effect of strain on the atom-projected density of states of the bulk LaBO3 and SrBO3 systems calculated as ±5%, ±2.5% and 0% of the DFT equilibrium volume. 5. Defining the d-band based on the effect of high tensile strain on the atomprojected density of states of the bulk LaBO3 and SrBO3 structures. 6. Derivation of the rectangular band model used in this work. Example of bulk electronic structure convergence with computational parameters. We performed a convergence study of the atom-projected density of states for k-point meshes in the range of 222 to 888 for bulk LaMnO3. The results are shown below. The integral properties, e.g. the d-band center, filling and d-band width, of the 666 and 888 are practically indistinguishable from each other. 8×8×8 6×6×6 4×4×4 2×2×2 Figure S1 Atom-projected density of states (DOS) for the Mn d-orbital (blue line) and the O s, p-orbital (green line) projections at different strains in the bulk LaMnO3 system using a plane-wave cutoff energy of 350 eV. The convergence calculations were tested relative to the Monkhorst-Pack k-point mesh. The shaded grey area indicates the occupied d-states up to the Fermi level (Ef). Table 1. Convergence results of atom-projected density of states of bulk LaMnO3 relative to k-point sampling at the equilibrium volume. 2×2×2 4×4×4 6×6×6 8×8×8 Total # d-states 8.9 8.92 8.93 8.93 # occupied d-states 3.76 3.99 4.05 4.08 Fractional d-band filling 0.42 0.45 0.45 0.46 d-band center (eV) 0.01 -0.24 -0.26 -0.25 d-band width (eV) 2.67 2.7 2.73 2.73 Comparison of DFT calculated lattice constants to experimental values The DFT calculated lattice constants for the LaBO3 and SrBO3 bulk systems employing a Monkhorst-Pack k-point grid of 6×6×6 and a plane-wave cutoff of 400 eV were in reasonable agreement with corresponding experimental values perovskites with an absolute mean error calculated as 0.08 Å. This is depicted in Error! Reference source not found. ( Table S 1). 4.10 DFT values 4.05 Parity line DFT Values (Å) 4.00 LaRhO3 LaTiO3 3.95 LaScO3 SrTiO3 LaCrO3 LaNiO3 SrVO3 3.85 SrCrO3 3.80 SrCuO3 LaGaO3 3.90 LaAlO3 3.75 3.75 SrFeO3 SrCoO3 SrMnO3 3.80 3.85 LaVO3 LaMnO3 LaCoO3 LaFeO3 3.90 3.95 4.00 4.05 Experimental values (Å) Figure S 1. Comparison of DFT lattice constants to experimental values. Table S 1. Comparison between DFT lattice constants and Experimental values. Perovskite DFT values (Å) LaAlO3 LaScO3 LaTiO3 LaVO3 LaCrO3 LaMnO3 LaFeO3 LaCoO3 LaNiO3 LaCuO3 SrTiO3 SrVO3 SrCrO3 SrMnO3 3.78 4.05 3.92 3.91 3.87 3.95 3.92 3.90 3.88 3.82 3.94 3.84 3.82 3.81 Experimental Values (Å) 3.80 3.94 3.95 3.88 3.85 3.83 3.83 3.83 3.84 3.01 3.91 3.84 3.82 3.81 Absolute Error (Å) 0.02 0.11 0.03 0.03 0.02 0.11 0.09 0.07 0.04 0.81 0.03 0.00 0.00 0.01 4.10 3.83 3.82 3.84 3.92 SrFeO3 SrCoO3 SrNiO3 SrCuO3 3.85 3.84 n/a 3.93 Average Error (Å) = 0.02 0.02 n/a 0.00 0.08 Strain dependent d-band filling The d-band filling was calculated to be roughly constant for the bulk LaBO3 and SrBO3 perovskites for all strains as shown in Figure S 2. (b) 1.2 LaScO3 LaCrO3 LaCoO3 1.0 LaTiO3 LaMnO3 LaNiO3 LaVO3 LaFeO3 LaCuO3 fractional d-band filling ratio (fd) fractional d-band filling ratio (fd) (a) 0.8 0.6 0.4 0.2 0.0 -5 -2.5 0 Strain ε (%) 2.5 5 1.2 SrTiO3 SrMnO3 SrNiO3 1.0 SrVO3 SrFeO3 SrCuO3 SrCrO3 SrCoO3 0.8 0.6 0.4 0.2 0.0 -5 -2.5 0 Strain ε (%) 2.5 5 Figure S 2. Strain dependence on the d-band filling of bulk LaBO3 and SrBO3 perovskites at ±5, ±2.5 and 0% of the DFT equilibrium volume. Effect of strain on the atom-projected density of states results for bulk LaBO3 and SrBO3 perovskites The effect of strain on the bulk electronic structure for various LaBO3 and SrBO3 (where B = Sc, Ti, V, Cr, Mn, Co, Ni and Cu) perovskites was computed using the atom-projected density of states of the bulk 3d transition metal perovskites. The states were obtained using an infinite cutoff radius and employed a Monkhorst-Pack grid of 6×6×6 and a plane-wave cutoff of 400 eV. The d-band properties such as the d-band width (Wd) were evaluated using the results illustrated in Figure S 3. LaScO3 ɛ = +5% ɛ = +2.5% ɛ = 0% ɛ = −2.5% ɛ = −5% LaTiO3 SrTiO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (d) LaVO3 (e) SrVO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (f) LaCrO3 (g) SrCrO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (h) LaMnO3 (i) SrMnO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (j) LaFeO3 (k) SrFeO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (l) LaCoO3 (m) SrCoO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (n) LaNiO3 (o) SrNiO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% (p) LaCuO3 (q) SrCuO3 ɛ = +5% ɛ = +5% ɛ = +2.5% ɛ = +2.5% ɛ = 0% ɛ = 0% ɛ = −2.5% ɛ = −2.5% ɛ = −5% ɛ = −5% Figure S 3. Atom-projected density of states (DOS) for the B d-orbital (blue line) and the O s, p-orbital (green dots) projections at different strains in the bulk LaBO3 and SrBO3 system using a 400 eV cutoff and a 6×6×6 Monkhorst-Pack k-point mesh. The shaded grey area indicates the occupied d-states up to the Fermi level (Ef). d-band evolution at high tensile strain on the atom-projected density of states of the bulk LaBO3 and SrBO3 structures The atom-projected density of states were computed at high tensile strain to study the effect of strain on the shift and width of the d-band. At high tensile strain, a reduced overlap between the d- and s,p-orbitals led to narrowing of the bands and consequently a high concentration at the Fermi level. In addition, the d-orbital projection of the B atom was computed alone to assess the effect of s,p-interaction and hybridization. Based on the analysis the appropriate d-band was selected. The results of the atom-projected density of states computed at high tensile strain are shown in Figure S 4 for the LaBO3 and Figure S 5 for the SrBO3 perovskites. LaScO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 5% ɛ = 0% LaTiO3 ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 10% ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaVO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaCrO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 10% ɛ = 5% ɛ = 0% LaMnO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaFeO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaCoO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaNiO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% LaCuO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 10% ɛ = 5% ɛ = 0% Figure S 4. (1)Atom-projected density of states for the B d-orbital (blue line) and the O s, porbital (green dots) projections of LaBO3 bulk perovskites on the left. The red lines at varying strain indicate the evolution of the d-band. (2) Atom-projected density of states for the corresponding B d-orbital (blue) alone on the right. The above DOS calculations were calculated at different tensile strains using 400 eV cutoff and a k-point grid of 6×6×6. The shaded grey area indicates the occupied d-states up to the Fermi level (Ef). SrTiO3 ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% SrVO3 ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% SrCrO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% SrMnO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 10% ɛ = 5% ɛ = 0% SrFeO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 5% ɛ = 0% SrCoO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 30% ɛ = 40% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 10% ɛ = 5% ɛ = 5% ɛ = 0% ɛ = 0% SrNiO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 10% ɛ = 5% ɛ = 0% SrCuO3 ɛ = 50% ɛ = 50% ɛ = 40% ɛ = 40% ɛ = 30% ɛ = 30% ɛ = 20% ɛ = 20% ɛ = 10% ɛ = 5% ɛ = 0% ɛ = 10% ɛ = 5% ɛ = 0% Figure S 5. (1)Atom-projected density of states for the B d-orbital (blue) and the O s, p-orbital (green) projections of SrBO3 bulk perovskites on the left. The red lines at varying strain indicate the evolution of the d-band. (2) Atom-projected density of states for the corresponding B dorbital (blue) alone on the right. The above DOS calculations were calculated at different tensile strains using 400 eV cutoff and a k-point grid of 6×6×6. The shaded grey area indicates the occupied d-states up to the Fermi level (Ef). (a) (b) 2.5 2.5 LaScO3 LaTiO3 LaVO3 LaCrO3 LaMnO3 LaFeO3 LaCoO3 LaNiO3 LaCuO3 1.5 1.0 0.5 0.0 0.0 2.0 d-band width (Wd) d-band width (Wd) 2.0 1.5 SrTiO3 SrVO3 SrCrO3 SrMnO3 SrFeO3 SrCoO3 SrNiO3 SrCuO3 1.0 0.5 0.0 0.5 1.0 1.5 s,p-band width (Wp) 0.0 2.0 (c) 0.5 1.0 1.5 s,p-band width (Wp) 2.0 (d) 8 5 d-band center (Ed) 6 4 2 0 -2 SrTiO3 SrVO3 SrCrO3 SrMnO3 SrFeO3 SrCoO3 SrNiO3 SrCuO3 4 d-band center (Ed) LaScO3 LaTiO3 LaVO3 LaCrO3 LaMnO3 LaFeO3 LaCoO3 LaNiO3 LaCuO3 3 2 1 0 -4 -8 -6 -4 s,p-band center (Ep) -2 -1 -7 -5 -3 s,p-band center (Ep) Figure S 6. Correlation between the d-band width and s, p-band width for (a) bulk LaBO3 and (b) bulk SrBO3 structures at varying strain. Correlation between the d-band center and s, p-band center for (c) bulk LaBO3 and (d) bulk SrBO3 structures at varying strain. Rectangular band model derivation In this work, we define the following quantities for the moments of the d-band: Ed d EdE dE d Wd d ( E Ed ) 2 dE dE d We assume a rectangular band of height h that contains ten states, with a fractional filling fd=Nelectrons/10 as shown below. With some algebra one can show that: Ed 0.5 (W12 W2 2 ) (W1 W2 ) and the d-band width is simply defined by the band edges: Wd 3/6(W1 -W2 ) . The band edges are determined by the equations: 10 h(W1 W2 ) hW2 10 Assuming the constraint that the total number of states in the band and the band-filling does fd not change with changes in band-width, this leads to the fact that the d-band center and width are correlated by the following equation: Wd Ed 3 1 . 6 0.5 f d Thus, for fd>0.5, the slope of the correlation should be negative, and for fd<0.5, the slope should be positive. At fd=0.5, the d-band center is equal to zero, leading to 0/0. The width is then simply defined to make fd=0.5 with the total number of states = 10.