LaAlO$_{3}$ ( a ), bulk LaNiO$_{3}$ ( b ), and LaNiO$_{3}$ on SrTiO$_{3}$ ( c ) along high symmetry lines in the  Brillouin given as  . For each strain state,  LaNiO$_{3}$ remains metallic. The role of strain on the electronic structure is to partially split the  orbital degeneracy between the majority spin  d$_{x}$ 2 -y $^{2}$ and  d$_{3z}$ 2 -r $^{2}$ orbitals (blue points) as indicated  at the -point. The Fermi level is denoted by the solid red line at 0 eV.  Supplemental References  $^{S1}$$_{ }$L. Pauling, J. Am. Chem. Soc.  51  1010 (1929)  Figure 10: Calculated electronic structure. The calculated band structure of LaNiO$_{3}$ on LaAlO$_{3}$ ( a ), bulk LaNiO$_{3}$ ( b ), and LaNiO$_{3}$ on SrTiO$_{3}$ ( c ) along high symmetry lines in the Brillouin given as Γ(0,0,0) → M(1/2,1/2,0) → X(1/2,0,0) → Γ(0,0,0). For each strain state, LaNiO$_{3}$ remains metallic. The role of strain on the electronic structure is to partially split the orbital degeneracy between the majority spin d$_{x}$ 2 −$_{y}$ 2 and d$_{3}$$_{z}$ 2 −$_{r}$ 2 orbitals (blue points) as indicated at the Γ-point. The Fermi level is denoted by the solid red line at 0 eV. Electronic band structure calculations We next plot the electronic band structures for the two strained films on STO and LAO using the experimental nickelate structures along the high symmetry lines in a non-primitive (2x2x1) unit cell of the monoclinic structure. This supercell doubles the number of bands, however, it makes the identification of the orbital contributions to the band structure more transparent. In Fig. 10a we show the calculated band structure for the experimentally determined nickelate film on the LAO substrate and compare it to the bulk experimental structure in Fig. 10b and to that on STO substrate in Fig. 10c. For each strain state the band structure is found to be fully metallic, with strain partially lifting the majority spin e$_{g}$ orbital degeneracy at the Γ-point around the Fermi level (set to zero here). The metallic nature of the films is evident in the resistivity behavior, shown in Fig. 11. 22