knowledge can help identify promising search spaces • Focus on stoichiometric, ordered compounds • Many previously synthesized • May contain hypotheticals alloys • Alloy compositions between known materials • Continuum search space - infinite possibilities • Present methods not efficient for alloys dielectric constant obtained from the preceding GW cal- culation. The k derivatives of the electron orbitals were determined using the finite difference approximation of Ref. [60] in the “perturbation expansion after discretiza- tion” formulation. For the calculation of optical properties, the k-point density was increased to 7000=nat within the full Brillouin zone, where nat is the number of atoms in the unit cell. In order to keep these calculations feasible, we reduced the energy cutoff for the response functions and reduced the number of bands to 32 × nat , as compared to 64 × nat for the band-gap calculations using a coarser grid with about 1000=nat k points. The resulting band-gap changes of less than 0.1 eV were corrected for in the spectra shown in Fig. 2(a). The absorption spectrum is subject to a finite Lorentzian broadening in these calcu- lations, and despite the increased k-point density, the subgap absorption due to the bound exciton was not accurately resolved. The low-energy part of the spectrum, where the absorption coefficient is significantly affected by the broadening, is omitted [Fig. 2(a)]. From the calculated effective masses, and dielectric constants (ε ¼ 8.1 and 7.8 for WZ-MnO and ZnO, respectively, including the ionic contribution), we expect a Wannier-type exciton with a binding energy similar to that in ZnO, i.e., about 60 meV. The electron effective masses were obtained directly from the band energies close to the conduction band minimum (CBM) at the Γ point of the Brillouin zone. Because of a larger nonparabolicity and anisotropy in the valence band, for hole carriers, we determined instead the density-of- states effective masses (cf. Ref. [61]) by integrating the density of states weighted with a Boltzmann distribution at 1000 K. 2. Models for alloys and the magnetic structure In order to model the alloy systems, we used special quasirandom structures (SQS) [62]. The SQS in this work were generated with the mcsqs utility in the Alloy Theoretic Automated Toolkit (ATAT) [63]. To calculate the mixing energy, we employed SQS with 64 atoms, without any constraints other than the composition being x ¼ 0=16; 1=16; …16=16, while keeping the underlying magnetic sublattices of the low-energy antiferromagnetic configuration “AF1” of wurtzite structure MnO [57]. A structural model of the atomic configuration for x ¼ 0.5 is shown in Fig. 6 (created with the VMD software [64]), showing also the calculated lattice parameters for the end compounds WZ MnO and ZnO. For the polaron calcu- lations, we used 64-atom SQS supercells with the shape close to a cube, as well as a 72-atom ZnO supercell for the MnZn impurity. At room temperature, MnO is paramagnetic (PM). It is important, however, to consider that in the PM phase the moments are not completely random, but the co-workers calculated the electronic structure for rocksalt MnO in the PM phase with the “disordered local moment” method [66]. Their results show that the insulating gap in the PM state is practically identical to that in the AFM phase. Thus, we conclude that our assumption of an AFM order is an appropriate model of the magnetic structure for computing the electronic structure in this system. For the GW calculations, we generated smaller 32-atom SQS for the alloy compositions x ¼ 0.25, 0.5, and 0.75, constructed to maintain the symmetry between the spin-up and spin- down density of states. Figure 7 shows the calculated local density of states (LDOS) for the valence band of the Mn 1−x Znx O alloys, as obtained from the GW quasiparticle energy calculations, where the contributions from all sites of the same atom type (Mn, Zn, or O) have been averaged. The energy scale is aligned with respect to the vacuum level, as in Fig. 4. We see that at high Zn compositions, Mn forms an impurity band in ZnO, but at x ¼ 0.75 and lower Zn compositions, the alloys exhibit a continuous valence band with domi- nating contributions from Mn-d and O-p. 3. Calculation of the small-polaron self-trapping energies The hole self-trapping energies are calculated using the ab initio theory for the small-polaron binding energies of Refs. [34,35]. This approach employs a potential term Vhs , i.e., the “hole-state potential,” which is added to the DFT Hamiltonian. A potential strength parameter λhs is then adjusted to recover the quasiparticle energy condition FIG. 6. Structural model of the SQS used to represent the Mn 0.5 Zn 0.5 O alloy. The inserted table shows the similarity of the calculated lattice parameters for WZ MnO and ZnO. DESIGN OF SEMICONDUCTING TETRAHEDRAL MN … PHYS. REV. X 5, 021016 (2015) undiscovered materials • Unchartered, under- explored chemical space • Requires stability analysis • Structure prediction tools are emerging