Computational Screening of Homovalent Lead Substitution in Organic

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Computational Screening of Homovalent Lead Substitution in Organic-Inorganic Halide Perovskites Marina R Filip, and Feliciano Giustino J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11845 • Publication Date (Web): 09 Dec 2015 Downloaded from http://pubs.acs.org on December 11, 2015

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The Journal of Physical Chemistry

Computational Screening of Homovalent Lead Substitution in Organic-Inorganic Halide Perovskites Marina R. Filip and Feliciano Giustino∗ Department of Materials, University of Oxford, Parks Road OX1 3PH, Oxford, UK E-mail: [email protected]

∗

To whom correspondence should be addressed

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Abstract Perovskite solar cells are gaining increasing popularity due to their unprecedented rise in power conversion efficiency. However, concerns over the potential environmental impact of CH3 NH3 PbI3 are stimulating experimental and theoretical searches for the replacement of lead by non-toxic elements. In this study we explore all homovalent metal ions which could substitute lead in a perovskite halide configuration, by performing a systematic combinatorial search over the entire periodic table. Our screening process selects compounds based on two concurrent criteria: the stability of the compound in a perovskite structure and the band gap. Using these search criteria we are able to reduce the number of possible compounds from 248 to 25, including 15 compounds which have not yet been proposed as semiconductors for optoelectronics. We identify Mg as a potential candidate for partial replacement of Pb, and show that the band gap of hypothetical magnesium iodide perovskites is tunable over a range of 0.8 eV via the size of the A-site cation.


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Introduction Solar cells based on organic-inorganic lead-halide perovskites are one of the most promising emerging photovoltaic materials of the last decade. 1–4 Only six years after the initial report of a working solar cell based on methylammonium lead-iodide (CH3 NH3 PbI3 ), 5 these devices are routinely reaching efficiencies above 15%, 4,6 with the record currently exceeding 20%. 7 However, the presence of Pb in these compounds is raising questions over the possible toxicity of these materials. 8 While the extent of the environmental impact of lead-halide perovskite solar cells is still debated, 8–10 these concerns are motivating the search for halide perovskites based on non-toxic and widely available metals with similar optoelectronic properties to lead-halide perovskites: optimum band gap for absorption of photons in the visible range, 11 direct band gap, 12,13 low electron and hole effective masses, 14–16 low exciton binding energy, 16–18 and long carrier lifetimes. 14,15 Replacement of Pb2+ with Sn2+ has already been successfully demonstrated, however the stability of these compounds is still an issue. 19,20 Furthermore, partial replacement of Pb2+ by Sn2+ as well as Sr2+ , Ca2+ and Cd2 +, 21 Bi-Tl based perovskites and chalcogenide perovskites have been explored both theoretically and experimentally. 22–26 In principle, the target element to act as replacement for Pb should be a metal which admits the oxidation state +2. This single criterion is met by more than 60% of the elements in the



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periodic table, 27 and yields 248 metal-halide combinations, without counting the enormous range of possibilities arising from the exchange of the A-site cation. 28 Based on this estimate, it is clear that a systematic high-throughput approach is required in order to search for novel metal-halide perovskite compounds. High-throughput computational screening 29,30 is a promising tool to assist the design and discovery of novel compounds. Previous computational searches of metal-halide perovskites have focused on mixed halide and cation combinations of Pb and Sn perovskites, 31 the replacement of Pb by other divalent metals in CH3 NH3 PbI3 , 32 or the replacement of the cation in leadhalide compounds. 28 Furthermore, Ref. 33 extended the search to binary and ternary compounds that do not have a perovskite structure, but have optoelectronic properties similar to CH3 NH3 PbI3 . The electronic properties of perovskites are known to be strongly dependent on the distortions of the crystal lattice such as tilting and deformations of the octahedra or ferroelectric distortions. 28 Given this delicate interplay between structure and electronic properties, we perform a search focusing both on the electronic band gap and the perovskite crystal structure. More specifically, we simultaneously search for metal-halide compounds with optical absorption onset in the visible range, and probe the stability of these compounds in a perovskite configuration. Therefore, in our approach we combine ideas from high-throughput computational screening 29 and randomstructure searches. 34 With these two criteria we are able to reduce the 248 4 ACS Paragon Plus Environment

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potential metal-halide combinations to 25 compounds, 15 of which have not yet been proposed for photovoltaic applications. In particular, we identify Mg as a potential candidate for the partial replacement of Pb in organic-inorganic lead-halide perovskites.

Results Organic-inorganic lead-halide perovskites have a structure of ABX3 type (as shown in the inset of Figure 1, where A+ is a molecular or atomic cation, B2+ is a divalent metal and X−1 is a halogen atom. The metal and halogen atom form a three-dimensional network of corner sharing octahedra, with the metal atoms at the center of the octahedra and the halogen atoms at the corners. The cation A is inside the cavity enclosed by the metal-halide octahedra. In the case of CH3 NH3 PbI3 , the organic cation CH3 NH+ 3 occupies the A site and has a disordered orientation at temperatures above 160 K. 35–37 In order to avoid possible complications arising from the orientation of the CH3 NH+ 3 we choose Cs+ as the central cation for the perovskite structures explored throughout this study. Broadly described, the synthesis methods used for lead-halide perovskites involve the reaction between the PbX2 and AX precursors in the presence of a solvent. 38 In this work we search for alternative metal-halide perovskites which are amenable to solution processing using a similar reaction. Therefore, we start by selecting all metals in the periodic table which have a known +2 5 ACS Paragon Plus Environment


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Figure 1: Schematic representation of the computational screening process. The arrows point to the order of the screening steps. The blue shading on the periodic table marks the elements which are considered at the start and at the end of the screening process. The numbers 1, 2 and 3 mark the steps of the screening process at which the number of compound combinations is reduced based on the following criteria: the DFT/LDA scalar relativistic band gap is smaller than 3.5 eV (1), the crystal structure retains the perovskite geometry after relaxation of the shaken configurations (2) and the fully relativistic band gap for the remaining structures is smaller than 2.0 eV (3). The inset shows a ball-and stick model of the ABX3 perovskite structure.

oxidation state and form a known BX2 salt with at least one halogen X = F, Cl, Br or I. At the same time we exclude all rare earth and radioactive metals which would be impractical in photovoltaic applications. This criterion is similar to the analysis presented in Ref., 39 and reduces the number of possible perovskite compounds from 248 to 116 before performing any calculations (as shown in the top left corner of Figure 1).


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Following this pre-screening, we construct a total of 116 (29 metals × 4 halogen atoms) orthorhombic metal-halide perovskite unit cells containing four ideal octahedra, using the procedure detailed in Ref. 28 A unique ideal orthorhombic perovskite unit cell can be constructed given two values for the apical (αa ) and equatorial (αe ) metal-halide-metal bond angles and the metal-halide bond lengths. 28 For each metal-halide combination we start the structural relaxations from five ideal unit cells constructed with the following pairs of metal-halide-metal bond angles: 1) αa = αe = 180◦ (perfect cubic perovskite), 2) αa = 180◦ , αe = 144◦ in phase (tetragonal), 3) out of phase (tetragonal), 4) αa = 148◦ , αe = 157.5◦ (orthorhombic), 5) αa = 148◦ , αe = 141◦ (orthorhombic). In the case of CH3 NH3 PbI3 it has been shown that structural optimizations are sensitive to the starting point geometry, 40–42 indicating that the total energy landscape for these structures exhibits many local minima. By starting relaxations from these five different geometries of the metal-halide octahedral network we reduce the likelyhood that the structures are trapped in unphysical local minima of the total energy. For each compound, we select the lowest energy configuration and calculate the band gap from scalar relativistic DFT/LDA, as shown in Figure 2a. The visible spectrum ranges approximately from 1.5 to 3.5 eV, and typical good light absorbers have band gaps between 1.3 eV and 1.7 eV. 43,44 Given that DFT/LDA is known to underestimate band gaps and that the spin-orbit coupling (which reduces the band gap) is not included in calculations at 7 ACS Paragon Plus Environment


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this stage, we can safely discard from the search the compounds with band gaps larger than 3.5 eV (Step 1 shown in Figure 1. These compounds are indicated as white squares in Figure 2a. Moreover, we restrict our search to all compounds which do not exhibit metallic behavior. Metallic compounds are indicated in Figure 2a as grey squares. Based on these criteria the number of compounds is reduced from 116 to 40. The next step of the search is to probe the dynamic stability of the newly formed compounds (Step 2 shown in Figure 1). We perform this test by first displacing (‘shaking’) the atomic positions and lattice parameters of each unit cell randomly, and by subsequently allowing the structure to relax, as described in detail in the Methods section. While the majority of structures retain the perovskite configuration upon shaking and relaxing, there are a few compounds which exhibit significant distortions. Figure S1 from the Supporting Information shows four representative examples of relaxed structures which either keep the perovskite configuration (CsMgI3 ), or undergo severe distortions and change coordination (CsZnCl3 , CsSnF3 and CsPtF3 ). In order to quantify the distortions occuring upon structural optimizations, we calculate the difference between the maximum and minimum metal-halide distance (Δ) within an octahedron for the lowest energy structures. For CsPbI3 , we obtain Δ = 0.03 ˚ A, indicating an almost perfect platonic octahedron, 28 as it is the case for perovskites in general. This is in agreement with experimental studies confirming that the perovskite structure is one of the crystal phases 8 ACS Paragon Plus Environment

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Figure 2: a. Scalar relativistic band gaps calculated for each structure at Step 1 shown in Figure 1. The composition of the structures represented in each square can be read on the horizontal and vertical axes respectively (i.e. Be and I for CsBeI3 ). The colour of each square represents the band gap as follows: white represents band gaps larger than 3.5 eV, grey represents metallic structures, and all other colours represent band gaps between 0 and 3.5 eV according to the colour bar on the side. All compounds with white and grey squares are discarded at the next step. b. Plot of the difference between the maximum and minimum metal-halide bond length within an octahedron (Δ) calculated for the crystal structures relaxed from the randomly shaken unit cells, for each of the remaining compounds selected at Step 1. The color of each square represents the value of Δ as follows: dark blue is 0, white is above 0.5 ˚ A and all other shades of blue represent values between 0 and 0.5 ˚ A indicated by the colour bar. The small squares represent the value of Δ calculated after the first set of shaking tests, and the large square is for the second set of shaking tests (see Methods). All compounds with at least one white square are discarded. c. Band gaps calculated for the remaining structures at Step 2, this time including spin-orbit coupling. The color of each square represents the value of the band gap, indicated by the colour bar. All compounds with white squares are discarded.



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of CsPbI3 . 45 By contrast, CsZnCl3 relaxes to a structure with 4-fold coordinated Zn cations (as shown in Figure S1 of the Supporting Information). In this case Δ = 1.6 ˚ A, suggesting that a perovskite structure is likely not stable for this compound. The values of Δ calculated for each of the compounds selected up to this step are shown in Figure 2b. Moving forward with the search, we discard all structures for which Δ exceeds 0.5 ˚ A (white squares in Figure 2b). This refinement reduces the number of compounds from 40 to 32. In order to establish the reliability of the shaking test described above we consult the Inorganic Crystal Structure Database (ICSD). 46 For each of the ABX3 compounds considered at this stage we compare with existing experimental data on compounds with the same stoichiometry, as available in ICSD (Table S1 of the Supporting Information). The majority of our predictions are consistent with data within ICSD (with the exception of the Mg, V, Mn and Ni compounds). In 10 cases we found no experimental data for compounds with the ABX3 stoichiometry and the comparison was not possible. In the case of Ni, V, Mn and Mg, the experimental structures found on ICSD resemble that of BaRuO3 (CsMnCl3 ) and BaNiO3 (for all other Mn and the Ni, V and Mg compounds). 46 These structures also exhibit a 6fold coordinated B-site, however the octahedra centered at the metal cation are face-sharing instead of corner sharing. We will analyze this category of compounds in more detail later, with a particular emphasis on CsMgI3 . 10 ACS Paragon Plus Environment

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We calculate the band gaps of the remaining structures within DFT/LDA including spin-orbit coupling (more details are available in the Methods section). In Figure 2c we plot the band gaps calculated for the remaining 31 compounds. At this stage we lower the band gap threshold from 3.5 eV to 2 eV in order to refine our search. The compounds that satisfy this criterion are CsMgI3 , CsVI3 , CsMnI3 , CsMnBr3 , CsNiBr3 , CsNiCl3 , CsCdI3 , CsCdBr3 , CsCdCl3 , CsHgBr3 , CsHgCl3 , CsHgF3 , CsGaCl3 , CsInBr3 , CsInCl3 as well as the Ge, Sn and Pb chlorides, bromides and iodides. The compounds based on Ge, Sn and Pb have been already proposed in previous studies, in combination with CH3 NH3 and Cs. 11,47 Therefore, we consider Mg2+ , V2+ , Mn2+ , Ni2+ , Cd2+ , Hg2+ , Ga2+ and In2+ as the novel candidates for the replacement of Pb in caesium metal-halide perovskites. Upon inspection of the band structures, we can classify the compounds identified in our search based on the qualitative features of their band edges. All Mg, Cd and Hg halides are direct band gap semiconductors (see for example CsCdI3 and CsHgCl3 in Figure S2 of the Supporting Information), while the compounds based on V, Mn, Ni, Ga and In exhibit indirect gaps (CsNiBr3 and CsInBr3 in Figure S2 of the Supporting Information). However, as we can see from Figure S2 of the Supporting Information, the difference between the direct and indirect band gaps in the V, Mn and Ni compounds is small (∼0.1-0.2 eV) in comparison with those of Ga and In (∼0.5 eV). In addition, we note that the Ga and In based compounds exhibit very dispersive bands, 11 ACS Paragon Plus Environment


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which could indicate good electron and hole transport properties that may be explored in optoelectronic applications. However, given their indirect band gap we do not consider Ga and In halides in the subsequent discussion. Furthermore, given the criterion for reduced toxicity set out at the beginning of this study, the compounds based Cd and Hg should also be removed from the list of potential candidates of Pb replacement. After this final refinement we are left with Mg, Mn, V and Ni as potential alternatives to Pb in lead-halide perovskites. While in our search we started from the working assumption that CsMgI3 , CsMnI3 , CsMnBr3 , CsVI3 , CsNiCl3 and CsNiBr3 can crystallize in the perovskite structure, the reported experimental structures are not perovskites. 48–51 This discrepancy can be rationalized using the empirical octahedral factor and tolerance factor. The octahedral factor is defined as μ = rB /rX , and the √ tolerance factor as t = (rA + rX )/[ 2(rB + rX )], where rA , rB and rX are the ionic radii of the cation A, metal B, and halogen X in the ABX3 perovskite. Empirical observations suggest that an ABX3 compound is likely to form in a perovskite structure if their corresponding t is between 0.7 and 1.1 and μ is above 0.4, respectively. 52 These limits define a ‘perovskite region’ in the (t, μ) parameter space. 52 For the Mg, Mn, V and Ni compounds above, we calculate μ between 0.32 and 0.46 and t between 0.90 and 1.02, placing these structures either just outside, or at the edge of the perovskite region. For reference, CsPbI3 falls right at the edge of the perovskite region with μ and 12 ACS Paragon Plus Environment

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t of 0.6 and 0.8, respectively. CsPbI3 is known to form two distinct crystal structures: a three-dimensional perovskite structure 45 (as considered here), and a structure with edge-sharing PbI6 octahedra (‘non-perovskite’). 47 The latter is shown in Figure S2a of the Supporting Information. We compare the total energies of these two structures and find that the non-perovskite is more stable than the perovskite configuration, by 28 meV/atom. This result is in agreement with experimental observations, 47 indicating that the perovskite structure is a metastable phase of CsPbI3 . Similarly to CsPbI3 , it is possible that the perovskite structures proposed here for CsMgI3 , CsMnBr3 , CsMnI3 , CsVI3 , CsNiCl3 and CsNiBr3 are also metastable phases of these compounds. In order to investigate this possibility further, we focus on CsMgI3 and calculate the total energy difference between the perovskite and non-perovskite structures. The non-perovskite CsMgI3 reported in Ref. 48 (Figure S2b of the Supporting Information) is indeed more stable, and the total energy difference between the two structures is of 40 meV/atom, which is comparable to the thermal energy at room temperature. However, this small total energy difference between the perovskite and non-perovskite phase of CsMgI3 is very close to that calculated for the case of CsPbI3 , for which a perovskite phase has been synthesized. 45 For this reason, we consider that the experimental synthesis of CsMgI3 in a perovskite phase is plausible and may require annealing at high temperature, as demostrated for CsPbI3 . 45 Alternatively, 13 ACS Paragon Plus Environment


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we also propose that the gradual substitution of Pb by Mg is a potential route for the stabilization of mixed Mg-Pb based halide perovskites, as it was demonstrated for Cs/Rb mixed cation perovskites. 28 A similar anlysis could be made for the V, Mn and Ni structures. However, as pointed out in the Methods, a more detailed study of their structural and magnetic properties would be required for these structures, and this is beyond the scope of the present study. In the following we focus on CsMgI3 and investigate its electronic properties. In Figure 3a-b we show the crystal structure and band structure of CsMgI3 calculated within DFT/LDA including spin-orbit coupling, as described in the Methods. This compound exhibits a direct band gap at Γ and a highly dispersive conduction band. Indeed, we calculate an isotropic effective mass of 0.37 electron masses (me ) for the electrons, while for the holes we obtain effective masses one order of magnitude larger. In Figure 3b-f we show that the band gap of magnesium-iodide perovskites can be tuned by using different A-site cations. In fact, we calculate 1.7 eV for CsMgI3 , 1.5 eV for CH3 NH3 MgI3 and 0.9 eV for CH(NH2 )2 MgI3 . Preliminary GW calculations 53,54 confirm this trend (see Methods for calculation details), rendering a variation of the quasiparticle band gap from 2.5 eV [CH(NH2 )2 MgI3 ] to 3.4 eV (CsMgI3 ). As shown in Figure 3 the octahedral tilt is also reduced as the size of the central cation increases, indicating an interplay between the electronic band gap and crystal structure similar to lead-iodide perovskites. 28 Moreover, the 14 ACS Paragon Plus Environment

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Figure 3: Ball-and-stick models and band structures of the hypothetical perovskites CsMgI3 (a-b), CH3 NH3 MgI3 (c-d) and CH(NH2 )2 MgI3 (e-f). The crystal structures of the latter two compounds are obtained via structural optimizations within DFT/LDA starting from the experimental crystal structure of CH3 NH3 PbI3 11 and the crystal structure of CH(NH2 )2 PbI3 reported in Ref., 28 respectively. For reference the tolerance factors calculated for CsMgI3 , CH3 NH3 MgI3 and CH(NH2 )2 MgI3 are 0.95, 1.02 and 1.07, respectively, while the octahedral factor is 0.32. The band structures were calculated within DFT/LDA including spin-orbit coupling for I.

band edges become more dispersive when Cs is replaced by larger cations, with electron effective masses decreasing to 0.31 me for CH3 NH3 and 0.21 me for CH(NH2 )2 . Given these low electron effective masses we expect that the



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hypothetical CH(NH2 )2 MgI3 perovskite may exhibit high electron mobilities and may act as an efficient electron conductor. The quasiparticle band gaps of the hypothetical Mg-based perovskites are over 1 eV larger than the leadhalide perovskites, suggesting that they are not likely to be efficient light absorbers for perovskite solar cells. However, in view of the partial replacement of Pb by Mg, we expect that the band gap of Pb-Mg mixes will increase with the concentration of Mg.

Conclusions In summary, we have performed a systematic computational screening of potential divalent metal atoms which could replace Pb in CH3 NH3 PbI3 . By taking into account the perovskite crystal structure and the band gap as two concurrent criteria, we were able to reduce the number of possible compounds from 248 to 25, 15 of which have not been proposed yet for photovoltaic applications. 65% of our predicted compounds in this combinatorial search matched existing experimental data in the ICSD database. In addition, potentially new meta-stable phases were identified for Mg, Ni, Mn and V halides with band gaps in the visible range. In particular, for CsNiCl3 and CsNiBr3 we obtained low electronic band gaps within DFT/LDA and dispersive band edges, attractive for photovoltaic applications. However, we note that further work is required in order to clarify the magnetic ordering of the Ni-based compounds and establish the reliability of these predictions. In the less prob16 ACS Paragon Plus Environment

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lematic case of Mg, we performed DFT/LDA and GW calculations including spin-orbit coupling, and showed that halide perovskites based on Mg exhibit highly tunable band gaps over almost 1 eV, and are larger than in lead-halide perovskites by more than 1 eV. In addition, we found that magnesium-iodide perovskites, and in particular CH(NH2 )2 MgI3 , may act as efficient electron conductors, due to low electron effective masses. Our overall conclusion from this study is that lead plays a fundamental role in the remarkable optoelectronic properties of organic-inorganic metal-halide perovskites, and is unique among all divalent metals in the periodic table. It is likely that the complete replacement of lead by other divalent metals will result in a loss of efficiency for photovoltaic devices, either due to a reduction in optical absorption or to a less efficient charge transport. Therefore, we propose that the partial replacement of Pb by Mg is a more promising route to reduce the toxicity of organic-inorganic metal-halide perovskite while retaining the unique contribution of Pb to the remarkable optoelectronic properties of these compounds. We hope that the results presented in this work will stimulate the synthesis and characterization of mixed-metal perovskites, and make progress toward the next generation of environmentally-friendly efficient photovoltaic devices.

Methods Density functional theory calculations We perform all calculations using the local density approximation (LDA) 55 to 17 ACS Paragon Plus Environment


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density functional theory (DFT) 56 as implemented in the Quantum ESPRESSO simulation package. 57 We use ultrasoft

58

and norm conserving 59 pseudopo-

tentials as available in the Quantum Espresso library as well as the Theos library 60 for all calculations. In all calculations employing ultrasoft pseudopotentials we use a kinetic cutoff of 60 Ry and a charge density cutoff of 300 Ry, while in the norm conserving case we use 80 Ry and 400 Ry respectively. Relaxations are performed by sampling the Brillouin zone over a 4 × 4 × 4 k-point grid centered at Γ (for the relaxations starting from the perfect perovskite structures) and a 6 × 6 × 6 grid (for the randomly displaced structures). For the band structure calculations the charge densities are calculated using a 6 × 6 × 6 k-point grid unless otherwise specified. We use fully relativistic pseudopotentials in all calculations including spin-orbit coupling, for all elements except Mg, Ca and V. Given the small size of these atoms we do not expect them to have a significant contribution to the spin-orbit coupling effect. Relaxations for randomly displaced structures In order to check the stability of the compounds against structural distortions we relax each structure starting from perovskite unit cells with randomly displaced (shaken) atomic positions and lattice parameters. We perform this test in two stages. In the first instance we construct 5 shaken configurations for each compound, with the displacement amplitude of 0.1 ˚ A for the atomic coordinates and 0.3 ˚ A for the lattice vectors, and allow the structures to relax. 18 ACS Paragon Plus Environment

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In the second stage, we double the amplitudes for both atomic positions and lattice parameters for 5 more configurations and allow them to relax. Finally, we compare the total energies of all configurations and retain the crystal structures with the smallest total energy. Calculations for transition metals For all transition metals (Ti, Zr, V, Cr, Mo, W, Mn, Fe, Co, Ni, Pd, Pt) and noble metals (Cu and Ag) we use LDA+U 61–63 in the formulation of Cococcioni and Gironcoli. 64 For consistency, we use a Hubbard U parameter of 4 eV for all elements. We use LDA+U for all calculations involving transition metals except for the initial relaxations of the perfect perovskite structures. For the magnetic transition metals (V, Cr, Mn, Fe, Co, Ni) we test the stability of ferromagnetic or antiferromagnetic configuration for the chloride compounds by performing spin-polarized calculations within local spin density approximation (LSDA). We obtain that all chlorides except for the Cr compounds have a preferential antiferromagnetic ‘rock salt’ configuration. For the case of Cr we obtain a ferromagnetic configuration, and Cr-halide compounds with a half-metallic behavior. We use the magnetic ordering identified for the chlorides for all other halides in subsequent calculations. Spin polarization is included in all calculations except in the initial relaxations starting from the ideal perovskite structures. It is worth noting that spin ordering has been investigated only in the unit cell containing four octahedra. The magnetic ordering in a supercell configuration as well as the influence of 19 ACS Paragon Plus Environment


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the magnetic ordering on the crystal structure properties of these compounds should be analyzed separately. Such a thorough analysis is beyond the scope of the current investigation. Therefore, for the compounds based on magnetic metals the structures we consider are tentative. For all ground state calculations which include transition metals as well as for the cases of Ga and In we use a gaussian smearing in order to converge the total energy of metallic systems. We increase the k-point sampling from 6×6×6 to 8×8×8 and 10×10×10 and gaussian smearings from 0.1 to 0.4 eV in order to achieve convergence of the total energy within 100 iterations. A number of systems fail to achieve convergence for a 10 × 10 × 10 k-point grids and 0.4 eV gaussian smearings. This is the case for CsTiF3 , CsTiI3 , CsZrF3 , CsMoBr3 , CsMoI3 , CsWBr3 , CsWI3 , CsCoBr3 and CsFeI3 . In addition, there is a number of compounds for which the calculated Fermi Level is within less than 0.1 eV from the nearest band edge: CsCoF3 , CsCoCl3 , CsCoI3 , CsFeF3 , CsFeCl3 , CsFeBr3 and CsWF3 . All these compounds are discarded after the first screening step on the basis that they are likely metallic. We test the metallic character of these compounds by recalculating their band structure after setting a fixed occupation of the eigenstates. For all compounds listed above except CsWBr3 and CsFeBr3 the total energy fails to converge within 100 iterations. Instead, for CsWBr3 and CsFeBr3 we obtain semiconducting band structures with gaps of 0.4 and 1.6 eV respectively. However, we note that the electronic structure of these compounds is extremely sensitive to the 20 ACS Paragon Plus Environment

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gaussian smearing and k-point sampling as well the Hubbard U parameter and magnetic ordering. We therefore discard all compounds listed in this paragraph (marked as grey squares in Figure 2a). The rest of the compounds highlighted in grey in Figure 2 of the main manuscript are expected to be metallic based on the calculated DFT band structure. GW calculations for Mg-based perovskites We performed GW calculations on CsMgI3 and CH(NH2 )2 MgI3 using a set of norm-conserving fully-relativistic pseudopotentials for Mg and I. For I we include the semicore 4d10 states while for Mg we take into account only the valence 3s2 states. For C, H, N and Cs we use norm-conserving scalar- or non-relativistic pseudopotentials as found in the Quantum Espresso library. We use a plane-wave cutoff of 150 Ry for the ground state calculation. We calculate the quasiparticle energies using the Yambo code. 54 The screened Coulomb interaction is described via the Godby-Needs plasmon pole model, 65 using a plasmon-pole parameter of 27.2 eV. The exchange self-energy is calculated using a plane-wave cutoff of 30 Ry. For the calculation of the correlation self-energy we sum over 1000 bands and use a plane-wave cutoff of 6 Ry for the calculation of the polarizability. Both the exchange and the correlation self-energies are obtained using a Γ-centered 2 × 2 × 2 k-point grid. Supporting Information The Supporting Information contains additional crystal and electronic struc21 ACS Paragon Plus Environment


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ture data relevant for the discussions presented in the manuscript, as well as a table comparing our computational predictions with data available on the ICSD. 46

Acknowledgement This work was supported by the Leverhulme Trust (Grant RL-2012-001), the European Research Council (EU FP7/ERC grant No. 239578), the UK Engineering and Physical Sciences Research Council (Grant No. EP/J009857/1), and the Graphene Flagship (EU FP7 grant No. 604391). The authors would like to thank Henry J. Snaith and Giles E. Eperon from the Department of Physics at the University of Oxford for useful discussions. The authors would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility 66 and the ARCHER UK National Supercomputing Service under the ‘AMSEC’ Leadership project in carrying out this work. Structural models were rendered using VESTA. 67

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Computational Screening of Homovalent Lead Substitution in Organic

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