Effects of the van der Waals Interactions on Structural and Electronic Properties of CH₃NH₃(Pb,Sn)(I,Br,Cl)₃ Halide Perovskites

Abstract

In hybrid perovskite materials like CH 3 NH 3 PbI 3 , methylammonium (MA) lead iodide (MAPI), the orientation of the MA + cations and their ordering can significantly affect the structure of the inorganic framework. Although the states near the band edges are known to be primarily derived from the Pb and halogen orbitals rather than from the organic ion, the latter may have an indirect effect through their impact on the structural relaxation. In this work, we investigate both the structural relaxation effects of the inorganic framework in response to the MA + orientation and their impact on the electronic structure near the band edges. Calculations are performed for MA(Pb,Sn) X 3 with ( X = I, Br, and Cl) materials for both Pb- and Sn-based compounds. The work focuses on the high-temperature α-phase, which is nominally cubic if averaged over all possible MA orientations and in which no alternating rotations of the octahedral occur, so that the unit cell is the smallest possible. The effects of van der Waals (vdW) corrections to density functional theory on the structural relaxation are investigated. Our results reveal that the vdW interactions between the MA + cation and the inorganic framework can strongly affect the optimized orientation and position of the molecule and the resulting distortion of the inorganic framework. Consequently, it also affects the electronic properties of the materials and specifically can change the band structure from direct to indirect band gaps. The robustness of this result is studied by comparing hybrid functional calculations and quasiparticle self-consistent GW calculations as well as spin–orbit coupling.

First-Principles Study on the Stability and Electronic Properties of Dion–Jacobson Halide A′(MA)n−1BnX3n+1 Perovskites

“…The band gaps of (BAC)­MA n –1 Pb n I 3 n +1 are 1.91, 1.74, 1.68, and 1.65 eV for n = 1–4, respectively, which converge toward the value of 3D perovskite MAPbI 3 (1.50 eV) as n increases. Compared with the previously reported experimental and theoretical values of 3D MAPbI 3 (1.55 eV), , our calculation results are reliable. Other calculated systems (that is, A′MA n –1 Pb n Cl 3 n +1 , A′MA n –1 Pb n Br 3 n +1 , and A′(MA) n −1 B n X 3 n +1 , A′ = PDMA/BAC, B = Sn/Ge, X = Cl/Br/I) also follow this rule, as shown in Table S1.…”

“…When n > 1, the small organic molecule MA appears in the structure. At this time, the orientation of MA also has a certain impact on the system. , Taking (BAC)­(MA)­Pb 2 I 7 as an example, we considered four cases where MA is parallel to the a -, b -, and c -axis and directly opposite to BX 3 , respectively, as shown in Figure . The results show that the energy of (BAC)­(MA)­Pb 2 I 7 is the lowest when the MA is along the b -axis, so we set MA parallel to the b for all calculations.…”

“…The band gap calculated with the PBE exchange-correlation functional of GGA is generally underestimated compared to the experimental data. , However, for some cases, the PBE shows that the band gap is very similar to the experimental value , due to the error elimination; that is, ignoring the spin–orbit coupling (SOC) caused band gap overestimation, thereby offsetting the underestimation error of the GGA calculation . For example, the band gap values of BA 2 PbI 4 and MAPbI 3 calculated by Liu Biao et al using PBE are only about 0.1 eV higher than those calculated using the Heyd–Scuseria–Ernzerh (HSE06) functional with SOC 3 and are consistent with the experimental data. , In our work, MAPbCl 3 and MASnI 3 are also calculated by HSE06 + SOC.…”

Do Lead Halide Hybrid Perovskites Have Hydrogen Bonds?

“…The H···I distance in MAPbI 3 may reach 3.5 Å, and the N–H···I angles may vary from 0 to 140° even if the structure is fixed, but the calculation method is changed . The H···X distance decreases to around 2.45 Å for Br and to 2.3 Å for Cl in MAPbX 3 . Experimentally, the H···I distances in FAPbI 3 were deduced from the atomic positions given by neutron powder diffraction performed at RT for the recovered crystals .…”

“…13 The H•••X distance decreases to around 2.45 Å for Br and to 2.3 Å for Cl in MAPbX 3 . 64 Experimentally, the H•••I distances in FAPbI 3 were deduced from the atomic positions given by neutron powder diffraction performed at RT for the recovered crystals. 14 These were found to be 2.992 and 2.770 Å for the different N−H hydrogen atoms involved and were accepted as H-bonds.…”