Excitons in metal-halide perovskites from first-principles many-body perturbation theory.

Metal-halide perovskites are a structurally, chemically, and electronically diverse class of semiconductors with applications ranging from photovoltaics to radiation detectors and sensors. Understanding neutral electron-hole excitations (excitons) is key for predicting and improving the efficiency of energy-conversion processes in these materials. First-principles calculations have played an important role in this context, allowing for a detailed insight into the formation of excitons in many different types of perovskites. Such calculations have demonstrated that excitons in some perovskites significantly deviate from canonical models due to the chemical and structural heterogeneity of these materials. In this Perspective, I provide an overview of calculations of excitons in metal-halide perovskites using Green's function-based many-body perturbation theory in the GW + Bethe-Salpeter equation approach, the prevalent method for calculating excitons in extended solids. This approach readily considers anisotropic electronic structures and dielectric screening present in many perovskites and important effects, such as spin-orbit coupling. I will show that despite this progress, the complex and diverse electronic structure of these materials and its intricate coupling to pronounced and anharmonic structural dynamics pose challenges that are currently not fully addressed within the GW + Bethe-Salpeter equation approach. I hope that this Perspective serves as an inspiration for further exploring the rich landscape of excitons in metal-halide perovskites and other complex semiconductors and for method development addressing unresolved challenges in the field.

Understanding the evolution of double perovskite band structure upon dimensional reduction.

Recent investigations into the effects of dimensional reduction on halide double perovskites have revealed an intriguing change in band structure when the three-dimensional (3D) perovskite is reduced to a two-dimensional (2D) perovskite with inorganic sheets of monolayer thickness (n = 1). The indirect bandgap of 3D Cs2AgBiBr6 becomes direct in the n = 1 perovskite whereas the direct bandgap of 3D Cs2AgTlBr6 becomes indirect at the n = 1 limit. Here, we apply a linear combination of atomic orbitals approach to uncover the orbital basis for this bandgap symmetry transition with dimensional reduction. We adapt our previously established method for predicting band structures of 3D double perovskites for application to their 2D congeners, emphasizing new considerations required for the 2D lattice. In particular, we consider the inequivalence of the terminal and bridging halides and the consequences of applying translational symmetry only along two dimensions. The valence and conduction bands of the layered perovskites can be derived from symmetry adapted linear combinations of halide p orbitals propagated across the 2D lattice. The dispersion of each band is then determined by the bonding and antibonding interactions of the metal and halide orbitals, thus affording predictions of the essential features of the band structure. We demonstrate this analysis for 2D Ag-Bi and Ag-Tl perovskites with sheets of mono- and bilayer thickness, establishing a detailed understanding of their band structures, which enables us to identify the key factors that drive the bandgap symmetry transitions observed at the n = 1 limit. Importantly, these insights also allow us to make the general prediction that direct → indirect or indirect → direct bandgap transitions in the monolayer limit are most likely in double perovskite compositions that involve participation of metal d orbitals at the band edges or that have no metal-orbital contributions to the valence band, laying the groundwork for the targeted realization of this phenomenon.

Chemical Mapping of Excitons in Halide Double Perovskites.

Halide double perovskites comprise an emerging class of semiconductors with tremendous chemical and electronic diversity. While their band structure features can be understood from frontier-orbital models, chemical intuition for optical excitations remains incomplete. Here, we use ab initio many-body perturbation theory within the GW and the Bethe-Salpeter equation approach to calculate excited-state properties of a representative range of Cs2BB'Cl6 double perovskites. Our calculations reveal that double perovskites with different combinations of B and B' cations display a broad variety of electronic band structures and dielectric properties and form excitons with binding energies ranging over several orders of magnitude. We correlate these properties with the orbital-induced anisotropy of charge-carrier effective masses and the long-range behavior of the dielectric function by comparing them with the canonical conditions of the Wannier-Mott model. Furthermore, we derive chemically intuitive rules for predicting the nature of excitons in halide double perovskites using computationally inexpensive density functional theory calculations.

Delocalized electronic excitations and their role in directional charge transfer in the reaction center of Rhodobacter sphaeroides.

In purple bacteria, the fundamental charge-separation step that drives the conversion of radiation energy into chemical energy proceeds along one branch-the A branch-of a heterodimeric pigment-protein complex, the reaction center. Here, we use first principles time-dependent density functional theory (TDDFT) with an optimally-tuned range-separated hybrid functional to investigate the electronic and excited-state structure of the six primary pigments in the reaction center of Rhodobacter sphaeroides. By explicitly including amino-acid residues surrounding these six pigments in our TDDFT calculations, we systematically study the effect of the protein environment on energy and charge-transfer excitations. Our calculations show that a forward charge transfer into the A branch is significantly lower in energy than the first charge transfer into the B branch, in agreement with the unidirectional charge transfer observed experimentally. We further show that the inclusion of the protein environment redshifts this excitation significantly, allowing for energy transfer from the coupled Qx excitations. Through analysis of transition and difference densities, we demonstrate that most of the Q-band excitations are strongly delocalized over several pigments and that both their spatial delocalization and charge-transfer character determine how strongly affected they are by thermally-activated molecular vibrations. Our results suggest a mechanism for charge-transfer in this bacterial reaction center and pave the way for further first-principles investigations of the interplay between delocalized excited states, vibronic coupling, and the role of the protein environment in this and other complex light-harvesting systems.

Emergence of Rashba-/Dresselhaus effects in Ruddlesden-Popper halide perovskites with octahedral rotations.

Ruddlesden-Popper halide perovskites are highly versatile quasi-two-dimensional energy materials with a wide range of tunable optoelectronic properties. Here we use the all-inorganic Csn+1PbnX3n+1Ruddlesden-Popper perovskites with X = I, Br, and Cl to systematically model the effect of octahedral tilting distortions on the energy landscape, band gaps, macroscopic polarization, and the emergence of Rashba-/Dresselhaus splitting in these materials. We construct all uniquen = 1 andn = 2 structures following from octahedral tilts and use first-principles density functional theory to calculate total energies, polarizations and band structures, backed up by band gap calculations using theGWapproach. Our results provide design rules for tailoring structural distortions and band-structure properties in all-inorganic Ruddlesden-Popper perovskites through the interplay of the amplitude, direction, and chemical character of the antiferrodistortive distortion modes contributing to each octahedral tilt pattern. Our work emphasizes that, in contrast to three-dimensional perovskites, polar structures may arise from a combination of octahedral tilts, and Rashba-/Dresselhaus splitting in this class of materials is determined by the direction and Pb-I orbital contribution of the polar distortion mode.

Tuning Defects in a Halide Double Perovskite with Pressure.

Dopant defects in semiconductors can trap charge carriers or ionize to produce charge carriers─playing a critical role in electronic transport. Halide perovskites are a technologically important semiconductor family with a large pressure response. Yet, to our knowledge, the effect of high pressures on defects in halide perovskites has not been experimentally investigated. Here, we study the structural, optical, and electronic consequences of compressing the small-bandgap double perovskites Cs2AgTlX6 (X = Cl or Br) up to 56 GPa. Mild compression to 1.7 GPa increases the conductivity of Cs2AgTlBr6 by ca. 1 order of magnitude and decreases its bandgap from 0.94 to 0.7 eV. Subsequent compression yields complex optoelectronic behavior: the bandgap varies by 1.2 eV and conductivity ranges by a factor of 104. These conductivity changes cannot be explained by the evolving bandgap. Instead, they can be understood as tuning of the bromine vacancy defect with pressure─varying between a delocalized shallow defect state with a small ionization energy and a localized deep defect state with a large ionization energy. Activation energy measurements reveal that the shallow-to-deep defect transition occurs near 1.5 GPa, well before the cubic-to-tetragonal phase transition. An analysis of the orbital interactions in Cs2AgTlBr6 illustrates how the bromine vacancy weakens the adjacent Tl s-Br p antibonding interaction, driving the shallow-to-deep defect transition. Our orbital analysis leads us to propose that halogen vacancies are most likely to be shallow donors in halide double perovskites that have a conduction band derived from the octahedral metal's s orbitals.

Charge Reservoirs in an Expanded Halide Perovskite Analog: Enhancing High-Pressure Conductivity through Redox-Active Molecules.

As halide perovskites and their derivatives are being developed for numerous optoelectronic applications, controlling their electronic doping remains a fundamental challenge. Herein, we describe a novel strategy of using redox-active organic molecules as stoichiometric electron acceptors. The cavities in the new expanded perovskite analogs (dmpz)[Sn2 X6 ], (X=Br- (1Br) and I- (1I)) are occupied by dmpz2+ (N,N'-dimethylpyrazinium), with the LUMOs lying ca. 1 eV above the valence band maximum (VBM). Compressing the metal-halide framework drives up the VBM in 1I relative to the dmpz LUMO. The electronic conductivity increases by a factor of 105 with pressure, reaching 50(17) S cm-1 at 60 GPa, exceeding the high-pressure conductivities of most halide perovskites. This conductivity enhancement is attributed to an increased hole density created by dmpz2+ reduction. This work elevates the role of organic cations in 3D metal-halides, from templating the structure to serving as charge reservoirs for tuning the carrier concentration.

Assessment of the Ab Initio Bethe-Salpeter Equation Approach for the Low-Lying Excitation Energies of Bacteriochlorophylls and Chlorophylls.

Bacteriochlorophyll and chlorophyll molecules are crucial building blocks of the photosynthetic apparatus in bacteria, algae, and plants. Embedded in transmembrane protein complexes, they are responsible for the primary processes of photosynthesis: excitation energy and charge transfer. Here, we use ab initio many-body perturbation theory within the GW approximation and Bethe-Salpeter equation (BSE) approach to calculate the electronic structure and optical excitations of bacteriochlorophylls a, b, c, d, and e and chlorophylls a and b. We systematically study the effects of the structure, basis set size, partial self-consistency in GW, and the underlying exchange-correlation approximation and compare our calculations with results from time-dependent density functional theory, multireference RASPT2, and experimental literature results. We find that optical excitations calculated with GW+BSE are in excellent agreement with experimental data, with an average deviation of less than 100 meV for the first three bright excitations of the entire family of (bacterio)chlorophylls. Contrary to state-of-the-art time-dependent density functional theory (TDDFT) with an optimally tuned range-separated hybrid functional, this accuracy is achieved in a parameter-free approach. Moreover, GW+BSE predicts the energy differences between the low-energy excitations correctly and eliminates spurious charge transfer states that TDDFT with (semi)local approximations is known to produce. Our study provides accurate reference results and highlights the potential of the GW+BSE approach for the simulation of larger pigment complexes.

Chemically Localized Resonant Excitons in Silver-Pnictogen Halide Double Perovskites.

Halide double perovskites with alternating silver and pnictogen cations are an emerging family of photoabsorber materials with robust stability and band gaps in the visible range. However, the nature of optical excitations in these systems is not yet well understood, limiting their utility. Here, we use ab initio many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation approach to calculate the electronic structure and optical excitations of the double perovskite series Cs2AgBX6, with B = Bi3+, Sb3+ and X = Br-, Cl-. We find that these materials exhibit strongly localized resonant excitons with energies from 170 to 434 meV below the direct band gap. In contrast to lead-based perovskites, the Cs2AgBX6 excitons are computed to be non-hydrogenic with anisotropic effective masses and sensitive to local field effects, a consequence of their chemical heterogeneity. Our calculations demonstrate the limitations of the Wannier-Mott and Elliott models for this class of double perovskites and contribute to a detailed atomistic understanding of their light-matter interactions.

First principles theoretical spectroscopy of methylene blue: Between limitations of time-dependent density functional theory approximations and its realistic description in the solvent.

Methylene blue [3,7-Bis(di-methylamino) phenothiazin-5-ium chloride] is a phenothiazine dye with applications as a sensitizer for photodynamic therapy, photoantimicrobials, and dye-sensitized solar cells. Time-dependent density functional theory (TDDFT), based on (semi)local and global hybrid exchange-correlation functionals, fails to correctly describe its spectral features due to known limitations for describing optical excitations of π-conjugated systems. Here, we use TDDFT with a non-empirical optimally tuned range-separated hybrid functional to explore the optical excitations of gas phase and solvated methylene blue. We compute solvated configurations using molecular dynamics and an iterative procedure to account for explicit solute polarization. We rationalize and validate that by extrapolating the optimized range separation parameter to an infinite amount of solvating molecules, the optical gap of methylene blue is well described. Moreover, this method allows us to resolve contributions from solvent-solute intermolecular interactions and dielectric screening. We validate our results by comparing them to first-principles calculations based on the GW+Bethe-Salpeter equation approach and experiment. Vibronic calculations using TDDFT and the generating function method account for the spectra's subbands and bring the computed transition energies to within 0.15 eV of the experimental data. This methodology is expected to perform equivalently well for describing solvated spectra of π-conjugated systems.

Revealing Local Disorder in a Silver-Bismuth Halide Perovskite upon Compression.

The halide double perovskite Cs2AgBiBr6 has emerged as a promising nontoxic alternative to the lead halide perovskites APbX3 (A = organic cation or Cs; X = I or Br). Here, we perform high-pressure synchrotron X-ray total scattering on Cs2AgBiBr6 and discover local disorder that is hidden from conventional Bragg analysis. While our powder diffraction data show that the average structure remains cubic up to 2.1 GPa, analysis of the X-ray pair distribution function reveals that the local structure is better described by a monoclinic space group, with significant distortion within the Ag-Br and Bi-Br octahedra and off-centering of the Cs atoms. By tracking the distribution of interatomic Cs-Br distances, we find that the local disorder is enhanced upon compression, and we corroborate these results with molecular dynamics simulations. The observed local disorder affords new understanding of this promising material and potentially offers a new parameter to tune in halide perovskite lattices.

Dimensional reduction of the small-bandgap double perovskite Cs2AgTlBr6.

Quantum confinement effects in lower-dimensional derivatives of the ABX3 (A = monocation, X = halide) single perovskites afford striking optical and electronic changes, enabling applications ranging from solar absorbers to phosphors and light-emitting diodes. Halide double perovskites form a larger materials family, known since the late 1800s, but lower-dimensional derivatives remain rare and prior work has revealed a minimal effect of quantum confinement on their optical properties. Here, we synthesize three new lower-dimensional derivatives of the 3D double perovskite Cs2AgTlBr6: 2D derivatives with mono- (1-Tl) and bi-layer thick (2-Tl) inorganic sheets and a quasi-1D derivative (1'-Tl). Single-crystal ellipsometry studies of these materials show the first clear demonstration that dimensional reduction can significantly alter the optical properties of 2D halide double perovskites. This large quantum confinement effect is attributed to the substantial electronic delocalization of the parent 3D Ag-Tl perovskite. Calculations track the evolution of the electronic bands with dimensional reduction and the accompanying structural distortions and show a direct-to-indirect bandgap transition as the 3D perovskite lattice is thinned to a monolayer in 1-Tl. This bandgap transition at the monolayer limit is also evident in the calculations for 1-In, an isostructural, isoelectronic analogue to 1-Tl in which In3+ replaces Tl3+, underscoring the orbital basis for the direct/indirect nature of the bandgap. Thus, in complement to the massive compositional diversity of halide double perovskites, dimensional reduction may be used as a systematic route for harnessing electronic confinement effects and obtaining new electronic structures.

Expanded Analogs of Three-Dimensional Lead-Halide Hybrid Perovskites.

Replacing the Pb-X octahedral building unit of AI PbX3 perovskites (X=halide) with a pair of edge-sharing Pb-X octahedra affords the expanded perovskite analogs: AII Pb2 X6 . We report seven members of this new family of materials. In 3D hybrid perovskites, orbitals from the organic molecules do not participate in the band edges. In contrast, the more spacious inorganic sublattice of the expanded analogs accommodates larger pyrazinium-based cations with low-lying π* orbitals that form the conduction band, substantially decreasing the band gap of the expanded lattice. The molecular nature of the conduction band allows us to electronically dope the materials by reducing the organic molecules. By synthesizing derivatives with AII =pyridinium and ammonium, we can isolate the contributions of the pyrazinium-based orbitals in the band gap transition of AII Pb2 X6 . The organic-molecule-based conduction band and the inorganic-ion-based valence band provide an unusual electronic platform with localized states for electrons and more disperse bands for holes upon optical or thermal excitation.

Tuning the bandgap of Cs2AgBiBr6 through dilute tin alloying.

The promise of lead halide hybrid perovskites for optoelectronic applications makes finding less-toxic alternatives a priority. The double perovskite Cs2AgBiBr6 (1) represents one such alternative, offering long carrier lifetimes and greater stability under ambient conditions. However, the large and indirect 1.95 eV bandgap hinders its potential as a solar absorber. Here we report that alloying crystals of 1 with up to 1 atom% Sn results in a bandgap reduction of up to ca. 0.5 eV while maintaining low toxicity. Crystals can be alloyed with up to 1 atom% Sn and the predominant substitution pathway appears to be a ∼2 : 1 substitution of Sn2+ and Sn4+ for Ag+ and Bi3+, respectively, with Ag+ vacancies providing charge compensation. Spincoated films of 1 accommodate a higher Sn loading, up to 4 atom% Sn, where we see mostly Sn2+ substitution for both Ag+ and Bi3+. Density functional theory (DFT) calculations ascribe the bandgap redshift to the introduction of Sn impurity bands below the conduction band minimum of the host lattice. Using optical absorption spectroscopy, photothermal deflection spectroscopy, X-ray absorption spectroscopy, 119Sn NMR, redox titration, single-crystal and powder X-ray diffraction, multiple elemental analysis and imaging techniques, and DFT calculations, we provide a detailed analysis of the Sn content and oxidation state, dominant substitution sites, and charge-compensating defects in Sn-alloyed Cs2AgBiBr6 (1:Sn) crystals and films. An understanding of heterovalent alloying in halide double perovskites opens the door to a wider breadth of potential alloying agents for manipulating their band structures in a predictable manner.

A pencil-and-paper method for elucidating halide double perovskite band structures.

Halide double perovskites are an important emerging alternative to lead-halide perovskites in a variety of optoelectronic applications. Compared to ABX3 single perovskites (A = monovalent cation, X = halide), A2BB'X6 double perovskites exhibit a wider array of compositions and electronic structures, promising finer control over physical and electronic properties through synthetic design. However, a clear understanding of how chemical composition dictates the electronic structures of this large family of materials is still lacking. Herein, we develop a qualitative Linear Combination of Atomic Orbitals (LCAO) model that describes the full range of band structures for double perovskites. Our simple model allows for a direct connection between the inherently local bonding between atoms in the double perovskite and the resulting delocalized bands of the solid. In particular, we show how bands in halide double perovskites originate from the molecular orbitals of metal-hexahalide coordination complexes and describe how these molecular orbitals vary within a band. Our results provide both an enhanced understanding of known perovskite compositions and predictive power for identifying new compositions with targeted properties. We present a table, which permits the position of the conduction band minimum and valence band maximum in most double perovskites to be immediately determined from the frontier atomic orbitals of the B-site metals. Using purely qualitative arguments based on orbital symmetries and their relative energies, the direct/indirect nature of the bandgap of almost all halide double perovskites can thus be correctly predicted. We hope that this theory provides an intuitive understanding of halide double perovskite band structures and enables lessons from molecular chemistry to be applied to these extended solids.

Small-Band-Gap Halide Double Perovskites.

Despite their compositional versatility, most halide double perovskites feature large band gaps. Herein, we describe a strategy for achieving small band gaps in this family of materials. The new double perovskites Cs2 AgTlX6 (X=Cl (1) and Br (2)) have direct band gaps of 2.0 and 0.95 eV, respectively, which are approximately 1 eV lower than those of analogous perovskites. To our knowledge, compound 2 displays the lowest band gap for any known halide perovskite. Unlike in AI BII X3 perovskites, the band-gap transition in AI2 BB'X6 double perovskites can show substantial metal-to-metal charge-transfer character. This band-edge orbital composition is used to achieve small band gaps through the selection of energetically aligned B- and B'-site metal frontier orbitals. Calculations reveal a shallow, symmetry-forbidden region at the band edges for 1, which results in long (µs) microwave conductivity lifetimes. We further describe a facile self-doping reaction in 2 through Br2 loss at ambient conditions.

Layered Halide Double Perovskites: Dimensional Reduction of Cs2AgBiBr6.

We investigate the consequences of dimensional confinement on halide double perovskites by synthesizing two-dimensional analogues of the recently reported three-dimensional double perovskite Cs2AgBiBr6. The layered perovskites (BA)4AgBiBr8 (1) and (BA)2CsAgBiBr7 (2) (BA = CH3(CH2)3NH3+) feature metal-halide sheets of mono and bilayer thickness, respectively, where the ordered double-perovskite lattice is partitioned by organic cations. Electronic structure calculations indicate that the indirect bandgap of Cs2AgBiBr6 becomes direct when the infinitely thick inorganic lattice is reduced to monolayer thickness. Calculations on model systems allow us to separate the effects of dimensional reduction from those of the accompanying structural distortions in the inorganic sublattice. Detailed optical characterization shows that the photophysical properties of 1 and 2 are markedly different than those of their well-studied lead-halide analogs. Hybrid layered derivatives of double perovskites substantially expand on the substitutional flexibility of halide perovskites to encompass greater compositional and electronic diversity.

Defect-Induced Band-Edge Reconstruction of a Bismuth-Halide Double Perovskite for Visible-Light Absorption.

Halide double perovskites have recently been developed as less toxic analogs of the lead perovskite solar-cell absorbers APbX3 (A = monovalent cation; X = Br or I). However, all known halide double perovskites have large bandgaps that afford weak visible-light absorption. The first halide double perovskite evaluated as an absorber, Cs2AgBiBr6 (1), has a bandgap of 1.95 eV. Here, we show that dilute alloying decreases 1's bandgap by ca. 0.5 eV. Importantly, time-resolved photoconductivity measurements reveal long-lived carriers with microsecond lifetimes in the alloyed material, which is very promising for photovoltaic applications. The alloyed perovskite described herein is the first double perovskite to show comparable bandgap energy and carrier lifetime to those of (CH3NH3)PbI3. By describing how energy- and symmetry-matched impurity orbitals, at low concentrations, dramatically alter 1's band edges, we open a potential pathway for the large and diverse family of halide double perovskites to compete with APbX3 absorbers.