Methylammonium Tetrel Halide Perovskite Ion Pairs and Their Dimers: The Interplay between the Hydrogen-, Pnictogen- and Tetrel-Bonding Interactions

The structural stability of the extensively studied organic-inorganic hybrid methylammonium tetrel halide perovskite semiconductors, MATtX₃ (MA = CH₃NH₃⁺; Tt = Ge, Sn, Pb; X = Cl, Br, I), arises as a result of non-covalent interactions between an organic cation (CH₃NH₃⁺) and an inorganic anion (TtX₃^-). However, the basic understanding of the underlying chemical bonding interactions in these systems that link the ionic moieties together in complex configurations is still limited. In this study, ion pair models constituting the organic and inorganic ions were regarded as the repeating units of periodic crystal systems and density functional theory simulations were performed to elucidate the nature of the non-covalent interactions between them. It is demonstrated that not only the charge-assisted N-H···X and C-H···X hydrogen bonds but also the C-N···X pnictogen bonds interact to stabilize the ion pairs and to define their geometries in the gas phase. Similar interactions are also responsible for the formation of crystalline MATtX₃ in the low-temperature phase, some of which have been delineated in previous studies. In contrast, the Tt···X tetrel bonding interactions, which are hidden as coordinate bonds in the crystals, play a vital role in holding the inorganic anionic moieties (TtX₃^-) together. We have demonstrated that each Tt in each [CH₃NH₃⁺•TtX₃^-] ion pair has the capacity to donate three tetrel (σ-hole) bonds to the halides of three nearest neighbor TtX₃^- units, thus causing the emergence of an infinite array of 3D TtX₆^4- octahedra in the crystalline phase. The TtX₄^4- octahedra are corner-shared to form cage-like inorganic frameworks that host the organic cation, leading to the formation of functional tetrel halide perovskite materials that have outstanding optoelectronic properties in the solid state. We harnessed the results using the quantum theory of atoms in molecules, natural bond orbital, molecular electrostatic surface potential and independent gradient models to validate these conclusions.

The Tetrel Bond and Tetrel Halide Perovskite Semiconductors

The ion pairs [Cs+•TtX3-] (Tt = Pb, Sn, Ge; X = I, Br, Cl) are the building blocks of all-inorganic cesium tetrel halide perovskites in 3D, CsTtX3, that are widely regarded as blockbuster materials for optoelectronic applications such as in solar cells. The 3D structures consist of an anionic inorganic tetrel halide framework stabilized by the cesium cations (Cs+). We use computational methods to show that the geometrical connectivity between the inorganic monoanions, [TtX3-]∞, that leads to the formation of the TtX64- octahedra and the 3D inorganic perovskite architecture is the result of the joint effect of polarization and coulombic forces driven by alkali and tetrel bonds. Depending on the nature and temperature phase of these perovskite systems, the Tt···X tetrel bonds are either indistinguishable or somehow distinguishable from Tt-X coordinate bonds. The calculation of the potential on the electrostatic surface of the Tt atom in molecular [Cs+•TtX3-] provides physical insight into why the negative anions [TtX3-] attract each other when in close proximity, leading to the formation of the CsTtX3 tetrel halide perovskites in the solid state. The inter-molecular (and inter-ionic) geometries, binding energies, and charge density-based topological properties of sixteen [Cs+•TtX3-] ion pairs, as well as some selected oligomers [Cs+•PbI3-]n (n = 2, 3, 4), are discussed.

The Pnictogen Bond, Together with Other Non-Covalent Interactions, in the Rational Design of One-, Two- and Three-Dimensional Organic-Inorganic Hybrid Metal Halide Perovskite Semiconducting Materials, and Beyond

The pnictogen bond, a somewhat overlooked supramolecular chemical synthon known since the middle of the last century, is one of the promising types of non-covalent interactions yet to be fully understood by recognizing and exploiting its properties for the rational design of novel functional materials. Its bonding modes, energy profiles, vibrational structures and charge density topologies, among others, have yet to be comprehensively delineated, both theoretically and experimentally. In this overview, attention is largely centered on the nature of nitrogen-centered pnictogen bonds found in organic-inorganic hybrid metal halide perovskites and closely related structures deposited in the Cambridge Structural Database (CSD) and the Inorganic Chemistry Structural Database (ICSD). Focusing on well-characterized structures, it is shown that it is not merely charge-assisted hydrogen bonds that stabilize the inorganic frameworks, as widely assumed and well-documented, but simultaneously nitrogen-centered pnictogen bonding, and, depending on the atomic constituents of the organic cation, other non-covalent interactions such as halogen bonding and/or tetrel bonding, are also contributors to the stabilizing of a variety of materials in the solid state. We have shown that competition between pnictogen bonding and other interactions plays an important role in determining the tilting of the MX6 (X = a halogen) octahedra of metal halide perovskites in one, two and three-dimensions. The pnictogen interactions are identified to be directional even in zero-dimensional crystals, a structural feature in many engineered ordered materials; hence an interplay between them and other non-covalent interactions drives the structure and the functional properties of perovskite materials and enabling their application in, for example, photovoltaics and optoelectronics. We have demonstrated that nitrogen in ammonium and its derivatives in many chemical systems acts as a pnictogen bond donor and contributes to conferring stability, and hence functionality, to crystalline perovskite systems. The significance of these non-covalent interactions should not be overlooked, especially when the focus is centered on the rationale design and discovery of such highly-valued materials.

Small practical cluster models for perovskites based on the similarity criterion of central location environment and their applications

Developing universal theoretical models for perovskites (often denoted as ABX₃) can contribute to the rational design of novel perovskite photovoltaic materials. However, few models can be successfully applied to study the intrinsic electronic structure due to the poor accuracy and unaffordable computational cost. Herein, we report the innovative construction of small practical cluster models through the similarity criterion of the central location environment, which retains only the central A-site as the original cation while the others are substituted by Cs to keep the clusters electrically neutral. The central cation has a chemical environment similar to that of the bulk perovskite. The binding energy between A and the BX framework, geometric structures (B-X distances and B-X-B angles), and the electronic structures (the gap and the spatial distribution of HOMO and LUMO, electron distribution) of these clusters have been investigated and compared with the corresponding properties of bulk materials. The results suggest that the cluster model with twelve B-atoms suitably describes these properties. The geometric structures and gaps are closer to the bulk situations than the quasi-one-dimensional and quasi-two-dimensional cluster models with all-primitive cations, respectively. Other organic cations, such as NH₃(CH₂)_nCH₃ (n = 1, 2, and 3 for EA, PA, and BA, respectively), and (NH₂)₂CH (FA) can, therefore, mimic perovskite materials. Clusters with different sizes of A indicate that PA and BA will distort the quasi-cubic structures, which is consistent with the judgment of the tolerance factor of bulk materials. The reliable cluster model provides the research foundation for some basic issues of perovskites, such as vibrational spectroscopy and hydrogen bonding strength, to gain detailed insight into the interactions between A and the BX framework.

A2AgCrBr6 (A = K, Rb, Cs) and Cs2AgCrX6(X = Cl, I) Double Perovskites: A Transition-Metal-Based Semiconducting Material Series with Remarkable Optics

With an interest to quest for transition metal-based halogenated double perovskites ABBX6 as high performance semiconducting materials for optoelectronics, this study theoretically examined the electronic structures, stability, electronic (density of states and band structures), transport (effective masses of charge carriers), and optical properties (dielectric function and absorption coefficients, etc.) of the series A2AgCrBr6 (A = K, Rb, Cs) using SCAN+rVV10. Our results showed that A2AgCrBr6 (A = Rb, Cs), but not K2AgCrBr6, has a stable perovskite structure, which was revealed using various traditionally recommended geometry-based indices. Despite this reservation, all the three systems were shown to have similar band structures, density of states, and carrier effective masses of conducting holes and electrons, as well as the nature of the real and imaginary parts of their dielectric function, absorption coefficient, refractive index, and photoconductivity spectra. The small changes observed in any specific property of the series A2AgCrBr6 were due to the changes in the lattice properties driven by alkali substitution at the A site. A comparison with the corresponding properties of Cs2AgCrX6 (X = Cl, I) suggested that halogen substitution at the X-site can not only significantly shift the position of the onset of optical absorption found of the dielectric function, absorption coefficient and refractive spectra of Cs2AgCrCl6 and Cs2AgCrI6 toward the high- and low-energy infrared regions, respectively; but that it is also responsible in modifying their stability, electronic, transport, and optical absorption preferences. The large value of the high frequency dielectric constants-together with the appreciable magnitude of absorption coefficients and refractive indices, small values of effective masses of conducting electrons and holes, and the indirect nature of the bandgap transitions, among others-suggested that cubic A2AgCrBr6 (A = Rb, Cs) and Cs2AgCrCl6 may likely be a set of optoelectronic materials for subsequent experimental characterizations.

C70 Fullerene Cage as a Novel Catalyst for Efficient Proton Transfer Reactions between Small Molecules: A Theoretical study

When acids are supplied with an excess electron (or placed in an Ar or the more polarizable N₂ matrix) in the presence of species such as NH₃, the formation of ion-pairs is a likely outcome. Using density functional theory and first-principles calculations, however, we show that, without supplying an external electron or an electric field, or introducing photo-excitation and -ionization, a single molecule of HCl or HBr in the presence of a single molecule of water inside a C₇₀ fullerene cage is susceptible to cleavage of the σ-bond of the Brønsted-Lowry acid into X⁻ and H⁺ ions, with concomitant transfer of the proton along the reaction coordinate. This leads to the formation of an X⁻···⁺HOH₂ (X = Cl, Br) conjugate acid-base ion-pair, similar to the structure in water of a Zundel ion. This process is unlikely to occur in other fullerene derivatives in the presence of H₂O without significantly affecting the geometry of the carbon cage, suggesting that the interior of C₇₀ is an ideal catalytic platform for proton transfer reactions and the design of related novel materials. By contrast, when a single molecule of HF is reacted with a single molecule of H₂O inside the C₇₀ cage, partial proton transfers from HF to H₂O is an immediate consequence, as recently observed experimentally. The geometrical, energetic, electron density, orbital, optoelectronic and vibrational characteristics supporting these observations are presented. In contrast with the views that have been advanced in several recent studies, we show that the encaged species experiences significant non-covalent interaction with the interior of the cage. We also show that the inability of current experiments to detect many infrared active vibrational bands of the endo species in these systems is likely to be a consequence of the substantial electrostatic screening effect of the cage.

Halogen Bonding: A Halogen-Centered Noncovalent Interaction Yet to Be Understood

In addition to the underlying basic concepts and early recognition of halogen bonding, this paper reviews the conflicting views that consistently appear in the area of noncovalent interactions and the ability of covalently bonded halogen atoms in molecules to participate in noncovalent interactions that contribute to packing in the solid-state. It may be relatively straightforward to identify Type-II halogen bonding between atoms using the conceptual framework of σ-hole theory, especially when the interaction is linear and is formed between the axial positive region (σ-hole) on the halogen in one monomer and a negative site on a second interacting monomer. A σ-hole is an electron density deficient region on the halogen atom X opposite to the R–X covalent bond, where R is the remainder part of the molecule. However, it is not trivial to do so when secondary interactions are involved as the directionality of the interaction is significantly affected. We show, by providing some specific examples, that halogen bonds do not always follow the strict Type-II topology, and the occurrence of Type-I and -III halogen-centered contacts in crystals is very difficult to predict. In many instances, Type-I halogen-centered contacts appear simultaneously with Type-II halogen bonds. We employed the Independent Gradient Model, a recently proposed electron density approach for probing strong and weak interactions in molecular domains, to show that this is a very useful tool in unraveling the chemistry of halogen-assisted noncovalent interactions, especially in the weak bonding regime. Wherever possible, we have attempted to connect some of these results with those reported previously. Though useful for studying interactions of reasonable strength, IUPAC’s proposed “less than the sum of the van der Waals radii” criterion should not always be assumed as a necessary and sufficient feature to reveal weakly bound interactions, since in many crystals the attractive interaction happens to occur between the midpoint of a bond, or the junction region, and a positive or negative site.

Significance of hydrogen bonding and other noncovalent interactions in determining octahedral tilting in the CH3NH3PbI3 hybrid organic-inorganic halide perovskite solar cell semiconductor

The CH₃NH₃PbI₃ (methylammonium lead triiodide) perovskite semiconductor system has been viewed as a blockbuster research material during the last five years. Because of its complicated architecture, several of its technological, physical and geometrical issues have been examined many times. Yet this has not assisted in overcoming a number of problems in the field nor in enabling the material to be marketed. For instance, these studies have not clarified the nature and type of hydrogen bonding and other noncovalent interactions involved; the origin of hysteresis; the actual role of the methylammonium cation; the nature of polarity associated with the tetragonal geometry; the unusual origin of various frontier orbital contributions to the conduction band minimum; the underlying phenomena of spin-orbit coupling that causes significant bandgap reduction; and the nature of direct-to-indirect bandgap transition features. Arising from many recent reports, it is now a common belief that the I···H–N interaction formed between the inorganic framework and the ammonium group of CH₃NH₃⁺ is the only hydrogen bonded interaction responsible for all temperature-dependent geometrical polymorphs of the system, including the most stable one that persists at low-temperatures, and the significance of all other noncovalent interactions has been overlooked. This study focussed only on the low temperature orthorhombic polymorph of CH₃NH₃PbI₃ and CD₃ND₃PbI₃, where D refers deuterium. Together with QTAIM, DORI and RDG based charge density analyses, the results of density functional theory calculations with PBE with and without van der Waals corrections demonstrate that the prevailing view of hydrogen bonding in CH₃NH₃PbI₃ is misleading as it does not alone determine the a⁻b⁺a⁻ tilting pattern of the PbI₆⁴⁻ octahedra. This study suggests that it is not only the I···H/D–N, but also the I···H/D–C hydrogen/deuterium bonding and other noncovalent interactions (viz. tetrel-, pnictogen- and lump-hole bonding interactions) that are ubiquitous in the orthorhombic CH₃NH₃PbI₃/CD₃ND₃PbI₃ perovskite geometry. Their interplay determines the overall geometry of the polymorph, and are therefore responsible in part for the emergence of the functional optical properties of this material. This study also suggests that these interactions should not be regarded as the sole determinants of octahedral tilting since lattice dynamics is known to play a critical role as well, a common feature in many inorganic perovskites both in the presence and the absence of the encaged cation, as in CsPbI₃/WO₃ perovskites, for example.