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.

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 CH₃NH₃PbI₃and 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 CH₃NH₃PbI₃is misleading as it does not alone determine thea⁻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/CD₃ND₃PbI₃perovskite 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/WO₃perovskites, for example.

Can two sites of positive electrostatic potential localized on the outer surfaces of two halogen atoms (and especially fluorine) in different molecular domains attract each other to form a non-covalent engagement? The answer, perhaps counterintuitive, is yes as shown here using the electronic structures and binding energies of the interactions for a series of 22 binary complexes formed between identical or different atomic domains in similar or related halogen-substituted molecules containing fluorine. These were obtained using various computational approaches, including density functional and ab initio first-principles theories with M06-2X, RHF, MP2 and CCSD(T). The physical chemistry of non-covalent bonding interactions in these complexes was explored using both Quantum Theory of Atoms in Molecules and Symmetry Adapted Perturbation Theories. The surface reactivity of the 17 monomers was examined using the Molecular Electrostatic Surface Potential approach. We have demonstrated inter alia that the dispersion term, the significance of which is not always appreciated, which emerges either from an energy decomposition analysis, or from a correlated calculation, plays a structure-determining role, although other contributions arising from electrostatic, exchange-repulsion and polarization effects are also important. The 0.0010 a.u. isodensity envelope, often used for mapping the electrostatic potential is found to provide incorrect information about the complete nature of the surface reactive sites on some of the isolated monomers, and can lead to a misinterpretation of the results obtained.

The definition of the term “tetrel bond” and instances of its occurance in chemical systems are proposed based on the evidence documented in the current literature.

A-Site doping with alkali ions, and/or metal substitution at the B and B′-sites, are among the key strategies in the innovative development of A₂BB′X₆ halide double perovskite semiconducting materials for application in energy and device technologies. To this end, we have investigated an intriguing series of five halide-based non-toxic systems, A₂AgRhCl₆ (A = Li, Na, K, Rb, and Cs), using density functional theory at the SCAN-rVV10 level. The lattice stability and bonding properties emanating from this study of A₂AgRhCl₆ matched well with those that have already been synthesized, characterized and discussed [viz. Cs₂AgBiX₆ (X = Cl, Br)]. Exploration of traditional and recently proposed tolerance factors has enabled us to identify A₂AgRhCl₆ (A = K, Rb and Cs) as stable double perovskites. The band structure and density of states calculations suggested that the electronic transition from the top of the valence band [Cl(3p)+Rh(4d)] to the bottom of the conduction band [(Cl(3p)+Rh(4d)] is inherently direct at the X-point of the first Brillouin zone. The (non-spin polarized) bandgap of these materials was found in the range 0.57–0.65 eV with SCAN-rVV10, which were substantially smaller than those computed with hybrid HSE06 and PBE0, and quasi-particle GW methods. This, together with the appreciable refractive index and high absorption coefficient in the region covering the range 1.0–4.5 eV, enabled us to demonstrate that A₂AgRhCl₆ (A = K, Rb, and Cs) are likely candidate materials for photoelectric applications. The results of our phonon calculations at the harmonic level suggested that the Cs₂AgRhCl₆ is the only system that is dynamically stable (no imaginary frequencies found around the high symmetry lines of the reciprocal lattice), although the elastic moduli properties suggested all five systems examined are mechanically stable.

Spin-unrestricted DFT-X3LYP/6-311++G(d,p) calculations have been performed on a series of complexes of the form [Co(H₂O)_6−n(NH₃)_n]²⁺ (n = 0–6) to examine their equilibrium gas-phase structures, energetics, and electronic properties in their quartet electronic ground states. In all cases Co²⁺ in the energy-minimised structures is in a pseudo-octahedral environment. The calculations overestimate the Co–O and Co–N bond lengths by 0.04 and 0.08 Å, respectively, compared to the crystallographically observed mean values. There is a very small Jahn–Teller distortion in the structure of [Co(H₂O)₆]²⁺ which is in contrast to the very marked distortions observed in most (but not all) structures of this cation that have been observed experimentally. The successive replacement of ligated H₂O by NH₃ leads to an increase in complex stability by 6 ± 1 kcal mol⁻¹ per additional NH₃ ligand. Calculations using UB3LYP give stabilisation energies of the complexes about 5 kcal mol⁻¹ smaller and metal–ligand bond lengths about 0.005 Å longer than the X3LYP values since the X3LYP level accounts for the London dispersion energy contribution to the overall stabilisation energy whilst it is largely missing at the B3LYP level. From a natural population analysis (NPA) it is shown that the formation of these complexes is accompanied by ligand-to-metal charge transfer the extent of which increases with the number of NH₃ ligands in the coordination sphere of Co²⁺ . From an examination of the topological properties of the electron charge density using Bader’s quantum theory of atoms in molecules it is shown that the electron density ρ_c at the Co–O bond critical points is generally smaller than that at the Co–N bond critical points. Hence Co–O bonds are weaker than Co–N bonds in these complexes and the stability increases as NH₃ replaces H₂O in the metal’s coordination sphere. Several indicators, including the sign and magnitude of the Laplacian of the charge density ∇²ρ_c , the ratio of the local potential and kinetic energy densities, |V_c|/G_c , the sign of the total energy density H_c, and the delocalisation index δ(Co,X), X = O, N, are used to show that whilst the metal–ligand bonds are predominantly ionic in nature, they gain covalent character as NH₃ replaces H₂O, and the Co–N bond is significantly more covalent than the Co–O bond. We have shown that the delocalisation index δ(Co,X), X = O, N, is strongly correlated with the zero-point corrected stabilisation energy E^c _d demonstrating that δ can be used as a measure of the bond stability in these complexes.