The future of topological analysis in experimental charge-density research

The electron density: a fidelity witness for quantum computation

There is currently no combination of quantum hardware and algorithms that can provide an advantage over conventional calculations of molecules or materials. However, if or when such a point is reached, new strategies will be needed to verify predictions made using quantum devices. We propose that the electron density, obtained through experimental or computational means, can serve as a robust benchmark for validating the accuracy of quantum computation of chemistry. An initial exploration into topological features of electron densities, facilitated by quantum computation, is presented here as a proof of concept. Additionally, we examine the effects of constraining and symmetrizing measured one-particle reduced density matrices on noise-driven errors in the electron density distribution. We emphasize the potential benefits and future need for high-quality electron densities derived from diffraction experiments for validating classically intractable quantum computations of materials.

Understanding Hygroscopicity of Theophylline via a Novel Cocrystal Polymorph: A Charge Density Study

The charge density distribution in a novel cocrystal (1) complex of 1,3-dimethylxanthine (theophylline) and propanedioic acid (malonic acid) has been determined. The molecules crystallize in the triclinic, centrosymmetric space group P1̅, with four independent molecules (Z = 4) in the asymmetric unit (two molecules each of theophylline and malonic acid). Theophylline has a notably high hygroscopic nature, and numerous cocrystals have shown a significant improvement in stability to humidity. A charge density study of the novel polymorph has identified interesting theoretical results correlating the stability enhancement of theophylline via cocrystallization. Topological analysis of the electron density highlighted key differences (up to 17.8) in Laplacian (∇²ρ) between the experimental (EXP) and single-point (SP) models, mainly around intermolecular-bonded carbonyls. Further investigation via molecular electrostatic potential maps reaffirmed that the charge redistribution enhanced intramolecular hydrogen bonding, predominantly for N(2') and N(2) (61.2 and 61.8 kJ mol^-1, respectively). An overall weaker lattice energy of the triclinic form (-126.1 kJ mol^-1) compared to that of the monoclinic form (-133.8 kJ mol^-1) suggests a lower energy threshold to overcome to initiate dissociation. Future work via physical testing of the novel cocrystal in both dissolution and solubility will further solidify the correlation between theoretical and experimental results.

Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions

Two pressure-induced phase transitions have been theoretically studied in the layered iron phosphorus triselenide (FePSe₃ ). Topological analysis of chemical bonding in FePSe₃ has been performed based on the results of first-principles calculations within the periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. The first transition at about 6 GPa is accompanied by the symmetry change from R 3 ¯ to C2/m, whereas the semiconductor-to-metal transition (SMT) occurs at about 13 GPa leading to the symmetry change from C2/m to P 3 ¯ 1 m . We found that the collapse of the band gap at about 13 GPa occurs due to changes in the electronic structure of FePSe₃ induced by relative displacements of phosphorus or selenium atoms along the c-axis direction under pressure. The results of the topological analysis of the electron density and its Laplacian demonstrate that the pressure changes not only the interatomic distances but also the bond nature between the intralayer and interlayer phosphorus atoms. The interlayer P-P interactions are absent in two non-metallic FePSe₃ phases while after SMT the intralayer P-P interactions weaken and the interlayer P-P interactions appear.

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18-Crown-6/Urea (1:5) Host-Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis

High-resolution synchrotron and neutron single-crystal diffraction data of 18-crown-6/(pentakis)urea measured at 30 K are combined, with the aim of better appreciating the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown-6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a cocrystal or host-guest system incorporating such a large number of unique molecules. The dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared to values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range of 10-19 GV m^-1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

Atomic Charges in Describing Properties of Aromatic Molecules

The performance of four frequently employed population analysis methods is assessed by comparisons with experimentally derived properties of monosubstituted benzene derivatives. The analysis is based on the expected dependence between site reactivities and electron densities at the respective ring carbon atoms. The correspondence between charges obtained from Mulliken, NPA, Hirshfeld, and QTAIM approaches and the σ⁰_m and σ⁰_p aromatic substituent constants is examined. The series of molecules investigated includes benzene and 18 monosubstituted derivatives. The atomic charges are derived using the B3LYP, ωB97X-D density functional, and MP2 MO methods combined with the 6-311++G(3df,2pd) basis set. A quantitative correspondence between Hirshfeld charges and σ⁰ constants is established. Application of Møller-Plesset second-order perturbation theory (MP2) wave functions appears to be essential in obtaining a more realistic electron density distribution. NPA and QTAIM charges provide in most cases a satisfactory description of the substituent effects. The net transfer of charges between substituents and the aromatic ring is assessed.

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.

Bond Ellipticity Alternation: An Accurate Descriptor of the Nonlinear Optical Properties of π-Conjugated Chromophores

Well-defined structure-property relationships offer a conceptual basis to afford a priori design principles to develop novel π-conjugated molecular and polymer materials for nonlinear optical (NLO) applications. Here, we introduce the bond ellipticity alternation (BEA) as a robust parameter to assess the NLO characteristics of organic chromophores and illustrate its effectiveness in the case of streptocyanines. BEA is based on the symmetry of the electron density, a physical observable that can be determined from experimental X-ray electron densities or from quantum-chemical calculations. Through comparisons to the well-established bond-length alternation and π-bond order alternation parameters, we demonstrate the generality of BEA to foreshadow NLO characteristics and underline that, in the case of large electric fields, BEA is a more reliable descriptor. Hence, this study introduces BEA as a prominent descriptor of organic chromophores of interest for NLO applications.

Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids

The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points, i.e. such that ∇ρ(x_c) = 0 and λ₁, λ₂, λ₃ ≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at x_c], towards degenerate critical points, i.e. ∇ρ(x_c) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of x_c and allows one to rationalize the occurrence of instability in terms of electron-density topology and Gibbs energy. The phase/state transitions that TiO₂ (rutile structure), MgO (periclase structure) and Al₂O₃ (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3-5% is observed between the theoretical model and experimental pressure/temperature of transformation.