Hirshfeld Atoms Research Articles

Cocrystal of 4,5′-dinitro-3′H-2,4′-bi(1,2,3-triazole) and imidazole: A promising strategy for development of heat-resistant energetic materials

Improving stability is one of the pursuits of exploring energetic materials, and co-crystallization technology is one of the research approaches to achieve this goal. A heat-resistant energetic cocrystal combining 4,5′-dinitro-3′H-2,4′-bi(1,2,3-triazole) (DNBTA) and imidazole was synthesized and confirmed by single-crystal X-ray diffraction. Its physicochemical properties were fully investigated and pleasantly found that it has excellent mechanical stabilities (IS > 40 J, FS > 360 N) and thermal stability (Td = 313 °C), which is much higher than the DNBTA (Td = 195 °C). It was well explained by crystal structures, noncovalent interaction (NCI), electrostatic potentials (ESP), Hirshfeld surface analysis and atoms in molecules (AIM) theory. This work highlights the influence of energetic properties by the co-crystallization technology and reaffirmed its important position in the field of heat-resistant energetic compounds.

Multi-aspect simulation insight on thermolysis mechanism and interaction of NTO/HMX-based plastic-bonded explosives: a new conception of the mixed explosive model.

Reactive molecular dynamics (RMDs) calculations were used to determine, for the first time, the process of thermolysis of the mixed explosives, including 3-nitro-1,2,4-triazol-5-one (NTO) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoline (HMX). Significantly, this is the first time that a layered model for mixed explosives, which is an extreme innovation of mixed explosive models was adopted. It is shown that a large amount of NO2 in the HMX and OH groups generated by the decomposition of HNO2 has a favorable effect on the thermolysis of NTO, as further validated by a reduction in the activation energy of NTO/HMX. The amount of H2O and N2 in the resulting products increased significantly, but the amount of NH3 changed slightly. The analysis results correspond to the change in chemical bonds. Whenever there is an increase in temperature, the time for the maximum number of clusters to appear is shortened accordingly. In addition, the acidity of NTO has been considered. An independent gradient model based on Hirshfeld partition (IGMH) and atoms in molecule (AIM) analysis of NTO/HMX was implemented. The relatively strong hydrogen bonds indicate that HMX can inhibit the acidity of NTO and is beneficial for the wide application of NTO/HMX-based plastic-bonded explosives (PBXs).

Insight into the effect of anions on cycloaddition of CO2 catalyzed by carboxylate anion-based ionic liquids: A theoretical study by QM and MD

Elucidating the mechanism of carbon dioxide (CO2) cycloaddition reaction catalyzed by ionic liquid (ILs) facilitates the rational design of efficient IL catalysts at the molecular level. To date, a great deal of research has been devoted to the halogen-containing ILs, however, the catalytic mechanism of halogen-free ILs remains unclear. In this contribution, an exhaustive theoretical study of the coupling reaction of CO2 with epichlorohydrin (ECH) catalyzed by three halogen-free ILs has been carried out for the first time by combining density functional theory (DFT) calculations with molecular dynamics (MD) simulations. Meanwhile, the effect of carboxylate anion structure on catalytic activity is deeply investigated. The final results provide a comprehensive catalytic mechanism of carboxylate anion-based ILs. The most favorable mechanism involves three steps, i.e., ring-opening of ECH, CO2 insertion, and ring-closure to form the product. Among them, the ring-opening of ECH is the rate-determining step (RDS). Additionally, the analytical results of the independent gradient model based on Hirshfeld partition (IGMH) and atoms in molecules (AIM) suggest that the electrophilic activation from carboxylate anions plays a critical role in promoting the ECH ring-opening process. The electrophilic activation of anions is investigated for the first time in this work. The results indicate that incorporating electrophilic groups into anions is a promising pathway to develop new robust and efficient halogen-free ILs.

Investigation of optical, TD-DFT calculation and electrical conductivity in semiconducting [(CH3)NH3]2ZnBr4

Hybrid Organic-inorganic materials are the most promising systems in the optoelectronic and photovoltaic fields with other potential applications. In this work, the [(CH3)NH3]2ZnBr4 compound was successfully prepared using a slow evaporation solution growth method at room temperature. The XRPD (X-ray powder diffraction) analysis showed the formation of a single-phase with monoclinic structure (P21/c space group). The morphology of the powder was examined using Scanning Electron Microscopy (SEM), and the Energy Dispersive X-ray Spectroscopy (EDS) analysis was performed for a chemical characterization. The optical absorption measurement was investigated by UV-vis absorption, confirming the semiconductor nature with a band gap around 2.87 eV. Additionally, absorption spectrum and HOMO-LUMO gap energy are calculated using TD-DFT method. The nature and the strength of intermolecular interactions between organic and inorganic species are discussed through Hirshfeld surfaces (HS) and Atoms In Molecules (AIM) analysis. The analysis of complex impedance spectra shows that the electrical properties of the material are heavily dependent on frequency and temperature, indicating a relaxation phenomenon and semiconductor-type behavior. The Nyquist plots (-Z″ vs. Z′) revealed the presence of two contributions at different temperatures associated with grain and grain boundary. The obtained results have been adjusted using two circuits in series containing each one a resistance in parallel to a CPE capacitance. The temperature dependence of the bulk conductivity was found to obey the Arrhenius law with activation energies are: Ea1= 1.55 eV in phase I and Ea2= 1.21 eV in phase II. The evolution of the dielectric constant as a function of temperature has been investigated in order to discuss the mechanism of the phase transition.

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review.

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate.

The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.

Interacting Subsystems and Their Molecular Ensembles

The molecular density-partition problem is reexamined and the information-theoretic (IT) justification of the stockholder division rule is summarized. The ensemble representations of the promolecular and molecular mixed states of constituent atoms are identified and the electron probabilities in the isoelectronic stockholder atoms-in-molecules (AIM) are used to define the molecular-orbital ensembles for the bonded Hirshfeld atoms. In the pure quantum state of the whole molecular system its interacting (entangled) fragments are described by the subsystem density operators, with the subsystem physical properties being generated by the partial traces involving the fragment density matrices.

Improved Atoms-in-Molecule Charge Partitioning Functional for Simultaneously Reproducing the Electrostatic Potential and Chemical States in Periodic and Nonperiodic Materials.

We develop a nonempirical atoms-in-molecules (AIM) method for computing net atomic charges that simultaneously reproduce chemical states of atoms in a material and the electrostatic potential V(r) outside its electron distribution. This method gives accurate results for a variety of periodic and nonperiodic materials including molecular systems, solid surfaces, porous solids, and nonporous solids. This method, called DDEC/c3, improves upon our previously published DDEC/c2 method (Manz, T. A.; Sholl, D. S. J. Chem. Theory Comput. 2010, 6, 2455-2468) by accurately treating nonporous solids with short bond lengths. Starting with the theory all AIM charge partitioning functionals with spherically symmetric atomic weights must satisfy, the form of the DDEC/c3 functional is derived from first principles. The method is designed to converge robustly by avoiding conditions that lead to nearly flat optimization landscapes. In addition to net atomic charges, the method can also compute atomic multipoles and atomic spin moments. Calculations performed on a variety of systems demonstrate the method's accuracy, computational efficiency, and good agreement with available experimental data. Comparisons to a variety of other charge assignment methods (Bader, natural population analysis, electrostatic potential fitting, Hirshfeld, iterative Hirshfeld, and iterative stockholder atoms) show that the DDEC/c3 net atomic charges are well-suited for constructing flexible force-fields for atomistic simulations.

A computational study on conformational geometries, chemical reactivity and inhibitor property of an alkaloid bicuculline with γ-aminobutyric acid (GABA) by DFT

Bicuculline – a plant alkaloid is an important molecule of current pharmaceutical interest. It is a competitive antagonist of γ-aminobutyric acid (GABA), particularly of GABAA receptor activation. The antagonistic behavior of BIC with GABAA receptor has been evaluated with the help of quantum chemical calculations. The equilibrium structures of bicuculline conformers have been obtained by geometry optimizations using density functional theory (DFT) calculations at the B3LYP/6-311G(d,p) level of theory. The conformational flexibility of bicuculline has been investigated because of its importance as an apparently specific antagonist of the neurotransmitter GABA. Dipole moment and first hyperpolarizability analysis of BIC have also been performed. For predicting inhibitor properties of BIC, the specific site of interaction of BIC with GABA receptor has been calculated with the help of global and local reactivity descriptors using DFT. Condensed Fukui functions, relative nucleophilicity and electrophilicity indices of BIC and GABA receptor for electrophilic or nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.

Crystal-field effects inL-homoserine: multipolesversusquantum chemistry

In contrast to an isolated molecule with identical geometry, the electron density of a molecule in the crystalline solid state is influenced by the field of surrounding molecules and by intermolecular hydrogen bonding. These influences have not yet found wide study on the level of the molecular electron-density distribution, which can be obtained both from high-resolution X-ray single-crystal diffraction as well as from ab initio quantum chemistry. To investigate this `crystal-field effect' on the non-standard amino acid l-homoserine, three approaches were taken: (i) an ab initio point-charge isolated-molecule model; (ii) structure refinement with Hirshfeld atoms with and without surrounding point charges and dipoles; (iii) benchmark periodic calculations using density functional theory. For (i) and (iii) multipole models were fitted to static structure factors. The difference between the electron density obtained from the respective in-crystal model and from the isolated-molecular calculations yields detailed information on the crystal-field effect and dipole-moment enhancements. The point-charge model produces features of interaction density which are in good agreement with those from periodic ab initio quantum chemistry. On the other hand the multipole model is unable to reproduce fine details of the interaction density for zwitterionic homoserine.

Electron number distribution functions with iterative Hirshfeld atoms

Electron number distribution functions (EDF) for the fuzzy domains of the recently defined iterative Hirshfeld or stockholder atoms are considered for the first time. We obtain these EDFs for a set of test molecules and compare them to those coming from other fuzzy (standard Hirshfeld) and exhaustive (Quantum Theory of Atoms in Molecules) partitionings of the real space. Our results show that iterative Hirshfeld EDFs are clearly better than the ones obtained with the standard Hirshfeld partitioning. However, due to the overlapping character of the self-consistent Hirshfeld densities, the highly ionic resonant structures are less populated than in the QTAIM EDFs. Electron correlation effects on the EDFs are also briefly discussed.

Entropic descriptors of the chemical bond in H2: local resolution of stockholder atoms

The information systems of the local spatial “events” of two-electrons in the stockholder atoms-in-molecules (AIM) are established for the three-representative states of the hydrogen molecule in the minimum basis set description: the ground (bonding, singlet) state, the singly-excited (non-bonding, triplet) state describing the free atoms of the system “promolecule”, and the doubly-excited (anti-bonding, singlet) state. The Hirshfeld atoms reflect the molecular electron densities thus reflecting the bonding and anti-bonding polarizations of AIM in the corresponding molecular states. Their integral entropy-covalency and information-ionicity descriptors are expressed in terms of the relevant Shannon entropies of the molecular/promolecular and atomic probability distributions of electrons, the numerical values of which have been previously reported. The resulting estimates of the information-theoretic bond indices provide the entropic “fingerprints” of the bonding conditions in these three prototype electron configurations, which reflect upon the associated displacements in the information contained in the molecular electronic distribution relative to the initial, promolecular reference. A brief discussion of such changes due to the AIM contraction and/or promotion in the molecule and their mutual polarizations implied by the bonding/antibonding character of the molecular state is presented. This analysis uncovers the information origins of the covalent bond in this prototype molecular system.

X-ray structure refinement using aspherical atomic density functions obtained from quantum-mechanical calculations

An approach is outlined for X-ray structure refinement using atomic density fragments obtained by Hirshfeld partitioning of quantum-mechanical density fragments. Results are presented for crystal structure refinements of urea and benzene using these 'Hirshfeld atoms'. Using this procedure, the quantum-mechanical non-spherical electron density is taken into account in the structural model based on the conformation found in the crystal. Contrary to current consensus in structure refinement, the anisotropic displacement parameters of H atoms can be reproduced from neutron diffraction measurements simply from a least-squares fit using the Hirshfeld atoms derived from the BLYP level of theory and including a simple point-charge model to treat the crystal environment.

Critical analysis and extension of the Hirshfeld atoms in molecules

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges.

Hartree–Fock Energy Partitioning in Terms of Hirshfeld Atoms

A Hirshfeld decomposition scheme of the Hartree-Fock total molecular energy into atomic energies is presented. The calculations are performed by direct numerical integration and the results are compared for a set of 28 molecules containing different kinds of atoms. The calculated atomic energies show a strong dependency on changes of atomic electron population and hybridization. Linear correlations are found between the energy and the population for H, these being related to the electronegativity of this atom and to the external potential created by the remaining atoms. The proposed energy partitioning scheme appears to be useful for studies such as proton acidity, the anomeric effect and group transferability, and allows atomic virial ratios to be obtained. Finally, the atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.

What Is an Atom in a Molecule?

The derivation of the Hirshfeld atoms in molecules from information theory is clarified. The importance for chemistry of the concept of atoms in molecules (AIM) is stressed, and it is argued that this concept, while highly useful, constitutes a noumenon in the sense of Kant.

Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density.

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.