Development of a multipopulation parallel genetic algorithm for structure solution from powder diffraction data

Previously, the genetic algorithm (GA) approach for direct-space crystal structure solution from powder diffraction data has been applied successfully in the structure determination of a range of organic molecular materials. In this article, we present a further development of our approach, namely a multipopulation parallel GA (PGA), which is shown to give rise to increased speed, efficiency, and reliability of structure solution calculations, as well as providing new opportunities for further optimizing our GA methodology. The multipopulation PGA is based on the independent evolution of different subpopulations, with occasional interaction (e.g., transfer of structures) allowed to occur between the different subpopulations. Different strategies for carrying out this interpopulation communication are considered in this article, and comparisons are made to the conventional single-population GA. The increased power offered by the PGA approach creates the opportunity for structure determination of molecular crystals of increasing complexity.     

Polymorph Identification and Crystal Structure Determination by a Combined Crystal Structure Prediction and Transmission Electron Microscopy Approach

Electron diffraction offers advantages over X‐ray based methods for crystal structure determination because it can be applied to sub‐micron sized crystallites, and picogram quantities of material. For molecular organic species, however, crystal structure determination with electron diffraction is hindered by rapid crystal deterioration in the electron beam, limiting the amount of diffraction data that can be collected, and by the effect of dynamical scattering on reflection intensities. Automated electron diffraction tomography provides one possible solution. We demonstrate here, however, an alternative approach in which a set of putative crystal structures of the compound of interest is generated by crystal structure prediction methods and electron diffraction is used to determine which of these putative structures is experimentally observed. This approach enables the advantages of electron diffraction to be exploited, while avoiding the need to obtain large amounts of diffraction data or accurate reflection intensities. We demonstrate the application of the methodology to the pharmaceutical compounds paracetamol, scyllo‐inositol and theophylline.     

Molecular structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid have been determined by gas-phase electron diffraction using results from quantum chemical calculations to inform the choice of restraints applied to some of the structural parameters. The results from the study presented here demonstrate that resonance hybrids are not as helpful in rationalizing the structures of 2-, 3-, and 4-hydroxybenzoic acids as are models based upon electrostatic effects.     

First experimental characterization of a non-nuclear attractor in a dimeric magnesium(I) compound

High-resolution X-ray diffraction data, coupled with theoretical calculations, are used to demonstrate the presence of a non-nuclear local maximum in the electron density of a dimeric Mg(I) molecule. This is the first time such a non-nuclear attractor (NNA) has been observed in a stable molecular species. Multipole modeling of the Mg(I) centers requires use of expansion/contraction (κ) coefficients taken from density functional theory (DFT), since accurate scattering factors for Mg(I) are not available. The model developed accurately accounts for the electron density in the Mg-Mg region and is in excellent agreement with directly calculated DFT data. Within the quantum theory of atoms in molecules (QTAIM), this molecule is not bound by a Mg-Mg bond but rather by two Mg-"pseudo-atom" bonds. The NNA is associated with a large region of negative Laplacian in the Mg-Mg internuclear region and arises from the overlap of 3s orbitals in this long, nonpolar "bond". The pseudoatomic basin associated with the NNA contains 0.8 electrons, which are highly delocalized and hence weakly bound. Possible implications of this unusual electronic structure for the chemistry of such molecules, including their use as excellent reducing agents, are discussed.     

Coulomb and overlap self-similarities: a comparative selectivity analysis of structure-function relationships for auxin-like molecules

Auxins are defined mainly by a set of physiological actions, but the structure-effect relationship still is based on chemical intuition. Currently a well-defined auxin molecular structure is not available. The existence of different auxin binding proteins and mechanisms of auxin action, the wide diversity of the auxin molecules, and the pleiotropic effects of auxin imply a completely different mechanism as described for the animal hormone concept. Here, we present a computational approach dealing with semiempirical optimizations of the auxin molecules themselves, which represent a number of about 250 different chemical structures. Our approach uses molecular quantum similarity measures and additional quantum variables for the analysis of auxin-like molecules. The finding of similarities in molecules by focusing basically on their electron structure results in new insights in the relationship of the different auxin groups. Additional statistical analysis allows the identification of relationships between similarity groups and their biological activity, respectively. It is postulated that the auxin-like molecular recognition depends more on specific molecular assembling states than on a specific ring system or side chain.     

A bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles

We describe a bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles. In this method, we apply a many-body scaling function (in similar manner as in the environment-modified total energy based tight-binding method) to the DFT-derived diatomic AO interaction potentials (like in the conventional orbital-based density-functional tight binding approach) strictly according to atomic valences acquired naturally in a bulk structure. This modification, (a) facilitates all atom orbital-based electronic structure calculations of charge carrier dynamics in nanoscale structures with a molecular acceptor, and (b) allows to closely match high-level density functional calculation data (previously adjusted to the available experimental findings) for bulk structures. To advance practical application of the BA-LCAO approach we parameterize the Hamiltonian of wurtzite CdSe by fitting its band structure to a high-level DFT reference, corrected for experimentally measured band edges. Here, unlike in conventional DFTB approach, we: (1) use hydrogen-like AOs for the basis as exact atomic eigenfunctions, while orbital energies of which are taken from experimentally measured ionization potentials, and (2) parameterize the many-body scaling functions rather than the atomic wavefunctions. Development of this approach and parameters is guided by our goals to devise a method capable of simultaneously treating the problems of (i) interfacial electron/hole transfer between finite, variable size nanoparticles and electron scavenging molecules, and (ii) high-energy electronic transitions (Auger transitions) that mediate multi-exciton decay in quantum dots. Electronic structure results are described for CdSe quantum dots of various sizes. © 2018 Wiley Periodicals, Inc.     

Quantum chemical geometry optimizations in proteins using crystallographic raw data

A method is developed for the combination of quantum chemical geometry optimizations and crystallographic structure refinement. The method is implemented by integrating the quantum chemical software Turbomole with the crystallographic software Crystallography and NMR System (CNS), using three small procedures transferring information between the two programs. The program (COMQUM-X)is used to study the binding of the inhibitor N-methylmesoporphyrin to ferrochelatase, and we show that the method behaves properly and leads to an improvement of the structure of the inhibitor. It allows us to directly quantify in energy terms how much the protein distort the structure of the bound inhibitor compared to the optimum vacuum structure (4-6 kJ/mol). The approach improves the standard combined quantum chemical and molecular mechanics (QC/MM) approach by guaranteeing that the final structure is in accordance with experimental data (the reflections) and avoiding the risk of propagating errors in the crystal coordinates. The program can also be seen as an improvement of standard crystallographic refinement, providing an accurate empirical potential function for any group of interest. The results can be directly interpreted in standard crystallographic terms (e.g., R factors or electron density maps). The method can be used to interpret crystal structures (e.g., the protonation status of metal-bound water molecules) and even to locally improve them.     

Representation of the molecular topology of cyclical structures by means of cycle graphs. 2. Application to clustering of chemical databases

The great size of chemical databases and the high computational cost required in the atom-atom comparison of molecular structures for the calculation of the similarity between two chemical compounds necessitate the proposal of new clustering models with the aim of reducing the time of recovery of a set of molecules from a database that satisfies a range of similarities with regard to a given molecule pattern. In this paper we make use of the information corresponding to the cycles existing in the structure of molecules as an approach for the classification of chemical databases. The clustering method here proposed is based on the representation of the topological structure of molecules stored in chemical databases through its corresponding cycle graph. This method presents a more appropriate behavior for others described in the bibliography in which the information corresponding to the cyclicity of the molecules is also used.     

Ab Initio prediction of possible crystal structures for general organic molecules

The performance of a new crystal packing procedure for the ab initio prediction of possible molecular crystal structures is presented. The method is based upon only molecular information, i.e., no unit cell parameters are assumed to be known. The search for the global crystal energy minimum and all local minima inside an energy window is derived from Monte Carlo simulated annealing methods and has been applied to various organic molecules containing heteroatoms and polar groups. A systematic evaluation of the search method and of the quality of the potential energy function has been established. It is demonstrated that the packing of general organic molecules is possible even with standard force fields like CHARMM provided that the charges defining the electrostatic interactions are based upon physical models rather than transferable empirical parameters. Concepts of crystal packing that were based till now upon assumptions and speculations could be proved or disproved by solving directly the extended global optimization problem related to crystal packing. Crystal structures of molecules as complex as those treated in this article have not been, till now, predicted by a computational approach. In one case, a disagreement between the predicted and experimental structure was evident and, based upon the computations, we suspect that the published structure is the wrong one. © 1992 by John Wiley & Sons, Inc.     

Quantum molecular mechanics—a noniterative procedure for the fast Ab Initio calculation of closed shell systems

In this article, we advance the foundations of a strategy to develop a molecular mechanics method based not on classical mechanics and force fields but entirely on quantum mechanics and localized electron‐pair orbitals, which we call quantum molecular mechanics (QMM). Accordingly, we introduce a new manner of calculating Hartree–Fock ab initio wavefunctions of closed shell systems based on variationally preoptimized nonorthogonal electron pair orbitals constructed by linear combinations of basis functions centered on the atoms. QMM is noniterative and requires only one extremely fast inversion of a single sparse matrix to arrive to the one‐particle density matrix, to the electron density, and consequently, to the ab initio electrostatic potential around the molecular system, or cluster of molecules. Although QMM neglects the smaller polarization effects due to intermolecular interactions, it fully takes into consideration polarization effects due to the much stronger intramolecular geometry distortions. For the case of methane, we show that QMM was able to reproduce satisfactorily the energetics and polarization effects of all distortions of the molecule along the nine normal modes of vibration, well beyond the harmonic region. We present the first practical applications of the QMM method by examining, in detail, the cases of clusters of helium atoms, hydrogen molecules, methane molecules, as well as one molecule of HeH⁺ surrounded by several methane molecules. We finally advance and discuss the potentialities of an exact formula to compute the QMM total energy, in which only two center integrals are involved, provided that the fully optimized electron‐pair orbitals are known. © 2012 Wiley Periodicals, Inc.     

Properties of liquid crystal molecules from first principles computer simulation

We explore the valence charge distribution, equilibrium geometry and harmonic force fields of the 4-pentyl-4-cyanobiphenyl (5CB) molecule and the benzene (C6H6) molecule, which provides an important mesogenic fragment, using first principles techniques adapted from large scale electronic structure calculations of periodic solids. We present for the first time accurate structural data for the isolated 5CB molecule and observe subtle broken symmetries relative to the constituent mesogenic fragments. The dynamic properties of these molecules are determined by diagonalization of dynamical matrices, the elements of which are obtained directly from quantum mechanical Hellmann-Feynman forces. Results for both molecules are in excellent agreement with available spectroscopic data, and for benzene are comparable to the most accurate quantum chemistry calculations to date. For 5CB we also present values for the molecular dipole and quadrupole moments.     

Application of potential constants: Molecular chemical potential changes on formation of heteronuclear diatomic molecules—VI

The harmonic and anharmonic potential (force) constants of heteronuclear diatomic molecules, which are usually available from normal coordinate analyses, are applied to problems of determining the molecular chemical potential changes on formation of such molecules. The approach developed here is mainly based on density—functional theory, that is, the respective atomic energies in a molecule are expanded with the numbers of electrons and the nuclear potentials. These expansions are allowable because the ground-state energy for a system of N electrons and given nuclear potential ν(r) is a functional of N and ν(r). To test the reliability of the approach, we have calculated the molecular chemical potentials of alkali halides and other heteronuclear diatomic molecules, and their results have been compared favorably with the data obtained from Sanderson's Principle and the ab initio SCF calculation. We have also estimated apparent chemical hardnesses as well as integral terms including Fukui functions that provide good measures for electron transfers between atoms on molecule formation. Brief discussions on the molecular chemical potential changes are given.     

Molecular structures of free quinuclidine and its adducts with metal trihydrides, MH3 (M=B, Al or Ga), studied by gas-phase electron diffraction, X-ray diffraction and quantum chemical calculations

The structure of quinuclidine, HC(CH(2)CH(2))(3)N, has been re-investigated by quantum chemical calculations and by gas-phase electron diffraction (GED). The GED data, together with published rotational constants, have been analysed using the SARACEN method to determine the most reliable structure (r(h1)) for the gaseous molecule. The structures of two adducts of quinuclidine with group 13 trihydride molecules, MH(3) (M=B, Al), have also been determined by GED and quantum chemical calculations. The effect of the coordination of these hydrides to the quinuclidine nitrogen atom has been investigated, and the structural changes and energetics of adduct formation are discussed. We also present the crystal structure of quinuclidine borane.     

Structure of small associates of glycyrrhizic acid with cholesterol in aqueous solution: Molecular dynamics simulation

In a recent work by Zelikman et al.(J. Struct. Chem., 2015, 56(1)), the molecular dynamics simulation of dimers of glycyrrhizic acid (GA) arising from the spontaneous collision of two GA molecules in water is performed. Several relatively stable dimer structures are found, and when a cholesterol molecule is inserted, associates are observed constituting a GA dimer with a cholesterol molecule “stuck” to it. Here, we simulate the associates consisting of three and four GA molecules and a cholesterol molecule. It appears that the cholesterol molecule, as a rule, also locates at the surface of the GA associate. Therewith, the trimers do not form any clear characteristic structures, as dimers do, and the tetramers can be two stuck dimers.     

Dynamic interaction of theory and experiment: total determination of the gas-phase molecular structure of tri-tert-butylphosphine oxide (OPBut3)

A new method to aid the determination of structures of sterically crowded molecules in the gas phase by dynamically linking the gas-phase electron diffraction (GED) refinement process with computational methods has been developed. The procedure involves refining the heavy-atom skeleton of the molecule using the GED data while continually updating the light-atom positions during the refinement using computational methods, in this case molecular mechanics. This removes errors associated with the assumption of local symmetry for the light-atom groups, which can affect the final values of the heavy-atom parameters. The refinement of the molecular structure of tri-tert-butyl phosphine oxide has been used to illustrate this new technique, which we call the DYNAMITE (DYNAMic Interaction of Theory and Experiment) method. Re-examination of the structure using this method has resulted in a shorter P-O distance than was found in a less sophisticated anaylsis, and is consistent with the molecule being regarded as O=PBut3, rather than O(-)-P+But3.     

Continuous symmetry numbers and entropy

Traditionally, entropy changes are corrected for rotational permutability only if the molecule is perfectly rotationally symmetric. By this approach, only a small fraction of all known molecules must be evaluated in terms of symmetry numbers, while all other molecules are totally exempt of these considerations. A general approach which encompasses all molecules, symmetric or not, is proposed here. It is based on introducing the notion of continuity to symmetry numbers and on allowing noninteger values. In the first part of the account, we provide arguments as to why continuity is needed and what difficulties one may encounter by adopting the "black-or-white" approach to symmetry. In the second part, we provide a working methodology of how to evaluate the symmetry number content of any molecule, symmetric or not. Finally, in the third part, we demonstrate the implications of this approach on entropy issues involving melting points, Jahn-Teller distortions (of fullerene) upon ionization, molecular distortion due to overcrowdedness, permutability of isotopes, and the structure of proton sponges. It is shown that continuous symmetry numbers provide entropy values, which better agree with experimental observations, and that they are capable of identifying correlations between symmetry and physical/chemical measurables.     

How to determine structures when single crystals cannot be grown: opportunities for structure determination of molecular materials using powder diffraction data

Many crystalline solids cannot be prepared as single crystals of sufficient size and/or quality for structure determination to be carried out using single crystal X-ray diffraction techniques. In such cases, when only polycrystalline powders of a material are available, it is necessary instead to tackle structure determination using powder X-ray diffraction. This article highlights recent developments in the opportunities for determining crystal structures directly from powder diffraction data, focusing on the case of molecular solids and giving particular attention to the most challenging stage of the structure determination process, namely the structure solution stage. In particular, the direct-space strategy for structure solution is highlighted, as this approach has opened up new opportunities for the structure determination of molecular solids. The article gives an overview of the current state-of-the-art in structure determination of molecular solids from powder diffraction data. Relevant fundamental aspects of the techniques in this field are described, and examples are given to highlight the application of these techniques to determine crystal structures of molecular materials.     

Tailoring the Cu(100) work function by substituted benzenethiolate self-assembled monolayers

The structure and electronic interface properties of five differently substituted benzenethiol based self-assembled monolayers (SAMs) on Cu(100) have been studied by means of low energy electron diffraction, thermal desorption spectroscopy, X-ray absorption spectroscopy (NEXAFS), and UV photoelectron spectroscopy. Because highly ordered SAMs are formed of which lateral density had been precisely determined, effective molecular dipole moments were derived from the measured work function shifts. These values are compared with gas phase dipole moments computed by quantum chemical calculations for the individual thiol molecules considering the molecular orientation determined from NEXAFS data. Furthermore, this comparison yields clear evidence for a coverage dependent depolarization effect of the adsorbed molecules within the SAMs.     

Evolving Opportunities in Structure Solution from Powder Diffraction Data—Crystal Structure Determination of a Molecular System with Twelve Variable Torsion Angles

The genetic algorithm approach , in which a population of trial structures is allowed to evolve subject to well-defined procedures for mating, mutation, and natural selection, was employed to solve the complex molecular crystal structure of Ph₂P(O)(CH₂)₇P(O)Ph₂ directly from powder diffraction data. The structure solution reveals an interesting (perhaps unexpected) molecular conformation (see picture), which emphasizes the importance of allowing complete conformational flexibility of the molecule in the structure solution calculation.     

Direct-Space Structure Determination of Covalent Organic Frameworks from 3D Electron Diffraction Data

Structure determination of covalent organic frameworks (COFs) with atomic precision is a bottleneck that hinders the development of COF chemistry. Although three-dimensional electron diffraction (3D-ED) data has been used to solve structures of sub-micrometer-sized COFs, successful structure solution is not guaranteed as the data resolution is usually low. We demonstrate that the direct-space strategy for structure solution, implemented using a genetic algorithm (GA), is a successful approach for structure determination of COF-300 from 3D-ED data. Structural models with different geometric constraints were considered in the GA calculations, with successful structure solution achieved from room-temperature 3D-ED data with a resolution as low as ca. 3.78 Å. The generality of this strategy was further verified for different phases of COF-300. This study demonstrates a viable strategy for structure solution of COF materials from 3D-ED data of limited resolution, which may facilitate the discovery of new COF materials in the future.