Direct-space Approach Research Articles

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

Direct space approach in action: Challenging structure solution of microcrystalline materials using the EXPO software

Despite recent advances, the crystal structure solution process from powder X-ray diffraction (PXRD) data is still a challenging task. In this article, we present case studies of structure solutions using direct-space methods based on a simulated annealing approach. Representative examples of applications of the software EXPO are described in detail to provide methodological and computational tools useful to face complex cases of structure solutions from powders. We focus on the main practical aspects regarding how to build a structure model compatible with the expected molecular geometry, which tricks to use in case of low-quality diffraction data, how to decide that the obtained solution is the correct one and how to treat the most frequent sources of errors. Through six case studies, regarding the solution process of diltiazem hydrochloride, tetracycline hydrochloride, selexipag form I, catena-(Aluminophosphate hexadecakis(2-hydroxyethylamine), poly[[di-μ-aqua-bis-(glycinato-κ2N,O)calcium(II)] monohydrate] and lanthanum titanium aluminate, we give the reader, expert or new in the field, the necessary instructions for solving structure using EXPO with the help of auxiliary programs. The article highlights some of the most critical aspects of the PXRD solution process with direct-space methods for providing deep insights into both the powers and limits.

Study on Quality of Pair Distribution Function for Direct Space Approach of Structure Investigation

Study on Quality of Pair Distribution Function for Direct Space Approach of Structure Investigation

Structural, spectroscopic and first-principles studies of new aminocoumarin derivatives.

The new aminocoumarin derivatives 3-[1-(3-hydroxyanilino)ethylidene]-3H-chromene-2,4-dione, (1), 3-[1-(4-hydroxyanilino)ethylidene]-3H-chromene-2,4-dione, (2), and 3-[1-(2-hydroxyanilino)ethylidene]-3H-chromene-2,4-dione, (3), all C17H13NO4, were synthesized by reacting an equimolar amount of 3-acetyl-4-hydroxycoumarin and the corresponding aminophenol in absolute ethanol. Structural and spectroscopic analysis of these phases revealed that derivatives (1) and (2) are isomers of previously reported (3) [Brahmia et al. (2013). Acta Cryst. E69, o1296]. The crystal structures of meta derivative (1) and para derivative (2) were ab initio determined from powder X-ray diffraction data using the direct-space approach. Both (1) and (2) adopt the orthorhombic space group P212121. These isomers show hydrogen bonds and rich π-π stacking, together with π...H interactions, which are built by conjugated systems of coumarin and phenol rings. In the crystalline lattice, the packing of (1) and (3) are mainly stabilized through O-H...O hydrogen bonding between neighbouring coumarin molecules, while hydrogen bonds between coumarin and water molecules build the stable crystal structure of derivative (2). A big similarity in the skeletons of the IR spectra of these isomers was noticed. Derivative (2) exhibits two weak bands which were not present in the spectra of the other two derivatives, at 2370 and 2948 cm-1, which can be assigned to the O-H vibrations of the solvent (H2O) trapped in the structure of (2). These aminocoumarin derivatives display absorption maxima in the visible region, attributed to π-π delocalization involving the whole electronic system of the compounds with a considerable charge-transfer character originating from the aminophenyl ring and pointing towards the coumarin system which is characterized by a high electron-accepting character. Additionally, the isolated molecular ground-state geometries were optimized at the PBE0/TZP level and the electronic properties, molecular electrostatic potential and Hirshfeld charges were determined.

Four interpenetrating hydrogen-bonded three-dimensional networks in divanillin

The crystal structure of divainillin (systematic name: 6,6'-dihydroxy-5,5'-dimethoxy-[1,1'-biphenyl]-3,3'-dicarbaldehyde), C16H14O6, was determined from laboratory powder X-ray diffraction data using the software EXPO2013 (direct methods) and WinPSSP (direct-space approach). Divanillin molecules crystallize in the orthorhombic space group Pba2 (No. 32), with two molecules per unit cell (Z' = 1/2). Each divanillin molecule, with twofold symmetry, is linked through strong alcohol-aldehyde hydrogen bonds to four equivalent molecules, defining a three-dimensional hydrogen-bonding network, with rings made up of six divanillin units (a diamond-like arrangement). Each molecule is also connected through π-π interactions to a translation-equivalent molecule along c. Four consecutive molecules stacked along [001] belong to four different three-dimensional hydrogen-bonding networks defining a quadruple array of interpenetrating networks. This complex hydrogen-bonding array is proposed as an explanation for the aging process experienced by divanillin powders.

Tailoring the particle microstructures of gefitinib by supercritical CO2 anti-solvent process

Supercritical CO2 anti-solvent (SAS) process is a green and effective method to produce particles with designated microstructures. In this study, the particle microstructures of gefitinib, a potent anticancer agent, are tailored by the SAS process to improve its aqueous solubility. The dichloromethane/ethanol (1:4, v/v) was selected as the suitable solvent from typical solvents used in the SAS process at first. Then, the effects of other SAS operating parameters, i.e., the flow rate of gefitinib solution (F), the concentration of gefitinib in the solution (C), the precipitation pressure (P) and the temperature (T), on the gefitinib particle size were investigated in detail. Lower F, lower C, higher P and suitable T were recommended for the formation of gefitinib particles with small particle size. The properties of the raw material and SAS processed samples of gefitinib were characterized by different methods. The results showed that a new polymorphic form (Form β) of gefitinib, which present different physicochemical properties, i.e., smaller particle size, narrower particle size distribution and higher solubility, with raw gefitinib (Form 1), was captured after the SAS process. The predicted structures of gefitinib crystals, which were consistent with the experiments, were performed from their experimental XRD data by the direct space approach using the Reflex module of Materials Studio. Meanwhile, the SAS processed gefitinib particles showed much higher solubility and faster dissolution rate than that of raw gefitinib, which had the potential to improve its bioavailability and decrease the dose-related adverse effects.

New polymorphs of 9-nitro-camptothecin prepared using a supercritical anti-solvent process

Recrystallization and micronization of 9-nitro-camptothecin (9-NC) has been investigated using the supercritical anti-solvent (SAS) technology in this study. Five operating factors, i.e., the type of organic solvent, the concentration of 9-NC in the solution, the flow rate of 9-NC solution, the precipitation pressure and the temperature, were optimized using a selected OA16 (45) orthogonal array design and a series of characterizations were performed for all samples. The results showed that the processed 9-NC particles exhibited smaller particle size and narrower particle size distribution as compared with 9-NC raw material (Form I), and the optimum micronization conditions for preparing 9-NC with minimum particle size were determined by variance analysis, where the solvent plays the most important role in the formation and transformation of polymorphs. Three new polymorphic forms (Form II, III and IV) of 9-NC, which present different physicochemical properties, were generated after the SAS process. The predicted structures of the 9-NC crystals, which were consistent with the experiments, were performed from their experimental XRD data by the direct space approach using the Reflex module of Materials Studio. Meanwhile, the optimal sample (Form III) was proved to have higher cytotoxicity against the cancer cells, which suggested the therapeutic efficacy of 9-NC is polymorph-dependent.

Factorial design analysis for optimizing the removal of cesium and strontium ions on synthetic nano-sized zeolite

Cesium and strontium ions removal from aqueous solution onto nano-sized zeolite was investigated using uni-variant and multi-variant procedures. Nano-zeolite Y was prepared using hydrothermal method and characterized by X-ray diffraction, X-ray fluorescence, transmission electron microscopy, and Fourier transformed infrared spectroscopy. Direct space approach was adopted to simulate the crystallographic structure and calculate the chemical formula. Removal kinetics and equilibrium isotherms were studied and the reaction nature, parameters, and most suitable models to predict sorption capacity were identified using linear and non-linear regression techniques. Multi-variant procedure was used to optimize the removal process and deduce equation to predict the removal efficiency. The results indicated that the prepared material belongs to nano-dehydrated zeolite Y family and referred to the possibility of metal ion entrapping within zeolite framework. Cs+ ions have higher removal than Sr2+, and the removal is controlled by external mass transfer through the boundary within the first 40 min then controlled by intra-particle diffusion. Temperature and pH are the most influential variables, whereas initial metal concentration and time affect the process to lesser extent. Cs+ removal was found more reliable under different operating conditions than Sr2+.

Solving surface and embedded structures without Fourier inversion: a 2-dimensional direct space approach

Abstract Two-dimensional equal atom structures or structure projections are determined applying the parameter space concept, either directly or supported by coordinate indications obtained from one or two separate runs on 1-d projection(s). By-passing the “phase problem” a grid-search based trial and error technique is used for optimizing model vs. experimental quasi-normalized structure amplitudes (or intensities) of a small number of reflections. The concept can also be applied to multi-wavelengths X-ray data exhibiting resonant scattering contrasts as well as to neutron data from structures including elements with differing signs of scattering powers. Unique results (or all possible combinations of atom sites meeting the data) are obtained from rather few reflections. They provide remarkable spatial resolution, but much more computing power is needed than for standard techniques. Considering the numbers of test models to be checked as a relative measure of computing time the computational efforts for different solution options and increasing numbers of independent atoms are assessed. In the examples given for symmetry p1 , where one atom defines the origin, up to 8 additional atoms were located within Δ(x, y) ≤ 0.025 from, e.g., 12 reflections with randomly generated maximum relative intensity errors of up to 20 %. All calculations were carried out with a standard PC.

Synthesis and crystal structure of the novel metal organic framework Zn(C3H5NO2S)2

The crystal structure of the novel metal organic framework (MOF) Zn(C3H5NO2S)2 is described. This MOF can serve as a model for active sites in metalloproteins, on diverse activities such as structural or catalytic functions. Each half of the amino acid act as a bidentate ligand to one Zn and as a monodentate ligand to another Zn, while the disulphide bond presents an important structural function, stabilizing the crystal packing. The structure has been obtained ab initio from synchrotron X-ray powder diffraction data. The compound crystallizes in the orthorhombic system (space group P212121), with a = 20.0906(7), b = 9.5842(3), c = 5.018 89(13), and V = 966.40(5) Å3, with Z = 4. The structure was determined using a direct space approach, by means of the Monte Carlo technique, followed by Rietveld refinement.

Ab initio and DFT study on Cu (II) complex salicylate derivative

X -ray diffraction becomes a routine process these decades for determining crystal structure of the materials. Most of the crystal structures solved nowadays is based on single crystal X-ray diffraction because it solves the crystal and molecular structures from small molecules to macro molecules without much human intervention. However it is difficult to grow single crystals of sufficient size and quality for conventional single-crystal X-ray diffraction studies. In such cases it becomes essential that structural information can be determined from powder diffraction data. With the recent developments in the direct-space approaches for structure solution, ab initio crystal structure analysis of molecular solids can be accomplished from X-ray powder diffraction data. It should be recalled that crystal structure determination from laboratory X-ray powder diffraction data is a far more difficult task than that of its single-crystal counterpart, particularly when the molecule possesses considerable flexibility or there are multiple molecules in the asymmetric unit. Salicylic acid and its derivatives used as an anti-inflammatory drug are known for its numerous medicinal applications. In our study, we synthesized mononuclear copper (II) complex of salicylate derivative. The structural characterization of the prepared compound was carried out using powder X-ray diffraction studies. Crystal structure of the compound has been solved by direct-space approach and refined by a combination of Rietveld method using TOPAS Academic V4.1. Density Functional Theory (DFT) calculations have to be carried in the solid state for the compound using GaussianW9.0 in the frame work of a generalized-gradient approximation (GGA). The geometry optimization was to be performed using B3LYP density functional theory. The atomic coordinates were taken from the final X-ray refinement cycle.

Four new polymorphic forms of suplatast tosilate

We found four new polymorphic forms (γ-, ε-, ζ-, and η-forms) of suplatast tosilate (ST) by recrystallization and seeding with ST-analogous compounds; three polymorphic forms (α-, β-, and δ-forms) of ST have been previously reported. The physicochemical properties of these new forms were investigated using infrared (IR) spectroscopy, solid-state nuclear magnetic resonance (NMR) spectroscopy, differential scanning calorimetry, and powder X-ray diffractometry. The presence of hydrogen bonds in the new forms was assessed from the IR and solid-state NMR spectra. The crystal structures of the ε- and η-forms were determined from their powder X-ray diffraction data using the direct space approach and the Monte Carlo method, followed by Rietveld refinement. The structures determined for the ε- and η-forms supported the presence of hydrogen bonds between the ST molecules, as the IR and solid-state NMR spectra indicated. The thermodynamic characteristics of the seven polymorphic forms were evaluated by determining the solubility of each form. The α-form was the most insoluble in 2-propanol at 35°C, and was thus concluded to be the most stable form. The ε-form was the most soluble, and a polymorphic transition from the ε- to the α-form was observed during solubility testing.

Dihydroxycoumarin Schiff base synthesis and structure determination from powder diffraction data

The titled compound with systematic name 4-hydroxy-3-((E)-1-(2-((E)-1-(4-hydroxy-2-oxo-2H-chromen-3-yl)ethylideneamino)ethylimino) ethyl)-2H-chromene-2-one is a new tetradentate (ONNO) Schiff-base which was synthesized by condensation of ethylenediamine and 3-acethyl 4-hydroxycoumarin. Its crystal structure was ab initio determined from laboratory X-ray powder diffraction data by using the direct space approach. The structure is monoclinic with space group P21/n and unit cell parameters a=10.4153(4)Å, b=12.8319(4)Å, c=7.48229(15)Å, β=98.892(3)Å, V=987.97(5)Å3. The asymmetric part of the structure contains one half of the centrosymmetric molecule. The obtained product was also characterized by infrared, UV–VIS and 1H NMR spectroscopy.

Crystal structure determination of three polycyclic compounds and comparative Rietveld refinement between MS and GSAS programs

The crystal structures of normethisterone, gestonoronacetat, and griseofulvin were directly determined from the X-ray powder diffraction (XRPD) using the direct space approach by means of material studio (MS), the Rietveld refinement (RR), based on MS and generalized structural analysis system (GSAS) programs, was examined to practice and expand the Rietveld (whole-profile) technique in the pharmaceutical field. The RR converges to Rwp=8.85%, 10.56%, and 5.92% for normethisterone (6.88%), gestonoronacetat (9.58%), and griseofulvin (5.24%), respectively. The crystallographic data obtained from the powder diffraction data were compared with the single-crystal X-ray diffraction (SXRD) data. The results showed that the maximum relative errors of lengths a, b, and c and volume were respectively 0.18%, 0.18%, 0.22%, and 0.39% between SXRD and XRPD. Thus, MS and GSAS programs were useful to powder diffractionists in determining the crystal structure of organic polycyclic molecules.

Ab initio crystal structure determination of two chain functionalized pyrroles from synchrotron X-ray powder diffraction data

The crystal structure of two chain functionalized pyrroles, methyl 1-benzyl-5-(1-(4-chlorobenzoyloxy)-2-methoxy-2-oxoethyl)-4-(4-chlorophenyl)-1H-pyrrole-2-carboxylate and methyl 1-benzyl-4-(biphenyl-4-yl)-5-(1-(4-biphenylcarbonyloxy)-2-methoxy-2-oxoethyl)-1H-pyrrole-2-carboxylate, which are both important active candidates as antitumoral agents, have been obtained ab initio from synchrotron X-ray powder diffraction data. Both compounds crystallize in the monoclinic system (space group P21/c), with a = 20.2544(3) Å, b = 6.80442(9) Å, c = 21.1981(3) Å, β = 111.6388(9)° and a = 29.7747(6) Å, b = 6.27495(14) Å, c = 18.8525(3) Å, β = 107.053(2)°, respectively. These structures were determined using a direct space approach, by means of Monte Carlo technique, followed by Rietveld refinement.

Periodic calculations of excited state properties for solids using a semiempirical approach

The semiempirical SCF MO method MSINDO (modified symmetrically orthogonalized intermediate neglect of differential overlap) [T. Bredow and K. Jug, Electronic Encyclopedia of Computational Chemistry, 2004] is extended to the calculation of excited state properties through implementation of the configuration interaction singles (CIS) approach. MSINDO allows the calculation of periodic systems via the cyclic cluster model (CCM) [T. Bredow et al., J. Comput. Chem., 2001, 22, 89] which is a direct-space approach and therefore can be in principle combined with all molecular quantum-chemical techniques. The CIS equations are solved for a cluster with periodic boundary conditions using the Davidson-Liu iterative block diagonalization approach. As a proof-of-principle, MSINDO-CCM-CIS is applied for the calculation of optical spectra of ZnO and TiO(2), oxygen-defective rutile, and F-centers in NaCl. The calculated spectra are compared to available experimental and theoretical literature data. After re-adjustment of the empirical parameters the quantitative agreement with experiment is satisfactory. The present approximate approach is one of the first examples of a quantum-chemical methodology for solids where excited states are correctly described as n-electron state functions. After careful benchmark testing it will allow calculation of photophysical and photochemical processes relevant to materials science and catalysis.

Structure Analysis of Molecular Compounds with Z′ = 2 Using Laboratory X-ray Powder Diffraction Data: 3-Phenylpropionic Acid and Its Derivatives

The structure determination of 3-phenylpropionic acid (1), 3-(3-methylphenyl) propionic acid (5), and 3-(3- methoxyphenyl) propionic acid (6), all three compounds crystallizing in the monoclinic space group P21/a (or P21/n) with Z′ = 2, has been accomplished from laboratory X-ray powder diffraction data following the direct space approach. The nature of intermolecular interactions in 1, 5, and 6 has been analyzed using the Hirshfeld surfaces and 2D fingerprint plots. While the two molecules (A and B) in the crystallographic asymmetric unit of 6 display almost identical conformation, those in 1 and 5 are significantly different due a rotation about the C–C bond linking the planar aromatic ring and propionic acid fragments. The presence of the COOH functional group in the compounds promotes the formation of cyclic R22(8) synthons via intermolecular O–H···O hydrogen bonds. Further linking of molecules through intermolecular C–H···O and C–H···π hydrogen bonds generates a three-dimensional supramolecular architecture in 1 and 5 and a two-dimensional molecular sheet in 6. Hirshfeld surface analyses of 1, 5, and 6 as well as a few substituted phenylpropionic acids retrieved from the Cambridge Structure Database (CSD) indicate that 94–99% of Hirshfeld surface areas in this class of compounds are due to H···H, O···H, and C···H contacts.

Structural Investigation on Thermoresponsive PVA/Poly(methacrylate-co-N-isopropylacrylamide) Microgels across the Volume Phase Transition

Characterization of switchable microgels is a major task in drug delivery science. The study of soft polymeric devices requires a combined use of spectroscopy, microscopy, and scattering approaches enabling the characterization of nanostructured features across a volume phase transition. In this work the structural changes of poly(vinyl alcohol) based thermoreversible microgel particles which incorporate p(NiPAAm-co-methacrylate) chains across the transition temperature occurring at 33 °C have been addressed by utilizing reciprocal and direct space approaches such as small angle neutron scattering, SANS, dynamic light scattering, DLS, soft transmittance X-ray microscopy, STXM, and confocal laser scanning microscopy, CLSM, respectively. The comparison between the results obtained from those approaches allows an evaluation of the driving forces acting in the transition and reveals the changes in the microgel structure at nanoscale level. The structure of the poly(vinyl alcohol) based microgel particles, inc...

Crystal structure determination of the β-cyclodextrin– p-aminobenzoic acid inclusion complex from powder X-ray diffraction data

The 1:1 inclusion complex of β-cyclodextrin and p-aminobenzoic acid was prepared and characterized by TG-DTA. The crystal structure of the complex was solved directly from powder X-ray diffraction data using the direct space approach and refined using Rietveld refinement techniques. The complex crystallizes in monoclinic P2 1 space group, with unit cell parameters a = 20.7890 Ǻ, b = 10.2084 Ǻ, c = 15.1091 Ǻ, β = 110.825°, V = 2997 Ǻ 3. The amino group is located at the wide side of the β-cyclodextrin cavity, forming hydrogen bonds with β-cyclodextrin, and the carboxyl group is located at the narrow side. The crystallographic data obtained from powder diffraction data were compared with the single crystallographic data, and the result shows that solving crystal structure of cyclodextrins inclusion complexes of such complexity is accessible to powder diffractionists to some extent.

Local ab initio methods for calculating optical band gaps in periodic systems. I. Periodic density fitted local configuration interaction singles method for polymers

We present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1D-periodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The one-electron part of the matrix-vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The contraction of the CIS vectors with the two electron integrals is performed in the direct space in the basis of localized occupied (Wannier) and virtual (projected atomic) orbitals. The direct space approach allows to utilize the sparsity of the integrals due to the local representation and locality of the exciton. The density fitting approximation employed for the two electron integrals reduces the nominal scaling with unit cell size to O(N(4)). Test calculations on a series of prototypical systems demonstrate that the method in its present stage can be used to calculate the excitonic band gaps of polymers with up to a few dozens of atoms in the cell. The computational cost depends on the locality of the exciton, but even relatively delocalized excitons occurring in the polybiphenyl in the parallel orientation, can be routinely treated with this method.