Gábor Oszlányi

Ab initio structure solution by charge flipping

In this paper, an extremely simple structure solution method termed charge flipping is presented. It works ab initio on high-resolution X-ray diffraction data in the manner of Fourier recycling. The real-space modification simply changes the sign of charge density below a threshold, while in reciprocal space the moduli F(obs) are retained resulting in an F(obs) map without weighting. The algorithm is tested using synthetic data for a wide range of structures, the solution statistics are analysed and the quality of reconstruction is checked. Finally, mathematical aspects of the algorithm are considered in detail, and these show that in this chaotic iteration process the solution is a limit cycle and not a fixed point.

Ab initio structure solution by charge flipping. II. Use of weak reflections.

The original charge flipping algorithm [Oszlanyi & Suto (2004). Acta Cryst. A60, 34-141] is an amazingly simple structure solution method which works ab initio on high-resolution X-ray diffraction data. In this paper, a new version of the algorithm is presented that complements the phase exploration in reciprocal space. Instead of prescribing observed moduli of all structure factors, weak reflections are treated separately. For these reflections, calculated moduli are accepted unchanged and calculated phases are shifted by a constant Deltaphi=pi/2. This means that the observed data of weak reflections are not used in the iteration, except for the knowledge that they are indeed weak. The improvement is drastic, in some cases the success rate is increased by a factor of ten, in other cases a previously unsolvable structure becomes solvable by the modified algorithm.

The charge flipping algorithm

This paper summarizes the current state of charge flipping, a recently developed algorithm of ab initio structure determination. Its operation is based on the perturbation of large plateaus of low electron density but not directly on atomicity. Such a working principle radically differs from that of classical direct methods and offers complementary applications. The list of successful structure-solution cases includes periodic and aperiodic crystals using single-crystal and powder diffraction data measured with X-ray and neutron radiation. Apart from counting applications, the paper mainly deals with algorithmic issues: it describes and compares new variants of the iteration scheme, helps to identify and improve solutions, discusses the required data and the use of known information. Finally, it tries to foretell the future of such an alternative among well established direct methods.

Imaging atom clusters by hard X-ray free-electron lasers

The ingenious idea of single-molecule imaging by hard X-ray Free Electron Laser (X-FEL) pulses was recently proposed by Neutze et al. (Nature 406 (2000) 752). However, in their numerical modelling of the Coulomb explosion, several interactions were neglected and no reconstruction of the atomic structure was given. In this work we carried out improved molecular-dynamics calculations including all quantum processes which affect the explosion. Based on this time evolution, we generated composite elastic-scattering patterns, and by using Fienups algorithm successfully reconstructed the original atomic structure. The critical evaluation of these results gives guidelines and sets important conditions for future experiments aiming at single-molecule structure solution.

Ab initio neutron crystallography by the charge flipping method.

In this paper, the charge flipping method is proposed for ab initio structure determination using neutron diffraction data alone. For this purpose, a new variant of the dual-space iterative algorithm is introduced, which is called band flipping. Unlike the basic algorithm, it reverses the sign of scattering density only within a zero-centred band, develops large plateaus without forcing positivity, and often leads to Babinet solutions. Its phasing power was tested on two organic structures. These behave similarly when using X-ray diffraction data and the basic algorithm but, with neutron data and band flipping, their solution becomes orders-of-magnitude more difficult and strongly dependent on the hydrogen content. Surprisingly, when the constraint of positivity is added, convergence speeds up to the point where structure determination using neutron diffraction data is not more difficult than the X-ray case. However, by following the evolution of the R factor, such a solution can be easily missed, and band flipping must be used both as a probe of convergence and as a tool for developing negative densities. Apart from demonstrating the feasibility of charge flipping for ab initio neutron crystallography, the present study also leads to an important byproduct: the type of traps that occasionally block the iterative process are identified and a mathematical analysis of their origin is given.

ENERGY GAP IN SUPERCONDUCTING FULLERIDES : OPTICAL AND TUNNELING STUDIES

Tunneling and optical transmission studies have been performed on superconducting samples of Rb{sub 3}C{sub 60}. At temperatures much below the superconducting transition temperature {ital T}{sub c}, the energy gap is 2{Delta}=5.2{plus_minus}0.2 meV, corresponding to 2{Delta}/{ital k}{sub B}{ital T}{sub c}=4.2. The low temperature density of states and the temperature dependence of the optical conductivity resemble BCS behavior, although there is an enhanced {open_quote}{open_quote}normal state{close_quote}{close_quote} contribution. The results indicate that this fulleride material is an {ital s}-wave superconductor, but the superconductivity cannot be described in the weak coupling limit. {copyright} {ital 1996 The American Physical Society.}

Structure and stability of C60Xy clathrates

Abstract A series of novel single crystalline C60Xy clathrates were prepared with various guest materials by crystallization from organic solvent-precipitant systems. Four different stoichiometric compositions ( y = 1, 3 4 , 2 3 and 1 2 ) were found. The stability of the clathrates was studied by thermoanalytical methods. The crystal structures were determined by X-ray diffraction. Based on the stoichiometry and structure, the clathrates are classified as members of two related homologous series with compositions of (C60)m+2X3 and (C60)n+1X2. The first observations of birefringence and phase transitions corresponding to orientational ordering are demonstrated.

A charge-flipping algorithm to handle incomplete data

Missing data are a general hindrance for all iterative, dual-space methods of structure determination. Charge flipping is no exception; its real-space perturbation may turn out to be too strong if the amount of diffraction data is not sufficient. To handle this situation, we introduce a variant of the basic algorithm which combines the original charge-flipping density modification in real space, the reflector of the Fourier-modulus projection in reciprocal space and the parameterless iteration scheme of averaged alternating reflections (AAR). This simple algorithm is a balance of increased perturbations and full negative feedback, with the extra freedom that it can be fine-tuned by a different treatment of different unobserved reflections. The efficiency of the method was tested using several single-crystal data sets and varying the amount of missing data at both high and low resolution. The results prove that many small-molecule structures can be solved by utilizing significantly less data than is standard in current crystallographic practice.

Molecular and crystal structure of the AC60 (A = K, Rb) dimer phase

Abstract Quantum chemical calculations, x-ray structural analysis and thermodynamic stability considerations are presented for the dimer phase of A C 60 . The relative stability of dimer and polymer phases was evaluated from thermodynamic data and critically compared to the results of quantum chemical calculations. The AM1 optimized geometry results in a high quality of Rietveld but the spatial distribution of excess charge of the dimer anion has no significant effect on the structural refinement.

Low-temperature phase transition in C60-n-pentane.

In this paper we report the results of x-ray powder diffraction experiments on C[sub 60]-[ital n]-pentane. This material is a typical C[sub 60] clathrate and shows orthorhombic symmetry at room temperature. At low temperature an orthorhombic to monoclinic phase transition can be observed which involves the distortion of the base plane from rectangular. A microscopic picture of the phase transition is given by molecular-dynamics calculations.