Andras Suto

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.

Percolation transition in the Bose gas: II

In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the notion of cycle percolation in the Bose gas and conjectured that it occurs if and only if there is Bose-Einstein condensation. Here we give a complete proof of this statement for the perfect and the imperfect (mean-field) Bose gas and also show that in the condensate there is an infinite number of macroscopic cycles.

Tunneling of quantum spins

Abstract A WKB formalism is presented whereby the tunneling rate of a quantum spin is obtained in the semiclassical limit when h → 0 and the spin quantum number S → ∞ in such a way that h S remains constant. The main idea is to single out one of t anisotropy axes, say the z-axis, to work in a representation with Sz, the z-component of the spin, diagonal and to describe quantum tunneling as a hopping process on the spectrum of Sz. This formalism enables us to efficiently handle tunneling problems, to incorporate dissipation, and to prove that the tunneling rate is universal, i.e. independent of the particular form of the anisotropy.

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.

The structure factor and dynamics of the helix-coil transition

Thermodynamical properties of the helix–coil transition were successfully described in the past by the model of Lifson, Poland and Sheraga. Here we compute the corresponding structure factor and show that it possesses a universal scaling behaviour near the transition point, even when the transition is of first order. Moreover, we introduce a dynamical version of this model, that we solve numerically. A Langevin equation is also proposed, to describe the dynamics of the density of hydrogen bonds. Analytical solution of this equation shows dynamical scaling near the critical temperature and predicts a gelation phenomenon above the critical temperature. In the case when comparison of the two dynamical approaches is possible, the predictions of our phenomenological theory agree with the results of the Monte Carlo simulations.

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.

Commensurate and incommensurate correlations in Haldane-gap antiferromagnets

We analyze the onset of incommensurabilities around the VBS point of the S=1 bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point

Semiclassical quantization and resonance in spin tunnelling

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Correlation inequalities for noninteracting Bose gases

. Moreover, the theory predicts another special point