Biomedical subjects

András Süto

Publications and source records attributed to András Süto.

5 recordsLinked to original sources

PubMed2006

Charge flipping at work: a case of pseudosymmetry.

Charge flipping (CF) is an amazingly simple structure solution method that uses single-crystal X-ray diffraction data. It is truly ab initio, no preliminary information on atom types, chemical composition, or space group symmetry is required. The algorithm is iterative and alternates between real and reciprocal spaces. Its simplest version only changes (flips) the sign of the electron density below a threshold, while in reciprocal space, it prescribes the moduli of observed structure factors. In this communication, we apply the algorithm in practice. The selected example presents a whole range of difficulties: it is large, contains only light atoms, is noncentrosymmetric, and shows a particularly awkward pseudosymmetry. To solve it with any of the traditional methods requires many hours of computer time, followed by a day of expert's handwork to find missing and to remove spurious atoms. In contrast, the CF algorithm provides the complete structure in a few seconds and without human intervention. It is also remarkable that the success rate is 100%, that is, any starting point in the high-dimensional phase space leads to the solution. The treatment of translational pseudosymmetry is obviously a favorable case. Similar resistant structures with pseudosymmetries or ambiguous space groups are the practical applications where the CF method could well complement standard software procedures.

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PubMed2005

Crystalline ground states for classical particles.

Pair interactions whose Fourier transform is non-negative and vanishes above a wave number K(0) are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three-dimensional example is an interaction of asymptotic form cosK(0)r/r(4). The result is obtained for densities rho > or = rho(d), where rho(1) = K(0)/2(pi), rho(2) = (sq.rt(3)/8)(K(0)/pi)(2), and rho(3) = (1/8sq.rt(2)) x (K(0)/pi)(3). At rho(d) there is a unique periodic GSC which is the uniform chain, the triangular lattice, and the bcc lattice for d = 1,2,3, respectively. For rho > rho(d), the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K(0), and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho > or = (1/6 sq.rt(3)) x (K(0)/pi)(3).

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PubMed2005

Equivalence of Bose-Einstein condensation and symmetry breaking.

Based on a classic paper by Ginibre [Commun. Math. Phys. 8, 26 (1968)] it is shown that, whenever Bogoliubov's approximation, that is, the replacement of a(0) and a*(0) by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |a(0)|(2)/V and a*(0)a(0)/V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation. Because the former was proved by Ginibre to hold for absolutely integrable superstable pair interactions, the latter is equally valid in this case. Apart from Ginibre's work, our proof uses only a simple convexity inequality due to Griffiths.

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PubMed2004

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.

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PubMed2004

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.

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