When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR 2 factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

The relationship between the structure and the properties of a drug or material is a key concept of chemistry. Knowledge of the three-dimensional structure is considered to be of such importance that almost every report of a new chemical compound is accompanied by an X-ray crystal structure - at least since the 1970s when diffraction equipment became widely available. Crystallographic software of that time was restricted to very limited computing power, and therefore drastic simplifications had to be made. It is these simplifications that make the determination of the correct structure, especially when it comes to hydrogen atoms, virtually impossible. We have devised a robust and fast system where modern chemical structure models replace the old assumptions, leading to correct structures from the model refinement against standard in-house diffraction data using no more than widely available software and desktop computing power. We call this system NoSpherA2 (Non-Spherical Atoms in Olex2). We explain the theoretical background of this technique and demonstrate the far-reaching effects that the improved structure quality that is now routinely available can have on the interpretation of chemical problems exemplified by five selected examples.

We have implemented a procedure that allows the use of non-spherical atomic form factors in a standard crystallographic X-Ray refinement. We outline the procedure for their use, alongside a mathematical justification of their viability.

This paper describes the mathematical basis for olex2.refine, the new refinement engine which is integrated within the Olex2 program. Precise and clear equations are provided for every computation performed by this engine, including structure factors and their derivatives, constraints, restraints and twinning; a general overview is also given of the different components of the engine and their relation to each other. A framework for adding multiple general constraints with dependencies on common physical parameters is described. Several new restraints on atomic displacement parameters are also presented.

Invariom partitioning and notation are used to estimate anisotropic hydrogen displacements for incorporation in crystallographic refinement models. Optimized structures of the generalized invariom database and their frequency computations provide the information required: frequencies are converted to internal atomic displacements and combined with the results of a TLS (translation-libration-screw) fit of experimental non-hydrogen anisotropic displacement parameters to estimate those of H atoms. Comparison with TLS+ONIOM and neutron diffraction results for four example structures where high-resolution X-ray and neutron data are available show that electron density transferability rules established in the invariom approach are also suitable for streamlining the transfer of atomic vibrations. A new segmented-body TLS analysis program called APD-Toolkit has been coded to overcome technical limitations of the established program THMA. The influence of incorporating hydrogen anisotropic displacement parameters on conventional refinement is assessed.

Refinement of model parameters against observed diffraction data is a widely used technique across many specializations of crystallography.In most cases gradient-driven minimization is employed, usually in combination with exact or approximate second derivatives.Ultimately, such methods are variations of Newton's method for iterative root finding and assume a quadratic model around the minimum.The parameter adjustments d in each iteration are determined as the ratios of 1 st and 2 nd derivatives: d = -f'/f", where f is the function to be minimized.While the success of this approach is evident through the innumerable results it has produced, it is obviously handicapped by singularities if f" approaches zero.In such cases naïve use of Newton's method leads to overestimated, unfeasible parameter adjustments.Consequently, all practical minimization algorithms include shift damping, line search, or trust region methods to achieve numerical stability.A systematic inspection of crystallographic target functions commonly used in the refinement of atomic coordinates reveals that near-zero or negative 2 nd derivatives occur systematically, well within the convergence radius.We observe that in this context a trigonometric (sine or cosine) function is always a better fit to the shape of the minimum, compared to the quadratic model underlying Newton's method.The trigonometric minimum model leads to the formula d = -w/π arctan(π/w f' / f") for the estimate of the parameter adjustment.This function is free of singularities; computer implementations use atan2().By design the maximum shift length is w, which is the halfwidth of the minimum.The trigonometric minimum model allows us to achieve numerical stability by injecting easily obtainable prior knowledge into the minimization procedure, through the parameter w.We will report results of systematically comparing conventional minimizations with minimizations using the trigonometric minimum model.

iotbx.cif is a new software module for the development of applications that make use of the CIF format. Comprehensive tools are provided for input, output and validation of CIFs, as well as for interconversion with high-level cctbx [Grosse-Kunstleve, Sauter, Moriarty & Adams (2002). J. Appl. Cryst. 35, 126-136] crystallographic objects. The interface to the library is written in Python, whilst parsing is carried out using a compiled parser, combining the performance of a compiled language (C++) with the benefits of using an interpreted language.

The Computational Crystallography Toolbox (cctbx

The Computational Crystallography Toolbox (cctbx) [1] opened a new era in crystallographic computing by providing a free, open and

Ab-initio crystal structure determination from powder diffraction data became more and more popular in the last 20 years, thanks to the development of effective novel methods and powerful experimental devices.These enhancements enable to solve, often routinely, organic, inorganic and metallo-organic crystal structures, even if not always they ensure the success because of unavoidable problems like peak overlap, preferred orientation and/or background estimation.EXPO2010, the evolution of EXPO2009 [1], is a package able to perform all the steps of the ab-initio structure determination process: indexing; space group determination; estimation of the reflection integrated intensities; structure solution (both in reciprocal and direct space) and structure refinement.Special procedures make more straightforward the crystal structure solution process, especially in case of low resolution data and/or organic compounds.They are: 1) a new figure of merit for identifying the correct cell among a set of plausible solutions; 2) new methods, working in direct and reciprocal space, able to correct the truncation effects on the electron density; 3) direct space techniques (simulated annealing and hybrid approach).Among the new algorithms implemented in EXPO2010 we quote:a. new procedures able to improve Direct Methods phasing via a suitable selection of the reflections to be phased; b. a new criterion for ranking the most plausible set of phases provided by Direct Methods.The main features of EXPO2010 and its application to experimental data are outlined.

Some years ago the direct-methods origin-free modulus sum function (S) [1] was adapted to the processing of intensity data from density functions with positive and negative peaks [2].That implementation used phase relationships explicitly.Although successfully applied to different situations where the number of reflections was small, its generalization to larger problems required avoiding the time-consuming manipulation of quartet terms.To circumvent this limitation, a modification of the more recent S-FFT algorithm [3] (that maximizes S with only Fourier transforms) was investigated.The resulting S 2 -FFT algorithm proved highly effective for crystal structures with positive and negative scatterers in the presence of at least one moderate scatterer in the unit cell [4].To increase its versatility, the S-FFT algorithm has been adapted now to density functions formed exclusively by positive and negative peaks of similar strength.The results are very promising and some examples describing different situations are analysed in detail.

New software, OLEX2 , has been developed for the determination, visualization and analysis of molecular crystal structures. The software has a portable mouse-driven workflow-oriented and fully comprehensive graphical user interface for structure solution, refinement and report generation, as well as novel tools for structure analysis. OLEX2 seamlessly links all aspects of the structure solution, refinement and publication process and presents them in a single workflow-driven package, with the ultimate goal of producing an application which will be useful to both chemists and crystallographers.

In current well-established crystallographic software packages, data refinement and other analytic fitting models are often embedded as a process engine.As such, they lack maintainability, extensibility and scalability; hence, the need for a mathematical programming infrastructure which offers a modelling design and is able to support the whole crystallographic modelling life-cycle, as well as keep separate model formulations from the optimisation process, bearing in mind that this separation is the key principle of modelling language design.In such a context and more specifically within small molecule crystallography software, this infrastructure will not only address the aforementioned drawbacks, but also allow for the investigation of solver performance of ill-conditioned problems and sensitivity analysis.This is made possible as one model formulation can work with numerous solvers, each of which implements one or more optimisation algorithms.We have defined a strategy and designed a toolkit for small molecule computational crystallography, which delivers optimisation components in general and refinement-based applications in particular, as applied to crystallographic computing.This design benefits from the major advances made in optimisation methods over recent decades, knowledge which is encoded in widely available software libraries and/or web-servers.We use the concept of a modelling environment, which consists of objective and constraint expressions, a concept that has become an essential tool for a wide range of optimisation and related problems.The toolkit provides users with an easy and efficient means to test ideas, construct new algorithms and models which can be readily adapted to any new situation, so by enabling users to develop and explore the full capabilities of crystallography, and upon which other researchers can build new applications.We discuss the concept of the toolkit and describe the adopted strategies, so as to combine the modelling facilities with a powerful object-oriented programming language, support the whole crystallographic modelling life-cycle (building model -refining -analysing -revising) and fulfil the common development practice issues, consisting of: (i) supporting model formulations and streamlining the construction of problem descriptions; (ii) handling automatic differentiation, to keep the user free from developing computational procedures for computing derivatives; (iii) handling restraints/constraints which can be provided as a symbolic form and (iv) interfacing the modelling environments with numerous solvers to take advantage of the different minimisation methods for a more accurate sensitivity analysis.

New software, OLEX2 , has been developed for the determination, visualization and analysis of molecular crystal structures. The software has a portable mouse-driven workflow-oriented and fully comprehensive graphical user interface for structure solution, refinement and report generation, as well as novel tools for structure analysis. OLEX2 seamlessly links all aspects of the structure solution, refinement and publication process and presents them in a single workflow-driven package, with the ultimate goal of producing an application which will be useful to both chemists and crystallographers.

improvement of the refinement can be obtained by eliminating the badly fitted reflections and/or by correcting the model, which could be too inaccurate or involve too subtle features to be modelled depending on the quality of the observations processed. A successfully recognition of the actually influencing reflections is represented by some statistical estimators based on leverage analysis (Belsey et al., 1980, Merli, 2005). Among several exploitable estimators, there are some of them that seem to be particularly suitable in crystallographic calculations: i) Cook distance (Cook, 1977), ii) DFFTIS and iii) DFBETASij (Belsey et al., 1980). In particular, estimator i) can be used to recognize an actual outlier of the refinement, whereas estimator ii) is useful to investigate the effects when a reflection is eliminated from the data set and iii) is able to recognize the variables that are mostly influenced by each reflection. The combined analysis of these diagnostics will be presented. It will be shown how successfully it yields to the recognition of a dangerous reflection and/or the inaccurate estimate of any particular variable. Belsey, Kuth & Welsh (1980) Regression diagnostics. J. Wiley & Sons Cook(1977) Technometrics, 19, 15-18 Merli (2005) Acta Cryst. A61, 471-477

Microsymposia(i) The theoretical developments made to analyse quantitatively the GISAXS patterns beyond the classical approximations, in particular to account for the profile of refraction index and the particle-particle correlations.(ii) The self similarity during the dynamic coalescence of Au/ TiO2(110) on the size distribution but also on the spatial ordering of the particles and its link with the randomness of the nucleation centers.(iii) The sintering of nanoparticles during the course of the CO oxidation reaction and the link between particle size and chemical reactivity measured by mass spectrometry.

Sessions 1renaming copies of files.The metadata module automatically collates information from the data collection and processing steps.This can then be edited and added to, before merging with the information generated by the refinement program employed to create a complete and correct cif file, if possible.The precompiled Olex2 executable can be downloaded free of charge by academic users from http:// www.olex2.org. 1. http://sourceforge.net/projects/olex2.