When default EXPO fails: strategies
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Crystal structures are solved by EXPO by default settings. In case of failure the user can modify the default pathway in order to improve the success rate. We give some suggestions to follow when Direct Methods fail.
- RBM Resolution Bias Modification (RBM).
Fourier syntheses usually suffer by truncation effects due to the limited data resolution (RES): the worst RES value, the less accurate is the electron density map. If RES is > 1 ? both the phasing and refinement process are difficult. The series termination errors are responsible for:
a) the presence of positive and negative ripples with decreasing amplitudes, located around each peak in the map;
b) the shift from the correct position and the broadening of each atomic peak, since the ripples overlap with other atomic peaks.
A new procedure (Altomare et al., 2008a, 2008b) has been introduced in EXPO, aiming at reducing the resolution bias effects and therefore at locating the peaks in more correct positions, eliminating false peaks and reducing the peak broadening.
The method has been successfully applied to a large set of experimental data that are expected to be a challenge for DM. The new approach is very effective particularly in case of organic structures (for them the resolution is usually far away the atomic one because of the rapid scattering factor decay) and enables EXPO to solve crystal structures previously not accessible by DM (Altomare et al., 2008a, 2008b). To apply RBM click on 'Refine' > 'Resolution Bias Modification (RBM, Direct Space)'

- The CFOM figure of merit is in practice an estimate of the probability that a trial solution is correct. If the highest CFOM does not correspond to the correct solution, subsequent different trials may be successful. This is particularly true when several nearly equivalent CFOM's are available for different trials. The Fourier map corresponding to sets different from the first one must be explored by graphical interface clicking on the list in the window 'Restart conditions'
accessible by menu 'Restart' > 'Explore other trials'. Eventually you can also apply the RBM.

By the check button 'E-map' you can select only the e-map. Modify the number of cycles of Fourier recycling by the entry 'Number of cycle(s)'.
Alternatively you can use the directive SET followed by the set number in the FOURIER command.
- It is important to provide good quality diffraction pattern. For example, it is recommended to reduce the pattern range in case of high noise signal at large 2theta values. Use the directive range in the command '%data' to select a portion of pattern or select 'Pattern' > 'Range' by the graphical interface.
- If a partial structure fragment has been located by the default run, it may be recycled in the extraction process (a graphic option must be selected). Click on 'Restart' > 'Recycle in extra'
The number of options is quite large. The optional strategies regard the improvement of both the decomposition process for carrying out more reliable reflection intensities and the Direct Methods performances and the structure model. We give some other secondary strategies.
About the improvement of the decomposition process
- The use of the 'RANDOM' directive in the EXTRACTION module activates the procedure for overcoming the Le Bail method tendency to equipartition the intensity of a group of strongly overlapped reflections. Based on a Monte Carlo approach, it may provide a set of more statistically meaningful intensities.
- If the default run has revealed pseudo symmetry effects and, in particular, if the percentage of electron density affected by pseudo is large, it may be very useful to exploit that information in the extraction process (a graphic option activates the procedure).
- In case of heavy atom structure, the use of prior information obtainable from the Patterson map can improve the quality of extraction (directive 'INVERSION' in the PATTERSON module).
- In some cases, the use of prior information from the structure invariant estimates can optimize the extracted intensities (directive 'ESTIMATE' in the INVARIANT module).
About the optimization of Direct Methods procedure
- Magic integers procedure is an effective and simple way for starting a multi-solution process.
A random approach may be alternatively chosen in the phasing process (directive 'RANDOM' in the PHASE module).
- Second representation formula for triplet invariants proved much more powerful than first representation formula therefore it is used as a default for estimating triplets. In case of failure, the user can choose P3 formula (directive 'COCHRAN' in the INVARIANT module) and/or conveniently increase the number of symbols in the phasing step (directive 'SYMBOLS' followed by the number of symbols to be used in the 'PHASE' module).
- A check for possible pseudotranslational symmetry is always made by EXPO: if PSEUDO keyword is not activated the information is given but not used in the normalization routine and in the phasing process. The user can decide to use it (directive 'PSEUDO' in the NORMAL module).
- the value of NREF (number of reflections actively used in the phasing process) is fixed by EXPO. For some special structures the ratio "number of active triplets/NREF" is too small (less than 10). Larger values of NREF may improve the phasing procedure (directive 'NREFLECTIONS' followed by the number of reflections in the NORMAL module).
- High (or low) resolution reflections may occasionally play a too important role in the first steps of convergence and divergence process. Fixing a thermal factor lower (or larger) than that automatically provided by the normalization routine may successfully change convergence and divergence process (directive 'BFACTOR' followed by the isotropic thermal factor in the NORMAL module).
- An alternative space group should be carefully considered (directive 'SPACEGROUP' in the DATA module).
- Sometimes the structure model is partial. Successive combined Fourier map calculations (Fo-Fc, 2Fo-Fc or Fo) and Rietveld refinements may be conveniently selected by graphical options.
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