Structure solution by Direct Methods

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Structure Solution in  EXPO2014 program

Typical X-ray diffraction experiments provide structure factor moduli, while the relative phases are lost. Recovery of the phase information is crucial for crystal structure solution and is referred in crystallography as the phase problem. In  EXPO2014 program,  the default strategy used to solve this problem is based on the application of the Direct Methods (DM) theory (Giacovazzo, 1998). DM are able to estimate phases directly from the structure factor amplitudes. The application of DM to powder data requires the previous decomposition of the full pattern to extract single diffraction intensities for each reflection in the measured 2theta range. Owing to the peak overlap the estimates of the diffraction moduli will be affected by unavoidable errors: this weakens the efficiency of DM (naively, wrong moduli will produce wrong phases), and still today makes crystal structure solution from powder data a challenge.

Load input file for Structure Solution by Direct Methods

When default EXPO2014 fails: strategies

Suggestions
Contact and References

Load input file for Structure Solution with Direct Methods

       To run  EXPO2014 for structure solution you need to create an input file (*.exp).  You can create an input file accessing by graphic interface by the menu "File" > "New".

You must specify the structure name, the profile count filename and its format, the type of radiation source. It is supposed that the cell parameters and the space group have been determined before so fill the frame 'Cell Parameters' and 'Space Group'. Activate the check button 'Structure Solution' if you intend to perform the crystal structure solution process with Direct Methods. Otherwise use the button 'Open' to import an existing input exp, for example you could load the file cime.exp already existing in the directory 'examples'. The following picture is an example of the input file for crystal structure determination of the cimetidine compound.



When you press the button 'Save' an input file cime.exp will be created and automatically loaded by the program for the structure solution process by DM.


%structure cime
%job structure cime
%init
%data
pattern cime.pow
content s 4 c 40 n 24 h 64
wave 1.52904
cell 10.6986  18.8181  6.8246  90.000  111.284  90.000
space p 21/n
sync

filetype counts
%continue


You can known the meaning of lines of the input file by looking at the chapter "command and their use" of this manual.

Alternatively you can edit a new input file or modify an exiting input file with a text editor and save it with extension '.exp'. Once a time the input file has been created, load the exp input file from menu 'File' > 'Load & Go'.


Press the button in the toolbar and the following steps of the structure solution process will be automatically performed:

1) Extraction of the integrated intensities from the powder diffraction pattern;

2) The integrated intensities are normalized via Wilson method (Wilson,1942);

3) Triplet invariants are calculated and their phases are estimated via P10 formula (Cascarano et al., 1984);

4) Phasing process: more plausible sets of phases are generated whose reliability is assessed via the CFOM figure of merit (Cascarano et al., 1992);

5) Twenty sets of phases with the largest CFOM values are stored and ranked in decreasing CFOM order. The first set of phases is automatically selected and used for computing an electron density map via an E-Fourier synthesis (E-map): the most intense peaks in the E-map are located and chemically interpreted. The obtained structure model is optimized and completed via the automatic structure model optimization.

More information about the structure solution process by Direct Methods are in the chapter 'The steps of structure solution procedure'.


When default  EXPO2014 fails: strategies


       A lot of crystal structures are solved by  EXPO2014 by default settings in few minutes and in completely automatic way.

Unfortunately not always you can obtain the correct structure solution in default. In this situation two different strategies are suggested and can be applied at the end of the default run.


Explore trials


In a typical Direct Methods procedure more sets of phases (trials) are generated and ranked according  to the combined CFOM figure of merit (estimating the quality of the trial) and only the best trial is used to calculate a Fourier map. Because of the unavoidable errors on the phases, the figure of merit can fail to evaluate the best trial, so it is strictly suggested to develop the other trials by menu 'Solve' > 'Explore trials'.

The following window will be opened (the procedure has been applied to 2-Mercaptobenzoic acid compound, whose input file is in the directory 'examples').



and the the CFOM value can be read. The highest CFOM value could not correspond to the correct solution while subsequent different trials may be successful. This is particularly true when several nearly equivalent CFOM's are available for different trials as in the picture. If the trial has been already developed (done='yes'), you can read the RF figure of merit value that quantifies the agreement between the structure factors extracted from the experimental pattern and calculated by the model.
Check the button in the first column to decide which trial will be developed and press the button If you check the button 'Select all new trials', all the trial not already explored will be automatically selected and developed.

You can choose three different actions for the structure model optimization (see later):
1)RBM: Resolution Bias Modification is the default action for organic and metal organic compounds.
2)Fourier: classical Fourier refinement, default choice for inorganic compounds.
3)E-map: the first electron density map calculated directly after the phasing process by Direct Methods.

4)COVMAP: the covariance principle based completion.

At the end of the procedure, all the trials will appear ordered according to the RF and the user can also view the model corresponding to each trial by mouse selection.



Alternatively to the graphical option, the use of the command %alltrials  in the input file  automatically activate the 'Explore trials' approach. An example of input file is here reported:


%Structure merca
%Initialize
%Job merca
%Data
       Cell       7.885  5.976   14.949  90.0  100.48  90
       SpaceGroup p 21/c
       Content    c 28 O 8 S 4 h 24
       Pattern    pd_0002.xy
       Wavelength 1.54056
%extra
%normal
%invar
%phase
%alltrials


Structure model optimization


The structure model obtained at the end of the default strategy, generally is a partially correct representation of the true model: some atoms are in correct positions but other are incorrectly positioned or completely false. In this situation the user can try to improve the quality of the Fourier map, as obtained at the end of Direct Methods, by using different optimization strategies implemented in the  EXPO2014 program:

  1. suitably weighted least squares (wLSQ) (Altomare et al., 2006), able to compensate the low accuracy of the intensities of strongly overlapped reflections. The procedure is automatically applied in case of inorganic compounds.
  2. the resolution bias correction algorithm (RBM) (Altomare et al., 2008a, 2008b; 2009, 2010a, 2010b)for reducing, in the electron density map, the errors caused by the limited experimental resolution: peak broadening, peak shift, intensity distorsion. The correction has been developed in direct space (it represents the default choice in case of organic and metal organic compounds), in reciprocal space and in both direct and reciprocal space;
  3. the procedure of electron density modification based on the concept of covariance between points of the map (COVMAP) (Altomare et al., 2012)  The procedure executes the following strategy: the structural model provided by the RBM procedure is submitted to COVMAP approach which suitably modifies the electron density map and successively submits the improved model to wLSQ analysis. The resulting new model is again modified by COVMAP and cyclically processed in the other two steps. The number of cycles depends on the structure complexityThe structure model obtained at the end of the default strategy can be partly correct with some atoms in correct position but other atoms are incorrectly positioned or completely false. In this situation the user can try to optimize del model by using different optimization strategies.

It is possible to graphically choice different RBM procedures for model optimization by the menu 'Resolution Bias Modification (RBM)', via 'Refine' button from the upper  EXPO2014 menu.



Apply the RAMM (RAndom Model based Method) procedure


The new method RAMM (Altomare et al., 2013) has been developed and implemented in the  EXPO2014 computing program for improving the ab initio crystal structure solution process. When the available information consists of only the experimental powder diffraction pattern and the chemical formula of the compound under study, the structure solution classical approach follows two main steps: 1) phasing by Direct Methods (or by Patterson methods) in order to obtain a structure model (this last is usually uncompleted and/or approximate); 2) improving the model by structure optimization techniques. The alternative RAMM approach skips step 1) and supplies a fully random model to step 2). Such model is then submitted to important structure optimization tools present in EXPO: wLSQ , RBM and COVMAP which are able to lead to correct structure. RAMM is based on a cyclic process generating several random models which are then optimized. The process stops automatically when recognizes the correct structure.


Click 'RAMM' on the menu 'Solve' to activate this alternative strategy for structure solution at the end of the default run of EXPO2014. The following pictures are related to 2-Mercaptobenzoic acid whose input file is in the directory 'examples'.



The procedure can take from some minutes to several hours depending on the complexity of problem (number of atoms, quality of data, data resolution). If more than one plausibile solution is found they will be ordered according to the R-structure factor in an interactive list.



The selected model will be visualized on the molecular viewer. Press 'OK' to accept the selected model.

When Direct Methods procedure fails, the RAMM approach can be a very useful tool to find the correct solution.

The use of the command %randomsolve  in the input file  automatically activate the 'Explore trials' approach. An example of input file is here reported:

%Structure merca
%Initialize
%Job merca
%Data
       Cell       7.885  5.976   14.949  90.0  100.48  90
       SpaceGroup p 21/c
       Content    c 28 O 8 S 4 h 24
       Pattern    pd_0002.xy
       Wavelength 1.54056
%randomsolve


Suggestions

The number of options in the program 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. We give some other secondary strategies.


About the improvement of the decomposition process


About the optimization of Direct Methods procedure


Contact

For suggestions and bugs contact:

angela.altomare@ic.cnr.it

annagrazia.moliterni@ic.cnr.it

rosanna.rizzi@ic.cnr.it

corrado.cuocci@ic.cnr.it


References

Altomare, A., Cuocci, C., Giacovazzo, C., Moliterni, A.G.G., Rizzi, R. (2006.) Powder diffraction: the new

automatic least-squares Fourier recycling procedure in EXPO2005. J. Appl. Cryst. 39 (2006) 558-562.

Altomare, A., Cuocci, C.,  Giacovazzo, C., Kamel, G. S.,  Moliterni, A. & Rizzi, R.  (2008a). Minimally

resolution biased electron-density maps. Acta Cryst. A64, 326-336. 

Altomare, A., Cuocci, C.,  Giacovazzo, C., Moliterni, A.  & Rizzi, R.  (2008b). Correcting resolution bias in electron density maps of organic molecules derived by direct methods from powder data. J. Appl. Cryst. 41, 592-599.

Altomare, A., Cuocci, C., Giacovazzo, C., Moliterni, A., Rizzi, R. (2009) Correcting electron-density

resolution bias in reciprocal space. Acta Cryst. A65, 183-189.

Altomare, A., Cuocci, C., Giacovazzo, C., Moliterni, A., Rizzi, R. (2010a) The dual-space resolution bias

correction algorithm: applications to powder data. J. Appl. Cryst. 43, 798-804.

Altomare, A., Cuocci, C., Giacovazzo, C., Moliterni, A., Rizzi, R. The dual-space resolution bias

correction in EXPO2010. Z. Kristallogr. 225, 548-551.

A. Altomare, C. Cuocci, C. Giacovazzo, A. Moliterni and R. Rizzi (2012). Covariance and correlation estimation in electron-density maps. Acta Cryst. A68, 244-255.

A. Altomare, C. Cuocci, C. Giacovazzo, A. Moliterni and R. Rizzi (2013). RAMM: a new random-model-based method for solving ab initio crystal structure using the EXPO package. J. Appl. Cryst. 46,

Cascarano, G., Giacovazzo, Camalli, M., Spagna, R., Burla, M. C, Nunzi, A.  & Polidori, G.  (1984). The method of representations of structure seminvariants. The strengthening of triplet relationships. Acta Cryst. A40, 278-283.

Cascarano G., Giacovazzo C. & Guagliardi A. (1992). Improved figures of merit for direct methods. Acta Cryst. A48, 859-865.

Giacovazzo, C. (1998). Direct Phasing in Crystallography. Oxford: IUCr/Oxford University Press.

Wilson, A. J. C. (1942). Determination of Absolute from Relative X-Ray Intensity Data. Nature, Load.

150, 152.

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