### Introduction to Sir2011 - Erice Crystallography 2011 IT Support

```Introduction to Sir2011
Giovanni Luca Cascarano
CNR- Istituto di Cristallografia – Bari - Italy
Erice 2011 Electron Crystallography – June 2-12 2011
The crystal structure solution
To solve a crystal structure, i.e. to obtain the atomic coordinates,
different methods are available.
We’ll focus our attention on Direct Methods, very popular and
effective, able to give in a short time and in automatic way the
solution to our problem: to compute the phases lost during the
diffraction experiment (the so called Phase Problem).
Once the phases are available it is possible to apply the Fourier
Transform and get the electron density map whose maxima
correspond to the atomic positions.
Erice 2011 Electron Crystallography – June 2-12 2011
The crystal structure solution
Esperiment
Crystallization
I = |F|2
=?
Beam
(X rays, electrons)
Crystal
Diffraction pattern
Atomic model
Crystallographic
Methodologies
Software
Erice 2011 Electron Crystallography – June 2-12 2011
Electron density map
The crystal structure solution
Esperiment
Crystallization
I = |F|2
=?
Beam
(X rays, electrons)
Crystal
Diffraction pattern
Atomic model
Crystallographic
Methodologies
Software
Erice 2011 Electron Crystallography – June 2-12 2011
Electron density map
The crystal structure solution
Esperiment
Crystallization
I = |F|2
=?
Beam
(X rays, electrons)
Crystal
Diffraction pattern
Atomic model
Crystallographic
Methodologies
Software
Erice 2011 Electron Crystallography – June 2-12 2011
Electron density map
The crystal structure solution
Esperiment
Crystallization
I = |F|2
=?
Beam
(X rays, electrons)
Crystal
Diffraction pattern
Atomic model
Crystallographic
Methodologies
Software
Erice 2011 Electron Crystallography – June 2-12 2011
Electron density map
The phase problem
If we define the structure factor Fh with indices h=(hkl)
N
Fh   f j exp(2hrj )  Fh exp(ih )
j 1
the electron density (r) for every point r in the unit cell is defined as:
 (r)  V 1  Fh exp(ih ) exp(2ihr)
h
In this formula the |Fh| value is known from experiment, the phase
of the structure factor h has to be recovered.
Erice 2011 Electron Crystallography – June 2-12 2011
The structural complexity
In Sir2011 the parameter related to the structural complexity governs most of
the algorithms used for the automatic structure solution.
In the program there is the following classification:
Very small size structures: up to 6 non-H atoms in asymmetric unit
Small size structures: 6-80 non-H atoms in asymmetric unit
Medium size structures: 81-300 non-H atoms in asymmetric unit
Large size structures: more than 300 non-H atoms in asymmetric unit
Erice 2011 Electron Crystallography – June 2-12 2011
Program flow chart
WILSON METHOD  (K, B)
STRUCTURE FACTORS NORMALIZATION
(|F||E|)
STRUCTURE INVARIANTS CALCULATION
(TRIPLETS AND QUARTETS)
TANGENT FORMULA
AND FIGURES OF MERIT
DIRECT SPACE REFINEMENT
AUTOMATIC STRUCTURE MODEL
REFINEMENT
Erice 2011 Electron Crystallography – June 2-12 2011
The multisolution approach
Usually random phase values are assigned to a subset of
strong reflections (those with the higher of |E|); by means of
the triplets and of the tangent formula almost all the strong
reflections can be phased.
This procedure is repeated n times changing the values of the
random phases and, for every obtained set of phases a suitable
Figure of Merit (eFOM) is computed. Higher is the eFOM
value, more likely the corresponding phase set is correct.
These trials, sorted with respect to the eFom value, will be
submitted to the automatic Direct Space Refinement (DSR).
Erice 2011 Electron Crystallography – June 2-12 2011
Program flow chart
WILSON METHOD  (K, B)
STRUCTURE FACTORS NORMALIZATION
(|F||E|)
STRUCTURE INVARIANTS CALCULATION
(TRIPLETS AND QUARTETS)
TANGENT FORMULA
AND FIGURES OF MERIT
DIRECT SPACE REFINEMENT
AUTOMATIC STRUCTURE MODEL
REFINEMENT
Erice 2011 Electron Crystallography – June 2-12 2011
Direct space refinement
The number of reflections phased by the tangent formula is, in
general, a small percentage of all reflections available.
To extend and refine for all suitable reflections (i.e. those for
which Fobs > 3(Fobs)) an iterative procedure is used, the Direct
Space Refinement.
The procedure is constituted by n cycles
    
where  is the electron density map and  is the set of calculated
phases.
Erice 2011 Electron Crystallography – June 2-12 2011
Direct space refinement
The electron density maps are calculated by using a number of
reflections cyclically increasing; a small fraction of  is used during the
inversion of the electron density map, the remaining part is set to zero.
To process a trial, EDM is applied a number of times, depending on
structural complexity.
Erice 2011 Electron Crystallography – June 2-12 2011
Program flow chart
WILSON METHOD  (K, B)
STRUCTURE FACTORS NORMALIZATION
(|F||E|)
STRUCTURE INVARIANTS CALCULATION
(TRIPLETS AND QUARTETS)
TANGENT FORMULA
AND FIGURES OF MERIT
DIRECT SPACE REFINEMENT
AUTOMATIC STRUCTURE MODEL
REFINEMENT
Erice 2011 Electron Crystallography – June 2-12 2011
The DLSQ procedure
Peaks are labelled in terms of atomic species according to
their intensity and to the chemical content of the unit cell;
the atomic coordinates and the isotropic thermal factor are
refined using a diagonal least squares algorithm. New
values of phases and weights are computed and used to
produce a new electron density map using (2Fobs-Fcalc)
coefficients.
The DLSQ procedure stops when the crystallographic
residual R increases.
Erice 2011 Electron Crystallography – June 2-12 2011
The DLSQ procedure
The DLSQ procedure stops when the crystallographic
residual R increases.
R =  | |Fobs| – |Fcalc| | /  |Fobs|
Fourier
Recycling
Erice 2011 Electron Crystallography – June 2-12 2011
Diagonal
Least
Squares
The Direct space refinement
The Direct Space Refinement procedure
stops when the R factor is smaller than a
given threshold (default value 25%)
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
Sir2011 is the latest product of the Sir family, in beta version at the moment.
It includes many new features that will be described in the following slides.
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
This is a new cyclic phasing algorithm which does not use
Direct or Patterson methods: it is based only on properties of a
new difference electron density and of the observed Fourier
synthesis. Owing to the central role of the difference Fourier
synthesis the method has been called VLD (vive la différence) .
In sinergy with the RELAX procedure, it has been applied with
success both to small/medium size molecules and to atomic
resolution proteins.
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
The VLD cycling process may be described by the following steps:
a) The difference Fourier q =  - p synthesis is calculated using
the following formula:
 e   A2
[(m R   A R p )  R' p (1  D)
2
 1 A

] exp(i p )

b) The difference map is suitably modified and inverted; the
corresponding Fourier coefficients are combined with the
normalized structure factors of the model structure by means of
the tangent formula:
tan 
R p sin  p  Rq sin q
R p cos p  Rq cosq
c) A new map using the observed structure factors and the phases 
defined in b) is submitted to EDM cycles.
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
DEDM
Tangent
EDM
NO
Solution?
Stop
YES
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
DM vs VLD: results
Average time in seconds and number of test structures
Method
Small < 80
Medium 80-200
Macro > 200
Direct Methods
5 (33/33)
319 (23/23)
1728 (16/35)
VLD
7 (33/33)
246 (23/23)
1844 (24/35)
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
Erice 2011 Electron Crystallography – June 2-12 2011
The VLD procedure
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Fourier map in part of the cell
Erice 2011 Electron Crystallography – June 2-12 2011
Fourier map in part of the cell: Jav
Erice 2011 Electron Crystallography – June 2-12 2011
Fourier map in part of the cell
Erice 2011 Electron Crystallography – June 2-12 2011
Fourier map in part of the cell: Jav
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
If the crystal size is in the nanometric range, X-ray crystallography
cannot be used because of both the weak interaction between X-ray
and matter and the damage induced by high energy X-ray photons.
Electrons interact with matter about 103-104 times stronger than Xray and are therefore the ideal source to study such small single
crystals.
Electron diffraction can provide data up to 0.5 Å (and even more) but
only 2D projections.
A pseudo 3D set of reflections can be obtained by tilting the sample
and merging different zone axes. Furthermore dynamical effects can
reduce the reliability of the measured intensities.
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
The PED techniques reduce the number of reflections which
are simultaneously excited and therefore allow to describe
the scattering by few beam approximations, however 2dimensional reflections from few well oriented zone axes are
usually collected.
More recently the combination of the ADT (Automated
Diffraction Tomography) technique with PED has increased
the data quality and completeness.
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
If PED techniques are used, the dynamical effects are no
more dominant but still present.
Two questions arise:
1) Is the average (over symmetry equivalent reflections) a
good representative of the correct intensity?
2) In absence of a theoretical formulation establishing which
of the equivalent reflections is less affected by dynamical
scattering, can one use a practical criterion for selecting
the best unique reflection?
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
BEA has some similarity with a criterion used in powder
crystallography during the phasing process:
when a structural model is not available the experimental
diffraction profile is decomposed according to LeBail or to
Pawley algorithms;
if a structural model is available, the experimental diffraction
profile is partitioned in a way proportional to the calculated
structure factors of the overlapping reflections.
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
In the BEA (Best Equivalent Amplitude) algorithm it is
selected as unique reflection that one which better agrees
with the current structural model.
The effect is certainly cosmetic (the final RESID value may
be much smaller than that obtained by using the average of
the equivalent amplitudes). But it may also be substantial:
i.e., the crystal structure solution becomes more
straightforward and the final structural model may be more
complete
Erice 2011 Electron Crystallography – June 2-12 2011
New features for electron diffraction data
Direct Methods applications, performed via the last version
of the program Sir2011 including BEA, show that such
algorithm is able to provide more complete structural models
and better crystallographic residuals.
More extended applications are needed to extrapolate the
usefulness of BEA for the final refinement stages.
Erice 2011 Electron Crystallography – June 2-12 2011
Test structure: Charoite
89 atoms in a.u.
I. Rozhdestvenskaya, E. Mugnaioli, M. Czank, W. Depmeier, U. Kolb, A. Reinholdt,
T. Weirich, Mineralogical Magazine 74 (2010), 159-177.
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
New procedure to select
the space group
A new algorithm has been developed for the automatic
identification of the Laue group and of the extinction symbol
from electron diffraction intensities.
The algorithm has a statistical basis, and tries to face the
severe problems arising from the often non-kinematical
nature of the diffraction intensities, from the limited
accuracy of the lattice parameters determined via electron
diffraction and from the limited amount of measured
intensities.
Erice 2011 Electron Crystallography – June 2-12 2011
New procedure to select
the space group
First step
Since the accepted unit cell may show a lattice symmetry
higher than the true one, all the crystal systems with unit
cells compatible with that experimentally estimated (we will
call them feasible systems) are taken into considerations for
the next steps.
For example, in case of aSecond
cell with
cubic geometry,
step
tetragonal,
monoclinic
and triclinic
systems
The list oforthorhombic,
the Laue groups
compatible
with each
feasible
are
considered
hexagonal and
trigonal are
crystal
systemfeasible,
is automatically
generated
(denoted as
excluded.
Erice 2011 Electron Crystallography – June 2-12 2011
New procedure to select
the space group
Third step
For each feasible crystal system the admitted Laue group
with minimal symmetry (say LGmin) is considered. For each
i-th admitted Laue group the internal residual factor Rint(i) is
calculated:
Rint

|F | |F

(i ) =
 F 
obsh
obsh
|

obsh
The probability of the i-th Laue group is:
PL (i)   [0.85- Rint (i)](n/2)
1/6
Erice 2011 Electron Crystallography – June 2-12 2011

2
New procedure to select
the space group
The final probabilistic formula for identifying the most
probable extinction symbol, and simultaneously, for
confirming the most probable Laue group and crystal
system is:
[ PEX (i, j )]sc  PL (i)[PEX ( j )]
1/ m
associated to the i-th admitted Laue group and the j-th
extinction symbol
Erice 2011 Electron Crystallography – June 2-12 2011
New procedure to select
the space group
Charoite
Cell 31.91 19.64 7.09 90 90 90
Space Group: P 21/m
Erice 2011 Electron Crystallography – June 2-12 2011
New procedure to select the space group
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Simulated Annealing
Erice 2011 Electron Crystallography – June 2-12 2011
Simulated Annealing
Erice 2011 Electron Crystallography – June 2-12 2011
Simulated Annealing
Erice 2011 Electron Crystallography – June 2-12 2011
What’s new
 VLD procedure
 Fourier map in a small volume
 New features for electron diffraction data
 New procedure to select the space group
 Simulated Annealing
 Integration with Jav, the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
Integration with Jav,
the new visualizer in 3D
Erice 2011 Electron Crystallography – June 2-12 2011
The program
J. Appl. Cryst. (2011), in preparation
Sir2011: a new program for crystal structure solution
M.C.Burla, R. Caliandro, M. Camalli, B. Carrozzini,
G.L. Cascarano, C. Giacovazzo, A. Mazzone, G. Polidori, R. Spagna
This program will be available, free of
Linux, Mac and MS Windows systems.
Erice 2011 Electron Crystallography – June 2-12 2011
The authors
R.Caliandro, B.Carrozzini, G.L.Cascarano,
C.Giacovazzo, A. Mazzone
Istituto di Cristallografia del CNR – Bari
M.Camalli, R.Spagna
Istituto di Cristallografia del CNR –Rome
M.C.Burla, G.Polidori
Dipartimento di Scienze della Terra,
University of Perugia
Erice 2011 Electron Crystallography – June 2-12 2011
Tutorial