Single Crystal Structure Determination of Organic and Organometallic Compounds

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Single Crystal Structure Determination of Organic
and Organometallic Compounds

• A.L. (Ton) Spek
• National Single Crystal
• Service Facility
• Utrecht University
• Amsterdam, 23-10-2007

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Single Crystal X-Ray Structure Determination
Nowadays THE technique in support of synthetic
chemistry either to confirm a proposed structure
or to solve a puzzle.
BLACK BOX
3D-Structure
Single Crystals
X-Ray Diffraction Experiment
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Some History

• The first X-ray structure determination was
  carried out around 1913 (Bragg).
• In the sixties, 40 years ago, a small molecule
  crystal structure determination still took in the
  order of half a year.
• Main problems were the time consuming data
  collection, the solution of the Phase Problem
  and the the scarce and slow university main frame
  computing facilities.
• We received in the late 70th an interesting
  request from a synthetic chemist interested in
  the 3D structure of a new compound .. Can you
  inject this sample in your diffractometer .., a
  request that looked naïve at the time.
• In hindsight he was visionary, since

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Announced Aug 2007 Tabletop Black Box Smart
X2S
Crystal
Structure ?
5
Current Status

• Data collection and evaluation procedures have
  now evolved to a level that a subset of the
  routine samples can indeed be analyzed
  automatically in a matter of hours.
• The problem is that many real world samples still
  turn out to be non-routine.
• Thus still a working knowledge is needed of what
  is in the box in order to get a reliable
  structure.

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Black Box gt Gray Box
Two sub-boxes
X-Ray Diffraction Experiment
Crystal

• Unitcell info
• H K L, I, ?(I)

-Solution of the phase problem -3D model x,y,z
Computation
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X-Ray Diffraction Experiment

• X-Ray Sources
• Sealed Tube (CuKa, MoKa) 1-3kW
• Rotating Anode (CuKa, MoKa) 10kW
• Rotating Anode Focussing Mirrors
• New Microsource 30W
• Low Temperature Unit for the best data

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X-Ray Diffraction Experiment

• Reflection RegistrationTechniques
• 2D-X-Ray Film (Weissenberg Camera etc.)
• 1D-Point Detector (Scientilation counter CAD4 -
  Automation
• 2D-Image Plate
• CCD 2D Detector (KappaCCD, APEX)
• Future? Real time 2D low noise, shutterless
  detectors

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X-Ray source, Goniometer Serial Detector
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LNT
CCD - Detector
X-ray
Crystal
Goniometer
X-ray source, goniometer crystal, N2-cooling
and CCD Detector
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One of the several hundreds of CCD images with
diffraction spots
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Data Collection

• Diffraction Condition (determines the position of
  the diffracted beams on the detector)
• 2 dhkl sin(Q) n l (Bragg Equation)
• Result
• - Cell Dimensions, a,b,c, a, b, g
• - Reflection intensities by planes (hkl) in
  the crystal I(hkl) (many thousands)

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Computation

• Data Reduction to hkl I and ?(I)
• Correction for absorption effects
• Determination of the Space Group
• Solution of the Phase Problem
• Abstraction of a Parameter Model from 3D-density
  map
• Refinement of the Structural Model
• Analysis of the geometry, intermolecular
  interactions
• Structure Validation

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Data Reduction

• Integration and scaling of the diffraction
  intensities
• E.g. with programs
• (Generally comes with the hardware)
• DENZO, EVAL-CCD, SAINT

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Correction for Absorption

• Numerical correction based on the description of
  the crystal in terms of its bounding faces.
• Correction based on Phi-scans (Serial Det.)
• Fitted Absorption Surface based on multiple
  measured reflections with different setting
  angles (SADABS, TWINABS, MULABS etc.)

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Determination of the Space Group

• Based on
• Cell Dimensions
• Laue Symmetry
• Intensity Statistics (Centro/Non-Centro)
• Systematic Extinctions
• Space Group Frequency in the CSD
• Note Not always a unique proposal

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Structure Determination

• Experiment ? Ihkl ? Fhkl Sqrt(Ihkl)
• Needed for 3D structure (approximate) Phases
  fhkl
• Fhkl fhkl Fhkl? 3D-Fourier Synthesis
• r(x,y,z) Shkl Fhkl exp-2pi(hx ky lz) /
  V
• x,y,z are fractional coordinates (range 0 ? 1)
• Example ? next slide

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Contoured 2D-Section Through the 3D Structure
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Solution of the Phase Problem

• Direct Methods
• e.g. SHELXS, SHELXD, SIR, CRUNCH
• Patterson Methods
• DIRDIF
• Fourier Difference Maps (Structure Completion)
• New Charge Flipping

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Abstracted and Interpreted Structure
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3D Parameter Model

• Extract the 3D Coordinates (x, y, z) of the
  atoms.
• Assign Atom Types (Scattering type C, O etc.)
• Assign Additional Parameters to Model the Thermal
  Motion (T) of the Atoms.
• Other Parameters Extinction, Twinning, Flack x
• Model Fhkl Sj1,n fj T exp2pi(hx ky lz)
• Non-linear Least-squares Parameter Refinement
  until Convergence.
• Minimize Shkl w (Fhklobs)2 (Fhklcalc)22
• Agreement Factor R S Fobs Fcalc / SFobs

22
Refinement of the Structural Model

• Refinement Steps (Programs SHELXL, Crystals, XTAL
  etc)
• Refine positional parameters isotropic U
• Refine positional anisotropic parameters
• Introduce H-atoms
• Refine H-atoms with x,y,z,U(iso) or riding on
  their carrier atoms
• Refine weighting scheme
• ORTEP presentation ?

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Analysis of the Geometry and Intermolecular
Interactions

• Programs PLATON, PARST etc
• Bond distances, angles, torsion angles, ring
  (puckering) geometry etc.
• Intermolecular Contacts
• Hydrogen Bonds (O-H..O, N-H..O, O-H..?)

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Structure Validation

• Refinement results in CIF File format.
• Final Fobs/Fcalc data in FCF File Format
• IUCr CHECKCIF tool
• PLATON Validation Tool
• Check in Cambridge Crystallographic Database for
  similar structures.

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Technical Issues and Problems

• Poor crystal quality (e.g. fine needle bundles)
• Determination of the correct Space Group Symmetry
• Pseudo-Symmetry
• Absolute Structure of light atom structures
• Twinning
• Positional and substitutional disorder of part
  (or even the whole) molecule
• Disordered Solvent
• Incommensurate structures
• Diffuse scattering, streaks, diffuse layers

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Tools offered by PLATON

• The program PLATON offers multiple tools that can
  be used to analyse and solve problems encountered
  in a single crystal structure determination
• ? Next slide Main Feature Menu PLATON

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Selected Tools

• ADDSYM Detection and Handling of Missed
  (Pseudo)Symmetry
• TwinRotMat Detection of Twinning
• SOLV Report of Solvent Accessible Voids
• SQUEEZE Handling of Disordered Solvents in
  Least Squares Refinement (Easy to use Alternative
  for Clever Disorder Modelling)
• BijvoetPair Post-refinement Absolute Structure
  Determination (Alternative for Flack x)
• VALIDATION PART of IUCr CHECKCIF

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ADDSYM

• About 1 of the 2006 2007 entries in the CSD
  need a change of space group.
• Often, a structure solves only in a space group
  with lower symmetry than the correct space group.
  The structure should subsequently be checked for
  higher symmetry.
• Next slides Recent examples of missed symmetry

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WRONG SPACEGROUP
J.A.C.S. (2000),122,3413 P1, Z 2
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CORRECTLY REFINED STRUCTURE
P-1, Z2
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Organic Letters (2006) 8, 3175
Correct Symmetry ?
P1, Z 8
CCo
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Correct Space Group
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After Transformation to P212121, Z 2
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Organometallics (2004) 23,2310
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Change of Space Group ALERT
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(Pseudo)Merohedral Twinning

• Options to handle twinning in L.S. refinement
  available in SHELXL, CRYSTALS etc.
• Problem Determination of the Twin Law that is in
  effect.
• Partial solution coset decomposition, try all
  possibilities
• (I.e. all symmetry operations of the lattice
  but not of the structure)
• ROTAX (S.Parson et al. (2002) J. Appl. Cryst.,
  35, 168.
• (Based on the analysis of poorly fitting
  reflections of the type F(obs) gtgt F(calc) )
• TwinRotMat Automatic Twinning Analysis as
  implemented in PLATON (Based on a similar
  analysis but implemented differently)

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TwinRotMat Example

• Originally published as disordered in P3.
• Solution and Refinement in the trigonal space
  group P-3 ?R 20.
• Run PLATON/TwinRotMat on CIF/FCF
• Result Twin law with an the estimate of the
  twinning fraction and the estimated drop in
  R-value
• Example of a Merohedral Twin ?

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Ideas behind the Algorithm

• Reflections effected by twinning show-up in the
  least-squares refinement with F(obs) gtgt F(calc)
• Overlapping reflections necessarily have the same
  Theta value within a tolerance.
• Generate a list of implied possible twin axes
  based on the above observations.
• Test each proposed twin law for its effect on the
  R-value.

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Possible Twin Axis
H H H
Candidate twinning axis (Normalize !)
H
H
Reflection with F(obs) gtgt F(calc)
Strong reflection H with theta close to theta of
reflection H
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Solvent Accessible Voids

• A typical crystal structure has only in the order
  of 65 of the available space filled.
• The remainder volume is in voids (cusps)
  in-between atoms (too small to accommodate an
  H-atom)
• Solvent accessible voids can be defined as
  regions in the structure that can accommodate at
  least a sphere with radius 1.2 Angstrom without
  intersecting with any of the van der Waals
  spheres assigned to each atom in the structure.
• Next Slide Void Algorithm Cartoon Style ?

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DEFINE SOLVENT ACCESSIBLE VOID
STEP 1 EXCLUDE VOLUME INSIDE THE VAN DER
WAALS SPHERE
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DEFINE SOLVENT ACCESSIBLE VOID
STEP 2 EXCLUDE AN ACCESS RADIAL VOLUME TO
FIND THE LOCATION OF ATOMS WITH THEIR CENTRE AT
LEAST 1.2 ANGSTROM AWAY
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DEFINE SOLVENT ACCESSIBLE VOID
STEP 3 EXTEND INNER VOLUME WITH POINTS
WITHIN 1.2 ANGSTROM FROM ITS OUTER BOUNDS
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Listing of all voids in the triclinic unit cell
Cg
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VOID APPLICATIONS

• Calculation of Kitaigorodskii Packing Index
• As part of the SQUEEZE routine to handle the
  contribution of disordered solvents in crystal
  structure refinement
• Determination of the available space in solid
  state reactions (Ohashi)
• Determination of pore volumes, pore shapes and
  migration paths in microporous crystals

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SQUEEZE

• Takes the contribution of disordered solvents to
  the calculated structure factors into account by
  back-Fourier transformation of density found in
  the solvent accessible volume outside the
  ordered part of the structure (iterated).
• Filter Input shelxl.res shelxl.hkl
• Output solvent free shelxl.hkl
• Refine with SHELXL or Crystals
• NoteSHELXL lacks option for fixed contribution
  to Structure Factor Calculation.

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SQUEEZE Algorithm

1. Calculate difference map (FFT)
2. Use the VOID-map as a mask on the FFT-map to set
   all density outside the VOIDs to zero.
3. FFT-1 this masked Difference map -gt contribution
   of the disordered solvent to the structure
   factors
4. Calculate an improved difference map with F(obs)
   phases based on F(calc) including the recovered
   solvent contribution and F(calc) without the
   solvent contribution.
5. Recycle to 2 until convergence.

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SQUEEZE In the Complex Plane
Fc(solvent)
Fc(total)
Fc(model)
Fobs
Solvent Free Fobs
Black Split Fc into a discrete and solvent
contribution Red For SHELX refinement,
temporarily substract recovered solvent
contribution from Fobs.
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Comment

• The Void-map can also be used to count the number
  of electrons in the masked volume.
• A complete dataset is required for this feature.
• Ideally, the solvent contribution is taken into
  account as a fixed contribution in the Structure
  Factor calculation (CRYSTALS) otherwise it is
  subtracted temporarily from Fobs2 (SHELXL) and
  re-instated afterwards with info saved beyond
  column 80 for the final Fo/Fc list.

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Publication Note

• Always give the details of the use of SQUEEZE in
  the comment section
• Append the small CIF file produced by PLATON to
  the main CIF
• Use essentially complete data sets with
  sufficient resolution only.
• Make sure that there is no unresolved charge
  balance problem.

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Absolute Structure DeterminationComplex
Scattering Factors

• Scattering factor f f0 f if
• Where
• f0 a function of diffraction angle Q and
  equal to the number of electrons in the atom at Q
  0.
• f and f atom type and l dependent
• i sqrt(-1)
• Note A phase shift is often represented
  mathematically as a complex number.

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Breakdown of Friedels Law

• It can be derived from the expression for the
  calculated structure factor that for
  non-centrosymmetric crystal structures
• Fhkl not necessarily equal to F-h-k-l
• for f gt 0, thus breaking the earlier
  assumed Friedel Law Fhkl F-h-k-l
• (The Friedel Law still holds for
  centro-symmetric structures containing racemic
  mixtures of chiral compounds).

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Friedel Pairs
H,K,L
-H,-K,-L
Friedel Pair of Reflections
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Selected f - values
f(CuKa) f(MoKa)
Se 1.14 2.23
Cl 0.70 0.16
S 0.56 0.12
O 0.032 0.006
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Flack Parameter

• The current official method to establish the
  absolute configuration of a chiral molecule
  calls for the determination of the Flack x
  parameter.
• Flack, H.D. (1983). Acta Cryst. A39, 876-881.
• Twinning Model (mixture model and image)
• Ihklcalc (1 x) Fhkl2 x F-h-k-l2
• Result of the least-squares refinement x(u)
• Where x has physically a value between 0 and
  1
• and u the standard uncertainty (esd)

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Interpretation of the Flack x

• H.D.Flack G. Bernardinelli (2000)
• J. Appl. Cryst. 33, 1143-1148.
• For a statistically valid determination of the
  absolute structure
• u should be lt 0.04 and x lt 2u
• For a compound with known enantiopurity
• u should be lt 0.1 and x lt 2u

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Post-Refinement Absolute Structure Determination

• Unfortunately, many pharmaceuticals contain in
  their native form only light atoms that at best
  have only weak anomalous scattering power and
  thus fail the strict Flack conditions.
• Alternative approaches are offered by PLATON with
  scatter plots and the determination of the Hooft
  y parameter ?

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Scatter Plot of Bijvoet Differences

• Plot of the Observed Bijvoet (Friedel)
  Differences against the Calculated Differences.
• A Least-Squares line is calculated
• The Green least squares line should run from the
  lower left to the upper right corner for the
  correct absolute structure.
• Vertical bars on data points indicate the su
• on the Bijvoet Difference. Example ?

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Excellent Correlation
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MoKa, P212121
Example Ammonium Bitartrate Test
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Ammonium BiTartrate (MoKa)
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Bayesian Approach

• Rob Hooft (Bruker) has developed an alternative
  approach for the analyses of Bijvoet differences
  that is based on Bayesian statistics. (Paper
  under review)
• Under the assumption that the material is
  enantiopure, the probability that the assumed
  absolute structure is correct, given the set of
  observed Bijvoet Pair Differences, is calculated.
• An extension of the method also offers the Fleq y
  (Hooft y) parameter to be compared with the Flack
  x.
• Example Ascorbic Acid, P21, MoKa data ?

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MoKa
Natural Vitamin C, L-()Ascorbic Acid
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L-() Ascorbic Acid
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Hooft y Proper Procedure

• Collect data with an essentially complete set of
  Bijvoet Pairs
• Refine in the usual way (preferably) with BASF
  and TWIN instructions (SHELXL)
• Structure Factors to be used in the analysis are
  recalculated in PLATON from the parameters in the
  CIF (No Flack x contribution).

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Do we need Validation ?Some Statistics

• Validation CSD Entries 2006 2007
• Number of entries 35760
• of likely Space Group Changes 384
• of structures with voids 3354
• Numerous problems with H, O, OH, H2O etc.
• Example ?

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Organometallics (2006) 25, 1511-1516
Next Slide This is why the reported density is
low and the R and Rw high ?
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Solvent Accessible Void of 235 Ang3 out
of 1123 Ang3
Not Accounted for in the Refinement Model
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SOLUTION

• A solution for the structure validation
  problem was pioneered by the International Union
  of Crystallography
• Provide and archive crystallographic data in the
  computer readable CIF standard format.
• Offer Automated validation, with a computer
  generated report for authors and referees.
• Have journals enforce a structure validation
  protocol.
• - The IUCr journals and most major journals now
  indeed implement some form of validation
  procedure.

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THE CIF DATA STANDARD

• Driving Force Syd Hall (IUCr/ Acta Cryst C)
• Early Adopted by XTAL SHELX(T)L.
• Currently WinGX,Crystals,Texsan, Maxus etc.
• Acta Cryst. C/E Electronic Submission
• Acta Cryst.Automatic Validation at the Gate
• CIF data available for referees for detailed
  inspection (and optional calculations).
• Data retrieval from the WEB for published papers
• CCDC Deposition in CIF-FORMAT.

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VALIDATION QUESTIONS

• Single crystal validation addresses three
• simple but important questions
• 1 Is the reported information complete?
• 2 What is the quality of the analysis?
• 3 Is the Structure Correct?

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IUCr CHECKCIF WEB-Service

• http//checkcif.iucr.org reports the outcome of
• IUCr standard tests
• Consistency, Missing Data, Proper Procedure,
  Quality etc.
• Additional PLATON based tests
• Missed Symmetry, Twinning, Voids, Geometry,
  Displacement Parameters, Absolute Structure etc.

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ALERT LEVELS

• ALERT A Serious Problem
• ALERT B Potentially Serious Problem
• ALERT C Check Explain
• ALERT G Verify or Take Notice

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ALERT TYPES

• 1 - CIF Construction/Syntax errors,
• Missing or Inconsistent Data.
• 2 - Indicators that the Structure Model
• may be Wrong or Deficient.
• 3 - Indicators that the quality of the results
• may be low.
• 4 - Cosmetic Improvements, Queries and
• Suggestions.

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EXAMPLE OF PLATON GENERATED ALERTS FOR A
RECENT PAPER PUBLISHED IN J.Amer.Chem.Soc. (2007)
Attracted special attention in Chemical and
Engineering News
Properly Validated ?
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Problems Addressed by PLATON/CIF-CHECK

• Missed Higher Space Group Symmetry
• Solvent Accessible Voids in the Structure
• Unusual Displacement Parameters
• Hirshfeld Rigid Bond test
• Misassigned Atom Type
• Population/Occupancy Parameters
• Mono Coordinated/Bonded Metals
• Isolated Atoms (e.g. O, H, Transition Metals)

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More Problems Addressed by PLATON

• Too Many Hydrogen Atoms on an Atom
• Missing Hydrogen Atoms
• Valence Hybridization
• Short Intra/Inter-Molecular Contacts
• O-H without Acceptor
• Unusual Bond Length/Angle
• CH3 Moiety Geometry
• To be extended with tests for new problems
  invented by authors.

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Additional Problems Addressed byPLATON/FCF-CHECK

• Information from .cif and .fcf files
• Report on the resolution of the data
• Report about randomly missing data
• Check the completeness of the data (e.g. for
  missing cusps of data
• Report on Missed (Pseudo) Merohedral Twinning
• Report on Friedel Pairs and Absolute Structure
• Next Slide ASYM VIEW Display for the inspection
  of the data completeness ?

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Section in reciprocal space
Missing cusp of data
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Incorrectly Oriented O-H

• The O-H moiety is generally, with very few
  exceptions, part of a D-H..A system.
• An investigation of structures in the CSD brings
  up many exceptions.
• Closer analysis shows that misplacement of the
  O-H hydrogen atom is in general the cause.
• Molecules have an environment in the crystal !
• Example ?

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Example of a PLATON/Check Validation Report Two
ALERTS related to the misplaced Hydrogen Atom
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Difference Electron Density Map
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Validation Looks at inter-molecular contacts
Unsatisfactory Hydrogen Bond Network
Correct !
ALERT !
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QUATERNION FIT

• In many cases, an automatic molecule fit can be
  performed
• A) Identical atom numbering
• B) Sufficient number of Unique Atoms
• C) By manual picking of a few atom pairs

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QUATERNION FIT
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Simulated Powder Patterns

• It is not always apparent that two crystal
  structures are identical. The assigned unit cell
  or space group can differ.
• Comparison of the associated calculated powder
  patterns should solve the issue.
• Example for the CSD

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Tetragonal
Orthorhombic
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THE MESSAGE

• Validation should not be postponed to the
  publication phase. All validation issues should
  be taken care of during the analysis.
• Everything unusual in a structure is suspect,
• mostly incorrect (artifact) and should be
  investigated and discussed in great detail and
  supported by additional independent evidence.
• - The CSD can be very helpful when looking for
  possible precedents.

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CONCLUSION

• Validation Procedures are excellent Tools to
• Set Quality Standards (Not just on R-Value)
• Save a lot of Time in Checking, both by the
  Investigators and the Journals (referees)
• - Point at Interesting Features
  (Pseudo-Symmetry,
• short Interactions etc.) to be discussed.
• Surface a problem that only an experienced
  Crystallographer might be able to Address
• Proof of a GOOD structure.

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Additional Info

• http//www.cryst.chem.uu.nl
• (including a copy of this powerpoint
  presentation)
• Thanks
• for your attention !!

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