Single Crystal Structure
Determination of Organic and
Organometallic Compounds
A.L. (Ton) Spek
National Single Crystal
Service Facility
Utrecht University
Amsterdam, 23-10-2007
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
Single Crystals
3D-Structure
X-Ray Diffraction Experiment
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 …
Announced Aug 2007: Tabletop
‘Black Box’ – Smart X2S
Crystal
Structure ?
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.
Black Box => Gray Box
Two sub-boxes
Crystal
X-Ray
Diffraction
Experiment
-Unitcell info
-H K L, I, (I)
Computation
-Solution of the
phase problem
-3D model x,y,z
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
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
X-Ray source, Goniometer & Serial Detector
LNT
CCD - Detector
X-ray
Crystal
Goniometer
X-ray source, goniometer + crystal, N2-cooling and CCD Detector
One of the several hundreds of CCD images with diffraction spots
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)
Computation
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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
Data Reduction
• Integration and scaling of the diffraction
intensities
• E.g. with programs
(Generally comes with the hardware)
DENZO, EVAL-CCD, SAINT
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.)
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
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
Contoured 2D-Section Through the 3D Structure
Solution of the Phase Problem
• Direct Methods
e.g. SHELXS, SHELXD, SIR, CRUNCH
• Patterson Methods
DIRDIF
• Fourier Difference Maps (Structure Completion)
• New: Charge Flipping
Abstracted and Interpreted Structure
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 = Sj=1,n fj T exp{2pi(hx + ky + lz)}
• Non-linear Least-squares Parameter Refinement
until Convergence.
• Minimize: Shkl w [(Fhklobs)2 – (Fhklcalc)2]2
• Agreement Factor: R = S |Fobs – Fcalc| / S|Fobs|
Refinement of the Structural
Model
Refinement Steps (Programs SHELXL, Crystals,
XTAL etc)
1. Refine positional parameters + isotropic U
2. Refine positional + anisotropic parameters
3. Introduce H-atoms
4. Refine H-atoms with x,y,z,U(iso) or riding on
their carrier atoms
5. Refine weighting scheme
6. ORTEP presentation 
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..p)
Structure Validation
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•
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•
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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.
Technical Issues and Problems
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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
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
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
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
WRONG SPACEGROUP
J.A.C.S. (2000),122,3413 – P1, Z = 2
CORRECTLY REFINED STRUCTURE
P-1, Z=2
Organic Letters (2006) 8, 3175
P1, Z’ = 8
C
C
o
Correct Symmetry ?
Correct Space Group
After Transformation to P212121, Z’ = 2
Organometallics (2004) 23,2310
Change of Space Group ALERT
(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) >> F(calc) )
• TwinRotMat Automatic Twinning Analysis as
implemented in PLATON (Based on a similar analysis but
implemented differently)
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 
Ideas behind the Algorithm
• Reflections effected by twinning show-up in the
least-squares refinement with F(obs) >> 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.
Possible Twin Axis
H” = H + H’
H
Reflection
with
F(obs) >>
F(calc)
Candidate twinning axis
(Normalize !)
H’
Strong reflection H’ with theta
close to theta of reflection H
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 
DEFINE SOLVENT ACCESSIBLE VOID
STEP #1 – EXCLUDE VOLUME INSIDE THE
VAN DER WAALS SPHERE
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
DEFINE SOLVENT ACCESSIBLE VOID
STEP # 3 – EXTEND INNER VOLUME WITH POINTS WITHIN
1.2 ANGSTROM FROM ITS OUTER BOUNDS
Listing of all voids in the triclinic unit cell
Cg
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
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
• Note:SHELXL lacks option for fixed contribution
to Structure Factor Calculation.
SQUEEZE Algorithm
1.
2.
3.
4.
5.
Calculate difference map (FFT)
Use the VOID-map as a mask on the FFT-map to set all
density outside the VOID’s to zero.
FFT-1 this masked Difference map -> contribution of the
disordered solvent to the structure factors
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.
Recycle to 2 until convergence.
SQUEEZE
In the Complex Plane
Fc(total)
Fc(solvent)
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.
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.
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.
Absolute Structure Determination
Complex 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.
Breakdown of Friedels Law
• It can be derived from the expression for the
calculated structure factor that for noncentrosymmetric crystal structures:
|Fhkl| not necessarily equal to |F-h-k-l|
for f “ > 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).
Friedel Pairs
H,K,L
-H,-K,-L
Friedel Pair of Reflections
Selected f” - values
f”(CuKα)
f”(MoKα)
Se
1.14
2.23
Cl
0.70
0.16
S
0.56
0.12
O
0.032
0.006
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) |Fhkl|2 + x |F-h-k-l|2
• Result of the least-squares refinement: x(u)
Where x has physically a value between 0 and 1
and u the standard uncertainty (‘esd’)
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 < 0.04 and |x| < 2u
• For a compound with known enantiopurity:
u should be < 0.1 and |x| < 2u
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 
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 
Excellent Correlation
MoKa, P212121
Example: Ammonium Bitartrate Test
Ammonium BiTartrate (MoKa)
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 
MoKa
Natural Vitamin C, L-(+)Ascorbic Acid
L-(+) Ascorbic Acid
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).
Do we need Validation ?
Some Statistics
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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 
Organometallics (2006) 25, 1511-1516
Next Slide: This is why the reported density is low and the R and Rw
high 
Solvent
Accessible
Void of
235 Ang3
out of
1123 Ang3
Not Accounted
for in the
Refinement
Model
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.
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.
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?
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.
ALERT LEVELS
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ALERT A – Serious Problem
ALERT B – Potentially Serious Problem
ALERT C – Check & Explain
ALERT G – Verify or Take Notice
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.
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 ?
Problems Addressed by
PLATON/CIF-CHECK
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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)
More Problems Addressed by
PLATON
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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.
Additional Problems Addressed by
PLATON/FCF-CHECK
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•
•
•
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 
Section in
reciprocal
space
Missing cusp
of data
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 OH hydrogen atom is in general the cause.
• Molecules have an environment in the crystal !
• Example 
Example of a PLATON/Check Validation Report: Two
ALERTS related to the misplaced Hydrogen Atom
Difference Electron Density Map
Validation Looks at
inter-molecular
contacts
Example of Misplaced Hydrogen Atom
Unsatisfactory Hydrogen Bond
Network
Satisfactory Hydrogen Bond Network with new H-position
Correct !
ALERT !
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
QUATERNION FIT
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:
Tetragonal
“Orthorhombic”
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.
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.
Additional Info
http://www.cryst.chem.uu.nl
(including a copy of this powerpoint presentation)
Thanks
for your attention !!