Absolute Structure Determination of Chiral Molecules:

State-of-the-Art X-ray Diffraction based Tools

A.L.Spek

Bijvoet Centre of Biomolecular Research

Utrecht University

The Netherlands

Organon, Oss, 25-January 2007

Outline of this Talk

• Introduction to who we are.• Intro to Single Crystal X-ray Structure Determination.• Concept of Absolute Structure (Absolute Configuration).• Resonant Scattering (Anomalous Dispersion).• Early Applications (Bijvoet, Peerdeman & van Bommel).• The Flack Parameter – The Current De-facto Absolute

Structure Analysis Tool (‘IUCr Approved’).• Absolute Structure Determination of Light Atom.

Structures: Problems and Tentative New Tools. • Concluding Remarks.

Who are we ?

• The National facility for ‘small molecule’ single crystal structure determination since 1971 in the Netherlands.

• Embedded within the Crystal and Structural Chemistry group in Utrecht.• Most of the Crystal and Structural Chemistry

research in Utrecht has moved from small molecule to protein crystallography (Structural Biology – Piet Gros).

Small molecule and Protein Xtallography:Utrecht

Some Statistics

• Collaboration of the National facility with most synthetic groups in the Netherlands (mostly academic and a few commercial) who send their samples for analysis to Utrecht.

• We handled over 3800 requests over the past 35 years. Mainly organometallic and coordination chemistry, but also from organic, pharmaceutical and mineralogical background.

• Up to now, the results have been reported in over 1200 (joint) papers.

People Involved

• The last years 3 to 4, mostly PHD’s, of which one on a postdoc position.

• Currently a permanent staff of 2 + 1 postdoc.• Dr. Martin Lutz (since 1997) • Dr. Lars von Chrzanowski (postdoc since Oct 15, 2006) Successor of Dr. Huub Kooijman (now SHELL)• In the past: a few trained chemists in the context

of their synthetic work.

Associated Functions

• Development of crystallographic software based on local needs: collected in the PLATON package.

• Crystal Structure Validation (IUCr)

• Co-Editor of Acta Cryst. C (involved in the handling of more than 1000 CIF-formatted papers).

Single Crystal Structure Determination ‘Routine’

• Select and Mount a Suitable Single Crystal, preferably taken from the mother liquor (typical size : 0.3 mm in all directions)

• Determine Lattice Parameters, Space Group Symmetry • Collect (Redundant) Set of Reflection Intensity Data,

preferably on a CCD based diffractometer system at 150 K (in N2 stream) (MoK X-rays)

• Solve the Phase Problem (I.e. Recover Phases Associated with the Measured Intensities)

• Least Squares Refinement of a Parameter Model (Coordinates, Displacement parameters, etc.)

• Analysis, Reporting & Archiving of the Data & Results

X-Ray source, Goniometer & Serial Detector

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( = n Bragg Equation)• Result: - Cell Dimensions, a,b,c, - Reflection intensities by planes (hkl) in

the crystal: I(hkl) (many thousands)

Structure Determination

• Experiment Ihkl |Fhkl| = Sqrt(Ihkl)• Needed for 3D structure (approximate) Phases: hkl

• Current Tools for Phase Recovery from |Ihkl| with:

- Patterson Techniques (heavy atom structures) (DIRDIF)

- Direct Methods (SHELXS, SIR)

- New: Charge Flipping:

Brute Force, Random Start, Ab-Initio (FFT, FFT-1)

- |Fhkl| + hkl = Fhkl 3D-Fourier Synthesis

(x,y,z) = [ hkl Fhkl exp{-2(hx + ky + lz)}] / V

Contoured 2D-Section Through the 3D Structure

Abstracted and Interpreted Structure

Refinement of a 3D 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 = j=1,n fj T exp{2i(hx + ky + lz)}• Non-linear Least-squares Parameter Refinement until

Convergence.• Minimize: hkl w [(Fhklobs)2 – (Fhklcalc)2]2

• Agreement Factor: R = |Fobs – Fcalc| / |Fobs|

ORTEP Presentation of Model Parameters

A-Priori Info Needed

• In principle nothing needs to be known about the composition.

• Any available (correct) info may speed up the analysis and interpretation.

• Often a service analysis turns up the structure of a different compound than intended, either boring or an interesting surprise. The only good crystal in a batch may be a contamination.

Newly Obtained Info

• Confirmation of proposed structure

• Unexpected new structure or chemistry

• Detailed info on the geometry (bonds, angles, torsion, ring puckering)

• Polymorphism

• Molecular interactions

• Absolute Configuration

X-ray Analysis Routine ?

Yes under optimal circumstances in the hands of a professional.

No in many cases due to:• Poor Crystal Quality (fine needle bundles etc.)• Complicated Twinning• Disorder in part of the molecule• Disordered (unknown) included lattice solvent• Pseudo Symmetry, Incommensurate Structures

Absolute Structure of Chiral Compounds

• Question before 1951: how to correlate microscopic absolute configurations to macroscopic properties such as the sign of the optical rotation of polarised light.

• Emil Fischer: relative system; assign ‘D’ configuration to (+) Glyceraldehyde.

• His ‘lucky’ choice was later ‘confirmed’ by calculations and physical methods.

Example of a Macroscopic Property

Absolute Structure

D-(+)-Glyceraldehyde

Emil Fisher: Arbitrary D assignments (50% chance to be correct)

Natural Isomer L-(R,R-(+) Tartaric Acid)

CIP-Nomenclature for Chiral Atoms: R,S

Prof. Dr. J.M. Bijvoet (1892-1980)

Bijvoet used Anomalous Dispersion (Resonant Scattering)to Solve the Absolute Structure Problem around 1950

Resonant Scattering

• X-rays interacting with the electrons in an atom scatter in all directions or in crystals in only certain directions due to interference.

• The phase of the waves scattered by the outer electrons of an atom is shifted by 180 degrees .

• This is no longer true for the inner electrons in heavier atoms resulting in a phase shift less than 180 degrees

• Therefore scattering factors are real numbers only in a first order approximation (I.e. with phase 0 or 180o)

• Second order effects become prominent when the frequency of the X-rays is close to the resonance frequency of the inner electrons of a heavy atom

(e.g. K shell).

Complex Scattering Factors

• Scattering factor: f = f0 + f ’ + if ’’ Where: f0 = a function of diffraction angle and equal to the

number of electrons in the atom at 0.f ‘and f ’’ atom type and dependent i = sqrt(-1)• Note: A phase shift is often represented mathematically

as a complex number.

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

Friedel Pairs

• 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 “ > 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).

H,K,L

-H,-K,-L

Friedel Pair of Reflections

Early Applications

• Around 1930: Coster, Knol & Prins determined that the shiny side of ZnS corresponds to the Sulfur layer and the dull side to the Zink layer.

• Around 1950: Bijvoet et al. generalized this method and showed that the arbitrarily assigned absolute L configuration of (+) tartaric acid was the correct one. Later this result was also confirmed with other techniques.

The First page of the famous 1951 Article

in Nature -

E. Fischerturned out to

have made the correct choice

by luck -

Nobel Price ?Dorothy Hodgkin

Experiments of Bijvoet et al.

• ‘Accurate measurement of the Intensities of Friedel Pairs’

• On Mixed salts of (+) Tartaric Acids

• NaRb Tartrate

• NaH Tartrate

• Using X-ray Film techniques

Qualitative

Long Exposures

Unstable X-Ray Sources

Quantitative Methods

• Hamilton Test: Refine both enantiomorph models and statistically test whether the difference in

R-value is significant.• Refine a multiplicative parameter with value in

the range –1 to 1 to f ”.• Beurskens B parameter (from DIRDIF)• Scatter Plot of Bijvoet Pair Differences• Refine Inversion Twin Parameter x (Flack,1983)

Scatter Plot of Bijvoet Differences

• Plot of the Observed Bijvoet Differences against the Calculated Differences.

• A Least-Squares line and Correlation Coefficient are calculated

• The Least-squares line should run from the lower left to to upper right corner for the correct enantiomorph and the Correlation close to 1.0

Excellent Correlation

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

Practical Aspects of Flack x

• The structure should contain atoms with sufficiently strong anomalous dispersion contributions for the radiation used (generally in the experiment (e.g. Br).

• Preferably, but not nesessarily, a full set of Friedel pairs is needed.

• Unfortunately, many relevant 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.

Light Atom Targets

Options for the Absolute Structure Determination of Light Atom Compounds

• Add HBr in case of tertiary N.• Co-crystallize with e.g. CBr4.• Co-crystallize with compound with known.

absolute configuration.• Alternative: Statistical analysis of Bijvoet

pair differences.

Dextro-Benzetimide HBr

My First Abs. Struct. DeterminationNature 1971

Statistical Analysis of Bijvoet Pairs

• Many experimentalists have the experience that the official Flack x method is too conservative, based on multiple carefully executed experiments with compounds with known absolute structure.

• The feeling is that also in light atom structures the average of thousands of small Bijvoet differences will point in the direction of the correct enantiomorph.

Example: Ammonium Bitartrate Test

Ammonium BiTartrate (MoK

Bayesian Approach

• Rob Hooft (Former PhD student in Utrecht now with Bruker-AXS) came up with a new statistical method based on Bayesian statistics.

• E.g. Assuming that the material is enantiopure, the probability that the assumed absolute structure is correct, given the set of observed Friedel Pair Differences, is calculated.

• This probability P2 is by a Delft colleague dubbed to be called ‘the swallow parameter’.

• An extension of the method offers the ‘Hooft y’ (or Fleq) parameter, comparable with the Flack x.

Natural Vitamin C, L-(+)Ascorbic Acid

L-(+) Ascorbic Acid

Current Status of the Bayesian Method

• Supporting Paper:

• ‘Determination of Absolute Structure using Bayesian Statistics on Bijvoet Differences’

• R.W.W. Hooft, L.H. Straver & A.L.Spek

• Rejected by J. Appl. Cryst., mainly on the basis of the verdict of one well-known crystallographer as a referee.

Concluding Remarks

• The ‘Rob Hooft’ approach works well for the multiple examples we tested but is not officially accepted (yet).

• Warning:The absolute structure determination on a single crystal is not necessarily representative for the absolute structure of all crystals in the batch. In principle, multiple crystals should be investigated by testing a number of representative Friedel Pair differences.

• An absolute structure determination is meaningless if not related to a macroscopic property such as the sign of the optical rotation or special crystal faces etc..

END

THANK YOU

http://www.cryst.chem.uu.nl