Experimental Aspects of Charge Density Studies

1. Jyväskylä Summer School on Charge Density August 2007 Experimental Aspects of Charge Density Studies Louis J Farrugia

2. Jyväskylä Summer School on Charge Density August 2007 What quality of data is required ?

3. Jyväskylä Summer School on Charge Density August 2007 What quality of data is required ? extinction coefficient incident beam intensity crystal volume absorption coefficient multiple scattering integrated reflectivity TDScoefficient background wavelength structure factor unit cell volume temperature factor atomic form factor

4. Jyväskylä Summer School on Charge Density August 2007 Data Collection Strategies • Use best crystal available – no disorder ! • Use highest intensity X-ray source available • Use lowest temperature available to minimise TDS • Use small crystal/short wavelength to minimise absorption & extinction • Use large crystal to maximise diffracted intensities • Use multiple measurements to get good statistics • Use rapid data collection to minimise sample decomposition • and environmental/mechanical variations

5. Jyväskylä Summer School on Charge Density August 2007 Data Collection Strategies Strategies may be limited by diffractometer software/hardware Strategy must ensure that both the low angle data and the high angle data are collected accurately. High redundancy essential (10-fold). Usually need to collect high angle data at least 3-4 times exposure of low angle data. • Potential problems • Low angle data are most intense, overflows possible especially for CCD (collect low angle data again at 1/10th exposure time) • High angle data with lab sources, 1-2 splitting may cause integration problems • Problem data e.g. obscured reflections, those close to spindle axis, at edge of detector etc should be removed.

6. Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation • Advantages • High intensity primary beam • Tunable and very monochromatic frequencies • Rapid data collection – area detectors essential ! • Small crystals used - minimise extinction/absorption • Ultra low temperature – minimises TDS Line X4A1 SUNY Brookhaven 0.394 Å, 28K, 6758 data Compared synchrotron data with conventional sealed tube Ag source, 0.5603 Å “some systematic errors remained.” Th(S2PMe2)4 P. Coppens et al (2005) Coord Chem Rev.249, 179 B. Iversen et al (1999) Acta CrystB55, 363

7. Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation • Advantages • High intensity primary beam • Tunable and very monochromatic frequencies • Rapid data collection – area detectors essential ! • Small crystals used - minimise extinction/absorption • Ultra low temperature – minimises TDS P. Luger et al (1998) Science.279, 356 “Accurate experimental electronic properties within 1 dayon DL-proline monohydrate” Line D3 HASYLAB, 0.496 Å, 100K, 6758 data Electrostatic potential blue 0.6, red –0.2 eÅ-1 from expt (A), theory (B) Shows polarization effects from crystal field

8. Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation • Advantages • High intensity primary beam • Tunable and very monochromatic frequencies • Rapid data collection – area detectors essential ! • Small crystals used - minimise extinction/absorption • Ultra low temperature – minimises TDS • Disadvantages • Primary beam instability - intensity variation during data collection • Inconvenience and expense

9. Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation Farrugia et al (2003) Acta Cryst B59, 234 Mn2(CO)10 difference Fourier Fobs - Fmult contours 0.1 eÅ-3 Daresbury SRS 0.4901Å Crystal size (mm) : 0.2 0.2 0.2 sin/max : 1.0788 Rint : 0.045 Redundancy : 8.0 % completeness : 99.9 R(F) (multipole) : 1.81 % GOF : 1.61 KappaCCD 0.71073 Å Crystal size (mm) : 0.45 0.45 0.4 sin/max : 1.0788 Rint : 0.035 Redundancy : 25.0 % completeness : 100 R(F) (multipole) : 1.34 % GOF : 1.51

10. Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation Farrugia et al (2003) Acta Cryst B59, 234 Mn2(CO)10 Daresbury SRS 0.4901Å Crystal size (mm) : 0.2 0.2 0.2 sin/max : 1.0788 Rint : 0.045 Redundancy : 8.0 % completeness : 99.9 R(F) (multipole) : 1.81 % GOF : 1.61 KappaCCD 0.71073 Å Crystal size (mm) : 0.45 0.45 0.4 sin/max : 1.0788 Rint : 0.035 Redundancy : 25.0 % completeness : 100 R(F) (multipole) : 1.34 % GOF : 1.51

11. Jyväskylä Summer School on Charge Density August 2007 Accurate data from a laboratory source • One day data collection • Rotating anode generator (18kW) • Rigaku R-Axis Rapid detector • Compound - pentaerythritol C5H12O4 • Open flow helium cryostat (15K) • Specialised integration software • Data averaged with SORTAV Crystal size (mm) : 0.3 0.3 0.25 sin/max : 1.323 Rint : 0.018 Redundancy : 10.4 % completeness : 89.5 R(F2) (multipole) : 1.34 % GOF : 1.51 Pinkerton et al (2005) J Appl Cryst38, 827

12. Jyväskylä Summer School on Charge Density August 2007 Accurate data from a laboratory source Cr(CO)6 KappaCCD 0.71073 Å Crystal size (mm) : 0.38 0.32 0.3 sin/max : 1.154 Rint : 0.026 Redundancy : 12 % completeness : 100 R(F) (multipole) : 0.92 % GOF : 1.684 Residuals :+0.21 :-0.13 e Å-3 Farrugia & Evans (2005) J. Phys Chem A109, 8834

13. Jyväskylä Summer School on Charge Density August 2007 Charge densities on reactive compounds KappaCCD/Stoe IPDS 0.71073 Å Rotating anode Crystal size (mm) : 0.5 0.25 0.1 sin/max : 1.097 Rint : 0.029 Redundancy : ~3 % completeness : 99.8 R(F) (multipole) : 2.68 % GOF : 2.439 Residuals :+0.46 :-0.34 e Å-3 Agostic interaction in EtTiCl3(dmpe) - hyperconjugative delocalisation of M-C bond Scherer et al (1998) JCS Chem Commun. 2471 Scherer et al (2003) Chem Eur. J.9, 6057 Scherer & McGrady (2004) Angew Chemie43, 1782

14. Jyväskylä Summer School on Charge Density August 2007 Low Temperature Data Collection • Advantages of data collection at low temperature are numerous • Minimizes thermal motion – easier to deconvolute from charge density effects. • Increases scattering at higher angles (at sin/=1.0Å-1 intensity increases by factor of 150 from 300K to 100K). • Minimizes thermal diffuse scattering TDS – not easy to correct for. • Minimizes anharmonicity – negligible at very low T. • Minimizes sample decomposition. Finn Larsen (1995) Acta Cryst.B51, 468

15. Jyväskylä Summer School on Charge Density August 2007 Low Temperature Devices Down to ~ 90K : Liquid N2 – Cryostream, Cryojet,Kryoflex,X-stream -air • Below 90K • Closed systems – Displex ~ 15K • Open flow systems – Helix, Helijet <15-30K • Closed system • Advantages • Low cost • Stable temperature at 15K • Disadvantages • Difficult sample environment • Vibrations Peter Luger group – Kapton film instead of Be

16. Jyväskylä Summer School on Charge Density August 2007 Low Temperature Devices • Temperature ~ 25-30K • Uses gaseous He only • Also works with N2 Helix - Oxford Cryosystems http://www.oxfordcryosystems.co.uk/

17. Jyväskylä Summer School on Charge Density August 2007 Low Temperature Devices • Temperature ~ 15K • Uses gaseous and liquid He • No vibration Helijet - Oxford Diffraction http://www.oxford-diffraction.com

18. Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors A number of studies have compared the relative quality of data obtained from CCD area detectors and serial scintillation detectors. Pinkerton & Martin (1998) Acta Cryst.B54, 471 Macchi et al (1998) J. Appl. Cryst.31, 583 Lecomte et al (1999) Acta Cryst.B55, 867 Larsen & Sørensen (2003) J. Appl. Cryst. 36, 931 CCD detectors do not discriminate photons by energy – so /2 contamination may be a potential problem. CONCLUSION : contribution from F22h,2k,2l to F2hkl is ~ 0.001 and hence negligible for normal structural studies. May be useful for charge density analyses. Kirschbaum et al (1997) J. Appl. Cryst.30, 514

19. Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors CCD detectors show a great variation of sensitivity, especially detectors with optical tapering. Area detectors in general have to be corrected for many deficiences and physical effects, e.g. incomplete absorption of X-rays by phosphor. Coppens et al (2002) J. Appl. Cryst.35, 356 Sensitivity map shows a 40% variation

20. Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors • Compared CAD4 (2 months) & KappaCCD (7 d) • CAD4 data gives better residuals • sytematic differences in intensities due to differing extinction (KappaCCD > CAD4) • Derived multipole parameters very similar top CAD4, bottom KappaCCD Larsen & Sørensen (2003) J. Appl. Cryst. 36, 931

21. Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors • Compared CAD4, Siemens SMART CCD & KappaCCD • Crystal used -spodumene LiAl(SiO3)2 • All gave data of sufficient quality for charge density studies • main differences between CCD data was in estimation of errors • “black box” nature of integration software a potential problem KappaCCD Lecomte et al (1999) Acta Cryst.B55, 867-881 SMART

22. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data Commercial integration packages : SAINT, Denzo, D*Trek – use the profile-fitting method Ford (1974) J Apply Cryst7, 555-564 Kabsch (1988) J Apply Cryst21, 916-924 Profiles obtained from neighbouring reflections in sub region of detector. Profile is essentially a weighting function for each pixel’s contribution to the total integrated intensity.

23. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data Commercial integration packages : EVALCCD – use the predicted profile method Duisenberg et al (2003) J Apply Cryst36, 220 Method uses ab-initio calculation of the three dimension reflection boundaries from crystal and instrumental parameters - a “ray-tracing” technique. Then integrates using the background-peak-background method, • In general : • I/s(I) better for high intensity data, but significantly worse for weak data • Overall residuals, e.g.R values, D(r) somewhat worse

24. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data

25. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data Academic/freely available integration packages Mainly designed for the macromolecular environment MOSFLM (Harry Powell) – http://www.mrc-lmb.cam.ac.uk/harry/mosflm XDS (Wolfgang Kabsch) – http://www.mpimf-heidelberg.mpg.de/~kabsch/xds HIPPO – seed-skewness method – developed explicitly for the accurate integration of Image-Plate data Bolotovsky et al (1995) J Appl Cryst28, 86 Bolotovsky & Coppens (1997) J Appl Cryst30, 244 Evaluations : Darovsky & Kezerashvili (1997) J Appl Cryst30, 128 Graafsma et al (1997) J Appl Cryst30, 957(CCD data)

26. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data HIPPO integration package The seed-skewness method is based on a statistical analysis (skewness) of the pixel intensities in the integration box. Skewness is the third moment of the distribution, which increases is a peak is present in the pixel intensity distribution. No peak in box Peak in box

27. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data • HIPPO integration package • Integration box placed around predicted position of Bragg peak (a) • Pixel intensities smoothed to suppress random noise • Initial skewness and  and mean background <B> and  estimated • Seed is constructed from pixels with smoothed intensity > [<B>+3(B)] (b) • All pixels not in seed are are tested for skewness and most intense are included until skewness reaches a minimum. This gives a mask, which defines the peak area (c) a b c

28. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data HIPPO integration package Method provides a purely statistical approach to deciding peak profile. Has other options for “special” cases, e.g. 1-2 splitting (a) (b) Intensity distributions (a) before and (b) after seed pixels have been removed Graafsma et al (1997) J Appl Cryst30, 957- CCD data compared with Denzo. HIPPO better for strong reflections, Denzo better for weak reflections.

29. Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data Multiple measurements - statistical averaging of data - SORTAV KappaCCD 0.71073 Å C12H24O21B2F8Na5Gd Crystal size (mm) : 0.5 0.4 0.3 sin/max : 1.152 Rint : 0.039 Redundancy : 36.6 % completeness : 99.9 R(F2) (SHELX) : 1.0 % GOF : 1.15 Blessing (1997) J Appl Cryst30, 421-426

30. Jyväskylä Summer School on Charge Density August 2007 Anharmonic Thermal Motion The anharmonic pdf is approximated in terms of zero and higher derivatives of the normal distribution P(u) = {1 + (1/3!)C jklH jkl +(1/4!)C jklmH jklm + …)P0 where H jkl … are 3-D Hermite polynomials - functions of U and u and C jkl … are refinable coefficients. The advantage of this Gram-Charlier expansion is that the Fourier transform is a simple power series expansion of the harmonic temperature factor. • Anharmonic vibrations of atoms increase with • Temperature • Core electron density

31. Jyväskylä Summer School on Charge Density August 2007 Anharmonic Thermal Motion Anharmonic coefficients and multipole parameters are usually strongly correlated Restori & Schwarzenbach (1996) Acta CrystA52, 369 In fact, it has been shown that Gram-Charlier coefficients can quite adequately model aspherical density, see study on [Fe(H2O)6]2+ Mallinson et al (1988) Acta CrystA44, 336 Model deformation maps with (a) anharmonic Fe (b) aspherical Fe

32. Jyväskylä Summer School on Charge Density August 2007 Accurate H-atom parameters ‘there is no possibility of deriving hydrogen vibrational parameters from the X-ray intensities’ F. Hirshfeld (1976) Acta Cryst, 32, 239 In principle, neutron diffraction data will give accurate H-atom parameters. Often there is a scaling problem between X-ray and neutron data, even for the same nominal temperature (differing extinction/TDS effects). Blessing (1995) Acta Cryst, B51, 816 In many cases, the positional parameters may be approximated from known (neutron derived) X-H distances. Thermal parameters are more problematical : Flaig et al (1998) J. Am. Chem. Soc. 120, 2227(from ab initio calcs) Bürgi & Capelli (2000) Acta CrystA56, 403 Bürgi et al (2000) Acta CrystA56, 413(from neutron data at other T) Roversi & Destro (2004) Chem Phys. Lett. 386, 472(from vibrational data) Sine Larsen et al (2004) Acta CrystA60, 550 (calculated rigid body motion +database) A. Ø Madsen (2006) J. Appl. Cryst.39, 757. Simple Hydrogen Anisotropic Displacement Estimator SHADE WEB SERVER http://shade.ki.ku.dk/

33. Jyväskylä Summer School on Charge Density August 2007 Other systematic errors in data Absorption Best corrected by face indexing methods, e.g. Gaussian quadrature Coppens et al (1965) Acta Cryst, 18, 1035 Empirical corrections using spherical harmonic functions – corrects for machine instabilities & mount medium absorption Blessing (1995) Acta Cryst, A51, 33 Sheldrick - SADABS Extinction Best avoided by using small crystal. Part of refinement procedure. Anisotropic extinction difficult to deal with in large data sets. Becker & Coppens (1974) Acta CrystA30, 129 Thermal Diffuse Scattering Best avoided by using ultra-low temperatures. No general correction is currently available, but some empirical methods are being developed. Stash & Zavodnick (1996) Crystallogr. Rep.41, 404 Sample instability Less serious because of low temperatures and (relatively) short data acquisition times. Treated in scaling procedures (SORTAV/SADABS)

34. Jyväskylä Summer School on Charge Density August 2007 The Role of Data Quality in Experimental Charge Density Studies Riccardo Destro et al (2004) Acta Cryst, A60, 365 “A quantitative and detailed discussion of the local properties of expt is meaningful solely when based on data of genuine high quality. If only data of a lower grade are available, the analysis of the electron distribution must be restricted to a qualitative level.” “Lower grade” = data collected at 19K on spherical organic crystal, carefully corrected for scan truncation losses, but tainted by little imperfections.