Jyvskyl Summer School on Charge Density August 2007

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

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

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 TDS coefficient wavelength background structure factor unit cell volume atomic form factor temperature factor

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

Jyväskylä Summer School on Charge Density August 2007 Data Collection 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 1/10 th 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.

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 X 4 A 1 SUNY Brookhaven 0. 394 Å, 28 K, 6758 data Th(S 2 PMe 2)4 Compared synchrotron data with conventional sealed tube Ag source, 0. 5603 Å “some systematic errors remained. ” P. Coppens et al (2005) Coord Chem Rev. 249, 179 B. Iversen et al (1999) Acta Cryst B 55, 363

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 day on DLproline monohydrate” Line D 3 HASYLAB, 0. 496 Å, 100 K, 6758 data Electrostatic potential blue 0. 6, red – 0. 2 eÅ-1 from expt (A), theory (B) Shows polarization effects from crystal field

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

Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation Mn 2(CO)10 Farrugia et al (2003) Acta Cryst B 59, 234 difference Fourier Fobs - Fmult contours 0. 1 eÅ-3 Daresbury SRS Crystal size (mm) sin / max Rint Redundancy % completeness R(F) (multipole) GOF 0. 4901Å : 0. 2 : 1. 0788 : 0. 045 : 8. 0 : 99. 9 : 1. 81 % : 1. 61 Kappa. CCD 0. 71073 Å Crystal size (mm) : 0. 45 0. 4 sin / max : 1. 0788 Rint : 0. 035 Redundancy : 25. 0 % completeness : 100 R(F) (multipole) : 1. 34 % GOF : 1. 51

Jyväskylä Summer School on Charge Density August 2007 Use of synchrotron radiation Mn 2(CO)10 Farrugia et al (2003) Acta Cryst B 59, 234 Daresbury SRS Crystal size (mm) sin / max Rint Redundancy % completeness R(F) (multipole) GOF 0. 4901Å : 0. 2 : 1. 0788 : 0. 045 : 8. 0 : 99. 9 : 1. 81 % : 1. 61 Kappa. CCD 0. 71073 Å Crystal size (mm) : 0. 45 0. 4 sin / max : 1. 0788 Rint : 0. 035 Redundancy : 25. 0 % completeness : 100 R(F) (multipole) : 1. 34 % GOF : 1. 51

Jyväskylä Summer School on Charge Density August 2007 Accurate data from a laboratory source • One day data collection • Rotating anode generator (18 k. W) • Rigaku R-Axis Rapid detector • Compound - pentaerythritol C 5 H 12 O 4 • Open flow helium cryostat (15 K) • Specialised integration software • Data averaged with SORTAV Crystal size (mm) : 0. 3 0. 25 sin / max : 1. 323 Rint : 0. 018 Redundancy : 10. 4 % completeness : 89. 5 R(F 2) (multipole) : 1. 34 % GOF : 1. 51 Pinkerton et al (2005) J Appl Cryst 38, 827

Jyväskylä Summer School on Charge Density August 2007 Accurate data from a laboratory source Cr(CO)6 Kappa. CCD Crystal size (mm) sin / max Rint Redundancy % completeness R(F) (multipole) GOF Residuals 0. 71073 Å : 0. 38 0. 32 0. 3 : 1. 154 : 0. 026 : 12 : 100 : 0. 92 % : 1. 684 : +0. 21 : -0. 13 e Å-3 Farrugia & Evans (2005) J. Phys Chem A 109, 8834

Jyväskylä Summer School on Charge Density August 2007 Charge densities on reactive compounds Kappa. CCD/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 Et. Ti. Cl 3(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 & Mc. Grady (2004) Angew Chemie 43, 1782

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 300 K to 100 K). • 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. B 51, 468

Jyväskylä Summer School on Charge Density August 2007 Low Temperature Devices Down to ~ 90 K : Liquid N 2 – Cryostream, Cryojet, Kryoflex, X-stream -air Below 90 K • Closed systems – Displex ~ 15 K • Open flow systems – Helix, Helijet <15 -30 K Closed system Advantages • Low cost • Stable temperature at 15 K Disadvantages • Difficult sample environment • Vibrations Peter Luger group – Kapton film instead of Be

Jyväskylä Summer School on Charge Density August 2007 Low Temperature Devices • Temperature ~ 25 -30 K • Uses gaseous He only • Also works with N 2 Helix - Oxford Cryosystems http: //www. oxfordcryosystems. co. uk/

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

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. B 54, 471 Macchi et al (1998) J. Appl. Cryst. 31, 583 Lecomte et al (1999) Acta Cryst. B 55, 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 F 22 h, 2 k, 2 l to F 2 hkl 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

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 Xrays by phosphor. Coppens et al (2002) J. Appl. Cryst. 35, 356 Sensitivity map shows a 40% variation

Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors Compared CAD 4 (2 months) & Kappa. CCD (7 d) • CAD 4 data gives better residuals • sytematic differences in intensities due to differing extinction (Kappa. CCD > CAD 4) • Derived multipole parameters very similar top CAD 4, bottom Kappa. CCD Larsen & Sørensen (2003) J. Appl. Cryst. 36, 931

Jyväskylä Summer School on Charge Density August 2007 Comparison of data quality from serial and CCD area detectors Compared CAD 4, Siemens SMART CCD & Kappa. CCD Crystal used -spodumene Li. Al(Si. O 3)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 Kappa. CCD Lecomte et al (1999) Acta Cryst. B 55, 867 -881 SMART

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 Cryst 7, 555 -564 Kabsch (1988) J Apply Cryst 21, 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.

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 Cryst 36, 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/ (I) better for high intensity data, but significantly worse for weak data • Overall residuals, e. g. R values, D(r) somewhat worse

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

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 Cryst 28, 86 Bolotovsky & Coppens (1997) J Appl Cryst 30, 244 Evaluations : Darovsky & Kezerashvili (1997) J Appl Cryst 30, 128 Graafsma et al (1997) J Appl Cryst 30, 957 (CCD data)

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

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 mean background <B> and estimated • Seed is constructed from pixels with smoothed intensity > [<B>+3 (B)] (b) • All pixels not in seed 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

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 - CCD data compared with Denzo. HIPPO better for strong reflections, Denzo better for weak reflections. Graafsma et al (1997) J Appl Cryst 30, 957

Jyväskylä Summer School on Charge Density August 2007 Accurate integration of area detector data Multiple measurements - statistical averaging of data - SORTAV Blessing (1997) J Appl Cryst 30, 421 -426 Kappa. CCD 0. 71073 Å C 12 H 24 O 21 B 2 F 8 Na 5 Gd Crystal size (mm) sin / max Rint Redundancy % completeness R(F 2) (SHELX) GOF : 0. 5 0. 4 0. 3 : 1. 152 : 0. 039 : 36. 6 : 99. 9 : 1. 0 % : 1. 15

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 jkl. H jkl +(1/4!)C jklm. H jklm + …)P 0 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

Jyväskylä Summer School on Charge Density August 2007 Anharmonic Thermal Motion Anharmonic coefficients and multipole parameters are usually strongly correlated Restori & Schwarzenbach (1996) Acta Cryst A 52, 369 In fact, it has been shown that Gram-Charlier coefficients can quite adequately model aspherical density, see study on [Fe(H 2 O)6]2+ Mallinson et al (1988) Acta Cryst A 44, 336 Model deformation maps with (a) anharmonic Fe (b) aspherical Fe

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, B 51, 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 Cryst A 56, 403 Bürgi et al (2000) Acta Cryst A 56, 413 (from neutron data at other T) (from vibrational data) et al (2004) Acta Cryst A 60, 550 (calculated rigid body motion +database) Roversi & Destro (2004) Chem Phys. Lett. 386, 472 Sine Larsen A. Ø Madsen (2006) J. Appl. Cryst. 39, 757. Simple Hydrogen Anisotropic Displacement Estimator SHADE WEB SERVER http: //shade. ki. ku. dk/

Jyväskylä Summer School on Charge Density August 2007 Absorption Other systematic errors in data 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, A 51, 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 Cryst A 30, 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)

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, A 60, 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 19 K on spherical organic crystal, carefully corrected for scan truncation losses, but tainted by little imperfections.