Crystal Structure Determination Crystal Structure Determination and Refinement Using the and Refinement Using the

Bruker AXS SMART APEX SystemBruker AXS SMART APEX System

Charles CampanaBruker Nonius

Flowchart for MethodFlowchart for Method

Interpret the results

Complete and refine the structure

Solve the structure

Data reduction

Measure intensity data

Evaluate crystal quality; obtain unit cell geometryand preliminary symmetry information

Select, mount, and optically align a suitable crystal

Adapted from William Clegg

“Crystal Structure Determination”

Oxford 1998.

Crystal Growing TechniquesCrystal Growing Techniques

Slow evaporation

Slow cooling

Vapor diffusion

Solvent diffusion

Sublimation

http://laue.chem.ncsu.edu/web/GrowXtal.html

http://www.as.ysu.edu/~adhunter/YSUSC/Manual/ChapterXIV.pdf

Examples of CrystalsExamples of Crystals

Growing CrystalsGrowing Crystals

Kirsten Böttcher and Thomas Pape

Select and Mount the CrystalSelect and Mount the Crystal

Use microscope

Size: ~0.4 (±0.2) mm

Transparent, faces, looks single

Epoxy, caulk, oil, grease to affix

Glass fiber, nylon loop, capillary

What are crystals ?What are crystals ?

Crystallographic Unit CellCrystallographic Unit Cell

Unit Cell Packing Diagram - YLID

7 Crystal Systems - Metric 7 Crystal Systems - Metric ConstraintsConstraints

Triclinic - none Monoclinic - = = 90, 90 Orthorhombic - = = = 90 Tetragonal - = = = 90, a = b Cubic - = = = 90, a = b = c Trigonal - = = 90, = 120, a = b

(hexagonal setting) or = = , a = b = c (rhombohedral setting)

Hexagonal - = = 90, = 120, a = b

X-Ray Diffraction Pattern X-Ray Diffraction Pattern from Single Crystalfrom Single Crystal

Rotation Photograph

X-Ray DiffractionX-Ray Diffraction

X-ray beam

1Å(0.1 nm)

~ (0.2mm)3 crystal~1013 unit cells, each ~ (100Å)3

Diffraction pattern onCCD or image plate

Bragg’s lawBragg’s law

We can think of diffraction as reflection at sets of planes running through the crystal. Only at certain angles 2 are the waves diffracted from different planes a whole number of wavelengths apart, i.e., in phase. At other angles, the waves reflected from different planes are out of phase and cancel one another out.

n = 2d sin()

d

Reflection IndicesReflection Indices

These planes must intersect the cell edges rationally, otherwise the diffraction from the different unit cells would interfere destructively.

We can index them by the number of times h, k and l that they cut each edge.

The same h, k and l values are used to index the X-ray reflections from the planes.

z

y

x

Planes 3 -1 2 (or -3 1 -2)

Diffraction PatternsDiffraction Patterns

Two successive CCD detector images with a crystal rotation of one degree per image

For each X-ray reflection (black dot), indices h,k,l can be assigned and an intensity I = F 2 measured

Reciprocal spaceReciprocal space

The immediate result of the X-ray diffraction experiment is a list of X-ray reflections hkl and their intensities I.

We can arrange the reflections on a 3D-grid based on their h, k and l values. The smallest repeat unit of this reciprocal lattice is known as the reciprocal unit cell; the lengths of the edges of this cell are inversely related to the dimensions of the real-space unit cell.

This concept is known as reciprocal space; it emphasizes the inverse relationship between the diffracted intensities and real space.

The structure factor The structure factor FF and and electron density electron density

Fhkl = V xyz exp[+2i(hx+ky+lz)] dV

xyz = (1/V) hkl Fhkl exp[-2i(hx+ky+lz)]

F and are inversely related by these Fourier transformations. Note that is real and positive, but F is a complex number: in order to calculate the electron density from the diffracted intensities, I = F2, we need the PHASE ( ) of F. Unfortunately it is almost

impossible to measure directly! F(h,k,l) = A + iB

The Crystallographic Phase The Crystallographic Phase ProblemProblem

The Crystallographic Phase The Crystallographic Phase ProblemProblem

In order to calculate an electron density map, we require both the intensities I = F 2 and the phases of the reflections hkl.

The information content of the phases is appreciably greater than that of the intensities.

Unfortunately, it is almost impossible to measure the phases experimentally !

This is known as the crystallographic phase problem and would appear to be insoluble

Real Space and Reciprocal Real Space and Reciprocal SpaceSpace

Real Space Unit Cell (a, b, c, ,

, ) Electron Density,

(x, y, z) Atomic Coordinates

– x, y, z Thermal Parameters

– Bij or Uij Bond Lengths (A) Bond Angles (º) Crystal Faces

Reciprocal Space Unit Cell (a*, b*,

c*, *, *, *) Diffraction Pattern Reflections – h,h,l Integrated Intensities

– I(h,k,l) Structure Factors –

F(h,k,l) Phase – (h,k,l)

Goniometer HeadGoniometer Head

3-Axis Rotation (SMART)3-Axis Rotation (SMART)

3-Axis Goniometer3-Axis Goniometer

SMART 6000 SystemSMART 6000 System

SMART APEX SystemSMART APEX System

SMART APEX SystemSMART APEX System

Kappa axes (X8)Kappa axes (X8)

Kappa RotationKappa Rotation

Kappa in X8APEXKappa in X8APEX

Short X-ray beam pathShort X-ray beam path

Kappa GoniometerKappa Goniometer

Bruker X8APEXBruker X8APEX

APEX detectorAPEX detector

CCD Chip SizesCCD Chip Sizes

Kodak 1K CCD 25x25 mm SMART 1000, 1500

& MSC Mercury

SITe 2K CCD 49x49 mmSMART 2000

4K CCD 62x62 mm

X8 APEX, SMART APEX, 6000, 6500

APEX detectorAPEX detector transmission of fiber-optic

taper depends on 1/M2

APEX with direct 1:1 imaging 1:1 is 6x more efficient than

2.5:1 improved optical transmission

by almost an order of magnitude

allowing data on yet smaller micro-crystals or very weak diffractors.

original SMART: 17 e/Mo photon; APEX: 170 e/Mo photon

project database

default settings

detector calibration

SMART

setup

sample screening

data collection

ASTRO

data collection strategy

SAINTPLUS

new project

change parameters

SAINT: integrate

SADABS: scale & empirical absorption correction

SHELXTL

new project

XPREP: space group determination

XS: structure solution

XL: least squares refinement

XCIF: tables, reports

                         

                          

George M. Sheldrick Professor, Director of Institute and part-time programming technician

1960-1966: student at Jesus College and Cambridge University, PhD (1966)    with Prof. E.A.V. Ebsworth entitled "NMR Studies of Inorganic Hydrides"1966-1978: University Demonstrator and then Lecturer at Cambridge University; Fellow of Jesus College, CambridgeMeldola Medal (1970),  Corday-Morgan Medal (1978)1978-now: Professor of Structural Chemistry at the University of GoettingenRoyal Society of Chemistry Award for Structural Chemistry (1981)Leibniz Prize of the Deutsche Forschungsgemeinschaft  (1989)Member of the Akademie der Wissenschaften zu Goettingen (1989)Patterson Prize of the American Crystallographic Association (1993) Author of more than 700 scientific papers and of a program called SHELX Interested in methods of solving and refining crystal structures (both small molecules and proteins) and in structural chemistry

email:  gsheldr@shelx.uni-ac.gwdg.defax:  +49-551-392582

SHELXTL vs. SHELX*SHELXTL vs. SHELX*http://shelx.uni-ac.gwdg.de/SHELX/index.htmlhttp://shelx.uni-ac.gwdg.de/SHELX/index.html

SHELXTL (Bruker Nonius) XPREP (space group

det’m) XS (structure solution) XM XE XL (least-squares

refinement) XPRO XWAT XP (plotting) XSHELL (GUI interface) XCIF (tables, reports)

SHELX (Public Domain)* None SHELXS SHELXD SHELXE SHELXL SHELXPRO SHELXWAT None None CIFTAB