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Crystal Structure Determination and Refinement Using the Bruker AXS SMART APEX System

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### Crystal Structure Determination and Refinement Using the Bruker AXS SMART APEX System

Charles Campana

Bruker Nonius

Crystal 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

Growing Crystals

Kirsten Böttcher and Thomas Pape

Select 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

Crystallographic Unit Cell

Unit Cell Packing Diagram - YLID

7 Crystal Systems - Metric Constraints

- 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 from Single Crystal

Rotation Photograph

X-Ray Diffraction

X-ray beam

1Å

(0.1 nm)

~ (0.2mm)3 crystal

~1013 unit cells, each ~ (100Å)3

Diffraction pattern on

CCD or image plate

Bragg’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 Indices

z

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.

y

x

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

Diffraction 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 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 lvalues. 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 F and electron density

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

xyz = (1/V) hklFhkl 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 Problem

- 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

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)

Real Space and Reciprocal SpaceCCD Chip Sizes

X8 APEX, SMART APEX, 6000, 6500

4K CCD 62x62 mm

Kodak 1K CCD 25x25 mm SMART 1000, 1500

& MSC Mercury

SITe 2K CCD 49x49 mm

SMART 2000

APEX 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

ASTRO

setup

data collection strategy

sample screening

data collection

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

project database

default settings

detector calibration

Professor, Director of Institute and part-time programming technician1960-1966: 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 chemistryemail: [email protected]: +49-551-392582

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

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