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Fasproblemet

Fasproblemet. Tungmetallderivat (MIR, SIR) Anomalous dispersion Patterson kartor. Vektorrepresentation av strukturfaktorer. Vektorrepresentation av strukturfaktorer. SIR. Multiple isomorphous replacement. MIR. Friedels Lag (hkl = -h –k –l). Anomalous dispersion. Anomalous dispersion.

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Fasproblemet

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  1. Fasproblemet • Tungmetallderivat (MIR, SIR) • Anomalous dispersion • Patterson kartor

  2. Vektorrepresentation av strukturfaktorer

  3. Vektorrepresentation av strukturfaktorer

  4. SIR

  5. Multiple isomorphous replacement

  6. MIR

  7. Friedels Lag (hkl = -h –k –l)

  8. Anomalous dispersion

  9. Anomalous dispersion

  10. Patterson map • Karta över vektorer mellan par av atomer • För varje topp finns det två atomer, visar atomer relativt till varandra ej relativt till enhetscellen • Varje atom bildar ett par (och vektor) med varje annan atom, dvs i en enhetscell med N atomer finns det N2 vektorer. N self vectors och n(n-1) andra vektorer • Intensitetet på toppen proportionell mot produkten av det ingående atomparet

  11. Patterson in plane group p2 a (0,0) b SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  12. Patterson in plane group p2 a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  13. Patterson in plane group p2 (-0.1,-0.2) a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  14. Patterson in plane group p2 (-0.1,-0.2) a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  15. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  16. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  17. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) What is the coordinate for the Patterson peak? Just take the difference between coordinates of the two happy faces. (x,y)-(-x,-y) or (0.1,0.2)-(-0.1,-0.2) so u=0.2, v=0.4 SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  18. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) (0.2, 0.4) What is the coordinate for the Patterson peak? Just take the difference between coordinates of the two happy faces. (x,y)-(-x,-y) or (0.1,0.2)-(-0.1,-0.2) so u=0.2, v=0.4 SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  19. Patterson in plane group p2 a (0,0) b (0.2, 0.4) If you collected data on this crystal and calculated a Patterson map it would look like this. PATTERSON MAP

  20. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? a (0,0) b Use our friends, the space group operators. The peaks positions correspond to vectors between smiley faces. (0.2, 0.4) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y x y -(-x –y) 2x 2y symop #1 symop #2 PATTERSON MAP

  21. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? a (0,0) b Use our friends, the space group operators. The peaks positions correspond to vectors between smiley faces. (0.2, 0.4) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y x y -(-x –y) 2x 2y symop #1 symop #2 PATTERSON MAP set u=2x v=2y plug in Patterson values for u and v to get x and y.

  22. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y a (0,0) b x y -(-x –y) 2x 2y symop #1 symop #2 (0.2, 0.4) set u=2x v=2y plug in Patterson values for u and v to get x and y. v=2y 0.4=2y 0.2=y u=2x 0.2=2x 0.1=x PATTERSON MAP

  23. Hurray!!!! SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y a (0,0) b x y -(-x –y) 2x 2y (0.1,0.2) symop #1 symop #2 set u=2x v=2y plug in Patterson values for u and v to get x and y. v=2y 0.4=2y 0.2=y u=2x 0.2=2x 0.1=x HURRAY! we got back the coordinates of our smiley faces!!!!

  24. Vektorrepresentation av strukturfaktorer

  25. Vektorrepresentation av strukturfaktorer

  26. Vektorrepresentation av strukturfaktorer

  27. Vektorrepresentation av strukturfaktorer

  28. Patterson map

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