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

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

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

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

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

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

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

8. Patterson in plane group p2 (0,0) a b a b (0.1,0.2) (-0.1,-0.2) SYMMETRY OPERATORS FOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL 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 (0.2, 0.4)

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

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

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

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

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