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Choice of origin: Difference between revisions
→Examples
(New page: The "problem" of choosing between possible origins occurs in all spacegroups (I believe!). It normally manifests itself when independantly calculating phases (e.g. by [[Molecular replaceme...) |
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* P1: There is only one operator (X, Y, Z) so there are no difference vectors between operators. In this case, any vector with components u,v,w may be added, meaning that any place in the unit cell may serve as an origin (or a molecule may be shifted anywhere and still give the same R-factor). | * P1: There is only one operator (X, Y, Z) so there are no difference vectors between operators. In this case, any vector with components u,v,w may be added, meaning that any place in the unit cell may serve as an origin (or a molecule may be shifted anywhere and still give the same R-factor). | ||
* P2<math>_1</math>: This has operators (X, Y, Z) and (-X, Y+1/2, Z). Difference operator is (2X, 1/2, 2Z). Any change of (X,Y,Z) by adding (0, v, 0) or (0.5, 0, 0) or (0, 0, 0.5), or any combination of these, will leave the difference operator alone (because 2*(X+0.5) = 2*X +1 which is the same as 2X in Patterson space). | * P2<math>_1</math>: This has operators (X, Y, Z) and (-X, Y+1/2, -Z). Difference operator is (2X, 1/2, 2Z). Any change of (X,Y,Z) by adding (0, v, 0) or (0.5, 0, 0) or (0, 0, 0.5), or any combination of these, will leave the difference operator alone (because 2*(X+0.5) = 2*X +1 which is the same as 2X in Patterson space, it's just in the next unit cell of the Patterson). In other words: in P2<math>_1</math> you may shift a molecule along the b axis, or by half a unit cell in a or c, and still get the same R-factor. | ||