Please note that only true hemihedral twinning can be deal with correctly in CNS. Data with pseudo-merohedral twinning can not be used (the program SHELXL is suggested instead).
Prior to refinement the twinning operator must be identified and the twinning fraction calculated. One of the best ways to do this is with Todd Yeates's web-based Merohedral Crystal Twinning Server. This is currently located at the following URL:
http://www.doe-mbi.ucla.edu/Services/TwinningExperimental diffraction data is given in either CIF or X-PLOR format. Various tests are performed for perfect or partial twinning.
Alternatively, twinning can be identified in CNS using the detect_twinning.inp task file:
cns_solve < detect_twinning.inp > detect_twinning.out [10 seconds]
Perfect twinning is tested for by analysis of intensity statistics:
| Statistic | Untwinned data | Twinned data |
| <I2>/<I>2 | 2.0 | 1.5 |
| <F>2/<F2> | 0.785 | 0.865 |
Partial twinning is tested by application of the possible twin laws and calculation of the twinning fraction. The possible hemihedral twinning operators for different point groups are:
| True point group | Twin operation | hkl related to |
| 3 | 2 along a,b | h,-h-k,-l |
| 2 along a*,b* | h+k,-k ,-l | |
| 2 along c | -h,-k , l | |
| 4 | 2 along a,b,a*,b* | h,-k ,-l |
| 6 | 2 along a,b,a*,b* | h,-h-k,-l |
| 321 | 2 along a*,b*,c | -h,-k , l |
| 312 | 2 along a,b,c | -h,-k , l |
| 23 | 4 along a,b,c | k,-h , l |
A listing file (detect_twinning.list) is produced:
==============================================================================
testing for perfect twinning
column 1: bin number
columns 2: upper resolution limit
columns 3: lower resolution limit
column 4: number of reflections in bin
column 5: average resolution in bin
column 6: <|I|^2> /(<|I|>)^2
column 7: (<|F|>)^2/<|F|^2>
column 8: fraction of theoretically complete data
<|I|^2> /(<|I|>)^2 is 2.0 for untwinned data, 1.5 for twinned data
(<|F|>)^2/<|F|^2> is 0.785 for untwinned data, 0.865 for twinned data
#bin | resolution range | #refl |
1 8.12 500.01 481 11.6016 1.8597 0.8063 0.9469
2 6.44 8.12 509 7.1613 1.8921 0.8264 0.9864
3 5.63 6.44 502 6.0042 1.6015 0.8615 0.9941
4 5.12 5.63 509 5.3576 1.8113 0.8416 0.9903
5 4.75 5.12 509 4.9234 1.6795 0.8545 0.9941
6 4.47 4.75 514 4.6003 1.9726 0.8228 0.9942
7 4.24 4.47 510 4.3488 1.6194 0.8617 0.9961
8 4.06 4.24 494 4.1487 1.6394 0.8653 0.9940
9 3.90 4.06 518 3.9796 1.6701 0.8542 0.9942
10 3.77 3.90 511 3.8322 1.6527 0.8594 1.0000
11 3.65 3.77 485 3.7096 1.6670 0.8597 1.0000
12 3.55 3.65 523 3.6004 2.0337 0.8147 0.9962
13 3.45 3.55 496 3.5000 1.6600 0.8540 1.0000
14 3.37 3.45 513 3.4134 1.7394 0.8433 1.0000
15 3.29 3.37 525 3.3305 1.6369 0.8724 1.0000
16 3.22 3.29 516 3.2567 1.6324 0.8653 1.0000
17 3.16 3.22 504 3.1882 1.5324 0.8773 1.0000
18 3.10 3.16 502 3.1285 1.5510 0.8686 1.0000
19 3.04 3.10 507 3.0710 1.5434 0.8649 1.0000
20 2.99 3.04 519 3.0172 1.5979 0.8639 1.0000
21 2.94 2.99 490 2.9684 1.6205 0.8555 1.0000
22 2.90 2.94 501 2.9218 1.6645 0.8544 1.0000
23 2.86 2.90 549 2.8778 1.7637 0.8524 1.0000
24 2.81 2.86 496 2.8342 1.5402 0.8710 1.0000
25 2.78 2.81 520 2.7956 1.5934 0.8699 1.0000
26 2.74 2.78 508 2.7584 1.6435 0.8508 1.0000
27 2.71 2.74 479 2.7245 1.5868 0.8674 1.0000
28 2.67 2.71 544 2.6904 1.5539 0.8720 1.0000
29 2.64 2.67 507 2.6584 1.6037 0.8625 1.0000
30 2.61 2.64 481 2.6283 1.5426 0.8727 1.0000
31 2.58 2.61 546 2.5990 1.6387 0.8533 1.0000
32 2.56 2.58 502 2.5710 1.6343 0.8585 1.0000
33 2.53 2.56 501 2.5443 1.6461 0.8594 1.0000
34 2.51 2.53 514 2.5190 1.7216 0.8447 1.0000
35 2.48 2.51 521 2.4938 1.7390 0.8439 1.0000
36 2.46 2.48 497 2.4710 1.6592 0.8554 1.0000
37 2.44 2.46 500 2.4479 1.5611 0.8739 1.0000
38 2.42 2.44 532 2.4256 1.6924 0.8597 1.0000
39 2.39 2.42 512 2.4049 1.6382 0.8568 1.0000
40 2.37 2.39 497 2.3840 1.5590 0.8614 1.0000
41 2.35 2.37 498 2.3645 1.6063 0.8553 1.0000
42 2.34 2.35 531 2.3455 1.6451 0.8616 1.0000
43 2.32 2.34 494 2.3267 1.5962 0.8643 1.0000
44 2.30 2.32 541 2.3088 1.7558 0.8438 1.0000
45 2.28 2.30 477 2.2910 1.6323 0.8609 1.0000
46 2.27 2.28 513 2.2744 1.5182 0.8894 1.0000
47 2.25 2.27 535 2.2580 1.5523 0.8878 0.9853
---------------------------averages-over-all-bins-----------------------------
<|I|^2> /(<|I|>)^2 = 1.6581 (2.0 for untwinned, 1.5 for twinned)
(<|F|>)^2/<|F|^2> = 0.8574 (0.785 for untwinned, 0.865 for twinned)
------------------------------------------------------------------------------
==============================================================================
testing for partial twinning (using statistical method of Yeates)
>>>> testing for twinning operator= h,-h-k,-l
<H> = 0.19495: twinning fraction= 0.305 (10554 reflections used)
<H2> = 0.05152: twinning fraction= 0.303 (10554 reflections used)
>>>> testing for twinning operator= h+k,-k,-l
<H> = 0.39128: twinning fraction= 0.109 (3670 reflections used)
<H2> = 0.21541: twinning fraction= 0.098 (3670 reflections used)
>>>> testing for twinning operator= -h,-k,l
<H> = 0.38104: twinning fraction= 0.119 (3878 reflections used)
<H2> = 0.20745: twinning fraction= 0.106 (3878 reflections used)
==============================================================================
The twinning operator h,-h-k,-l indicates a high twinning fraction (0.304). This is used in the subsequent refinement steps.
If the twinning fraction is greater than 0.45 it becomes very difficult to detwin the data. In such cases it may be better to average twin related reflections to generate perfectly twinned data. For further information see T.O. Yeates, Detecting and Overcoming crystal twinning, Meth. Enzym. 276, 344-358 (1997)
Script to run this tutorial