PLATON incorperates a significantly extented/modified implementation of the powerful MISSYM (C) algorithm invented by Y. Le Page for the detection of possibly MISsed ADDitional SYMmetry in a given coordinate set.
Missed symmetry is a serious problem. For a recent discussion see D.Marsh, Acta Cryst. (1997). B53, 317-322.
Major extensions include explicit transformation matrices, proposed alternative space group and the detection of approximate higher symmetry due to either missing atoms or a few atoms that do not comply with the higher symmetry (either real or refinement artifact).
In order not to confuse this implementation of the MISSYM (C) algorithm with the official (copyrighted) MISSYM implementation in the NRCVAX (C) package, it is named ADDSYM.
Given a name.res or name.cif formatted file, the test for possibly missed symmetry can be run (either from the keyboard or by mouse clicks on the proper menu items) as:
platon name.res
with the sole instruction:
CALC ADDSYM
See the TEST/ADDSYM_EXAMPLE subdirectory (on xraysoft.chem.uu.nl) for some examples and and additional README.
PLATON should produce a transformed shelx file with:
CALC ADDSYM SHELX
or a PLUTON DRAWING of the averaged/transformed structure with
CALL ADDSYM PLOT
CALC ADDSYM (element_name/EQUAL) (SHELX/PLOT) (ang d1 d2)
where:
Example 1
In the order of 10 % of the structures published in Space group Cc can be shown to be better described with higher symmetry. A common case is the omission of an inversion centre. This example shows how to detect and correct automatically for that problem.
TITL AACRUB Cc R=0.0380 CELL 14.2460 6.9040 17.6870 90.000 97.190 90.000 CESD 0.0020 0.0010 0.0020 0.000 0.010 0.000 SPGR Cc Ru(1) 0.22852 0.15210 0.36523 Ru(2) 0.12035 0.34630 0.40847 O(1) 0.22860 0.32200 0.27210 O(2) 0.33730 0.30800 0.42380 O(3) 0.22800 -0.00410 0.45390 O(4) 0.12660 -0.00400 0.30750 O(5) 0.12440 0.52300 0.31530 O(6) 0.22860 0.49900 0.46410 O(7) 0.11900 0.17000 0.49890 O(8) 0.02400 0.17600 0.35380 O(9) 0.33580 -0.06800 0.32270 O(10) 0.00210 0.52300 0.44990 C(1) 0.18130 0.46000 0.26420 C(2) 0.17370 0.61600 0.20200 C(3) 0.31360 0.45900 0.46460 C(4) 0.39210 0.55600 0.50520 C(5) 0.17690 0.01400 0.50280 C(6) 0.16480 -0.08500 0.57740 C(7) 0.04180 0.04600 0.31500
ADDSYM OUTPUT FOR EXAMPLE 1
ADDSYM - CHECK (cf. MISSYM (C): Le Page, Y., J. Appl. Cryst. (1987), 20,
264-269; J. Appl. Cryst. (1988), 21, 983-984)
------------------------------------------------------------------------------
- This ADDSYM Search is run on ALL NON-H Chemical Types
- Number of Input Atoms Included in Search = 25
- The Structure implies the following Symmetry Elements subject to the Criteria:
1.00 Deg., (metric) 0.25 Ang. (distances) and 0.45 Ang. (inv. and transl.)
Symm. Input Reduced (Ang) (Deg) (Ang) Input Cell
Elem Cell Row Cell Row d Type Dot Angle Max. dev. x y z
--------------------------------------------------------------------------------
c [ 0 1 0] [-1 0 0] 6.903 2 2 0.00 0 through 0 0 0
Glide = 0 0 1/2
-1 * ====================================== 0.270 at 0.174 0.249 0.387
F3 -F4
Reduced->Convent Input->Reduced T = Input->Convent: a' = T a
--------------------------------------------------------------------------------
( -1 2 0 ) ( 0 1 0 ) ( 1 0 0 ) Det(T)
( 1 0 0 ) X ( 1/2 1/2 0 ) = ( 0 1 0 ) =
( 0 0 -1 ) ( 0 0 -1 ) ( 0 0 1 ) 1.000
Cell Lattice a b c alpha beta gamma Volume CrystalSystem Laue
--------------------------------------------------------------------------------
Input mC 14.246 6.904 17.687 90.00 97.19 90.00 1726 Monoclinic 2/m
Reduced P 6.903 7.915 17.687 83.53 90.00 64.15 863
Convent mC 14.246 6.904 17.687 90.00 97.19 90.00 1726 Monoclinic 2/m
Conventional, New or Pseudo Symmetry
================================================================================
Space Group C2/c No: 15, Laue: 2/m [Hall: -C 2yc ]
Lattice Type mC, Centric, Monoclinic, Order 8( 2) [Shoenflies: C2h^6 ]
Nr ***** Symmetry Operation(s) *****
1 X , Y , Z
2 X , - Y , 1/2 + Z
3 - X , - Y , - Z
4 - X , Y , 1/2 - Z
5 1/2 + X , 1/2 + Y , Z
6 1/2 + X , 1/2 - Y , 1/2 + Z
7 1/2 - X , 1/2 - Y , - Z
8 1/2 - X , 1/2 + Y , 1/2 - Z
:: Origin shifted to: 0.424, 0.499, 0.387 after transformation
:: * Symmetry Elements preceded by an Asterisk are New and indicate
:: Missed/Pseudosymmetry Summary
:: M/P AACRUB Cc R=0.0380 mC => mC 0.000 0.00 0.500 100% C2/c
:: note: glide plane codes are with reference to input cell !!
:: An SPF-style file is written to be used for the cell transformation.
Example 2
This example shows how to detect and correct for missed symmetry for a structure initially solved and refined as a structure in space group Cc. The structure is actually taken from the Cambridge Crystallographic Database and was shown by Marsh & Herbstein (Acta Cryst (1988), B44, 77-88) to be better described in space group Fdd2.
TITL CcToFdd2 Cc (Anonymous Example from CSD) CELL 0.71073 6.6260 41.0800 6.6000 90.000 120.110 90.000 ZERR 1 0.0030 0.0200 0.0030 0.000 0.050 0.000 LATT -7 SYMM X , - Y , 0.50000 + Z SFAC C H S UNIT 56 80 16 S1 3 0.21990 0.21930 0.19410 11.0000 0.1000 S2 3 0.57670 0.14380 -0.14760 11.0000 0.1000 C1 1 0.31270 0.19010 -0.11180 11.0000 0.1000 C2 1 0.10530 0.19950 -0.09000 11.0000 0.1000 C3 1 0.50640 0.19980 0.31840 11.0000 0.1000 C4 1 0.53620 0.19040 0.11230 11.0000 0.1000 C5 1 0.68580 0.16180 0.14100 11.0000 0.1000 C6 1 0.29050 0.16190 -0.27040 11.0000 0.1000 C7 1 0.49320 0.21550 -0.06860 11.0000 0.1000 H1 2 -0.00400 0.18300 -0.11100 11.0000 0.0500 H2 2 -0.01900 0.22400 -0.20400 11.0000 0.0500 H3 2 0.58900 0.21600 0.41300 11.0000 0.0500 H4 2 0.50900 0.18200 0.38400 11.0000 0.0500 H5 2 0.64100 0.14200 0.24000 11.0000 0.0500 H6 2 0.81500 0.16700 0.19300 11.0000 0.0500 H7 2 0.25600 0.16600 -0.43500 11.0000 0.0500 H8 2 0.15500 0.14300 -0.31100 11.0000 0.0500 H9 2 0.44100 0.23600 -0.07100 11.0000 0.0500 H10 2 0.61400 0.21300 -0.14300 11.0000 0.0500 S3 3 0.56400 0.03100 -0.11710 11.0000 0.1000 S4 3 1.26330 0.10620 0.22630 11.0000 0.1000 C8 1 0.96450 0.05950 0.19380 11.0000 0.1000 C9 1 0.73190 0.05000 0.16440 11.0000 0.1000 C10 1 0.73020 0.04990 -0.23680 11.0000 0.1000 C11 1 0.95900 0.05970 -0.03760 11.0000 0.1000 C12 1 1.08120 0.08900 -0.06300 11.0000 0.1000 C13 1 1.09330 0.08840 0.34010 11.0000 0.1000 C14 1 1.09940 0.03490 0.14280 11.0000 0.1000 H11 2 0.73700 0.04400 0.31000 11.0000 0.0500 H12 2 0.64900 0.07000 0.15800 11.0000 0.0500 H13 2 0.76500 0.03100 -0.33000 11.0000 0.0500 H14 2 0.66400 0.06800 -0.31900 11.0000 0.0500 H15 2 0.96400 0.10000 -0.20500 11.0000 0.0500 H16 2 1.15500 0.08300 -0.11000 11.0000 0.0500 H17 2 1.17300 0.08100 0.47500 11.0000 0.0500 H18 2 0.93000 0.10400 0.32300 11.0000 0.0500 H19 2 1.02700 0.02000 0.09600 11.0000 0.0500 H20 2 1.26800 0.04000 0.26600 11.0000 0.0500 HKLF 4 1 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 END
ADDSYM OUTPUT for Example 2:
ADDSYM - CHECK (cf. MISSYM (C): Le Page, Y., J. Appl. Cryst. (1987), 20,
264-269; J. Appl. Cryst. (1988), 21, 983-984)
--------------------------------------------------------------------------
- This ADDSYM Search is run on ALL NON-H Chemical Types
- Number of Input Atoms Included in Search = 18
- The Structure implies the following Symmetry Elements subject to the Criteria:
1.00 Deg., (metric) 0.25 Ang. (distances) and 0.45 Ang. (inv. and transl.)
Symm. Input Reduced (Ang) (Deg) (Ang) Input Cell
Elem Cell Row Cell Row d Type Dot Angle Max. dev. x y z
--------------------------------------------------------------------------------
n [ 0 1 0] [ 1 1 2] 41.080 2 2 0.00 0 through 0 3/4 0
Glide = 1/2 0 1/2
d * [ 1 0 2] [ 1-1 0] 11.418 2 2 0.02 0.026 through 0.894 0 0.788
C13 -C6 Glide = 1/4 1/4 0
2 * [ 1 0 0] [-1-1 0] 6.626 2 2 0.02 0.026 through 0.269 1/8 0.538
C13 -C6
Reduced->Convent Input->Reduced T = Input->Convent: a' = T a
--------------------------------------------------------------------------------
( 1 1 2 ) ( 0 0 -1 ) ( 0 -1 0 ) Det(T)
( -1 1 0 ) X ( 1 0 1 ) = ( 1 0 2 ) =
( -1 -1 0 ) ( -1/2 -1/2 0 ) ( -1 0 0 ) 2.000
Cell Lattice a b c alpha beta gamma Volume CrystalSystem Laue
--------------------------------------------------------------------------------
Input mC 6.626 41.080 6.600 90.00 120.11 90.00 1554 Monoclinic 2/m
Reduced P 6.600 6.602 20.806 94.59 94.58 119.75 777
Convent oF 41.080 11.419 6.626 90.02 90.00 90.00 3108 Orthorhombic mmm
:: Cell Angles differ 0.02 Deg. from (90/120)
Conventional, New or Pseudo Symmetry
================================================================================
Space Group Fdd2 No: 43, Laue: mmm [Hall: F 2 -2d ]
Lattice Type oF, Acentric, Orthorhombic, Order 16( 4) [Shoenflies: C2v^19 ]
CHIRAL - See P.G. Jones, Acta Cryst. (1986), A42, 57.
Nr ***** Symmetry Operation(s) *****
1 X , Y , Z
2 - X , - Y , Z
3 3/4 - X , 3/4 + Y , 1/4 + Z
4 1/4 + X , 1/4 - Y , 1/4 + Z
5 X , 1/2 + Y , 1/2 + Z
6 - X , 1/2 - Y , 1/2 + Z
7 3/4 - X , 1/4 + Y , 3/4 + Z
8 1/4 + X , 3/4 - Y , 3/4 + Z
9 1/2 + X , Y , 1/2 + Z
10 1/2 - X , - Y , 1/2 + Z
11 1/4 - X , 3/4 + Y , 3/4 + Z
12 3/4 + X , 1/4 - Y , 3/4 + Z
13 1/2 + X , 1/2 + Y , Z
14 1/2 - X , 1/2 - Y , Z
15 1/4 - X , 1/4 + Y , 1/4 + Z
16 3/4 + X , 3/4 - Y , 1/4 + Z
:: Origin shifted to:-0.125, 0.269, 0.000 after transformation
:: * Symmetry Elements preceded by an Asterisk are New and indicate
:: Missed/Pseudosymmetry Summary
:: M/P CcToFdd2 Cc (Anonymous ExamC => oF 0.000 0.02 0.026 100% Fdd2
:: note: glide plane codes are with reference to input cell !!
:: An SPF-style file is written to be used for the cell transformation.
:: Change of Crystal System indicated. (Maxdev. = 0.026 Ang.)
See also Abstract ACA97-Talk on MISSED SYMMETRY
22-09-98