Structure solution when the Space Group is not certain.
DF41 is an example of the relatively rare P2₁2₁2 (No.18) Space Group.

The problem here is - how do you find the correct Space Group?
CrysAlis Pro suggested P222₁ and Platon/Addsym (defaults) gave different results before and after refinement in P1
 
Three possible strategies are described here:

(1) Use Absen to look carefully at the systematic absences.
(2) Solve the structure in P1 and Search for symmetry in the atom list
(3) Use the derivesymmetry output from Superflip to look for symmetry in the P1 electron density.

You will see that the three methods suggest the correct space group. In most cases it is best to go back and solve the structure in the correct space group.

Using Oscail/Absen the default Orthorhombic choices are:

The 00l 2n+1 absence looks likely but when the cut levels are raised x2

there are possible absences on 0k0 and 00l and Space Group 18 now looks likely. This is the correct choice. Back to the top

Solving the structure in P1 and looking for symmetry in the atom list.

When the space group is set to P1 solution the solution contains two full molecules in the unit cell.

Using the well known ADDSYM function in PLATON two 2₁s are found before the structure is refined in P1 and just one after refinement.
In the Oscail ChkSym run there are two 2₁s before and after refinement.
The following is the ChkSym symmetry analysis output with the space group set to P1.

If an sof of 1 is assumed for all atoms then
the number of atoms in the asymmetric unit is reasonable.
SYMMETRY in the selected Space Group
P1 (no. 1)
Origin Arbitrary
Symmetry Operations
---------------------------------------------------------------
SYMMETRY in the atom list Tol.Angst. 0.050 (xyz) 0.010 0.002 0.009
Q1 1 to Q5 5 a 2-fold at y 0.007 z 0.867 to 1, 8 contr.
Q3 3 to Q4 4 a 2-fold at y -0.493 z 0.364 to 5, 10 contr.
2-fold axis on a contributors 8 at y 0.007 z 0.867
x axis translation required before SYMM reduction
2-fold axis on a contributors 10 at y -0.493 z 0.364
x axis translation required before SYMM reduction
Q1 1 to Q4 4 b 2(1) at x 0.483 z 0.615 to 1, 14 contr.
Q1 1 to Q3 3 c 2(1) at x 0.483 y -0.244 to 1, 14 contr.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Summary of Symmetry Properties
---------------------------------------------------------------
Inversion centres
Space Group 1 is acentric
In the atom list there are 0 centre(s) max.contrib. 0
Space Group a b c Atom List a  b  c
mirrors     0 0 0           0  0  0
2-folds     0 0 0          10  0  1
2(1)s       0 0 0           1 17 19
glides      0 0 0           0  0  0
n-glides    0 0 0           1  0  0
d-glides    0 0 0           0  0  0
Atom List symmetry parallel to the axes
Along a 2-fold
Along b 2(1)
Along c 2(1)
>>>>2-fold found on unexpected a axis ?axis swap?
>>>>2(1) found on unexpected b axis ?axis swap?
>>>>2(1) found on unexpected c axis ?axis swap?

There are two 2₁s and a 2 in the atom list The numbers in the list are the numbers of contributing pairs.
Using ViewSGfreq. the closest match is No. 18 P2₁2₁2

The LST file gives the number of entries in the Jan 2009 update of the CSD.

 16 P222       21 Acentric
 17 P2221      51 Acentric
 18 P21212   1947 Acentric
 19 P212121 36484 Acentric
 

When the space group is set to No. 18 the ChkSym output is:

If an sof of 1 is assumed for all atoms then
there are (approx.) 4 times too many atoms in the asymmetric unit.
SYMMETRY in the selected Space Group
P21212 (no. 18)
Origin at 112 in 2(1)2(1) plane
Symmetry Operations
2-fold along c at x 0.000 y 0.000 (Origin)
2-fold along c at x 0.500 y 0.500
2(1) along a at y 0.250 z 0.000
2(1) along b at x 0.250 z 0.000
---------------------------------------------------------------
SYMMETRY in the atom list Tol.Angst. 0.050 (xyz) 0.010 0.002 0.009
N2 1 to N1 4 a 2-fold at y 0.006 z 0.861 to 1, 10 contr.
N4 2 to N3 3 a 2-fold at y -0.494 z 0.368 to 2, 8 contr.
2-fold axis on a contributors 10 at y 0.006 z 0.861
x axis translation required before SYMM reduction
2-fold axis on a contributors 8 at y -0.494 z 0.368
x axis translation required before SYMM reduction
N2 1 to N3 3 b 2(1) at x 0.482 z 0.614 to 1, 17 contr.
N2 1 to N4 2 c 2(1) at x 0.484 y -0.244 to 1, 19 contr.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Summary of Symmetry Properties
---------------------------------------------------------------
Inversion centres
Space Group 18 is acentric
In the atom list there are 0 centre(s) max.contrib. 0
Space Group a b c Atom List a  b  c
mirrors     0 0 0           0  0  0
2-folds     0 0 1          10  0  0
2(1)s       1 1 0           1 17 19
glides      0 0 0           0  0  0
n-glides    0 0 0           1  0  0
d-glides    0 0 0           0  1  0
Atom List symmetry parallel to the axes
Along a 2-fold
Along b 2(1)
Along c 2(1)
>>>>2-fold found on unexpected a axis ?axis swap?
>>>>2(1) found on unexpected c axis ?axis swap?

An axis swap is required to put the 2₁s and the 2 in the standard positions. Click and select -cba on the dialog.

Click OK and repeat the symmetry analysis. There is a 2-fold at x 0.862 y 0.006 this should be moved to the origin. Click and enter the required translations on the dialog.

Click OK. The symmetry equivalent atoms need to be removed. Click Setup and set the SYMM Reduction Tol. to 0.5.

Click the symmetry reduction button . The output is:

Symmetry Reduction
Tolerance (Angstroms) 0.500000
Symmetry Reduction
Current Total atoms    46
Symmetry related atoms 34
Atoms Written to file  12
Symmetry Reduced atom list implemented

The picture on screen shows the unique "half molecule" broken up.

This is easily reassembled using Ortex.
On exit from ChkSym the HKL file is backed up and a new transformed one is written.
N.B. Full details of all changes are in the _cs.LST file.
The procedure described here allows refinement to continue in P2₁2₁2.
Exit ChkSym and run Ortex. In Ortex edit mode select an atom in the largest piece and click SEL.Frg.

On the dialog select Auto Assemble to Fragment and click OK. Select defaults and then click ShelxL. Repeat auto assemble if necessary.

The full molecule (using the extend function in Ortex) is.

Final Structure Factor Calculation for DF41
Total number of l.s. parameters = 110 Maximum vector length = 511 Memory required = 1420 / 25046
wR2 = 0.1345 before cycle 13 for 2076 data and 2 / 110 parameters
GooF = S = 1.068; Restrained GooF = 1.068 for 0 restraints
Weight = 1 / [ sigma^2(Fo^2) + ( 0.0404 * P )^2 + 0.28 * P ] where P = ( Max ( Fo^2, 0 ) + 2 * Fc^2 ) / 3
R1 = 0.0569 for 1638 Fo > 4sig(Fo) and 0.0707 for all 2076 data
wR2 = 0.1345, GooF = S = 1.068, Restrained GooF = 1.068 for all data

The final ShelxL output is quite satisfactory. Back to the top

Using the derivesymmetry function in Superflip gives the following output (examine the .LST file)

#####################################
# Checking the density for symmetry #
#####################################

Symmetry operations compatible with the lattice and centering:
             Symmetry operation agreement factor
2_1(0,1,0):    -x1  1/2+x2    -x3   0.187 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  2(1,0,0):     x1     -x2    -x3   2.992 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
2_1(0,0,1):    -x1     -x2 1/2+x3   2.993 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  m(1,0,0):    -x1      x2     x3  60.306 XXXXXXXXXXXXXXXXXXXX
        -1:    -x1     -x2    -x3  62.727 XXXXXXXXXXXXXXXXXXX
  a(0,1,0): 1/2+x1     -x2     x3  79.344 XXXXXXXXXX
  b(0,0,1):     x1  1/2+x2    -x3  83.607 XXXXXXXX
  m(0,1,0):     x1     -x2     x3  86.469 XXXXXXX
  2(0,0,1):    -x1     -x2     x3  87.354 XXXXXX
  m(0,0,1):     x1      x2    -x3  89.723 XXXXX
  n(1,0,0):    -x1  1/2+x2 1/2+x3  90.633 XXXXX
  n(0,1,0): 1/2+x1     -x2 1/2+x3  93.856 XXX
  n(0,0,1): 1/2+x1  1/2+x2    -x3  95.674 XX
  c(0,1,0):     x1     -x2 1/2+x3 102.683 X
  b(1,0,0):    -x1  1/2+x2     x3 104.008 X
2_1(1,0,0): 1/2+x1     -x2    -x3 113.979 X
  2(0,1,0):    -x1      x2    -x3 115.446 X
  a(0,0,1): 1/2+x1      x2    -x3 118.247 X
  c(1,0,0):    -x1      x2 1/2+x3 122.861 X

-------------------------------------------------
Space group derived from the symmetry operations:
-------------------------------------------------
HM   symbol: P22121
Hall symbol: p 2bc 2
Fingerprint: 3300223}000qW3 (0,0,0)
Symmetry operations:
1          :  x1     x2     x3
2_1(0,0,1) : -x1 1/2-x2 1/2+x3
  2(1,0,0) :  x1    -x2    -x3
2_1(0,1,0):  -x1 1/2+x2 1/2-x3

This clearly also suggests space group 18. Notice that the errors on the first three symm ops are much lower than the others Back to top