FIRST EXAMPLE (ags4)

The first example (provided as the file ags4.ins) is the final refinement job for the polymeric inorganic structure Ag(NCSSSSCN)₂ AsF₆. This structure is described by H.W. Roesky, T. Gries, J. Schimkowiak and P.G. Jones in Angew. Chem. 98 (1986) 93-94 [Int. Edn. 25 (1986) 84-85] and was also used as the cover picture for the SHELXS-86 manual. Each ligand bridges two Ag⁺ ions so each silver is tetrahedrally coordinated by four nitrogen atoms. The silver, arsenic and one of the fluorine atoms lie on special positions. Normally the four unique heavy atoms (from Patterson interpretation using SHELXS) would have been refined first isotropically and the remaining atoms found in a difference synthesis, and possibly an intermediate job would have been performed with the heavy atoms anisotropic and the light atoms isotropic. For test purposes we shall simply input the atomic coordinates which assumes isotropic U's of 0.05. In this job all atoms are to be made anisotropic (ANIS). We shall further assume that a previous job has recommended the weighting scheme used here (WGHT) and shown that one reflection is to be suppressed in the refinement because it is clearly erroneous (OMIT).

The first 9 instructions (TITL...UNIT) are the same for any SHELXS and SHELXL-93 job for this structure and define the cell dimensions, symmetry and contents. The Siemens SHELXTL program XPREP can be used to generate these instructions automatically for any space group etc. SHELXL-93 knows the scattering factors for the first 94 neutral atoms in the Periodic Table. Ten least-squares cycles are to be performed, and the ACTA instruction ensures that the CIF files 'ags4.cif' and 'ags4.fcf' will be written for archiving and publication purposes. ACTA also sets up the calculation of bond lengths and angles (BOND) and a final difference electron density synthesis (FMAP 2) with peak search (PLAN 20). The HKLF 4 instruction terminates the file and initiates the reading of the 'ags4.hkl' intensity data file.

Users migrating from SHELX-76 should note that it is still legal to set up special position constraints on the x,y,z-coordinates, occupation factors, and U_ij components (for upwards compatibility). However it is totally unnecessary because the program will do this automatically for any special position in any space group, conventional or otherwise. Similarly the program recognizes polar space groups (P-4 is non-polar) and applies appropriate restraints (H.D. Flack and D. Schwarzenbach, Acta Cryst., A44 (1988) 499-506), so it is no longer necessary to worry about fixing one or more coordinates to prevent the structure drifting along polar axes. It is not necessary to set the overall scale factor using an FVAR instruction for this initial job, because the program will itself estimate a suitable starting value. Comments may be included in the '.ins' file either as REM instructions or as the rest of a line following '!'; this latter facility has been used to annotate this example.

 
TITL AGS4 in P-4                         ! title of up to 76 characters
CELL 0.71073 8.381 8.381 6.661 90 90 90  ! wavelength and unit-cell
ZERR 1 .002 .002 .001 0 0 0              ! Z (formula-units/cell), cell esd's
LATT -1                              ! non-centrosymmetric primitive lattice
SYMM -X, -Y, Z
SYMM Y, -X, -Z              ! symmetry operators (x,y,z must be left out)
SYMM -Y, X, -Z
SFAC C AG AS F N S          ! define scattering factor numbers
UNIT 4 1 1 6 4 8            ! unit cell contents in same order
 
L.S. 10                     ! 10 cycles full-matrix least-squares
ACTA                        ! CIF-output, bonds, Fourier, peak search
OMIT -2 3 1                 ! suppress bad reflection
ANIS                        ! convert all (non-H) atoms to anisotropic
WGHT 0.037 0.31             ! weighting scheme
AG  2  .000  .000  .000
AS  3  .500  .500  .000
S1  6  .368  .206  .517     ! atom name, SFAC number, x, y, z (usually
S2  6  .614  .966  .736     ! followed by sof and U(iso) or U_ij); the
C   1  .278  .095  .337     ! program automatically generates special
N   5  .211  .030  .214     ! position constraints
F1  4  .596  .325 -.007
F2  4  .500  .500  .246
HKLF 4                      ! read h,k,l,F_o²,sigma(F_o²) from 'ags4.hkl'

The '.lst' listing file starts with a head followed by an echo of the above '.ins' file. After reading TITL...UNIT the program calculates the cell volume, F(000), absorption coefficient, cell weight and density. If the density is unreasonable, perhaps the unit-cell contents have been given incorrectly. The next items in the '.lst' file are the connectivity table and the symmetry operations used to include a shell of symmetry equivalent atoms (so that all unique bond lengths and angles can be found):

 
Covalent radii and connectivity table for  AGS4 in P-4
 
C    0.770
AG   1.440
AS   1.210
F    0.640
N    0.700
S    1.030
 
Ag - N N_$4 N_$5 N_$3
As - F2 F2_$6 F1_$7 F1_$6 F1_$1 F1
S1 - C S2_$1
S2 - S2_$2 S1_$1
C - N S1
N - C Ag
F1 - As
F2 - As
 
 
Operators for generating equivalent atoms:
 
$1   -x+1, -y+1, z
$2   -x+1, -y+2, z
$3   -x, -y, z
$4   y, -x, -z
$5   -y, x, -z
$6   y, -x+1, -z
$7   -y+1, x, -z

Note that in addition to symmetry operations generated by the program, one can also define operations with the EQIV instruction and then refer to the corresponding atoms with _$n in the same way. Thus:

 EQIV $1 1-x, 1-y, z
 EQIV $2 x, y-1, z
 EQIV $3 1-x, -y, z
 CONF S1 S2_$1 S2_$2 S1_$3

could have been included in 'ags4.ins' to calculate the S-S-S-S torsion angle. Only one new operator would have been required if S2 were bonded to S1 in the original atom list. If EQIV instructions are used, the program renumbers the other symmetry operators accordingly.

The next part of the output is concerned with the data reduction:

 
   1475  Reflections read, of which     0  rejected
 
  0 =< h =< 10,     -9 =< k =< 10,      0 =< l =<  8,   Max. 2-theta =   55.00
 
      0  Systematic absence violations
 
 
Inconsistent equivalents etc.
 
  h   k   l       Fo^2    Sigma(Fo^2)  Esd of mean(Fo^2)
 
  3   4   0      387.25       8.54       47.78
 
      1  Inconsistent equivalents
 
    904  Unique reflections, of which      1  suppressed
 
R(int) = 0.0165     R(sigma) = 0.0202      Friedel opposites not merged
 
Maximum memory for data reduction =   955 /    9083

Throughout this documentation, Sigma with a capital S means a summation, and sigma with a small s is an esd. F_o² means the EXPERIMENTAL measurement, and so, despite the square, may possibly be slightly negative if the background is higher than the peak as a result of statistical fluctuations etc. R(int) and R(sigma) are defined as follows:

R(int) = Sigma | F_o² - F_o²(mean) | / Sigma [ F_o² ]

where both summations involve all input reflections for which more than one symmetry equivalent is averaged, but not the remaining reflections, and:

R(sigma) = Sigma [ sigma(F_o²) ] / Sigma [ F_o² ]

over all reflections in the merged list. Since these R-indices are based on F², they will tend to be about twice as large as the corresponding indices based on F. The 'esd of the mean' (in the table of inconsistent equivalents) is the rms deviation from the mean divided by the square root of (n-1), where n equivalents are combined for a given reflection. In estimating the sigma(F²) of a merged reflection, the program uses the value obtained by combining the sigma(F²) values of the individual contributors, unless the esd of the mean is larger, in which case it is used instead.

The memory statistics which appear at various points in the output give the highest elements of the A and B arrays used for the given calculation. Although it is easy to adjust these dimensions, it requires recompiling the program and will rarely be required. For example there is no limit on the number of reflections in this sort/merge stage - if there is less physical memory the program makes more use of the disk, which of course is slower.

Special position constraints are then generated and the statistics from the first least-squares cycle are listed (the output has been compacted to fit the page). The maximum vector length refers to the number of reflections processed simultaneously in the rate-determining calculations; usually the program utilizes all available memory to make this as large as possible, subject to a maximum of 511. This maximum may be reduced (but not increased) by means of the fourth parameter on the L.S. (or CGLS) instruction; this may be required to prevent unnecessary disk transfers when large structures are refined on virtual memory systems with limited physical memory. The number of parameters refined in the current cycle is followed by the total number of refinable parameters (here both are 55).

 
Special position constraints for Ag
x =  0.0000         y =  0.0000         z =  0.0000         U22 = 1.0 * U11
U23 = 0             U13 = 0             U12 = 0             sof = 0.25000
 
Special position constraints for As
x =  0.5000         y =  0.5000         z =  0.0000         U22 = 1.0 * U11
U23 = 0             U13 = 0             U12 = 0             sof = 0.25000
 
Special position constraints for F2
x =  0.5000         y =  0.5000         U23 = 0             U13 = 0
sof = 0.50000
 
 
Least-squares cycle 1  Maximum vector length =511  Memory required =1095/82388
 
wR2 =  0.5042 before cycle   1 for    903 data and   55 /   55 parameters
 
GooF = S =     3.480;     Restrained GooF =      3.480  for      0 restraints
 
Weight = 1/[sigma^2(Fo^2)+(0.0370*P)^2+0.31*P] where P=(Max(Fo^2,0)+2*Fc^2)/3
 
** Shifts scaled down to reduce maximum shift/esd from   17.32  to   15.00 **
 
    N      value        esd    shift/esd  parameter
 
    1     2.38015     0.04260    32.401    OSF
    2     0.08362     0.00224    14.993    U11 Ag
    5     0.02864     0.00580    -3.679    U33 As
   11     0.08546     0.00781     4.543    U33 S1
   23    -0.01788     0.00444    -4.027    U12 S2
   47     0.14422     0.01515     6.218    U33 F1
   52     0.13288     0.02330     3.558    U11 F2
 
Mean shift/esd =   2.053    Maximum =  32.401 for  OSF
 
Max. shift = 0.055 A for C      Max. dU = 0.049 for F2

Only the largest shift/esd's are printed. More output could have been obtained using MORE 2 or MORE 3. The largest correlation matrix elements are printed after the last cycle, in which the mean and maximum shift/esd have been reduced to 0.002 and 0.012 respectively. This is followed by the full table of refined coordinates and U_ij's with esd's (too large to include here, but similar to the corresponding table in SHELX-76 except that U_eq and its esd are also printed) and by a final structure factor calculation:

 
Final Structure Factor Calculation for  AGS4 in P-4
 
Total number of l.s. parameters = 55        Maximum vector length = 511
 
wR2 =  0.0779 before cycle  11 for    903 data and    2 /   55 parameters
 
GooF = S =     1.063;     Restrained GooF =      1.063  for      0 restraints
 
Weight = 1/[sigma^2(Fo^2)+(0.0370*P)^2+0.31*P] where P=(Max(Fo^2,0)+2*Fc^2)/3
 
R1 =  0.0322 for    818 Fo > 4.sigma(Fo)  and  0.0370 for all    904 data
wR2 =  0.0834,  GooF = S =   1.138,  Restrained GooF =    1.138  for all data
 
Flack x parameter =   0.0224   with esd  0.0260   (expected values are 0
(within 3 esd's) for correct and +1 for inverted absolute structure)

There are some important points to note here. The weighted R-index based on F_o² is (for compelling statistical reasons) much higher than the conventional R-index based on F_o with a threshold of say F_o > 4*sigma(F_o). For comparison with structures refined against F the latter is therefore printed as well (as R₁). Despite the fact that wR₂ and not R₁ is the quantity minimized, R₁ has the advantage that it is relatively insensitive to the weighting scheme, and so is more difficult to manipulate.

Since the structure is non-centrosymmetric, the program has automatically estimated the Flack absolute structure parameter x in the final structure factor summation. In this example x is within one esd of zero, and its esd is also relatively small. This provides strong evidence that the absolute structure has been assigned correctly, so that no further action is required. The program would have printed a warning here if it would have been necessary to 'invert' the structure. For further details see the section on absolute structure below. The two parameters 'refined' ( 2 / 55 ) but not applied in the final structure factor cycle in this case are related to the overall scale and the Flack x parameter; no parameters are 'refined' in the final structure factor cycle for a centrosymmetric structure.

This is followed by a list of principal mean square displacements U for all anisotropic atoms. It will be seen that none of the smallest components (in the third column) are in danger of going negative [which would make the atom 'non positive definite' (NPD)] but that the motion of the two unique fluorine atoms is highly anisotropic (not unusual for an AsF₆ anion). The program suggests that the fluorine motion is so extended in one direction that it would be possible to represent each of the two fluorine atoms as disordered over two sites, for which x, y and z coordinates are given; this may safely be ignored here (although there may well be some truth in it). The two suggested new positions for each 'split' atom are placed equidistant from the current position along the direction (and reverse direction) corresponding to the largest eigenvalue of the anisotropic displacement tensor.

This list is followed by the analysis of variance (reproduced here in squashed form), recommended weighting scheme (to give a flat analysis of variance in terms of F_c²), and a list of the most disagreeable reflections (which clearly shows that the one reflection suppressed by OMIT is indeed an aberration). For a discussion of the analysis of variance see the second example.

 
Principal mean square atomic displacements U
 
  0.1067   0.1067   0.0561   Ag
  0.0577   0.0577   0.0386   As
  0.1038   0.0659   0.0440   S1
  0.0986   0.0515   0.0391   S2
  0.0779   0.0729   0.0391   C
  0.1004   0.0852   0.0474   N
  0.3029   0.0954   0.0473   F1
     may be split into  0.5965  0.3173  0.0288  and  0.5946  0.3324 -0.0369
  0.4778   0.1671   0.0457   F2
     may be split into  0.5320  0.5089  0.2462  and  0.4680  0.4911  0.2462
 
Analysis of variance for reflections employed in refinement
K = Mean[Fo^2] / Mean[Fc^2]  for group
 
Fc/Fc(max)     0.000 0.026 0.039 0.051 0.063 0.082 0.103 0.147 0.202 0.306 1.0
 
Number in group    94.   89.   90.   91.   89.   91.   89.   91.   88.   91.
 
           GooF  1.096 1.101 0.997 1.078 1.187 1.069 1.173 0.922 1.019 0.966
 
            K    1.560 1.053 1.010 1.004 1.007 1.021 1.026 1.002 0.997 0.984
 
 
Resolution(A)  0.77  0.81  0.85  0.90  0.95  1.02  1.10  1.22  1.40  1.74  inf
 
Number in group    97.   84.   92.   91.   89.   90.   89.   90.   93.   88.
 
           GooF  1.067 0.959 0.935 0.895 1.035 1.040 1.115 1.149 1.161 1.228
 
            K    1.047 1.010 1.009 0.991 1.004 0.996 0.989 1.012 0.997 0.982
 
            R1   0.166 0.100 0.069 0.059 0.051 0.036 0.033 0.027 0.020 0.020
 
 
Recommended weighting scheme:  WGHT   0.0329   0.3591
 
 
Most Disagreeable Reflections (* if suppressed)
 
    h   k   l       Fo^2        Fc^2  Delta(F^2)/esd  Fc/Fc(max)  Resolution(A)
 
*  -2   3   1         43.53          7.44      11.14       0.029       2.19
    4   4   4         18.32         33.30       3.51       0.062       1.11
   -4   1   3         15.79          4.17       3.39       0.022       1.50
    0   2   2         41.60         57.32       3.16       0.082       2.61
    2   5   0        124.72        100.33       3.06       0.108       1.56
    2   3   0         64.43         48.46       3.03       0.075       2.32
   -5   4   1         11.04          2.57       2.90       0.017       1.28
    2   5   3         42.27         55.48       2.60       0.080       1.27
    6   5   2          6.43          1.02       2.56       0.011       1.02
    4   6   2         20.16         11.98       2.55       0.037       1.10
    6   1   1         55.45         42.28       2.51       0.070       1.35
    6   0   5        104.65        126.19       2.49       0.121       0.96
    4   1   2        139.30        116.95       2.44       0.117       1.74
    9   0   3         39.34         26.06       2.44       0.055       0.86
    2   4   4        371.53        327.01       2.36       0.195       1.24
    4   3   5         55.69         43.02       2.33       0.071       1.04
   -3   6   0          7.51          3.10       2.25       0.019       1.25
   -1   4   2        142.05        120.53       2.22       0.119       1.74
    0  10   1          2.01          8.31       2.21       0.031       0.83
   -2   1   2       1497.02       1361.86       2.20       0.399       2.49

After the table of bond lengths and angles (BOND was implied by the ACTA instruction), the data are merged (again) for the Fourier calculation after correcting for dispersion (because the electron density is real). In contrast to the initial data reduction, Friedel's law is assumed here; the aim is to set up a unique reflection list so that the (difference) electron density can be calculated on an absolute scale.

The algorithm for generating the 'asymmetric unit' for the Fourier calculations is general for all space groups, in conventional settings or otherwise. The rms electron density (averaged over all grid points) is printed as well as the maximum and minimum values so that the significance of the latter can be assessed. Since PLAN 20 was assumed, only a peak list is printed (and written to the .res file), followed by a list of shortest distances between peaks (not shown below); PLAN -20 would have produced a more detailed analysis with 'printer plots' of the structure. The last 40 peaks and some of the interatomic distances have been deleted here to save space. In this table, 'distances to nearest atoms' takes symmetry equivalents into account.

 
Bond lengths and angles        [severely squashed to fit 80 columns!]
 
Ag -   Distance     Angles
N     2.279(0.006)
N_$4  2.279(0.006) 113.08(0.15)
N_$5  2.279(0.006) 113.08(0.15) 102.47(0.29)
N_$3  2.279(0.006) 102.47(0.29) 113.08(0.16) 113.08(0.15)
         Ag -        N            N_$4         N_$5
 
As -   Distance     Angles
F2    1.640(0.007)
F2_$6 1.640(0.007)180.00(0.00)
F1_$7 1.672(0.004) 89.08(0.41) 90.92(0.41)
F1_$6 1.672(0.004) 89.08(0.41) 90.92(0.41)178.18(0.82)
F1_$1 1.672(0.004) 90.92(0.41) 89.08(0.41) 90.01(0.01) 90.01(0.01)
F1    1.672(0.004) 90.92(0.41) 89.08(0.41) 90.01(0.01) 90.01(0.01)178.18(0.82)
         As -        F2          F2_$6       F1_$7       F1_$6       F1_$1
 
S1 -   Distance     Angles
C     1.682(0.007)
S2_$1 2.063(0.003)  98.61(0.20)
         S1 -        C
 
S2 -   Distance     Angles
S2_$2 2.011(0.003)
S1_$1 2.063(0.003) 105.37(0.07)
         S2 -        S2_$2
 
C -    Distance     Angles
N     1.147(0.007)
S1    1.682(0.007) 175.67(0.49)
         C -         N
 
N -    Distance     Angles
C     1.147(0.007)
Ag    2.279(0.006) 152.38(0.45)
         N -         C
 
F1 -   Distance     Angles
As    1.672(0.004)
         F1 -
 
F2 -   Distance     Angles
As    1.640(0.007)
         F2 -
 
 
FMAP and GRID set by program
 
FMAP   2   3  18
GRID    -3.333  -2  -1     3.333   2   1
 
R1 =  0.0370 for    590 unique reflections after merging for Fourier
Highest memory used    768 /    6109
 
 
Electron density synthesis with coefficients Fo-Fc
 
Maximum = 0.32,   Minimum = -0.35 e/A^3,   Highest memory used = 768/13827
Mean = 0.00,   Rms deviation from mean = 0.07 e/A^3
 
 
Fourier peaks appended to .res file
 
         x       y       z       sof     U    Peak  Dist to nearest atoms
 
Q1  1  0.0000  0.0000  0.5000  0.25000  0.05  0.32  2.60 N  2.69 C  3.33 AG
Q2  1  0.5691  0.3728  0.1623  1.00000  0.05  0.27  1.20 F1  1.34 F2  1.62 AS
Q3  1  0.5685  0.3851 -0.1621  1.00000  0.05  0.24  1.19 F1  1.25 F2  1.56 AS
Q4  1  0.4075  0.4717  0.2378  1.00000  0.05  0.23  0.81 F2  1.78 AS  1.79 F1
Q5  1  0.5848  0.2667  0.0312  1.00000  0.05  0.23  0.55 F1  2.09 AS  2.47 F1
Q6  1  0.5495  0.3425 -0.1122  1.00000  0.05  0.21  0.83 F1  1.57 AS  1.65 F2
Q7  1  0.2617 -0.1441  0.1446  1.00000  0.05  0.20  1.59 N  2.17 F1  2.40 C
Q8  1  0.7221  0.1898  0.0030  1.00000  0.05  0.20  1.55 F1  2.39 N  2.54 N
Q9  1  0.1997  0.0293  0.1024  1.00000  0.05  0.19  0.75 N  1.79 C  1.82 AG
Q10 1  0.5394  1.0113  0.8165  1.00000  0.05  0.19  0.91 S2  1.41 S2  2.82 S1

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