**3. Examples
of Small Molecule Refinements with SHELXL**

Two test structures supplied with the SHELXL-97 are
intended to provide a good illustration of routine small moiety structure
refinement. The output discussed here should not differ significantly from
that of the test jobs, except that it has been abbreviated and there may
be differences in the last decimal place caused by rounding errors.

The first example (provided as the files *ags4.ins*
and *ags4.hkl*) is the final refinement job for the polymeric inorganic
structure Ag(NCSSSSCN)_{2} AsF_{6}, determined by Roesky,
Gries, Schimkowiak & Jones (1986). 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 isotropically first 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 for all atoms. 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 job for this structure and define the cell dimensions,
symmetry and contents. The SHELXTL program XPREP can be used to generate
these instructions automatically for any space group etc. SHELXL 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.

It is possible to set up special
position constraints on the x,y,z-coordinates, occupation factors, and
Uij components by hand. However this 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 is non-polar)
and applies appropriate restraints (Flack & Schwarzenbach, 1988), 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 .386 .034 .736 ! followed
by sof and U(iso) or Uij); 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,Fo^2,sigma(Fo^2)
from 'ags4.hkl'**

The *.lst* listing file
starts with a header 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_$3 N_$4 N_$2**

**As - F2 F2_$6 F1_$7 F1_$6
F1_$5 F1**

**S1 - C S2**

**S2 - S2_$1 S1**

**C - N S1**

**N - C Ag**

**F1 - As**

**F2 - As**

**Operators for generating equivalent
atoms:**

**$1 -x+1, -y+1, z**

**$2 -x, -y, z**

**$3 y, -x, -z**

**$4 -y, x, -z**

**$5 -x+1, -y+1, 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, -y, z**

**CONF S1 S2 S2_$1 S1_$1**

could have been included in *ags4.ins* to calculate
the S-S-S-S torsion angle. 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 1 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**

**903 Unique reflections, of
which 0 suppressed**

**R(int) = 0.0165 R(sigma) =
0.0202 Friedel opposites not merged**

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 msgizes 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=1092/82899**

**wR2 = 0.5042 before cycle
1 for 903 data and 55 / 55 parameters**

**GooF = S = 8.127; Restrained
GooF = 8.127 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 17.64 to 15.00 ****

**N value esd shift/esd parameter**

**1 2.31065 0.04324 9.042 OSF**

**2 0.07314 0.00206 11.250 U11
Ag**

**11 0.07309 0.00669 3.453 U33
S1**

**47 0.11304 0.01391 4.533 U33
F1**

**Mean shift/esd = 1.238 Maximum
= 11.250 for OSF**

**Max. shift = 0.045 A for C
Max. dU = 0.033 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 0.003 and 0.017 respectively. This
is followed by the full table of refined coordinates and Uij'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 = 0.0780 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 0.0367 for all 903 data**

**wR2 = 0.0780, GooF = S = 1.063,
Restrained GooF = 1.063 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*_{o}2
is (for compelling statistical reasons) much higher than the conventional
*R*-index based on *F*_{o} with a threshold of say *F*_{o}
> 4
(*F*_{o}).
For comparison with structures refined against *F* the latter is therefore
printed as well (as *R*1). Despite the fact that *wR*2 and not
*R*1 is the quantity minimized, *R*1 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 or to refine
it as a racemic twin.

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 AsF_{6} 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*_{c}2),
and a list of the most disagreeable reflections. 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 0.0314 0.3674**

**Most Disagreeable Reflections
(* if suppressed or used for Rfree)**

**h k l Fo^2 Fc^2 Delta(F^2)/esd
Fc/F(max) Resolution(A)**

**4 4 4 18.32 33.30 3.62 0.062
1.11**

**-4 1 3 15.79 4.17 3.50 0.022
1.50**

**0 2 2 41.60 57.32 3.26 0.082
2.61 etc.**

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 page!]**

**Ag - Distance Angles**

**N 2.2788(0.0058)**

**N_$2 2.2788(0.0058) 113.08(0.15)**

**N_$4 2.2788(0.0058) 113.08(0.15)
102.47(0.29)**

**N_$3 2.2788(0.0058) 102.47(0.29)
113.08(0.15) 113.08(0.15)**

**Ag - N N_$3 N_$4**

**As - Distance Angles**

**F2 1.6399(0.007)**

**F2_$6 1.6399(0.007)180.00(0.00)**

**F1_$7 1.6724(0.0037) 89.08(0.41)
90.92(0.41)**

**F1_$6 1.6724(0.0037) 89.08(0.41)
90.92(0.41)178.15(0.82)**

**F1_$5 1.6724(0.0037) 90.92(0.41)
89.08(0.41) 90.01(0.01) 90.01(0.01)**

**F1 1.6724(0.0037) 90.92(0.41)
89.08(0.41) 90.01(0.01) 90.01(0.01)178.15(0.82)**

**As - F2 F2_$6 F1_$7 F1_$6
F1_$5**

**S1 - Distance Angles**

**C 1.6819(0.0069)**

**S2 2.0633(0.0025) 98.61(0.20)**

**S1 - C**

**S2 - Distance Angles**

**S2_$1 2.0114(0.0028)**

**S1 2.0633(0.0025) 105.37(0.07)**

**S2 - S2_$1**

**C - Distance Angles**

**N 1.1472(0.0074)**

**S1 1.6819(0.0069) 175.67(0.49)**

**C - N**

**N - Distance Angles**

**C 1.1472(0.0074)**

**Ag 2.2788(0.0058) 152.38(0.45)**

**N - C**

**F1 - Distance Angles**

**As 1.6724(0.0037)**

**F1 -**

**F2 - Distance Angles**

**As 1.6399(0.0075)**

**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**

**Electron density synthesis
with coefficients Fo-Fc**

**Highest peak 0.32 at 0.0000
0.0000 0.5000 [2.60 A from N]**

**Deepest hole -0.36 at 0.5000
0.5000 0.1863 [0.40 A from F2]**

**Mean = 0.00, Rms deviation
from mean = 0.07 e/A^3 Highest memory used 1133/13851**

**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 0.5690 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 0.4606 -0.0113 0.8165
1.00000 0.05 0.19 0.91 S2 1.41 S2 2.82 S1**

In the second example (provided as the files *sigi.ins*
and *sigi.hkl*) a small organic structure is refined in the space
group P. Only the features
that are different from the ags4 refinement will be discussed in detail.
The structure consists of a five-membered lactone [-C7-C11-C8-C4(O1)-O3-]
with a -CH_{2}-OH group [-C5-O2] attached to C7 and a =C(CH_{3})
(NH_{2}) unit [=C9(C10)N6] double-bonded to C8.

Of particular interest here
is the placing and refinement of the 11 hydrogen atoms via HFIX instructions.
The two -CH_{2}- groups (C5 and C11) and one tertiary CH (C7) can
be placed geometrically by standard methods; the algorithms have been improved
relative to those used in SHELX-76, and the hydrogen atoms are now idealized
before each refinement cycle (and after the last). Since N6 is attached
to a conjugated system, it is reasonable to assume that the -NH_{2}
group is coplanar with the C8=C9(C10)-N6 unit, which enables these two
hydrogens to be placed as ethylenic hydrogens, requiring HFIX (or AFIX)
9n; the program takes into account that they are bonded to nitrogen in
setting the default bond lengths. All these hydrogens are to be refined
using a 'riding model' (HFIX or AFIX m3) for x, y and z.

The -OH and -CH_{3} groups
are trickier, in the latter case because C9 is sp^{2}-hybridized,
so the potential barrier to rotation is low and there is no fully staggered
conformation available as the obvious choice. Since the data are reasonable,
the initial torsion angles for these two groups can be found by means of
difference electron density syntheses calculated around the circles which
represent the loci of all possible hydrogen atom positions. The torsion
angles are then refined during the least-squares refinement. Note that
in subsequent cycles (and jobs) these groups will be re-idealized geometrically
with retention of the current torsion angle; the circular Fourier calculation
is performed only once. Two 'free variables' (2 and 3 yes, they still exist!)
have been assigned to refine common isotropic displacement parameters for
the 'rigid' and 'rotating' hydrogens respectively. If these had not been
specified, the default action would have been to hold the hydrogen U values
at 1.2 times the equivalent isotropic U of the atoms to which they are
attached (1.5 for the -OH and methyl groups).

The *sigi.ins* file (which is provided as a
test job) is as follows. Note that for instructions with both numerical
parameters and atom names such as HFIX and MPLA, it does not matter whether
numbers or atoms come first, but the order of the numerical parameters
themselves (and in some cases the order of the atoms) is important.

**TITL SIGI in P-1**

**CELL 0.71073 6.652 7.758 8.147
73.09 75.99 68.40**

**ZERR 2 .002 .002 .002 .03
.03 .03**

**SFAC C H N O**

**UNIT 14 22 2 6 ! no LATT and
SYMM needed for space group P-1**

**L.S. 4**

**EXTI 0.001 ! refine an isotropic
extinction parameter**

**WGHT .060 0.15 ! (suggested
by program in last job); WGHT**

**OMIT 2 8 0 ! and OMIT are
also based on previous output**

**BOND $H ! include H in bond
lengths / angles table**

**CONF ! all torsion angles
except involving hydrogen**

**HTAB ! analyse all hydrogen
bonds**

**FMAP 2 ! Fo-Fc Fourier**

**PLAN -20 ! printer plots and
full analysis of peak list**

**HFIX 147 31 O2 ! initial location
of -OH and -CH3 hydrogens from**

**HFIX 137 31 C10 ! circular
Fourier, then refine torsion, U(H)=fv(3)**

**HFIX 93 21 N6 ! -NH2 in plane,
xyz ride on N, U(H)=fv(2)**

**HFIX 23 21 C5 C11 ! two -CH2-
groups, xyz ride on C, U(H)=fv(2)**

**HFIX 13 21 C7 ! tertiary CH,
xyz ride on C, U(H)=fv(2)**

**EQIV $1 X-1, Y, Z ! define
symmetry operations for H-bonds**

**EQIV $2 X+1, Y, Z-1**

**HTAB N6 O1 ! outputs H-bonds
D-H...A with esds**

**HTAB O2 O1_$1 ! _$1 and _$2
refer to symmetry equivalents**

**HTAB N6 O2_$2**

**! l.s. planes through 5-ring
and through**

**MPLA 5 C7 C11 C8 C4 O3 O1
N6 C9 C10 ! CNC=CCC moiety, then find deviations**

**MPLA 6 C10 N6 C9 C8 C11 C4
O1 O3 C7 ! of last 4 and 3 named atoms resp. too**

**FVAR 1 .06 .07 ! overall scale
and free variables for U(H)**

**REM name sfac# x y z sof(+10
to fix it) U11 U22 U33 U23 U13 U12 follow**

**O1 4 0.30280 0.17175 0.68006
11.00000 0.02309 0.04802 =**

**0.02540 -0.00301 -0.00597
-0.01547**

**O2 4 -0.56871 0.23631 0.96089
11.00000 0.02632 0.04923 =**

**0.02191 -0.00958 0.00050 -0.02065**

**O3 4 -0.02274 0.28312 0.83591
11.00000 0.02678 0.04990 =**

**0.01752 -0.00941 -0.00047
-0.02109**

**C4 1 0.10358 0.23458 0.68664
11.00000 0.02228 0.02952 =**

**0.01954 -0.00265 -0.00173
-0.01474**

**C5 1 -0.33881 0.18268 0.94464
11.00000 0.02618 0.03480 =**

**0.01926 -0.00311 -0.00414
-0.01624**

**N6 3 0.26405 0.17085 0.33925
11.00000 0.03003 0.04232 =**

**0.02620 -0.01312 0.00048 -0.01086**

**C7 1 -0.25299 0.33872 0.82228
11.00000 0.02437 0.03111 =**

**0.01918 -0.00828 -0.00051
-0.01299**

**C8 1 -0.03073 0.27219 0.55976
11.00000 0.02166 0.02647 =**

**0.01918 -0.00365 -0.00321
-0.01184**

**C9 1 0.05119 0.24371 0.39501
11.00000 0.02616 0.02399 =**

**0.02250 -0.00536 -0.00311
-0.01185**

**C10 1 -0.10011 0.29447 0.26687
11.00000 0.03877 0.04903 =**

**0.02076 -0.01022 -0.00611
-0.01800**

**C11 1 -0.26553 0.36133 0.63125
11.00000 0.02313 0.03520 =**

**0.01862 -0.00372 -0.00330
-0.01185**

**HKLF 4 ! read intensity data
from 'sigi.hkl'; terminates '.ins' file**

**END**

The data reduction reports 1904
reflections read (one of which was rejected by OMIT) with indices -7
<=
*h*
<=
7,
-8 <= *k*
<= 9 and -9
<=
*l* <= 9.
Note that these are the limiting index values; in fact only about 1.5 times
the unique volume of reciprocal space was measured. The maximum 2
was 50.00, and there were no systematic absence violations, 34 (not seriously)
inconsistent equivalents, and 1296 unique data. R(int) was 0.0196 and R(sigma)
0.0151.

The program uses different default distances to hydrogen
for different bonding situations; these may be overridden by the user if
desired. These defaults depend on the temperature (set using TEMP) in order
to allow for librational effects. The list of default X-H distances is
followed by the (squashed) circular difference electron density syntheses
to determine the C-OH and C-CH_{3} initial torsion angles:

**Default effective X-H distances
for T = 20.0 C**

**AFIX m = 1 2 3 4 4[N] 3[N]
15[B] 8[O] 9 9[N] 16**

**d(X-H) = 0.98 0.97 0.96 0.93
0.86 0.89 1.10 0.82 0.93 0.86 0.93**

**Difference electron density
(eA^-3x100) at 15 degree intervals for AFIX 147 group attached to O2. The
center of the range is eclipsed (cis) to C7 and rotation is clockwise looking
down C5 to O2**

**2 -2 -6 -9 -8 -5 -1 0 0 0
1 0 -2 -2 0 9 23 39 48 42 29 16 9 5**

**Difference electron density
(eA^-3x100) at 15 degree intervals for AFIX 137 group attached to C10.
The center of the range is eclipsed (cis) to N6 and rotation is clockwise
looking down C9 to C10**

**50 47 39 28 19 15 20 30 38
41 39 37 34 29 25 27 33 35 29 19 12 15 29 43**

**After local symmetry averaging:
40 41 36 28 21 20 24 33**

It will be seen that the hydroxyl
hydrogen is very clearly defined, but that the methyl group is rotating
fairly freely (low potential barrier). After three-fold averaging, however,
there is a single difference electron density maximum. The (squashed) least-squares
refinement output follows:

**Least-squares cycle 1 Maximum
vector length=511 Memory required=1836/136080**

**wR2 = 0.1130 before cycle
1 for 1296 data and 105 / 105 parameters**

**GooF = S = 1.140; Restrained
GooF = 1.140 for 0 restraints**

**Weight = 1/[sigma^2(Fo^2)+(0.0600*P)^2+0.15*P]
where P=(Max(Fo^2,0)+2*Fc^2)/3**

**N value esd shift/esd parameter**

**1 0.97891 0.00384 -10.702
OSF**

**2 0.04044 0.00261 -7.494 FVAR
2**

**3 0.07317 0.00394 0.805 FVAR
3**

**4 0.01781 0.00946 1.777 EXTI**

**Mean shift/esd = 0.747 Maximum
= -10.702 for FVAR 2**

**Max. shift = 0.028 A for H10A
Max. dU =-0.020 for H5A**

**.......... etc (cycles 2 and
3 omitted) .........**

**Least-squares cycle 4 Maximum
vector length = 511 Memory required =1836/136080**

**wR2 = 0.1035 before cycle
4 for 1296 data and 105 / 105 parameters**

**GooF = S = 1.016; Restrained
GooF = 1.016 for 0 restraints**

**Weight = 1/[sigma^2(Fo^2)+(0.0600*P)^2+0.15*P]
where P=(Max(Fo^2,0)+2*Fc^2)/3**

**N value esd shift/esd parameter**

**1 0.97902 0.00358 -0.003 OSF**

**2 0.03605 0.00176 0.012 FVAR
2**

**3 0.07345 0.00376 -0.031 FVAR
3**

**4 0.02502 0.01081 -0.010 EXTI**

**Mean shift/esd = 0.008 Maximum
= -0.244 for tors H10A**

**Max. shift = 0.004 A for H10A
Max. dU = 0.000 for H2**

**Largest correlation matrix
elements**

**0.509 U12 O2 / U22 O2 0.507
U12 O3 / U11 O3**

**0.509 U12 O2 / U11 O2 0.500
U12 O3 / U22 O3**

**Idealized hydrogen atom generation
before cycle 5**

**Name x y z AFIX d(X-H) shift
Bonded Conformation**

**to determined by**

**H2 -0.6017 0.2095 0.8832 147
0.820 0.000 O2 C5 H2**

**H5A -0.2721 0.0676 0.9001
23 0.970 0.000 C5 O2 C7**

**H5B -0.2964 0.1554 1.0576
23 0.970 0.000 C5 O2 C7**

**H6A 0.3572 0.1389 0.4085 93
0.860 0.000 N6 C9 C8**

**H6B 0.3073 0.1559 0.2347 93
0.860 0.000 N6 C9 C8**

**H7 -0.3331 0.4598 0.8575 13
0.980 0.000 C7 O3 C5 C11**

**H10A -0.0176 0.2947 0.1525
137 0.960 0.000 C10 C9 H10A**

**H10B -0.2042 0.4192 0.2692
137 0.960 0.000 C10 C9 H10A**

**H10C -0.1764 0.2036 0.2964
137 0.960 0.000 C10 C9 H10A**

**H11A -0.3575 0.2948 0.6198
23 0.970 0.000 C11 C8 C7**

**H11B -0.3198 0.4943 0.5737
23 0.970 0.000 C11 C8 C7**

The final structure factor calculation, analysis of variance etc. produces the following edited output:

**Final Structure Factor Calculation
for SIGI in P-1**

**Total number of l.s. parameters
= 105 Maximum vector length = 511**

**wR2 = 0.1035 before cycle
5 for 1296 data and 0 / 105 parameters**

**GooF = S = 1.016; Restrained
GooF = 1.016 for 0 restraints**

**Weight = 1/[sigma^2(Fo^2)+(0.0600*P)^2+0.15*P]
where P=(Max(Fo^2,0)+2*Fc^2)/3**

**R1 = 0.0364 for 1189 Fo >
4.sigma(Fo) and 0.0397 for all 1296 data**

**wR2 = 0.1035, GooF = S = 1.016,
Restrained GooF = 1.016 for all data**

**Occupancy sum of asymmetric
unit = 11.00 for non-hydrogen and 11.00 for**

**hydrogen atoms.**

**Principal mean square atomic
displacements U**

**0.0504 0.0254 0.0188 O1**

**0.0492 0.0229 0.0189 O2**

**0.0513 0.0194 0.0165 O3**

**0.0326 0.0208 0.0159 C4**

**0.0376 0.0204 0.0190 C5**

**0.0439 0.0319 0.0214 N6**

**0.0329 0.0201 0.0185 C7**

**0.0276 0.0190 0.0181 C8**

**0.0289 0.0220 0.0191 C9**

**0.0493 0.0352 0.0181 C10**

**0.0353 0.0215 0.0183 C11**

**Analysis of variance for reflections
employed in refinement**

**K = Mean[Fo^2] / Mean[Fc^2]
for group**

**Fc/Fc(max) 0.000 0.009 0.017
0.027 0.038 0.049 0.065 0.084 0.110 0.156 1.0**

**Number in group 135. 125.
131. 139. 119. 132. 131. 128. 131. 126.**

**GooF 1.034 1.000 1.085 1.046
1.093 0.999 0.937 0.995 1.027 0.931**

**K 1.567 1.127 0.964 1.023
1.008 0.992 0.997 0.998 1.008 1.010**

**Resolution(A) 0.84 0.88 0.90
0.95 0.99 1.06 1.14 1.25 1.44 1.79 inf**

**Number in group 136. 127.
128. 128. 136. 124. 128. 130. 130. 129.**

**GooF 0.978 0.881 0.854 0.850
0.850 0.921 0.874 1.088 1.242 1.434**

**K 1.024 1.013 1.017 0.990
0.991 0.989 1.013 0.995 1.037 1.004**

**R1 0.061 0.049 0.050 0.046
0.034 0.034 0.031 0.039 0.038 0.037**

**Recommended weighting scheme:
WGHT 0.0545 0.1549**

The analysis of variance
should be examined carefully for indications of systematic errors. If the
*Goodness of Fit* (GooF) is significantly higher than unity and the
scale factor K is appreciably lower than unity in the extreme right columns
in terms of both *F* and resolution, then an extinction parameter
should be refined (the program prints a warning in such a case). This does
not show here because an extinction parameter is already being refined.
The scale factor is a little high for the weakest reflections in this example;
this may well be a statistical artifact and may be ignored (selecting the
groups on *F*_{c} will tend to make *F*_{o}^{2}
greater than *F*_{c}^{2} for this range). The increase
in the GooF at low resolution (the 1.79 to infinity range) is caused in
part by systematic errors in the model such as the use of scattering factors
based on spherical atoms which ignore bonding effects, and is normal for
purely light-atom structures (this interpretation is confirmed by the fact
that difference electron density peaks are found in the middle of bonds).
In extreme cases the lowest or highest resolution ranges can be conveniently
suppressed by means of the SHEL instruction; this is normal practice in
macromolecular refinements, but refining a diffuse solvent model with SWAT
may be better, inadequate solvent modeling for macromolecules produces
similar symptoms to lack of extinction refinement for small molecules.

The weighting scheme suggested by the program is
designed to produce a flat analysis of variance in terms of *F*_{c},
but makes no attempt to fit the resolution dependence of the GooF. It is
also written to the end of the *.res* file, so that it is easy to
update it before the next job. In the early stages of refinement it is
better to retain the default scheme of WGHT 0.1; the updated parameters
should not be incorporated in the next *.ins* file until all atoms
have been found and at least the heavier atoms refined anisotropically.

The list of most disagreeable reflections and tables of bond lengths and angles (BOND $H - omitted here) and torsion angles (CONF) are followed by the HTAB (hydrogen bonds) and MPLA (least-squares planes) tables:

**Selected torsion angles**

**-175.08 ( 0.12) C7 - O3 -
C4 - O1**

**5.73 ( 0.15) C7 - O3 - C4
- C8**

**109.69 ( 0.12) C4 - O3 - C7
- C5**

**-11.65 ( 0.15) C4 - O3 - C7
- C11**

**171.12 ( 0.10) O2 - C5 - C7
- O3**

**-72.04 ( 0.15) O2 - C5 - C7
- C11**

**-1.46 ( 0.24) O1 - C4 - C8
- C9**

**177.61 ( 0.12) O3 - C4 - C8
- C9**

**-176.27 ( 0.14) O1 - C4 -
C8 - C11**

**2.80 ( 0.16) O3 - C4 - C8
- C11**

**3.08 ( 0.22) C4 - C8 - C9
- N6**

**176.93 ( 0.13) C11 - C8 -
C9 - N6**

**-177.23 ( 0.13) C4 - C8 -
C9 - C10**

**-3.39 ( 0.22) C11 - C8 - C9
- C10**

**176.05 ( 0.13) C9 - C8 - C11
- C7**

**-9.39 ( 0.14) C4 - C8 - C11
- C7**

**12.37 ( 0.14) O3 - C7 - C11
- C8**

**-104.74 ( 0.13) C5 - C7 -
C11 - C8**

**Specified hydrogen bonds (with
esds except fixed and riding H)**

**D-H H...A D...A <(DHA)**

**0.86 2.23 2.8486(18) 129.3
N6-H6A...O1**

**0.82 2.04 2.8578(16) 174.0
O2-H2...O1_$1**

**0.86 2.17 2.9741(19) 155.1
N6-H6B...O2_$2**

**Least-squares planes (x,y,z
in crystal coordinates) and deviations from them**

**(* indicates atom used to
define plane)**

**2.3443 (0.0044) x + 7.4105
(0.0042) y - 0.0155 (0.0053) z = 1.9777 (0.0044)**

*** -0.0743 (0.0008) C7**

*** 0.0684 (0.0008) C11**

*** -0.0418 (0.0009) C8**

*** -0.0062 (0.0008) C4**

*** 0.0538 (0.0008) O3**

**-0.0061 (0.0020) O1**

**-0.0980 (0.0028) N6**

**-0.0562 (0.0023) C9**

**-0.0314 (0.0030) C10**

**Rms deviation of fitted atoms
= 0.0546**

**2.5438 (0.0040) x + 7.3488
(0.0040) y - 0.1657 (0.0042) z = 1.8626 (0.0026)**

**Angle to previous plane (with
approximate esd) = 2.45 ( 0.07 )**

*** 0.0054 (0.0008) C10**

*** 0.0082 (0.0008) N6**

*** -0.0052 (0.0012) C9**

*** -0.0337 (0.0012) C8**

*** 0.0135 (0.0008) C11**

*** 0.0118 (0.0009) C4**

**0.0568 (0.0019) O1**

**0.0214 (0.0018) O3**

**-0.1542 (0.0020) C7**

**Rms deviation of fitted atoms
= 0.0162**

**Hydrogen bonds with H..A <
r(A) + 2.000 Angstroms and <DHA > 110 deg.**

**D-H d(D-H) d(H..A) <DHA
d(D..A) A**

**O2-H2 0.820 2.041 174.05 2.858
O1 [ x-1, y, z ]**

**N6-H6A 0.860 2.225 129.29
2.849 O1**

**N6-H6B 0.860 2.172 155.06
2.974 O2 [ x+1, y, z-1 ]**

All esds printed by the program are calculated rigorously from the full covariance matrix, except for the esd in the angle between two least-squares planes, which involves some approximations. The contributions to the esds in bond lengths, angles and torsion angles also take the errors in the unit-cell parameters (as input on the ZERR instruction) rigorously into account; an approximate treatment is used to obtain the (rather small) contributions of the cell errors to the esds involving least-squares planes.

There follows the difference electron density synthesis and line printer 'plot' of the structure and peaks. The highest and lowest features are 0.27 and -0.17 eA-3respectively, and the rms difference electron density is 0.04. These values confirm that the treatment of the hydrogen atoms was adequate, and are indeed typical for routine structure analysis of small organic molecules. This output is too voluminous to give here, and indeed users of the Siemens SHELXTL molecular graphics program XP will almost always suppress it by use of the default option of a positive number on the PLAN instruction, and employ interactive graphics instead for analysis of the peak list.