Ab initio structure determination of monoclinic 2,2-dihydroxymethylbutanoic acid from synchrotron radiation powder diffraction data: Combined use of direct methods and the Monte Carlo method

Article abstract of DOI:10.1107/S0108768100018905

The crystal structure of 2,2-dihydroxymethylbutanoic acid (C₆H₁₂O₄) in monoclinic form has been determined ab initio from synchrotron radiation powder diffraction data. Two O and five C atoms were first derived by direct methods. Two missing O atoms and one C atom were found by the Monte Carlo method without applying constraint to their relative positions. Positional and isotropic displacement parameters of these non-H atoms were refined by the Rietveld method. Molecules are linked by hydrogen bonds and they make sheet-like networks running parallel to the (010) plane. The Monte Carlo method is demonstrated to be a powerful tool for finding missing atoms in partially solved structure.

Full text of DOI:10.1107/S0108768100018905

research papers
Acta Crystallographica Section B
Structural
Science
Ab initio structure determination of monoclinic 2,2-
dihydroxymethylbutanoic acid from synchrotron
radiation powder diffraction data: combined use of
direct methods and the Monte Carlo method
ISSN 0108-7681
a
Received 12 September 2000
Yusaku Tanahashi, Hisayoshi
The crystal structure of 2,2-dihydroxymethylbutanoic acid
(C H O ) in monoclinic form has been determined ab initio
6 12 4
a
a
Accepted 27 November 2000
Nakamura, Satoru Yamazaki,
b
c
from synchrotron radiation powder diffraction data. Two O
and ®ve C atoms were ®rst derived by direct methods. Two
missing O atoms and one C atom were found by the Monte
Carlo method without applying constraint to their relative
positions. Positional and isotropic displacement parameters of
these non-H atoms were re®ned by the Rietveld method.
Molecules are linked by hydrogen bonds and they make sheet-
like networks running parallel to the (010) plane. The Monte
Carlo method is demonstrated to be a powerful tool for
Yuko Kojima, Hideshi Saito,
a
a
Takashi Ida and Hideo Toraya *
a
Ceramics Research Laboratory, Nagoya Institute
of Technology, Asahigaoka, Tajimi 507-0071,
b
Japan, Yokohama Research Center, Mitsubishi
Chemical Corporation, Kamoshida-cho, Aoba-
c
ku, Yokohama 227-8502, Japan, and Research
and Development Center, Nippon Kasei
Chemical Co. Ltd, Takayama, Onahama, Iwaki
®nding missing atoms in partially solved structure.
971-8101, Japan
Correspondence e-mail: toraya@crl.nitech.ac.jp
1
. Introduction
In the coating industry the development of environment-
friendly materials is strongly required and one of the solutions
is to replace volatile organic materials with water-soluble
materials. 2,2-Dihydroxymethylbutanoic acid, C H O
4
6
12
(hereinafter DMBA), having a tertiary carboxyl group and
two reactive primary hydroxyl groups, has been developed as a
new waterborne coating material. DMBA also has excellent
solubility in an organic solvent, such as acetone, with a
magnitude of more than one order compared with that of 2,2-
dihydroxymethylpropanoic acid, C H O (DMPA). DMBA
5
10
4
can be polymerized without protecting the tertiary carboxyl
group, giving easy handing in the polymerization process.
Therefore, DMBA is expected to be a promising material as a
monomer for water-soluble polyurethane and water-soluble
polyester.
DMBA is known to be crystallized in two forms with
triclinic and monoclinic symmetries, depending on crystal-
lization conditions. The crystal structure of triclinic DMBA (t-
DMBA) has been determined by one of the authors (YK)
using a single-crystal method. It has a space group and
contains two independent molecules of C H O in an asym-
6
12
4
metric unit (Kojima, 2001). It was, however, dif®cult to obtain
a single-crystal of monoclinic DMBA (m-DMBA) for struc-
ture analysis. Therefore, in the present study synchrotron
radiation powder diffraction data are used for the structure
determination of m-DMBA.
With developments of whole-powder-pattern decomposi-
tion methods (Pawley, 1981; Le Bail et al., 1988) and computer
softwares for phasing (Cascarano et al., 1992; Altomare et al.,
1
994, 1995), a number of crystal structures have been solved
ab initio from powder diffraction data. Direct methods,
modi®ed for treating powder diffraction data, have been used
as major tools for solving crystal structures (see, for example, a
#
2001 International Union of Crystallography
Printed in Great Britain ± all rights reserved
ꢀ
184 Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid
Acta Cryst. (2001). B57, 184±189

research papers
review by Giacovazzo, 1996), while many other techniques
have also been developed over the past decade (see, for
example, a review by Harris & Tremayne, 1996). Direct
methods require extraction of integrated intensities of indi-
vidual re¯ections from the powder diffraction pattern and
whether a structure can be solved or not depends on the
percentage of independently resolved re¯ections (Estermann
technique was used in a capillary-specimen transmission
geometry.
After having derived a structure model of m-DMBA, we
had another chance of collecting intensity data with synchro-
Ê
tron radiation at ꢀ = 1.2085 (2) A using MDS. Diffraction data
Ê
had much higher intensity than those collected at ꢀ = 0.7086 A
and they were used for Rietveld re®nement. In the following
Ê
&
Gramlich, 1993). On the other hand, the Monte Carlo
intensity data sets collected at ꢀ = 0.7086 and 1.2085 A are
method (Harris et al., 1994) and the simulated annealing
method (Tremayne et al., 1996) directly ®t the calculated
pattern to the observed pattern and they do not require the
designated SR07 and SR12, respectively, according to their
wavelength values. Absorption correction was not necessary
even for SR12, since ꢂr < 0.1 (a packing density 33%). The
details of the synchrotron radiation experiments are described
in Table 1.
1
integrated intensities. Therefore, these methods are applic-
able not only to well resolved patterns, but also low-resolution
data as often exhibited by organic materials. In these methods
the rigid-body model is usually introduced for grouping atoms,
to reduce the number of unknown parameters and to avoid
falling into false minima. In the present study, the Monte Carlo
method has been applied to ®nding missing atoms in the
structure, partially solved by direct methods, without using the
rigid-body model.
2.3. Data collection with laboratory X-rays
Powder diffraction data of m-DMBA + Si specimen were
measured using Cu Kꢃ radiation monochromated with a
1
Johansson-type Ge(111) crystal, which was mounted on the
incident-beam side of a powder diffractometer (Rigaku Co.,
RINT1500). A ꢁ±2ꢁ step-scan technique was used in a ¯at-
specimen re¯ection geometry. Experimental details are given
in Table 1.
2. Experimental
2
.1. Sample preparation
3
. Structure solution and refinement
The present sample of m-DMBA was synthesized by
following the procedure established as an industrial process.
,2-Dihydroxymethylbutanal was ®rst synthesized by the
3
.1. Crystallographic data
Peak positions of the ®rst 40 re¯ections from the low-angle
side of SR07 were determined by the computer program
PROFIT (Version 3.00) for individual pro®le ®tting (Toraya,
1986). They were used by the computer program ITO for auto-
indexing based on the zone-®nding method (Visser, 1969): a
monoclinic cell with the dimensions a = 6.400, b = 11.085, c =
2
condensation reaction of 2-hydroxymethylbutanal with
formaldehyde (HCHO) at temperatures of 323±333 K, using
triethylamine as a catalyst. Then DMBA was synthesized by
oxidizing 2,2-dihydroxymethylbutanal with hydrogen
peroxide (H O ). The product was a white-coloured powder.
2
2
Ê
ꢁ
11.200 A and ꢄ = 106.12 was derived at a ®gure-of-merit of
86.1.
m-DMBA was obtained by crystallization at < 278 K in
-methyl-2-pentanone solution. On the other hand, t-DMBA
was obtained by crystallization in ethyl acetate solution
4
ꢁ
Overlapping re¯ections of SR07 in the 2ꢁ range of 5±30
were resolved by the computer program WPPF (Version 3.00)
for whole powder-pattern decomposition based on the Pawley
algorithm (Toraya, 1986). The split-type pseudo-Voigt func-
tion was used for modeling the pro®le shape. An output list of
re®ned integrated intensity parameters for 320 re¯ections
indicated systematic absences of re¯ections with indices of
l = 2n + 1 (n: integer) for h0l, k = 2n + 1 for 0k0, and l = 2n + 1
(
Kojima, 2001).
A sample for the re®nement of unit-cell parameters was
prepared by mixing m-DMBA with Si powder used as an
internal standard reference material (National Institute of
Standards and Technology, Standard Reference Material
6
40b) in a m-DMBA/Si weight ratio of 4:1.
for 00l, deriving uniquely a space group of P2 /c.
1
Unit-cell parameters of m-DMBA were re®ned by WPPF
ꢁ
2
.2. Synchrotron radiation experiment
using laboratory X-ray data in the 2ꢁ range 5±145 . The
Synchrotron radiation powder diffraction data were
collected at the beamline BL-4B with a bending magnet light
systematic peak shift Á(2ꢁ) was corrected with the function
Áꢂ2ꢁ† ˆ t ‡ t cos 2ꢁ ‡ t sin 2ꢁ ‡ t tan ꢁ. Following the
2
0
1
2
3
source at the Photon Factory in Tsukuba. Synchrotron
Ê
procedure proposed by Toraya (1993), the unit-cell para-
meters of m-DMBA and the parameters t ±t in Á(2ꢁ) were
re®ned simultaneously, while the unit-cell parameter of the Si
radiation with a wavelength ꢀ of 0.7086 (1) A was obtained
0
3
with a water-cooled double-crystal Si(111) monochromator
and it was focused horizontally by a cylindrical mirror installed
after the monochromator. Diffracted intensities were
measured using a powder diffractometer with a multiple-
detector system (MDS; Toraya et al., 1996). A 2ꢁ-step scan
Ê
powder was ®xed at a literature value of a = 5.430940 (35) A
(
Rasberry, 1987) during the whole powder-pattern ®tting.
From a comparison of calculated density of m-DMBA with
� 3
that of t-DMBA (D = 1.31 g cm ), the number of chemical
x
1
formula units, Z, was estimated to be four. Crystal data are
given, together with those of t-DMBA, in Table 2.
The Monte Carlo method and the simulated annealing method can also be
applied to an integrated intensity data set rather than pro®le intensities.
ꢀ
Acta Cryst. (2001). B57, 184±189
Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid 185

research papers
Table 1
Experimental details.
used as input data for the
computer program SIRPOW97
for direct methods (Altomare et
al., 1994). From an estimated Z
value of 4, six C and four O
atoms were assumed to be
present as asymmetric units in a
unit cell, whereas H atoms were
ignored in solving structure.
Data collection
Temperature
Crystal form
Crystal color
Wavelength (A)
Radiation type
Diffractometer
297
Powder
White
0.7086 (1)
Synchrotron
MDS²
Si(111) double crystal
Ge(111) ¯at crystal
Ê
1.2085 (2)
1.540562
Laboratory X-ray (Cu Kꢃ
Rigaku RINT1500
Johansson-type Ge(111) crystal
1
)
Monochromator
Analyzer
±
Data collection method
Measurement mode
Specimen mounting
2ꢁ step scans
Capillary specimen transmission
Glass capillary 1.0 mm '
ꢁ±2ꢁ step scans
Flat specimen re¯ection
Flat specimen holder
1
5.0±145.0
0.02
20
±
Positional parameters of ten
C atoms and three O atoms were
derived from SIRPOW97, giving
the Rwp value of 30.4%.
Comparisons of a molecular
structure thus derived with
those of t-DMBA and 1,1,1-
�
1
)
Specimen rotation (r s
ꢁ
1
1
2
ꢁ range ( )
2.0±154.9
0.004
3.5
2.0±154.8
0.004
3.5
Ê
Step size, 2ꢁ (A)
Step counting time (s)
Absorption correction
None
None
Re®nement
Re®nement on pro®le
intensities
Pro®le shape function
Structure re®nement
program
tris(hydroxymethyl)
(TRMP) (Sake Gowda et al.,
982) clearly indicated that the
propane
Pseudo-Voigt function
PFLS (Toraya, 2000)
1
positions of ®ve C and two O
atoms were correctly found,
whereas those of the remaining
six atoms, some of which have
much longer bond lengths than
the literature values, were
considered to be ghosts.
No. of re¯ections
876
64
No. of parameters re®ned
Weighting scheme
Preferred orientation
correction
Source of atomic scattering
factors
e
oi
w ˆ 1=y (e = 2.2)
i
Symmetrized harmonic expansion
International Tables for X-ray Crystallography (1974, Vol. IV)
R
R
R
R
p
0.0707
0.0709
0.0927
0.0927
wp
Bragg
F
3.3. Finding missing atoms by
the Monte Carlo method
P
P
P
P
P
P
P
P
2
2
oi
1=2
1=2
1=2
1=2
cj
Rp
ˆ
i
jy � y j=
oi
ci
i
yoi; R ˆ ‰ w ꢂy � y † =
wp
i
i
oi
ci
i
w y Š ; RBragg
i
ˆ
j
jI � I j=
oj
cj
j
I ; R ˆ
oj
f
j
jIoj � Icj j=
j
I
.
The Monte Carlo method,
used in the present study,
follows the procedure described
by Harris et al. (1994), using the
²
MDS: synchrotron radiation powder diffractometer with multiple-detector system.
3
.2. Application of direct methods
Metropolis importance sampling algorithm. The objective
function was the weighted reliability index given by
Integrated intensity parameters of 320 re¯ections of SR07
ꢁ
2
2
1=2
oi
(
|
2ꢁ range 5±30 ) were converted into structure amplitudes
F(hkl)| with appropriate corrections for Lorentz±polarization
Rwp ˆ 100  f‰Æw ꢂY � Y † Š=Æw Y g
;
i
oi
ci
i
and the multiplicity of re¯ections. Among them, 123 re¯ec-
tions were equi-partitioned (38% of total re¯ections). Values
of 0.01 were assigned to |F(hkl)| of 39 re¯ections with zero or
negative intensities (12%). A set of |F(hkl)| thus obtained was
where Yoi and Yci are the observed and calculated pro®le
intensities at the ith step, respectively, and w is the weight
i
�
1
assigned to the ith observation in the form w ˆ Y . The
i
oi
computer program MCS (Version 1.00) for the Monte Carlo
calculation, which has been developed by
the authors' group (Nakamura et al.,
2
and two O atoms in m-DMBA by using
001), was used to ®nd the missing one C
ꢁ
SR07 (2ꢁ range 5±30 ). In calculating
initial and trial con®gurations, relative
positions of seven independent atoms,
derived by direct methods, were kept
®xed as a group in a unit cell. In each
Monte Carlo move, nine positional para-
meters (three sets of x, y, z for three
missing atoms) were varied, under the
constraint of symmetry operations of the
Figure 1
Final ®tting result of Rietveld re®nement. Filled squares and solid lines represent the observed
space group P2 /c, by random amounts in
1
and calculated pro®le intensities, respectively. The diagram at the bottom gives weighted
)
1/2
difference plots by 5 Â (w
i
(Yoi � Yci). Short vertical bars represent Bragg re¯ection positions.
random directions within the maximum
ꢀ
186 Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid
Acta Cryst. (2001). B57, 184±189

research papers
Table 2
Crystal data of m-DMBA and t-DMBA.
Table 3
Fractional atomic coordinates and isotropic displacement parameters
(
Ê
2
A ).
m-DMBA
t-DMBA
x
y
z
U
iso
Chemical formula
Chemical formula weight
Cell setting
C
6
H
12
O
4
6 12 4
C H O
148.158
Triclinic
148.158
Monoclinic
P2 /c
6.3980 (1)
11.0866 (2)
11.2095 (4)
90
106.108 (2)
90
763.90 (4)
4
1.29
C1
C2
C3
C4
C5
C6
O1
O2
O3
O4
0.1145 (9)
0.074 (1)
0.2466 (8)
� 0.111 (1)
0.2582 (9)
0.470 (1)
0.1170 (6)
� 0.0208 (5)
0.3057 (5)
� 0.2531 (5)
0.3836 (5)
0.4302 (6)
0.4863 (4)
0.3434 (5)
0.2590 (5)
0.2776 (4)
0.5383 (3)
0.3626 (3)
0.4345 (3)
0.4432 (3)
0.2402 (4)
0.3555 (5)
0.1909 (4)
0.1487 (5)
0.2744 (5)
0.3769 (5)
0.3907 (3)
0.4214 (3)
0.0831 (3)
0.1259 (3)
0.012 (1)
0.041 (2)
0.024 (2)
0.036 (1)
0.045 (3)
0.040 (1)
0.041 (2)
0.031 (1)
0.035 (1)
0.031 (1)
ꢀ
P1
Space group
Ê
1
a (A)
Ê
10.282 (2)
10.712 (2)
6.835 (1)
91.49 (1)
92.94 (2)
90.47 (2)
753.6 (2)
4
b (A)
Ê
c (A)
ꢁ
ꢃ ( )
ꢁ
ꢄ ( )
ꢁ
ꢅ ( )
Ê
3
V (A )
Z
D
�
3
x
(Mg m
)
1.31
conformation as those in t-DMBA, whereas their orientations
in the unit cell are greatly different from those in t-DMBA.
As shown in Fig. 3(a), two carboxyl groups in m-DMBA
face each other, and two molecules, related by the centers of
Ê
displacement of 1.2 A. An acceptance level was set so as to
keep the acceptance rate of ꢃ40%.
Structural parameters for a con®guration, which gave the
minimum of 29.7% during 10000 Monte Carlo moves, were
further re®ned by the Rietveld method, reducing the value to
1
1
symmetry at (0, 0, 0) and (0, , ), are linked strongly by
2
2
Ê
hydrogen bonds O1Á Á ÁO2 having a distance of 2.596 (5) A in
the (100) plane. The formation of molecular pairs in m-DMBA
explains why the protection of the carboxyl groups is unne-
cessary during the polymerization process of m-DMBA.
In m-DMBA the molecular pairs are linked by two
1
2.1%.
3
.4. Rietveld refinement
Ê
hydrogen bonds of O3Á Á ÁO4 having distances of 2.647 (5) A in
Positional and isotropic displacement parameters of six C
and four O atoms were re®ned by the Rietveld method using
SR12 (2ꢁ range of 5±77 ) and the computer program PFLS
the (100) plane (Fig. 3a) and also by two hydrogen bonds of
Ê
ꢁ
O3Á Á ÁO4 [2.730 (5) A] along the a axis (Fig. 3b), while there
are no hydrogen bonds along the b axis. On the other hand,
individual molecules in t-DMBA have six hydrogen bonds of
(
Version 5.00; Toraya, 2000), adopting the same pro®le model
as that of WPPF. The contribution of 12 H atoms was not
included in the re®nement. An intensity correction for
preferred orientation was applied by employing the function
for symmetrized harmonic expansion (J aÈ rvinen, 1993).
Ê
Ê
O1AÁ Á ÁO3B [2.704 (2) A], O2AÁ Á ÁO3B [2.604 (2) A],
Ê
Ê
O4AÁ Á ÁO4A [2.720 (3) A], O1BÁ Á ÁO3A [2.762 (2) A],
Ê
Ê
O2BÁ Á ÁO3A [2.602 (2) A] and O4BÁ Á ÁO4B [2.697 (3) A],
which are all approximately parallel to the (001) plane (Fig.
Ê
In the least-squares ®tting the weight function w , proposed
i
3
c), and one hydrogen bond of O4AÁ Á ÁO4B [2.691 (3) A]
by Toraya (1998) for taking systematic error into account, was
e
�
along the c axis (Fig. 3d). Therefore, as shown by dotted lines
assigned to Y . The function has the form w ˆ Y , and the
oi
i
oi
parameter e can be optimized in order to obtain uniform
2
distributions of the mean weighted residuals hw ꢂY � Y † i
i
oi
ci
1
=2
and weighted difference plots by w ꢂY � Y †. The optimi-
i
oi
ci
zation of the weight function was obtained at e = 2.2.
Final reliability indices are given in Table 1. Details of the
re®nement procedure will be found elsewhere (Toraya, 2000).
4. Results and discussion
A ®nal ®tting result of Rietveld re®nement is shown in Fig. 1.
Final atomic parameters are given in Table 3. Fig. 2 shows the
conformation of a molecule of C H O in m-DMBA. Selected
6
12
4
bond lengths and bond angles are given in Table 4.
4
.1. Structure of m-DMBA
Figs. 3(a)±(d) show crystal structures of m-DMBA and t-
DMBA, each of which is projected along the [100] and [001]
directions. Two independent molecules in t-DMBA, desig-
nated A and B, respectively, are approximately in mirror
symmetry. The molecule in m-DMBA and its mirror image,
generated by the c glide plane, have virtually the same
Figure 2
6 12 4
Conformation of the molecule C H O in m-DMBA.
ꢀ
Acta Cryst. (2001). B57, 184±189
Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid 187

research papers
Table 4
Selected bond lengths (A) and bond angles ( ) of m-DMBA.
m-DMBA remains as aggregates of ®ne crystals and of low
crystallinity.
Ê
ꢁ
C1ÐC2
C1ÐC3
C1ÐC4
C1ÐC5
C5ÐC6
1.482 (9)
1.607 (8)
1.583 (7)
1.645 (8)
1.525 (7)
O1ÐC2
O2ÐC2
O3ÐC3
O4ÐC4
1.265 (8)
1.314 (8)
1.477 (7)
1.412 (7)
4
.2. The Monte Carlo method for finding missing atoms
To obtain a complete structure solution becomes dif®cult
with increasing the number of severely overlapping re¯ections
and the degradation of the quality of re¯ection data is the
principal problem in applying direct methods to structure
solution using powder diffraction data. In the present sample
re¯ections in 38% of the total re¯ections were equi-parti-
tioned and three atoms among ten atoms in the asymmetric
unit could not be found after the application of direct
methods.
C2ÐC1ÐC3
C2ÐC1ÐC4
C2ÐC1ÐC5
C3ÐC1ÐC4
C3ÐC1ÐC5
C4ÐC1ÐC5
106.7 (4)
108.4 (5)
108.0 (4)
116.8 (4)
111.0 (4)
105.4 (4)
C1ÐC5ÐC6
C1ÐC3ÐO3
C1ÐC4ÐO4
C1ÐC2ÐO1
C1ÐC2ÐO2
O1ÐC2ÐO2
112.8 (4)
106.4 (4)
108.6 (4)
121.8 (6)
120.5 (5)
117.4 (6)
in Figs 3(a)±(d), the molecules in m-DMBA constitute a sheet-
like network parallel to the (010) plane. On the other hand,
the molecules in t-DMBA constitute a three-dimensional
network. t-DMBA has a greater number of hydrogen bonds
and a smaller unit-cell volume by 1.6% than m-DMBA. These
facts suggest that t-DMBA is probably energetically more
stable than m-DMBA. Differences in these structural features
of t- and m-DMBA may be responsible for the fact that t-
DMBA could be grown up to large crystals with enough sizes
for single-crystal structure analysis. On the other hand,
Several techniques have been proposed to overcome this
dif®culty. Some persist in using direct methods to obtain the
complete structure solution by improving observed structure
amplitudes. Techniques, included in this category, are the fast
iterative Patterson squaring (FIPS) method for a sophisticated
whole powder-pattern decomposition (Estermann et al., 1992),
the computer software EXTRA, which feeds back various
types of information to the whole powder-pattern decom-
position process (Altomare et al., 1995, 1998; Carrozzini et al.,
1997) etc. A rather classical approach is the use of difference
Fourier synthesis to ®nd
missing atoms using integrated
intensities obtained by the
Rietveld
decomposition
formula (Rietveld, 1969). In
many cases in which we need
to ®nd missing atoms,
however, the quality of inten-
sity data is often not enough to
synthesize
difference Fourier maps. The
Monte Carlo method,
well
resolved
employing the rigid-body
model, has been used success-
fully for structure solutions of
organic compounds from
powder
(
diffraction
Harris & Tremayne, 1996).
data
However, the applicability of
the method has been limited in
cases where we have informa-
tion to construct the rigid-
body model itself. In the
present study, the Monte Carlo
method is demonstrated to be
a powerful tool for ®nding
missing atoms in the structure
partially solved by direct
methods. The method can be
applied not only to organic
materials, but also inorganic
materials, as has been shown
in the structure analysis of
Figure 3
(
a) [100] and (b) [001] projections of m-DMBA. (c) [001] and (d) [100] projections of t-DMBA.
ꢀ
188 Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid
Acta Cryst. (2001). B57, 184±189

research papers
tobermorite: a zeolitic Ca atom and three water molecules in
Ca Si O Á2H O] frameworks were found by the Monte Carlo
The authors wish to thank Mr Tetsugo Kawakami of
Mitsubishi Chemical Corporation for his assistance in engi-
neering crystal growth. They also thank Mr Hisashi Hibino of
Nagoya Institute of Technology and the staff of the Photon
Factory for their assistance in synchrotron radiation experi-
ments.
[
method (Yamazaki & Toraya, 2001).
4
6
17
2
4
.3. Accuracy of refined positional parameters
Pattison et al. (2000) discussed the accuracy of positional
parameters, re®ned by the Rietveld method, of m-¯uoro-
benzoic (C H FO ) acid (m-FBA) at room temperature and
References
7
3
2
Altomare, A., Burla, M. C., Cascarano, G., Giacovazzo, C.,
Guagliardi, A., Moliterni, A. G. G. & Polidori, G. (1995). J. Appl.
Cryst. 28, 842±846.
Altomare, A., Cascarano, G., Giacovazzo, C., Guagliardi, A., Burla,
M. C., Polidori, G. & Camalli, M. (1994). J. Appl. Cryst. 27, 435±436.
Altomare, A., Foadi, J., Giacovazzo, C., Moliterni, A. G. C., Burla,
M. C. & Polidori, G. (1998). J. Appl. Cryst. 31, 74±77.
1
00 K. m-FBA consists of ten independent non-H atoms in a
monoclinic unit cell and the maximum range of synchrotron
radiation powder diffraction data used for Rietveld re®ne-
�
1
Ê
ment was 0.51 A . Therefore, Rietveld re®nement conditions
are mostly the same as those in the present study. Pattison et
al. (2000) reported that the average deviation in bond lengths
Carrozzini, B., Giacovazzo, C., Guagliardi, A., Rizzi, R., Burla, M. C.
&
Ê
from single-crystal values is 0.025 A for room-temperature
data. In the present study, the average deviation of nine bond
Polidori, G. (1997). J. Appl. Cryst. 30, 92±97.
Cascarano, G., Favia, L. & Giacovazzo, C. (1992). J. Appl. Cryst. 25,
310±317.
Ê
lengths from single-crystal values of t-DMBA was 0.046 A,
Estermann, M. A. & Gramlich, V. (1993). J. Appl. Cryst. 26, 396±404.
Estermann, M. A., McCusker, L. B. & Baerlocher, C. (1992). J. Appl.
Cryst. 25, 539±543.
Giacovazzo, C. (1996). Acta Cryst. A52, 331±339.
Harris, K. D. M. & Tremayne, M. (1996). Chem. Mater. 8, 2554±2570.
Harris, K. D. M., Tremayne, M., Lightfoot, P. & Bruce, P. (1994). J.
Am. Chem. Soc. 116, 3543±3547.
J aÈ rvinen, M. (1993). J. Appl. Cryst. 26, 525±531.
Kojima, Y. (2001). In preparation.
Le Bail, A., Duroy, H. & Fourquet, J. L. (1988). Mater. Res. Bull. 23,
being about twice as large as that of m-FBA, although we must
take into account the fact that the referenced single-crystal
values are not of m-DMBA, but of t-DMBA and that the
contribution of H atoms was ignored in the Rietveld re®ne-
ment.
In a recent study on the accuracy of Rietveld re®nement it
was pointed out that important factors for obtaining high
accuracy are:
(
(
(
(
(
i) suf®ciently large sin ꢁ=ꢀ in the range > 0.8,
ii) adequate counting statistics,
iii) correct pro®le modeling,
iv) proper weighting and
v) high-resolution diffraction data (Toraya, 2000).
447±452.
Nakamura, H., Yamazaki, S., Ida, T. & Toraya, H. (2001). Powder
Diff. In the press.
Pattison, P., Knudsen, K. D. & Fitch, A. N. (2000). J. Appl. Cryst. 33,
82±86.
Pawley, G. S. (1981). J. Appl. Cryst. 14, 357±361.
Rasberry, S. D. (1987). NIST Certi®cate for SRM640b Si powder.
Rietveld, H. M. (1969). J. Appl. Cryst. 2, 65±71.
Sake Gowda, D. S., Federlein, N. & Rudman, R. (1982). J. Chem.
Phys. 77, 4659±4665.
Toraya, H. (1986). J. Appl. Cryst. 19, 440±447.
Toraya, H. (1993). J. Appl. Cryst. 26, 583±590.
Toraya, H. (1998). J. Appl. Cryst. 31, 333±343.
Toraya, H. (2000). J. Appl. Cryst. 33, 95±102.
Toraya, H., Hibino, H. & Ohsumi, K. (1996). J. Synchrotron Rad. 3,
75±83.
In the present study the accuracy of positional parameters
could be signi®cantly improved by optimizing the weighting
on observations in the Rietveld re®nement. A still greater
average deviation in bond length of m-DMBA than that of m-
FBA is primarily due to the broadening of diffraction lines of
m-DMBA: a minimum value of the full-width at half maximum
ꢁ
(
FWHM) was 0.055 for m-DMBA (FWHM for the instru-
mental function of MDS using a 1.0 mm '-capillary specimen
ꢁ
at the BL-4B beamline was ꢃ0.018 ). On the other hand, the
2
Tremayne, M., Kariuki, B. M. & Harris, K. D. M. (1996). J. Appl.
Cryst. 29, 211±214.
Visser, J. W. (1969). J. Appl. Cryst. 2, 89±95.
Yamazaki, S & Toraya, H. (2001). Submitted.
ꢁ
FWHM of m-FBA is reported to be 0.012 , indicating that the
sample of m-FBA is well crystallized, whereas the m-DMBA is
of low crystallinity.
ꢀ
Acta Cryst. (2001). B57, 184±189
Tanahashi et al.
2,2-Dihydroxymethylbutanoic acid 189