research papers
Journal of
Applied
Crystallography
Generation and applications of structure envelopes
for porous metal–organic frameworks
ISSN 0021-8898
Received 26 July 2012
Accepted 14 December 2012
Andrey A. Yakovenko,* Joseph H. Reibenspies, Nattamai Bhuvanesh and Hong-Cai
Zhou*
Chemistry Department, Texas A&M University, College Station, TX 77843, USA. Correspondence
e-mail: ayakovenko@chem.tamu.edu, zhou@chem.tamu.edu
# 2013 International Union of Crystallography
Printed in Singapore – all rights reserved
The synthesis of polycrystalline, as opposed to single-crystalline, porous
materials, such as zeolites and metal–organic frameworks (MOFs), is usually
beneficial because the former have shorter synthesis times and higher yields.
However, the structural determination of these materials using powder X-ray
diffraction (PXRD) data is usually complicated. Recently, several methods for
the structural investigation of zeolite polycrystalline materials have been
developed, taking advantage of the structural characteristics of zeolites.
Nevertheless, these techniques have rarely been applied in the structure
determination of a MOF even though, with the electron-density contrast
between the metal-containing units and pore regions, the construction of a
structure envelope, the surface between high- and low-electron-density regions,
should be straightforward for a MOF. Herein an example of such structure
solution of MOFs based on PXRD data is presented. To start, a Patterson map
was generated from powder diffraction intensities. From this map, structure
factor phases for several of the strongest reflections were extracted and a
structure envelope (SE) of a MOF was subsequently constructed. This envelope,
together with all extracted reflection intensities, was used as input to the
SUPERFLIP software and a charge-flipping (CF) structure solution was
performed. This structure solution method has been tested on the PXRD data of
both activated (solvent removed from the pores; dmin = 0.78 Å) and assynthesized (dmin = 1.20 Å) samples of HKUST-1. In both cases, our method has
led to structure solutions. In fact, charge-flipping calculations using SE provided
correct solutions in minutes (6 min for activated and 3 min for as-synthesized
samples), while regular charge flipping or charge flipping with histogram
matching calculation provided meaningful solutions only after several hours. To
confirm the applicability of structure envelopes to low-symmetry MOFs, the
structure of monoclinic PCN-200 has been solved via CF+SE calculations.
1. Introduction
Metal–organic frameworks (MOFs) (Férey, 2008; Kitagawa et
al., 2004; Makal et al., 2011; Yaghi et al., 2003) are porous
materials based on coordination of metal or metal-containing
units with organic linkers. MOFs are very important in the
development of new technologies and the study of gas storage
and separation (Chen et al., 2005; D’Alessandro et al., 2010;
Hu et al., 2009; Kuppler et al., 2009; Li et al., 2011; Sculley et al.,
2011; Uemura & Kitagawa, 2010). Understandably, knowledge
about a MOF structure allows the prediction of its properties.
Most MOFs are synthesized solvothermally; under such
reaction conditions obtaining a powder crystalline product is
more probable than getting single crystals. Consequently, it is
not always possible to determine a MOF structure by
employing single-crystal X-ray diffraction. In these cases the
structure determination has to be accomplished using powder
diffraction data. To date, little effort (Fujii et al., 2010; Kawano
346
doi:10.1107/S0021889812050935
et al., 2008; Martı́-Rujas et al., 2011; Matsuda et al., 2005) has
been devoted to crystal structure determination of MOFs from
powder diffraction data. To find new ideas for method
development, the starting point in our research was the
analysis of the structure determination methods recently used
for other types of porous materials such as zeolites.
McCusker & Baerlocher (2009) have shown that it is
possible to facilitate structure solution of porous materials by
identifying the areas within the unit cell that are most likely to
contain atoms. By assigning correct structure factor phases
’hkl to the normalized structure factor amplitudes |Ehkl| of just
a few strong low-order reflections, a surface that divides
regions with high and low electron density can be generated.
Such a surface is called a structure envelope (SE; Brenner et
al., 1997, 2002). Since these reflections are located in low-angle
regions, it is highly probable that there exists very little
overlap among them in the powder pattern, which can then be
J. Appl. Cryst. (2013). 46, 346–353
research papers
used for the selection of these reflections and generation of
the SE.
An SE can be built by applying an equation similar to that
for electron density:
P
ðx; y; zÞ ¼ Ehkl cos½2ðhx þ ky þ lzÞ ’0hkl : ð1Þ
hkl
The summation in equation (1) is typically performed for only
a small number of reflections (less than ten). These reflections
are usually selected by applying three simple criteria (Brenner
et al., 2002): (i) strong and low order, (ii) at least 0.5 FWHM
from neighboring reflections and (iii) selected such that all
directions in the reciprocal space are represented. The threedimensional surface at (x, y, z) = 0 will form the SE. In the
case of porous materials, the SE describes the pore system,
with the framework atoms located on the positive side of the
surface.
Evidently SEs can be used to advance structure solution by
restricting the generated electron density to regions of the
framework. In other words, SEs will provide reduction of
space in the asymmetric unit where atoms are likely to be
located. In fact, the test structure solutions have shown that
the use of SEs in dual space structure solution methods such as
Focus (Grosse-Kunstleve et al., 1997) allows researchers to
solve the structure of porous zeolites, such as ITQ-1, RUB-2
and Sigma-2, in minutes, while similar calculations without SE
restrictions solve the same structures in hours or in some cases
not at all (McCusker et al., 2001).
The most exciting application of SEs is that they can be used
in combination with charge flipping (CF) (Oszlányi & Süto
,
2004). An algorithm using CF+SE is presented in Fig. 1, in
which several low-angle reflections with known phases are
used to construct the SE. Subsequently, the SE restrictions are
applied to calculated electron density in CF runs, which should
provide a correct structure. The CF+SE method [in combination with histogram matching (HM)] was first introduced for
the solution of complex structures of zeolites such as IM-5
(Baerlocher et al., 2007) and SSZ-74 (Baerlocher et al., 2008).
It was mentioned that only a few reflections were used to
generate the SE. However, the evaluation of the structure
factor phases is not so straightforward. Sometimes the most
intense peaks in a powder pattern can be used as the set of
origin-defining reflections (Ladd & Palmer, 2003) and can be
used for SE generation without ’hkl investigation. However,
occasionally these reflections alone might not be sufficient.
This can occur if there are not enough reflections that are
origin defining or if the origin-defining reflections have weak
intensities. In such cases, additional structure factor phase
investigation should be completed.
One way to determine ’hkl is to use the Sayre (1952)
equation. This method was used in the SayPerm (Brenner et
al., 2002) software and is valid for structures with identical and
resolved atoms. Hence, for zeolite SiO4, tetrahedral building
units were used as pseudo-atoms. The use of this program
allows the estimation of structure phases in zeolites with small
to medium unit cells, such as ZSM-5 and ITQ-1.
Another unique feature of zeolites is their high stability
under an electron beam, making it possible to record a
magnified image of the sample surface using a transmission
electron microscope. Currently, it is even possible to record
images at the atomic level using high-resolution transmission
electron microscopy (HRTEM) (Dorset, 1995). The subsequent Fourier transform of the HRTEM images yields a list of
structure factor phases in the corresponding diffraction
pattern. Therefore, these phases can be used to generate an
SE. Using this approach the crystal structures of complicated
zeolites, such as TNU-9 (Gramm et al., 2006) and IM-5
(Baerlocher et al., 2007), have been determined.
Since MOFs are porous materials containing distinct
regions of high and low electron densities in the metalcontaining units and pores, respectively, the generation and
Figure 2
Figure 1
Diagram illustrating the use of charge flipping with the SE technique.
J. Appl. Cryst. (2013). 46, 346–353
(a) Crystal structure of HKUST-1, projected onto the (100) plane; (b)
scheme of its synthesis.
Andrey A. Yakovenko et al.
Structure envelopes for porous MOFs
347
research papers
use of SEs has the potential to dramatically aid their structure
solution by CF techniques. However, on the other hand, the
existing methods for SE generation, which take advantage of
the unique properties of zeolites, cannot always be applied for
MOFs. In this article, we describe our attempt to develop a
method for the generation of SEs specifically for MOF
materials.
The generation of an SE for MOF materials should include the
following steps: (i) X-ray powder data recording, (ii) pattern
indexing and reflection intensity extraction, (iii) reflection
selection, and (iv) phase extraction and SE generation. To
illustrate this procedure, crystalline powder samples of
HKUST-1 (Chui et al., 1999) were used. The structure of this
well known MOF was previously determined from singlecrystal data; it is formed from the coordination of dicopper
Figure 3
Final Le Bail whole pattern decomposition plots for the (a) HKUST-1a
and (b) HKUST-1syn samples.
Andrey A. Yakovenko et al.
Final R factors and main refinement parameters for the Le Bail whole
pattern decompositions for the HKUST-1 samples.
HKUST-1a
HKUST-1syn
Rp
Rwp
Rexp
2
a (Å)
dmin (Å)
0.059
0.061
0.072
0.075
0.067
0.059
1.14
1.60
26.2976 (2)
26.3103 (6)
0.78
1.20
paddlewheel secondary building units (SBUs) with benzene1,3,5-tricarboxylate (BTC) linkers (Fig. 2a).
2. Method development
348
Table 1
Structure envelopes for porous MOFs
2.1. Sample preparation and intensity extraction
HKUST-1 is quite stable in air and can be easily synthesized
in crystalline powder form in a conventional microwave oven
(770 W for 1 min) from a solution of Cu(NO3)22.5H2O and
H3BTC (Fig. 2b) in N,N-diethylformamide (DEF).
To activate the sample, solvent exchange (with MeOH and
CH2Cl2) procedures were performed to remove the co-crystallized dimethylformamide solvent molecules, followed by
pumping of the sample at 393 K under a dynamic vacuum. By
measuring N2 adsorption at 77 K (Langmuir surface area
1882 m2 g1), it was confirmed that the activated sample
remains porous and does not have guest solvent molecules in
the pores. To see how solvent removal might affect SE
generation and/or structure determination, we decided to
generate SEs for two samples of HKUST-1: (i) an activated
sample (HKUST-1a) and (ii) an as-synthesized sample
(HKUST-1syn).
Both samples were submitted to Argonne National
Laboratory where high-resolution synchrotron powder
diffraction data were collected using beamline 11-BM at the
Advanced Photon Source (APS) using an average wavelength
of 0.458755 Å.
Indexing of the resulting patterns indicates that these
samples crystallized in cubic space group Fm3m with the unitcell parameter a close to 26 Å. These data were then used for
pattern decomposition and reflection intensity extraction by
the Le Bail method (Le Bail et al., 1988) using FULLPROF
(Rodrı́guez-Carvajal, 1993).
The final Le Bail whole pattern decomposition plots for the
HKUST-1a and HKUST-1syn samples are presented in Fig. 3;
the final R factors and major refinement parameters can be
found in Table 1 (data in CIF format are provided as supplementary material1). It can be seen that in both cases the fit
is good: Rwp is very close to Rexp and 2 is close to 1. It can also
be seen that upon activation the unit-cell parameters did not
change substantially. However, the quality of the activated
powder pattern is much better; therefore the resolution at
which reflections were available is much higher for the
HKUST-1a sample. The reason for this is presumably the
removal of disordered solvent from the pores of the framework, which leads to an increase of the overall order in the
sample as well as an increase of the number of regular repeat
1
Supplementary data for this paper are available from the IUCr electronic
archives (Reference: FS5026). Services for accessing these data are described
at the back of the journal.
J. Appl. Cryst. (2013). 46, 346–353
research papers
of porous materials, because only
MOFs contain electron-rich metal
clusters that can be easily located from
Patterson maps.
This algorithm has been used for the
generation of SEs for the two HKUST1 data sets (Fig. 6). SEs were generated
by using just the six most intense lowangle reflections: 420, 422, 200, 220, 222
and 440. The phase information for
these reflections can be easily extracted by introducing the Cu coordinates
into the SHELXTL (Sheldrick, 2008)
software and running the refinement
(XL) with the command LIST 2. In
Figure 4
Patterson maps in the (100) crystallographic planes for (a) HKUST-1a and (b) HKUST-1syn.
such a refinement, it is often helpful to
fix the coordinates and displacement
parameters of the metal atoms and just refine the scale factor.
distances in the structure. Thus, we can compare the SE
It can be seen that the two SEs are very similar to each
generation and structure solution for the same framework
other; therefore the data-resolution difference did not affect
with high- and low-resolution data sets.
the quality of the SEs. In addition, the similarity of the two
2.2. Structure envelope generation
envelopes suggests that the framework structure of HKUST-1
did not change upon activation. Comparison of SEs generated
It is evident that extracted reflection intensities can be used
from the powder X-ray diffraction data with the crystal
for the generation of a Patterson map. Since this map is
structure of HKUST-1 (Figs. 2a and 6) revealed that all three
created by using only intensities (or |Fhkl|2), no structure factor
of them represent the same pore system.
phase information is needed. However, this map is very useful
in the determination of the atomic positions of the heaviest
elements in the structure. In fact, from the Patterson maps
3. Structure determination tests
(Fig. 4) generated for both HKUST-1 data sets, it is straightforward to find the dicopper positions.
The SEs generated above were used in the structure-deterThe locations of Cu atoms can be found easily because Cu
mination tests for the HKUST-1 samples by the CF+SE
contains the largest number of electrons among all other
method using the SUPERFLIP (Palatinus & Chapuis, 2007)
elements present in the structure. It should also be noted that,
software. During the charge-flipping calculations, we used 20
because metal atoms in MOFs are usually located in very
separate runs, each producing an electron-density map of its
compact metal clusters, these metal-containing SBU regions
own. The selection of the best electron-density map is usually
contain the highest electron density. This should help locate
based on comparison of their R factors. However, our initial
the SBU positions in the framework by building Patterson
attempts revealed that the electron-density maps with the
maps, even from low-resolution data. The metal-containing
lowest R factors did not yield the most useful information
SBUs include the majority of the electron density in the
about the MOF structure. Therefore, we decided to select the
structure; consequently they should contribute more to the
phase angle associated with each reflection in the X-ray
powder pattern. Therefore, we can conclude that the positions
of metal-containing SBUs should probably provide correct
structure factor phase information for the most intense
reflections, which can be used for the SE generation.
The foregoing discussion is the basis of a new MOF-specific
method for SE construction. The algorithm of this method is
presented in Fig. 5. In this method, first structure factor
amplitudes (or intensities) are extracted from powder or
single-crystal X-ray diffraction data. These intensities are used
in Patterson and/or direct methods to find the location of the
metal-containing SBUs. These SBU positions are then used
for the reverse Fourier transform that determines the phases
of the most intense reflections. Combining this information
with structure factor amplitudes for selected strong reflections
allows SE generation. It should be noted that this method
Figure 5
works only for MOF data and cannot be used for other types
Diagram illustrating the new algorithm for MOF SE generation.
J. Appl. Cryst. (2013). 46, 346–353
Andrey A. Yakovenko et al.
Structure envelopes for porous MOFs
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research papers
Table 2
atoms can be identified (Fig. 7a). The electron-density map
was generated after only 6 min of calculation, which included
20 runs and 250 CF cycles in each run. This result has been
compared with the outcomes of structure determinations
No. of No. of No. of
Best ED Computation No. of atoms
performed by the CF and CF with histogram matching
Method cycles runs
best EDs Rf (%)
time
not found
(CF+HM) methods (see supplementary information, Fig. 1S).
CF+SE
250
20
18
33.05
6 min
0
The structure of HKUST-1 itself was used as a ‘similar strucCF
250
20
20
33.68
6 min
4
ture’ in the CF+HM method. Comparison of the final results
CF+HM
250
20
2
28.72
11 min
1
and calculation parameters can be found in Table 2 (here ED
CF
10000 1000
1
19.47
>72 h
4
CF+HM 10000
50
3
28.19
11 h
0
denotes electron-density map). In the first set of tests we used
the same number of cycles and runs as for the CF+SE structural determinations. The time needed to complete the CF and
best electron-density maps by comparing the coordinate shifts
CF+HM calculations was comparable to that for the CF+SE
(x, y, z) of the highest electron-density peaks with the
method. However, in the electron-density maps from the CF
Cu-atom positions: the map for which such shifts were minimal
or CF+HM calculations, several atomic peaks were missing
was chosen as the best electron-density map. The final electron(Figs. 1Sa and 1Sb). Only when the calculation time was
density maps for the HKUST-1a and HKUST-1syn samples
increased to 11 h (50 runs, 10 000 cycles) did the CF+HM
generated from CF+SE calculations are presented in Fig. 7.
method yield a reasonably good electron-density map. In the
In the case of the activated sample data (HKUST-1a, dmin =
case of CF calculations, even after 72 h the structure deter0.78 Å), the positions of all six symmetrically independent
mination did not produce any acceptable result (Figs. 1Sc and 1Sd).
After performing CF+SE calculations for the HKUST-1syn sample data
(dmin = 1.20 Å), four out of six symmetrically independent atom positions
were found from the final electrondensity map (Fig. 7b). Peaks corresponding to the solvent-coordinated O
and carboxylate C atoms were missing;
all atom positions corresponding to the
BTC benzene ring and carboxylate O
atoms were found. Hence the positions
of missing atoms can be deducted from
geometry and observations. This map
has been generated by using 20 runs, of
500 CF cycles each, which took about
3 min of computational time; increasFigure 6
ing the number of cycles or calculation
SEs generated from the (a) HKUST-1a and (b) HKUST-1syn data sets.
time did not improve the final electrondensity map. Comparison with the CF
and CF+HM calculations (Table 3 and
Fig. 2S) has shown results similar to
those for the HKUST-1a structure
determinations. In fact, the use of the
same parameters (20 runs, 500 cycles)
in CF and CF+HM calculations failed
to reveal any atom positions of the
BTC ligands (Figs. 2Sa and 2Sb). Only
after a dramatic increase in the number
of cycles and runs (100 runs with 10 000
CF cycles) did the CF+HM calculation repeat the results of the CF+SE
calculations; this result was generated
after 7 h (Fig. 2Sd). The outcome of
simple CF calculations did not change
Figure 7
even after increasing the number of
Final electron-density maps generated from CF+SE calculations from the (a) HKUST-1a and (b)
cycles.
HKUST-1syn data sets.
Comparison of final results and calculation parameters of HKUST-1a
structure determinations completed by the CF+SE, CF+HM and CF
methods.
350
Andrey A. Yakovenko et al.
Structure envelopes for porous MOFs
J. Appl. Cryst. (2013). 46, 346–353
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Table 3
found and the structure of the MOF has been solved.
However, in the case of the HKUST-1syn sample only one
atom of the benzene ring fragment can be found in the
difference density map.
No. of No. of No. of
Best ED Computation No. of atoms
Another method is to use the conventional powder differMethod cycles runs
best EDs Rf (%)
time
not found
ence Fourier procedure. For this method, described above, the
CF+SE
500
20
9
32.31
3 min
2
Rietveld refinement procedure was performed and then the
CF+HM
500
20
1
29.20
5 min
4
Rietveld |Fobs|2 values were used in CF calculations, instead of
CF
500
20
2
32.12
3 min
5
the original intensities extracted via Le Bail refinement. This
CF+HM 10000 100
1
26.72
7h
2
CF
10000 100
2
31.01
2h
5
method improves estimates of overlapping peak intensities
and its effect can be seen right away. Fig. 5S represents the
best electron-density maps for both HKUST-1 samples
generated in a simple CF calculation but by using Rietveld
4. Rietveld refinement
2
|F
obs| . In these calculations we have used the same parameters
Finally, Rietveld refinements (Young, 1993) were performed
for the CF calculations as we used previously for the CF+SE
in JANA2006 (Petricek et al., 2006) to confirm that the
calculations (HKUST-1a: 20 runs, 250 cycles; HKUST-1syn: 20
determined structures of HKUST-1a and HKUST-1syn are
runs, 500 cycles). It can be seen that in the case of the highcorrect. In both cases, we obtained relatively good fits (Fig. 3S);
resolution HKUST-1a data almost all atoms (except solventall R factors were in a reasonable range (see supplementary
coordinated oxygen) have been identified. At the same time,
information, Table 1S), which confirms that the determined
in the case of HKUST-1syn we are still missing three atoms
structures of the frameworks in both cases are correct. In
from the structure.
addition, the overlap of the envelopes with the refined strucThe last technique with which we compared our structure
tures (Fig. 8) confirms the very high quality of the SEs
solution
results is based on introduction of the Cu-atom
generated using our method. This implies that similar techpositions
directly into the CF calculations. This technique
niques can now be applied to generate SEs for more compliallows
use
of the structure factor phases, which are defined by
cated MOFs to assist their structure solution and refinement.
Cu atoms at the beginning of each run in CF calculations. The
structure solution results should be improved, since Cu-atom
5. Alternative approaches to structure solution
positions contribute to the majority of ’hkl. For these types of
CF calculations we used the same parameters as in the
There are also many alternative ways to solve the structure of
HKUST-1 without use of the structure envelope; hence the
previous example, and the best resulting electron-density
structure solution results achieved by the CF+SE methods
maps for both HKUST-1 samples are presented in Fig. 6S. In
should be compared with those techniques. The easiest one is
this case we see a similar situation to the two previous cases.
The electron-density map for HKUST-1a is missing a peak for
the introduction of the Cu-atom positions into the Rietveld
one carboxylate C atom, while the map for HKUST-1syn
refinement and the generation of a difference Fourier density
contains peaks for only two light atoms.
map. This type of Rietveld refinement was performed in the
Comparison of the results from these methods with the
JANA2006 software and the resulting Fobs Fcalc density
results of CF+SE calculations yields three main conclusions:
maps were generated for both HKUST-1 data sets (Fig. 4S). It
(i) For high-resolution diffraction data all techniques perform
can be clearly seen that in the case of HKUST-1a the positions
well and yield a reasonable structure of HKUST-1; at the same
of all light atoms, except solvent-coordinated oxygen, were
time, CF+SE calculations provide the
positions of all atoms in the framework
of HKUST-1, while the electrondensity maps from all other methods
are missing peaks for at least one atom.
(ii) In the case of low-resolution data,
CF+SE calculations provide the best
and most easily recognizable structure
for the HKUST-1 framework; even
with the use of Cu-atom positions, the
electron-density maps for other techniques are missing peaks for at least
three atoms. (iii) The densities
provided by the CF+SE method are
‘cleaner’ and do not contain a large
number of extra peaks.
As we can see, there are a number of
Figure 8
structure solution techniques that can
Final refined structures of (a) HKUST-1a and (b) HKUST-1syn overlapped with their SEs.
Comparison of final results and calculation parameters of HKUST-1syn
structure determinations completed by the CF+SE, CF+HM and CF
methods.
J. Appl. Cryst. (2013). 46, 346–353
Andrey A. Yakovenko et al.
Structure envelopes for porous MOFs
351
research papers
be used to improve and simplify determination of MOF
structures. CF+SE calculations can be a valuable source for
structural information for unknown MOFs; however, the best
structure solution results would probably be produced by
combination of CF+SE with several other structure solution
techniques.
6. Structure solution of a low-symmetry MOF
With the example of HKUST-1 we have shown that the use of
SEs in CF calculations indeed promotes structure solution. At
the same time, even though HKUST-1 has large unit-cell
parameters, it crystallizes in a very high symmetry space
group, which may simplify its structure solution. It is not clear
that this method will extend to other more complex lowsymmetry structures based on the first example in this paper.
To investigate this, we applied the SE technique to the structure solution of the activated phase of PCN-200 (PCN-200a;
Fig. 9) (Wriedt et al., 2012).
PCN-200 is constructed from Cu2+ ions connected through
tetrazolate-5-carboxylate and 1,3-di(4-pyridyl)propane ligands
(Fig. 9d). It crystallizes in a low-symmetry monoclinic crystal
system, which was ideal for our structure determination test.
Upon activation, this MOF goes through a phase transition, so
the structure of its activated phase is different from the as-
synthesized phase. We originally solved the structure of PCN200a using FOX (Favre-Nicolin & Černý, 2002) and, therefore,
we knew the initial unit-cell parameters for the whole pattern
decomposition (Wriedt et al., 2012). Synchrotron powder
diffraction data were collected using beamline 1-BM at the
APS, with an average wavelength of 0.6065 Å. The sample of
PCN-200 was loaded into a Kapton capillary and heated to
373 K in a helium stream to generate the activated phase of
PCN-200. Subsequently, the sample was cooled to 295 K and
the powder diffraction data were collected with a mar345
imaging plate over the angular range 1–25 2. The structure
solution was complicated as a result of the collection of lowresolution data (dmin = 1.4 Å).
Pawley (1981) whole pattern decomposition for the PCN200a data was performed with TOPAS 4.2 (Bruker, 2009). The
determined unit cell was consistent with previous results and
was found to be monoclinic with parameters a = 28.692 (1), b =
9.2640 (4), c = 9.3215 (5) Å and = 116.084 (3) . Systematic
absences were found to correspond to the space group C2/c.
The refinement converged with satisfactory R values (Rp =
0.026, Rwp = 0.038, Rexp = 0.012) and the final plot is presented
in Fig. 9(a). The procedure yielded 429 reflection intensities,
which were used for the following calculations.
The reflection list was transferred to SHELXTL and the
Patterson technique easily produces correct Cu-atom posi-
Figure 9
Structure determination of PCN-200a: (a) final Pawley whole pattern decomposition plot; (b) SE generated from the PCN-200a data set; (c) final
electron-density map generated from CF+SE calculations; (d) final refined structure of PCN-200a.
352
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Structure envelopes for porous MOFs
J. Appl. Cryst. (2013). 46, 346–353
research papers
tions, which were used in the estimation of structure factor
phases for reflections in the powder pattern. The seven most
intense and non-overlapping reflections (200, 111, 310, 311,
511, 510 and 311) were used for SE generation (Fig. 9b). It can
be easily seen that the structure envelope produced by our
technique has the same pore distribution as in the structure of
PCN-200a.
This envelope was used in CF+SE structure solution
calculations. Because the number of reflections was limited,
we used 5000 CF cycles and 20 runs. After 2 min of computational time, this CF+SE procedure produces the electrondensity map presented in Fig. 9(c). It can be clearly seen that
the majority of the atoms in the structure have been determined. The density map is missing only four out of 17 non-H
atoms in the structure; hence the structure of PCN-200a was
solved. This solution was used as the starting point for the
Rietveld refinement (JANA2006), and the final structure of
PCN-200a is presented in Fig. 9(d), while the final Rietveld
refinement plot and R factors can be found in the supplementary information (Fig. 7S).
7. Conclusion
In this article we have demonstrated a new technique for
structure envelope generation for MOF materials. This technique is based on the fact that, in the case of MOFs, determination of heavy-metal SBU positions is usually simple;
therefore, these metal positions can be used as estimations of
the structure factor phases needed for envelope generation. It
also can be seen that use of SEs in charge-flipping calculations
shortens and simplifies structure determination of MOF
materials. This technique provides excellent MOF models,
which can be used as a good starting point for their refinement.
The authors thank Dr Mario Wriedt for providing the
sample of PCN-200, Dr Gregory Halder for help with
recording the powder X-ray diffraction data for the activated
sample of PCN-200, and Mr Trevor Makal for discussion and
review of the manuscript. This work was supported by the US
Department of Energy (DOE DE-SC0001015, DE-FC3607GO17033 and DE-AR0000073), the National Science
Foundation (NSF CBET-0930079) and the Welch Foundation
(A-1725). Use of the Advanced Photon Source at Argonne
National Laboratory was supported by the US Department of
Energy, Office of Science, Office of Basic Energy Sciences,
under contract No. DE-AC02-06CH11357.
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