Breathing and twisting: An investigation of framework deformation and guest packing in single crystals of a microporous vanadium benzenedicarboxylate

Article abstract of DOI:10.1021/ic1025087

The structural details of the compounds vanadium benzenedicarboxylate VO(bdc)?Guest, where the Guests are the absorbed six-ring molecules: benzene, 1,4-cyclohexadiene, 1,3-cyclohexadiene, cyclohexene and cyclohexane, have been determined from single cryst

Full text of DOI:10.1021/ic1025087

2028 Inorg. Chem. 2011, 50, 2028–2036
DOI: 10.1021/ic1025087
Breathing and Twisting: An Investigation of Framework Deformation and Guest
Packing in Single Crystals of a Microporous Vanadium Benzenedicarboxylate
Xiqu Wang,*,† Juergen Eckert,‡ Lumei Liu,† and Allan J. Jacobson*,†
†Department of Chemistry, University of Houston, Houston, Texas 77204-5003, United States, and ‡Materials
Research Laboratory, University of California, Santa Barbara, California 93106-5121, United States
Received December 15, 2010
The structural details of the compounds vanadium benzenedicarboxylate VO(bdc) Guest, where the Guests are the
3
absorbed six-ring molecules: benzene, 1,4-cyclohexadiene, 1,3-cyclohexadiene, cyclohexene and cyclohexane, have
been determined from single crystal X-ray data. All of the six-ring guest molecules show a high degree of ordering
inside the channels of VO(bdc). The interactions between the guests and the host framework are dominated by van
der Waals bonding. The six-ring molecules are all packed in two columns in the channels, either in herringbone or close
to parallel patterns. The packing changes the space group symmetry of VO(bdc) from Pnma to the noncentrosym-
metric space group P212121. The VO(bdc) framework deforms to closely adapt to the shape and thickness changes of
the double columns of the guest molecules. In addition to the well studied breathing deformation, a twisting
deformation mechanism that involves a cooperative rotation of the octahedral chains accompanied by bending of the
bdc ligand is apparent in the detailed structural data. More quantitative information on the remarkable flexibility of the
VO(bdc) framework was obtained from ab initio calculations.
Introduction
oxide units with different dimensionalities.4-6 Among them,
a group of compounds with the general framework formula
The remarkable progress in the synthesis of inorganic-
organic hybrid compounds has greatly enhanced the chemical
and structural diversity of crystalline microporous materials
and the potential for novel applications. The design of
metal-organic open frameworks (MOFs) can take advan-
tage of both the variety of organic linkers and specific
physical properties of the inorganic core structural units.1,2
Relative to conventional inorganic porous solids such as
zeolites, hybrid organic-inorganic porous frameworks
have the advantage of flexibility upon loading and unloading
of guest species. The high flexibility can give rise to tunable
adsorption selectivity by using changes in external conditions
to adjust pore shapes. Compounds with such properties
have been categorized as “third generation” microporous
materials.3
ꢀ
MX(bdc), first reported by Ferey and co-workers, are based
on chains of trans corner-sharing octahedra MX2O4 (M =
V,7 Cr,8 Al,9,10 Fe,11,12 In,13 Ga,14 Mn15 and X = O, OH, F)
cross-linked by 1,4-benzene dicarboxylate. The framework
that results contains one-dimensional wide channels. Upon
removal or adsorption of guest species inside the channels of
the structure, large deformations occur without changes in
the topology of the framework. Interesting adsorption prop-
erties of several members of the family have attracted great
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pounds with high porosity and various pore sizes have been
synthesized by using this ligand to connect together metal
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*To whom correspondence should be addressed. Tel.: 713-743-2785. Fax:
713-742-2787. E-mail: ajjacob@uh.edu (A.J.J.), xiqu.wang@mail.uh.edu
(X.W.).
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pubs.acs.org/IC
Published on Web 01/12/2011
2011 American Chemical Society

Article
Inorganic Chemistry, Vol. 50, No. 5, 2011 2029
interest because of potential applications including storage of
gases such as H2, CO2, and CH4; molecule separations, for
example, vapor phase adsorption and separation of xylene
isomers; and drug delivery.16-31 Functional groups of var-
ious polarities, hydrophilicities, and acidities were recently
introduced through substitution in the framework phenyl
groups, and their effects on pore opening and the host-guest
interactions were reported.32-34
We have reported the synthesis of [VO(bdc)](H2bdc)0.71
(traditionally designated as MIL-477) in the form of large
single crystals.35 After removal of the guest acid molecules by
heating the crystals of [VO(bdc)](H2bdc)0.71 in the air, we
observed that the VO(bdc) structure is sufficiently flexible
to undergo single-crystal-to-single-crystal transformations
upon the adsorption of aniline, acetone, thiophene, and other
molecules enabling the details of the guest structure, frame-
work-guest interactions, and framework deformations to
be determined from single crystal X-ray diffraction data.
Furthermore, we have observed the rapid and highly selective
adsorption of organic sulfur molecules from methane or
octane by VO(bdc), a process relevant to clean fuels.36,37
The details of the crystal structures show the importance of
noncovalent interactions in determining the guest molecule
packing within the nanochannels and are valuable in helping
to understand the adsorption properties. Most recently, Leus
et al. reported remarkable catalytic activity of VO(bdc) in the
epoxidation of cyclohexene.38
We have extended our earlier study to other guest mole-
cules with different shapes and chemical bonding possibili-
ties. In the structural study of the VO(bdc) framework loaded
with different six-ring organic molecules, a twisting deforma-
tion mode accompanied by a cooperative rotation of the
octahedral chains and bending of the bdc ligands has been
observed. This deformation mode is complementary to the
well investigated breathing deformation which corresponds
to a cooperative translation of the octahedral chains. In the
present work, we show that combinations of the twisting and
breathing deformations occur when different molecules are
absorbed into the VO(bdc) framework. Quantitative insights
into these deformations and the remarkable flexibility of the
VO(bdc) framework have been obtained from ab initio
calculations.
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Experimental Section
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Crystalline [VO(bdc)](H2bdc)0.71, 1, was synthesized as
previously reported.35 For the adsorption measurements,
red prismatic crystals of 1 were heated in the air to 380 °C
using a 10 °C min-1 heat-up rate to remove H2bdc and to
form VO(bdc), 2. X-ray diffraction measurements on both
powder and single crystalsamples afterheatingconfirmed the
integrity of the structure of VO(bdc). Adsorption experi-
ments were carried out by immersing crystals of 2 in liquid
benzene, 1,4-cyclohexadiene, 1,3-cyclohexadiene, cyclohex-
ene, or cyclohexane in the air at room temperature. After
immersing the VO(bdc) crystals in the corresponding guest
liquid for ∼1 h, a suitable crystal for each intercalation com-
poundwas selectedand sealedina capillaryintheair together
with the guest liquid and mounted on a Bruker Apex-II
diffractometer for X-ray data collection. Structure determi-
nation and refinements were performed using the Bruker
SHELXTL software package.39 Data collection and struc-
ture refinement details are listed in Table 1. Volumes of vari-
ous voids within the structures are calculated using the
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program PLATON and the van der Waals radii: C, 1.70 A;
40
˚
H, 1.20 A; O, 1.52 A; V, 2.13 A.
˚
˚
In order to obtain more quantitative information on the
remarkable flexibility of the VO(bdc) framework revealed
in our crystallographic studies, we carried out ab initio cal-
culations. All energy calculations were performed with the
DFT-based code VASP41-45 using the more recent PAW
potentials46 and the PBE functional.47 An energy cutoff of
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6499–6503.

2030 Inorganic Chemistry, Vol. 50, No. 5, 2011
Wang et al.
Table 1. Crystal Data and Structure Refinement for [VO(bdc)](benzene)-LT, 3; [VO(bdc)](benzene)-RT, 4; [VO(bdc)](1,4-cyclohexadiene), 5; [VO(bdc)](1,3-
cyclohexadiene), 6; [VO(bdc)](cyclohxene), 7; and [VO(bdc)](cyclohexane), 8
compound
guest
guest/V mol. ratio
formula
fw
3
4
5
6
7
8
benzene
0.795(8)
C12.75H8.75O5V
292.89
223(2)
0.71073
P212121
6.7884(7)
13.231(1)
16.636(2)
1494.1(3)
4
benzene
1.0
C14H10O5 V
309.16
296(2)
0.71073
P212121
6.8018(4)
13.5344(9)
16.416(1)
1511.2(2)
4
1,4-cyclohexadiene
0.76(2)
C12.72H10.29O5V
294.08
296(2)
1,3-cyclohexadiene
1.0
C14H12O5V
311.18
296(2)
cyclohexene
0.81(1)
C13.43H13.02O5V
305.30
296(2)
0.71073
P212121
6.827(8)
13.965(16)
16.073(18)
1532(3)
cyclohexane
0.924(4)
C13.54H15.09O5V
308.79
296(2)
temp/K
wavelength/A
˚
0.71073
P212121
6.802(1)
0.71073
P212121
0.71073
P212121
space group
˚
a/A
6.8050(3)
13.9793(7)
15.9447(8)
1516.8(1)
4
6.8127(3)
13.7142(7)
16.0701(8)
1501.44(13)
4
˚
b/A
13.912(3)
16.052(3)
1519.1(5)
4
˚
c/A
˚
V/A
3
Z
4
data/params
goodness-of-fit
R1/wR2 [I>2σ(I)]a
R1/wR2 [all data]a
3407/170
1.067
0.0336/0.0901
0.0380/0.0925
2558/152
1.057
0.0282/0.0810
0.0301/0.0824
3590/178
1.052
0.0373/0.0994
0.0426/0.1022
3563/181
1.057
0.0284/0.0766
0.0304/0.0778
2355/140
1.071
0.0535/0.1237
0.0913/0.1381
3557/182
1.046
0.0283/0.0765
0.0298/0.0772
P
P
P
P
a R1 = ||Fo| - |Fc||/ |Fo|, wR2 = [ (w(Fo2 - Fc2)2)/ (wFo2)2]1/2
.
Figure 1. Crystal structure views along channel axis [100] for VO(bdc),
2; [VO(bdc)](benzene)-LT, 3; [VO(bdc)](1,4-cyclohexadiene), 5; [VO-
(bdc)](1,3-cyclohexadiene), 6; [VO(bdc)](cyclohxene), 7; and [VO(bdc)]-
(cyclohexane), 8. Vanadium, oxygen, carbon, and hydrogen atoms are
plotted in green, red, gray, and dark gray, respectively.
Figure 2. Structure views along [043] for [VO(bdc)](benzene)-LT, 3;
[VO(bdc)](benzene)-RT, 4; [VO(bdc)](1,4-cyclohexadiene), 5; [VO(bdc)]-
(1,3-cyclohexadiene), 6; [VO(bdc)](cyclohexene), 7; and [VO(bdc)](cyclo-
hexane), 8. The two disordered orientations of guest molecules in 4 and 5
are plotted with yellow and blue bonds, respectively.
400 eV for the plane wave basis set was used. We did calculate
the relative energies of theempty framework structures with a
larger energy cutoff (450 eV) and found that the differences in
the relative energies were well within the uncertainties ex-
pected for this type of calculation; the energy cutoff did not
affect the energetic ordering of the structures. The k-points
were generated using a 2 ꢀ 2 ꢀ 2 Monkhorst-Pack setting.
In the first step, we performed single-point energy calcula-
tions on each of the framework structures using the atomic
positions from the single crystal diffraction results for the
different guest-host systems by ignoring the guest molecules.
C-H bond distances were, however, corrected to the ex-
These are taken to be the difference in the single-point
energies (based on experimental crystal structures) of the
framework including guests to the sum of energies of the
empty framework and the guests themselves (in the config-
uration found in the framework).
Results and Discussion
Six host/guest structures [VO(bdc)](benzene)-LT, 3; [VO-
(bdc)](benzene)-RT, 4; [VO(bdc)](1,4-cyclohexadiene), 5; [VO-
(bdc)](1,3-cyclohexadiene), 6; [VO(bdc)](cyclohxene), 7; and
[VO(bdc)](cyclohexane), 8, were refined from the single
crystal data. As shown in Figures 1 and 2, in all six structures,
the guest molecules are packed in two columns inside each
channel of the VO(bdc) framework. Most noticeably, as the
shape of the guest molecules changes from the flat benzene
˚
pected value of 1.01 A because of the well-known foreshor-
tening observed in X-ray diffraction. We also obtained esti-
mates of the host/guest binding energies for selected phases.
(46) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys.
1999, 59, 1758–1775.
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Article
Inorganic Chemistry, Vol. 50, No. 5, 2011 2031
˚
with the period of the channel, i.e., 6.788 A, while the
distance from a benzene ring center of one column to a
neighboring benzene ring center of the other column is
˚
5.04 A. In contrast, the shortest distance between the
benzene ring center and the center of bdc ligands of the
˚
framework is 4.62 A, which is still much longer than those
molecule to the more spherical cyclohexane, the framework
deforms through cooperative rotation of the octahedral
chains together with progressive bending of the channel
walls. When viewed along the channel axis, the deformation
appears to be caused by twisting neighboring octahedral
chains relative to each other. This “twisting” deformation
is in contrast to the well studied breathing deformation in
other phases of the MIL-47 and MIL-53 families.48 A typical
example of a breathing deformation is found for [VO-
(bdc)](acetone) in which the diamond shaped host channels
close up substantially by cooperative translation of the
octahedral chains upon adsorption of guest acetone mole-
cules, but there is no rotation of the octahedral chains. The
V-O-C-C torsion angles of the framework vary like hinges
to facilitate the breathing mechanism, and the bdc ligands
stay practically flat.35 Structural details of 3-8 described in
the following sections indicate that the “twisting” deforma-
tion is mainly a result of adaption of the framework to the
space requirements of the guest molecule packing. There is
little change observed in the V-O bond lengths after adsorp-
tion, indicating that the adsorption of the guest molecules
does not change the tetravalent state of the vanadium atoms.
The vanadium atoms are tetravalent in all of the compounds
(3-8) studied.
for typical π-π interactions but indicates somewhat
stronger interaction between the guest and the host than
between the guests. The shortest distances from the
benzene hydrogen atoms to the neighboring benzene ring
˚
centers of guest benzene and host bdc are 3.30 and 3.01 A,
respectively, indicating very weak CH π interactions.
3 3 3
It seems that van der Waals interactions are the dominant
forces determining the packing of the benzene molecules
inside the channels. The herringbone pattern and similar
atom distances are also found in the local structure of
crystalline benzene.49
The two columns of benzene molecules are oriented
roughly perpendicular to one pair of the channel walls
and are close to parallel to the other pair. The latter pair is
slightly bent toward the outside of the channel, while the
former pair is bent toward the inside, presumably due to
the space requirement of the guest benzene columns. Such
bending of the channel walls facilitates and probably is
also strengthened by weak electrostatic interactions be-
tween the benzene hydrogen atoms and the oxygen atoms
The Porous Structure of VO(bdc), 2. The structure of
VO(bdc), 2, has been briefly described in the literature.7,35
It contains single chains of VO6 octahedra cross-linked by
bdc ligands. The octahedral chains have a -OdV-
OdV- backbone with alternating short and long V-O
apical bonds of the VO6 octahedra and a V-O-V angle
of 128.7°. The equatorial corners of the VO6 octahedra
are shared with the bdc ligands. The 1D channels parallel
to the octahedral chains have a diamond-shaped cross-
of the framework with CH O distances in the range
3 3 3
˚
2.90-2.99 A. Similar interactions have been reported for
zeolite/guest systems.50,51 In addition to bending, the
inclination of bdc ligands toward the channel axis in-
creased to 9.0° from the value of 3.7° found in VO(bdc), 2,
and in such a way that a four-column herringbone pattern
is formed by the two columns of guest benzene molecules,
and the two channel walls closely parallel to them.
The guest benzene molecules in neighboring channels
are oriented nearly perpendicular to each other, and
the polar axes of their herringbone pattern are in opposite
directions. The packing features of the guest benzene
molecules are not compatible with the mirror and glide
plane symmetry of the initial framework, and the space
group of the structure is lowered from centrosym-
metric Pnma to chiral P212121 after absorption. Similar
symmetry changes caused by absorbing other molecules
have been reported previously35 and are also observed in
structures 4-8.
˚
section with an aperture of ∼7.6 ꢀ 7.7 A. The structure
has a space group symmetry of Pnma with [100] parallel to
the octahedral chains and [010] perpendicular to the plane
running through the zigzag -OdV-OdV- backbone.
The bdc ligands are flat with their benzene ring plane
almost parallel to the channel axis. The angle between the
bdc benzene ring and the channel axis is only 3.7°.
However, this small inclination of bdc toward the channel
axis causes a slight fluctuation of the channel aperture
along the channel axis. It also makes individual channels
polar but the polarities of neighboring channels are in
opposite directions. The angle between the long axis of
the bdc ligand and the octahedral chain is 86.6°, less than
the 90° angle found in the closely related M(OH)(bdc)
structures. The deviation is presumably related to the
polar feature of individual octahedral chains of VO(bdc)
caused by alternating short and long V-O bonds. These
orientation features of the framework bdc play a subtle
role in the packing patterns of the absorbed guest mole-
cules and in symmetry changes of the structures upon
absorption.
The occupancy of the benzene molecules was refined to
0.795(8) per vanadium atom. Therefore, about one-fifth
of the guest benzene positions are randomly vacant. The
3
˚
calculated packing density is 173 A per benzene mole-
cule, assuming a full occupancy of the benzene positions,
3
which is lower than in liquid benzene (148 A ).
˚
The Crystal Structure of [VO(bdc)](benzene)-RT, 4. An
apparent difference between the room temperature 4 and
low temperature 3 structures is the random orientational
disorder of the guest benzene molecules in the former
(Figure 2). Roughly two-thirds of the benzene molecules in
4 are packed and oriented very similarly to the arrangement
The Crystal Structure of [VO(bdc)](benzene)-LT, 3. At
223 K, the absorbed benzene molecules form two col-
umns packed in a herringbone arrangement in each
channel of the VO(bdc) framework (Figures 1 and 2).
The angle between the benzene ring planes of the two
columns is 43.8°. The distance between the centers of
neighboring benzene rings in each column is commensurate
(49) Bacon, G. E.; Curry, N. A.; Wilson, S. A. Proc. R. Soc. London, Ser.
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2032 Inorganic Chemistry, Vol. 50, No. 5, 2011
Wang et al.
in 3, while the remaining one-third are flipped to the
opposite direction of the channel axis. The disorder is
presumably caused by local structures where the guests in
neighboring channels all have the same orientation in-
stead of being related by a 21 axis. Another possibility is
the formation of local structures with parallel packed
double columns of benzene rings in individual channels,
but the observed distances between the benzene carbon
The Crystal Structure of [VO(bdc)](1,3-cyclohexadi-
ene), 6. At room temperature, an ordered packing of the
absorbed 1,3-cyclohexadiene molecules is observed. As
expected, the 1,3-cyclohexadiene molecules have a non-
planar conformation, but the butadiene fragment is
nearly flat with a CdC-CdC torsion angle of 3.9°.53
One alkyl carbon atom is above and the other below the
butadiene plane. Therefore, the molecule has a twisted
wedge shape. The 1,3-cyclohexadiene molecules are packed
in two columns in each channel of VO(bdc) with the buta-
diene fragments almost parallel to each other and to the
channel axis (Figure.2). The two columns are shifted relative
to each other so that the thick alkyl fragments in one column
fit the space near the thin butadiene fragments in the other
˚
sites are too short (3.17 A) to favor this possibility. The
angle between the two herringbone columns of benzene
molecules decreases from 43.7° in 3 to 39.1° and 32.6° in
4 for the orientations with high and low occupancies,
respectively, which might be related to the slightly ex-
panded period of the framework along the channel axis
and the higher guest content of 4. The observed atom
distances indicate much weaker interactions between the
guests and between the guest and host benzene rings in 4
than in 3. However, the shortest distance between guest
benzene hydrogen atoms and the host bridging oxygen
column. This facilitates a C-H CdC interaction net-
3 3 3
work between the two columns with relatively short inter-
˚
molecular distances (C-H CdC: 2.87-3.04 A). Rela-
3 3 3
tively strong guest/host interactions are indicated by the
short distances from the hydrogen atoms of the guests to the
carbon atoms of the framework benzene rings (2.78-
˚
˚
atoms is 2.76 A, shorter than the 2.90 A observed in 3.
Compared to 3, the unit cell volume of 4 increases by
1.1%. The total occupancy of the two orientations of the
benzene molecules in 4 was refined very close to 1.0 and
was fixed to 1.0 per vanadium atom. The channels of 4 are
more open, as indicated by the larger channel diagonal
ratio of 13.534/16.417 compared to 13.231/16.636 of 3,
and by the smaller inclination angle of the bdc ligand of
6.2° compared to 9.0° of 3. The calculated packing density
˚
2.82 A), and to the bridging oxygen atoms of the framework
(2.87 A). The former are typical CH π interactions.54
˚
3 3 3
The strengthened intermolecular interactions between the
guests and between the guest and host may account for the
absence of disorder in 6.
The channel diagonal ratio, 13.98:15.95, of 6 indicates
enhanced channel opening compared to 5. The bending of
the channel walls in 6 is more pronounced than in 3-5,
probably because of the increased thickness of the guest
molecules. On the other hand, the cell volume of 6 is
slightly smaller than that of 5, due to the stronger inter-
actions between the guests and the host in 6.
The Crystal Structure of [VO(bdc)](cyclohexene), 7.
The conformation of the absorbed cyclohexene molecules
is a half-chair with a twist angle of 52.5°. The half-chair
conformation of cyclohexene with twist angles close to
60° occurs exclusively in many other crystal structures
and is consistent with results from quantum chemical
calculations.55,56 The cyclohexene molecules are packed
in two columns related to each other by a 2-fold screw axis
in each channel of VO(bdc) (Figure 2). The shortest
3
˚
for the guests in 4 is 178 A per benzene molecule, slightly
lower than the low temperature structure 3.
The Crystal Structure of [VO(bdc)](1,4-cyclohexadi-
ene), 5. The absorbed 1,4-cyclohexadiene molecules are
nearly planar with the maximum shift of carbon atoms
˚
from the ideal plane less than 0.04 A, which is closely
similar to the planar conformation found in the structure
of crystalline 1,4-cyclohexadiene.52 At room tempera-
ture, the 1,4-cyclohexadiene molecules inside the channels
of VO(bdc) show a herringbone packing pattern and an
orientational disorder similar to the benzene molecules in
4 (Figure 2). One orientation of the guest 1,4-cyclohex-
adiene molecules has a refined occupancy of 47.1%, for
which the angles between the two herringbone columns is
21.4°. The other orientation has a refined occupancy of
28.8% and a much larger angle of 38.6° between the two
intermolecular H C distances between the guests is
3 3 3
˚
3.48 A, indicating no significant bonding other than
van der Waals interactions. However, the packing of the
guests seems to fill space most efficiently with the chair
backs of one column fitting the double bond part of the
other column. Similar to 5 and 6, relatively strong guest/
host interactions are indicated by the short distances from
the hydrogen atoms of the cyclohexene molecules to the
herringbone columns. The nearest H C distances be-
3 3 3
tween neighboring guest molecules for both orientations
˚
are larger than 3.36 A, indicating mainly intermolecular
van der Waals interactions. In contrast, there are rela-
˚
tively short distances (2.92-3.20 A) from the hydrogen
˚
atoms of the guests to the framework carbon atoms. The
distances from the hydrogen atoms of the guests to the
nearest bridging oxygen atoms of the framework are
carbon atoms of the framework (2.90-3.23 A) and to the
bridging oxygen atoms of the framework (2.99 A).
˚
The occupancy of the cyclohexene molecule was refined
to 0.81(1), rather close to the guest occupancies in 3 and 5.
The channel opening and the bending of the channel walls in
7 are both slightly decreased compared to 6 in spite of the
large molecule size and the large intermolecular distances of
˚
between 2.75 and 2.79 A for the two orientations, respec-
tively, indicating relatively strong guest/host interactions.
The channels of 5 are further opened up compared to 4,
as indicated by the larger channel diagonal ratio 13.912/
16.052 of 5 compared to 13.534/16.417 of 4, probably
because features of the 1,4-cyclohexadiene molecules are
more bulky than the benzene molecules.
(53) Shishkin, O. V. J. Struct. Chem. 2000, 41, 383–387.
(54) Suezawa, H.; Yoshida, T.; Umezawa, Y.; Tsuboyama, S.; Nishio, M.
Eur. J. Inorg. Chem. 2002, 3148–3155.
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2002, 354, 428–434.
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2008, 8, 512–518.
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Chem. Soc. 1988, 110, 7218–19.

Article
Inorganic Chemistry, Vol. 50, No. 5, 2011 2033
Figure 3. The “breathing” (left) and the “twisting” (right) deformation mode of the VO(bdc) framework. The angle φ is a measure of twisting.
Breathing and Twisting, Two Different Framework De-
formations. Compared to the breathing deformation, the
“twisting” deformation of the VO(bdc) framework ob-
served above has less effect on the volume of the cell and
on the aperture of the channels but does significantly vary
the channel shape by changing the curvature of the
channel walls. The magnitude of the breathing deforma-
tion is directly reflected in the ratio of the two channel
diagonals measured between the metal atoms. For the
pure breathing deformation observed on adsorption of
acetone, this ratio changes from 14.00:16.07 in VO(bdc)
to 10.21:18.41 in [VO(bdc)](acetone). In comparison,
the ratio is 13.71:16.07 in [VO(bdc)](cyclohexane). The
two deformation mechanisms are illustrated in Figure 3.
If the VO(bdc) framework is considered an expanded
ReO3 structure, the twisting deformation is similar to the
a0a0cþ in-phase tilting deformation of the perovskite
Figure 4. Deformations of the VO(bdc) framework loaded with differ-
ent guest molecules. Δ and φ are measures of the breathing and the
twisting deformation modes, respectively. dmsulfide, dimethylsulfide;
H2bdc, 1,4-benzenedicarboxylic acid; bz, benzene; 14chdiene, 1,4-cyclo-
hexadiene; 13chdiene, 1,3-cyclohexadiene; chexene, cyclohexene; chex-
ane, cyclohexane.
structures.57
The framework deformations observed to date for
different guest molecules can be described by various
combinations of the breathing and the twisting modes.
In order to quantitatively characterize the deformation,
we define the following parameters (see Figure 3):
the guests in the former. This is probably related to the dif-
ferent shapes and occupancies of the guest molecules in the
Δ=|(b/c)-(b0/c0)|, variation of channel diagonal
ratio (b/c) from that of 2 with empty channels (b0/c0),
a measure of the breathing deformation
two phases. The unit cell volume of 7 is larger than other
phases mainly due to an expansion along the channel axis.
The Crystal Structure of [VO(bdc)](cyclohexane), 8.
The absorbed cyclohexane molecules have a typical chair
conformation. Their packing pattern and orientations are
similar to the cyclohexene molecules in 7 (Figure 2). The
φ: angle between the zigzag -VdO-VdO- backbone
planes of two neighboring octahedral chains, a mea-
sure of cooperative rotation of the octahedral chains
and the twisting deformation. The variation of Δ
versus φ for VO(bdc) is shown in Figure 4 for VO(bdc)
frameworks loaded with different guest molecules.
There is no substantial framework deformation upon
the adsorption of dimethylsulfide that is found to be
highly disordered in the VO(bdc) channels.37 [VO-
(bdc)](acetone) shows a breathing deformation only,
while phases 5-8 are dominated by twisting deforma-
tions. The other phases show different combinations of
both breathing and twisting modes.
shortest intermolecular H C distances between the
3 3 3
˚
cyclohexane guests is 3.41 A, while the shortest distances
from the hydrogen atoms of the cyclohexane molecules to
˚
the framework carbon and oxygen atoms are 3.09 A and
˚
3.00 A, respectively. Therefore, they are held together
mainly by van der Waals interactions. Compared to the
other guest molecules, cyclohexane is the most volumi-
nous but has the least extension along the six-ring plane.
Therefore, the packed cyclohexane molecules have larger
space requirement along the six-ring thickness direction
and less space requirement along the six-ring plane.
The requirement is met by the highest degree of bending
of the channel walls, which also tends to maximize the
number of van der Waals contacts between the guests and
the host. The channel wall bending is accompanied by a
cooperative rotation of the octahedral chains to release
the strain.
Since the two deformation modes are accompanied by
different bending of the bdc ligands, we further define the
following parameters in order to study the correlations
(57) Mitchell, R. H. Perovskites Modern and Ancient; Almaz Press:
Thunderbay, Canada, 2002.

2034 Inorganic Chemistry, Vol. 50, No. 5, 2011
Wang et al.
Figure 6. Correlation between the cooperative rotation of the octahe-
dral chains and the bending of the channel walls of the VO(bdc) frame-
work loaded with different guest molecules. Abbreviations are the same as
in Figure 4.
Figure 5. The relationship between η1 and η2 for the VO(bdc) frame-
work loaded with different guest molecules, showing that the channel
walls bend differently for different deformation modes. Abbreviations are
the same as in Figure 4.
We may attempt to relate the observed structural
deformations to the relative energies of the various frame-
works. Table 2 lists relative single point energies (kcal/
mol) from our VASP calculations of the empty VO-
(bdc) frameworks (after “removal” of the different guest
molecules) on the basis of results from the single crystal
X-ray diffraction data. The energy of VO(bdc), 2, with-
out guest loading was taken as the reference (i.e., energy
=0.0 kcal/mol).
between the deformation mode and shapes of channel
walls:
η1, η2: bending angles of the (V1)2-bdc-(V2)2 channel
wall, defined as the angle between the line through
the two benzene C atoms on the bdc long axis and the
best plane fitting the two V-O bonds on V1 and V2
respectively, |η1| g |η2|. If the V atoms are all on the
same side of the bdc plane, both η1and η2 are positive;
otherwise, η1 is positive and η2 is negative.
The relative energies of five of the structures, including
that of the empty framework, fall within about 2 kcal/
mol. Such small differences are not likely to be significant.
Three other structures differ by less than 10 kcal/mol
from the one with the lowest energy, while the framework
for the acetone inclusion compound is 26.2 kcal/mol
higher in energy. These results may be correlated to some
degree with the details of the framework distortions
observed in the single crystal X-ray diffraction data,
and described above. Reference to Figure 4, where the
breathing (Δ) and twisting deformations (φ) of the differ-
ent framework structures are displayed, reveals that five
of the structures found to have the lowest energies (dms,
aniline, thiophene, benzene LT, and the empty frame-
work) roughly fall on a diagonal with modest values of Δ
and φ. The other structures, which deviate in energy by
more significant amounts, either exhibit a large breathing
deformation (acetone) with no twisting deformation or
(1,4-cyclohexadiene, cyclohexene, 1,3-cyclohexadiene,
and cyclohexane) show little or no breathing deformation
accompanied by various degrees of twisting. Figure 5
shows that the latter frameworks are those closer to a C
shape, while the acetone framework is one with a pro-
nounced S shape. The low energy structures in turn have a
framework closest to an L shape.
ε1, ε2: hinge angles of the (V1)2-bdc-(V2)2 channel
wall, defined as the angle between the carboxylate
plane and the best plane fitting the two V-O bonds
on V1 and V2, respectively, |ε1| g |ε2|. If the V atoms
are all on the same side of the bdc plane, both ε1and ε2
are positive; otherwise, ε1 is positive and ε2 is negative.
ψ: bending angle of the bdc ligand, the angle between
the two C-C single bonds of bdc. As shown in Figure 5
where η1 is plotted against η2, the channel walls bend
differently for the breathing and twisting modes. For
breathing, the wall bends to an “S” shape because the
V atoms on the two edges of the wall shift to the
opposite sides of the bdc plane, while for twisting they
tend to shift to the same side so that the wall bends to a
“C” shape. Some of the phases with combined defor-
mation of both breathing and twisting modes have
walls approaching an “L” shape.
Assuming the octahedral chains are rigid, the rotation
angle φ of the octahedral chains is expected to be equal to
the sum of the bending angles η1 þ η2. Αs shown in Figure
6, this is indeed the case for most of the phases. In fact,
even for the most twisted phase [VO(bdc)](cyclohexane),
8, the VO6 octahedron changes very little from that of
VO(bdc), 2. The maximum difference in corresponding
O-V-O angles between the two frameworks is less than
1°. The bending of the V-bdc-V channel walls consists
of two parts: the hinging angles and the bending of the bdc
ligand. As shown in Figure 7, the net bending of the
channel walls η1 þ η2 is approximately equal to the net
hinge angles ε1 þ ε2 plus the bending angle of the bdc
ligand ψ. Bending of the bdc ligand ψ is somewhat less
than the net hinge angles ε1 þ ε2. Both increase as the
degree of twisting increases (Figure 7).
In an effort to separate the effects of structural distor-
tions from that of the binding of guest molecules, we
obtained estimates of the binding energies for three host/
guest systems listed in Table 3. These are taken to be the
difference in the single-point energies (based on experi-
mental crystal structures) of the framework including
guests to the sum of energies of the empty framework
and the guests themselves (in the configuration found in
the framework). It should be noted, however, that the

Article
Inorganic Chemistry, Vol. 50, No. 5, 2011 2035
Figure 7. Left: The net bending of the channel walls (η1 þ η2), which is approximately equal to the net hinge angles (ε1þ ε2) plus the bending angle of the
bdc ligand (j). Right: Correlation between ε1 þ ε2 and j of the VO(bdc) framework loaded with different guest molecules. Abbreviations are the same as in
Figure.4.
Table 2. Relative Single Point Energies of the Empty VO(bdc) Framework
Structures with the Respective Guest Molecules Removed on the Basis of Single
Crystal X-Ray Diffraction Dataa
Table 3. Estimate of the Binding Energies of Guest Molecules for Three Frame-
work Structures (See Text)
phase
binding energy (kcal/mol)
framework
relative energy (kcal/mol)
[VO(bdc)](benzene)-LT
[VO(bdc)](thiophene)
[VO(bdc)](acetone)
4.1
4.5
4.9
[VO(bdc)](cyclohexene)
[VO(bdc)](dms)
[VO(bdc)](aniline)
[VO(bdc)](thiophene)
[VO(bdc)](benzene)-LT
VO(bdc)
-7.6
-2.1
-1.2
-0.54
-0.47
0.0
phenyl rings in VO(bdc) and MIL-53(Cr) were unveiled
using the 2H NMR method most recently.58
We may add that it is the VO(bdc) framework which we
found to have the lowest energy of the five structures after
relaxation in the manner described above. It is also no
surprise, of course, that these frameworks will reduce in
volume in the absence of guest molecules and may, in fact,
change shape and ultimately collapse. The relative en-
ergies of the synthesized frameworks without guest mo-
lecules must therefore be treated with caution.
As discussed in previous sections, the twisting deforma-
tions are mainly related to adaption of the framework to
the packing of the guests so that the van der Waals interac-
tions between the host and the guest can be maximized. In
the case of strong breathing deformations, pronounced
interactions between guests and the octahedral chains of
the framework can be identified. In [VO(bdc)](acetone),
dipole-dipole interactions between the acetone molecules
and the caboxylate groups of the framework were observed,
which tend to pull a pair of opposite octahedral chains to the
channel axis. Similarly, in [Al(OH)(bdc)](H2O), which
shows a very large breathing deformation, significant hydro-
gen bonding between the guest water molecules and the
framework oxygen atoms was observed.59 The adsorption-
induced stress exerted on the host framework may acts as a
stimulus that triggers breathing transitions.60
[VO(bdc)](1,3-cyclohexadiene)
[VO(bdc)](1,4-cyclohexadiene)
[VO(bdc)](cyclohexane)
[VO(bdc)](acetone)
4.4
5.5
15.2
26.2
a The energy of VO(bdc) before loading guests was taken as the
reference (i.e. energy = 0.0 kcal/mol).
values obtained in this manner are likely to underestimate
binding energies of the guest molecules, as this type of
calculation does not adequately account for dispersion
forces, as such corrections are not currently supported in
VASP. The values for the three systems investigated in
this manner were all between 4 and 5 kcal/mol, largely
independent from the extent to which the host framework
was distorted. This result suggests that additional factors
play a role in the distortion of the framework upon the
inclusion of guest molecules, which could be of a kinetic
nature during the synthesis.
In an effort to investigate this point further, and to
understand why the empty framework structure is not the
one with the lowest energy, we performed full geometry
relaxation (atomic positions and, subsequently the cell para-
meters) of five of the structures, VO(bdc), [VO(bdc)](dms),
[VO(bdc)](thiophene), [VO(bdc)](cyclohexane), and [VO-
(bdc)](acetone), without the presence of guest molecules.
In all three cases, the structures became more distorted,
decreased in cell volume, and reached minimum energies
more than 75 kcal/mol lower than those of the corresponding
empty framework but had not converged after 500 optimiza-
tion steps. Perhaps the most noteworthy aspect of the relaxed
structures is that in all cases the bdc linker turns more
inclined to the channel axis (Figure 8), akin to what is the
case for MOF-5, for example. Dynamic flips of the bdc
The deformation parameters defined in the last section
can also be used to help describe framework deformation
of other members of the MIL-47 and MIL-53 families. In
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V.; Devic, T.; Serre, C.; Ferey, G. Angew. Chem., Int. Ed. Engl. 2010, 49,
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2036 Inorganic Chemistry, Vol. 50, No. 5, 2011
Wang et al.
Figure 8. (a) VO(bdc), diffraction data (top left), relaxed (top right). (b). [VO(bdc)] (cyclohexane) cell crystal structure (bottom left), relaxed (bottom
right).
some monoclinic phases such as [Al(OH)(bdc)]-LT61and
[Fe(OH)(bdc)](pyridine),12 neighboring MO6 octahedra
of each individual chain are slightly rotated relative to
each other, usually coupled with increased inclination of
the bdc ligands toward the channel axis. The breathing or
twisting deformation parameters of such frameworks can
also be determined by cooperating translation or rotation
of neighboring octahedral chains. In the system [Al(OH)-
(bdc)](pyridine)x, depending on the value of x, the guest
packing can be switched between two different patterns,
and accordingly, the framework shows different defor-
mation modes. For x=1, the pyridine molecules are
packed in two columns in each channel very similarly to
benzene molecules in [VO(bdc)](benzene)-LT, and the
framework shows mainly a twisting deformation. If x
decreases to 0.8, the pyridine molecules are packed per-
pendicular to the channel axis in a single column, and the
framework is deformed in the breathing mode. In con-
trast, for the system [Ga(OH,F)(bdc)](pyridine)x, when x
changes from 1 to 0.85, the framework shows increased
breathing deformation but no twisting, although the
packing of the guest pyridine molecules changes drama-
tically.14 These observations suggest that both breath-
ing and twisting deformations should be considered in
studies of the adsorption of various molecules, especially
by computer simulations.
Conclusion
All of the six-ring guest molecules show a high degree of
ordering inside the channels of VO(bdc). The interactions
between the guests and the host framework are dominated by
van der Waals bonding; therefore, the packing of the guest
molecules adopts patterns that tend to maximize the van der
Waals contacts. The six-ring molecules are all packed in two
columns in each channel, either in herringbone or close to
parallel patterns. Such packing is not compatible with the
space group symmetry Pnma of the VO(bdc) framework, and
all of the phases have the noncentrosymmetric space group
P212121. The VO(bdc) framework deforms so that it closely
fits the shape and thickness changes of the double columns of
the guest molecules. In addition to the well studied breathing
deformation, the phases reported here show a much more
pronounced twisting deformation, associated with coopera-
tive rotations of the octahedral chains accompanied by bend-
ing of the bdc ligand.
Acknowledgment. We (X.W., L.L., A.J.J.) thank the R.
A. Welch Foundation (#E-0024), NHARP;Chemistry
003652-0092-2007, and NSF DMR-0706072 for support
of this work. One of us (J.E.) wishes to acknowledge
support from the Office of Energy Efficiency and Renew-
able Energy, U.S. DOE.
Supporting Information Available: Crystallographic informa-
tion files in CIF format. This material is available free of charge
via the Internet at http://pubs.acs.org.
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D. A.; Brown, C. M. J. Am. Chem. Soc. 2008, 130, 11813–11818.