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Volume 2 | Number 4 | 21 February 2012 | Pages 1191–1676
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Cite this: RSC Advances, 2012, 2, 1618–1631
PAPER
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Ab initio investigations on the crystal structure, formation enthalpy,
electronic structure, chemical bonding, and optical properties of
experimentally synthesized isoreticular metal–organic framework-10 and its
analogues: M-IRMOF-10 (M = Zn, Cd, Be, Mg, Ca, Sr and Ba){
Li-Ming Yang,*a Ponniah Ravindran,b Ponniah Vajeestonb and Mats Tilset*a
Received 20th May 2011, Accepted 31st October 2011
DOI: 10.1039/c1ra00187f
The equilibrium solid-state structure, electronic structure, formation enthalpy, chemical bonding, and
optical properties of IRMOF-10 and its alkaline earth metal analogues M-IRMOF-10 (M = Cd, Be,
Mg, Ca, Sr, Ba) have been investigated with density functional calculations. The unit cell volume and
atomic positions were fully optimized with the GGA functional. This supplements the incomplete
experimental structural parameters available for Zn-IRMOF-10. The calculated bulk moduli decrease
monotonically from Zn to Cd, and from Be to Ba, and indicate that Zn-IRMOF-10 and its analogues
are relatively soft materials. The estimated bandgap values are in the range 2.9 to 3.0 eV, indicating
nonmetallic character. Importantly, the bandgaps within the M-IRMOF-10 series (containing a
rather long 4,49-biphenyldicarboxylate linker) are smaller than those within the M-IRMOF-1 series
(shorter benzene dicarboxylate linker). The optical properties (dielectric function e(v), refractive
index n(v), absorption coefficient a(v), optical conductivity s(v), reflectivity R(v), and electron
energy-loss spectrum L(v)) of the M-IRMOF-10 series were computed. The observation of very small
reflectivities over a wide energy range suggests possible uses in hybrid solar cell applications. The
main characteristics of the optical properties are similar for the whole series although differences are
seen in the details. An analysis of chemical bonding in the M-IRMOF-10 series reveals as might be
anticipated that M–O bonds are largely ionic whereas C–O, C–H and C–C exhibit mainly covalent
interactions. The BOP values of M–O decrease through the series when going from Zn to Cd, and
from Be to Ba, i.e. the ionicity increases and the covalency decreases for the M–O bonds.
I. Introduction
MOFs constitute a rather new class of porous materials that are
considered for many applications, including catalysis, petrochemistry, gas adsorption and storage (e.g., H2, CH4, CO2, etc.),
selective separation, sensing, molecular recognition, and much
more.1 Within the huge MOF family of structures, the series of
isoreticular metal–organic frameworks (IRMOF-1–16), prepared
by Yaghi and coworkers,2–4 may have attracted most attention.
Systematic changes in linker size and linker functionalization
affects the adsorptive and diffusive properties of the material.
a
Center of Theoretical and Computational Chemistry, Department of
Chemistry, University of Oslo, P.O.Box 1033 Blindern, N-0315, Oslo,
Norway. E-mail: mats.tilset@kjemi.uio.no; l.m.yang@kjemi.uio.no;
Fax: +47 22855441
b
Center for Materials Science and Nanotechnology, Department of
Chemistry, University of Oslo, P.O.Box 1033, Blindern, N-0315, Oslo,
Norway
{ Electronic supplementary information (ESI) available: The calculated
charge density, charge transfer, and electron localization function (ELF)
plots, the total density of states (TDOS) and partial density of states
(PDOS), the optical properties and band structures for M-IRMOF-10
(M = Cd, Be, Mg, Ca, Sr and Ba). See DOI: 10.1039/c1ra00187f
1618 | RSC Adv., 2012, 2, 1618–1631
Interestingly, MOFs have been recently considered as suitable
preconcentrators for detection of explosive compounds,5 i.e.
detection at parts per trillion levels.6 In this respect, several
MOFs have shown effective selective preconcentration properties, i.e., IRMOF-1,7–10 IRMOF-3,8 IRMOF-8,11 and IRMOF10.8,12 A predictive understanding of the relationship between
MOF structure and its corresponding physicochemical properties will help match MOFs to a particular application. Optical
and electronic properties may be of relevance concerning the
suitability of MOFs to act as sensors when exposed to adsorbing
species. Currently, limited experimental or computational
techniques are used to establish structure/property relationships,
mostly on a case-by-case basis.
Compared to the ‘‘prototypical’’ IRMOF-1 (also known as
MOF-5) in which tetranuclear Zn clusters are linked by a
benzene-1,4-dicarboxylate unit, IRMOF-1013 with its longer
4,49-biphenyldicarboxylate linker has received much less attention concerning its physicochemical properties. IRMOF-10 was
first synthesized by Yaghi and coworkers.2–4,13 The higher
surface area and pore sizes of IRMOF-1014 is a key feature for its
use for gas absorption and separation and hydrogen storage.15–23
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Interestingly, exceptional negative thermal expansion has been
reported for Zn-IRMOF-10.24 Other than adsorption and separation properties, scarce attention has been paid to other properties
of IRMOF-10, e.g., structural stability, mechanical properties,
chemical bonding, optical properties, etc. Interestingly, even its
solid-state structure remains to be well characterized: The crystals
of Zn-IRMOF-10 were too small for collection of quality X-ray
intensity data and instead, the structure was assigned by a simple
simulation (see ref. 13, supplementary info p.70): The unit cell
constants and space group information of a related IRMOF-12
was used to build the IRMOF-10 structure. The simulated powder
diffraction pattern of the predicted structure was in reasonable, but
far from perfect, agreement with the measured PXRD patterns of
IRMOF-10 and IRMOF-12. Under such circumstances, structural
optimization based on computational calculations should be an
indispensable tool to determine and/or confirm the solid-state
structure since many experimentally determined MOF structures
are relatively coarse. In this respect, the contributions from MellotDraznieks and coworkers to predict structures by computational
tools are particularly noteworthy.25–32
Recent reports on MOFs as semiconductors33,34 have triggered intense research in this area and is a motivation for
studying their electronic and optical properties. The quantum
confinement of inorganic semiconductor entities (such as dots or
wires) in close contact with organic molecules makes the optical
properties of MOFs particularly interesting. To our knowledge,
there are until now no detailed theoretical reports on these
aspects of M-IRMOF-10 available.
Herein, we present a comprehensive computational study on the
solid-state structure, stability, electronic structure, formation
energy, chemical bonding, and mechanical properties of the
experimentally known Zn-IRMOF-10 using DFT calculations
with the GGA-PBE functional as implemented in the VASP
code.35,36 Moreover, analogues of Zn-IRMOF-10, i.e.,
M-IRMOF-10 with M = Cd, Be, Mg, Ca, Sr, and Ba are studied
systematically. The optical properties of this whole M-IRMOF-10
series were calculated using the CASTEP module37 of the Material
Studio 5.0 program.38 The acquired insight should be valuable for
future uses of the M-IRMOF-10 series of materials as photocatalysts, photoactive materials for photovoltaic cells, and
components for electroluminescence devices.
Computational details are provided in the following section.
The details of the results and discussions are then described,
including structural details, formation energies, electronic
structures, chemical bonding, calculated band structures, and
finally optical properties. In order to conveniently present the
comprehensive results in this work, we use the experimentally
synthesized, Zn-based IRMOF-10 as the main line for the
discussion and analysis for the whole series. Moreover, we
compare and discuss the analogues (i.e., M-IRMOF-10, with M
? Zn) with IRMOF-10 (M = Zn)39 and try to elucidate
systematic trends in the properties for the whole series. The
findings for M-IRMOF-10 will also be compared with data for
the M-IRMOF-1 analogues, recently published by us.40,41
II. Computational details
The Vienna ab initio simulation package (VASP)35,36 has been
used for the total-energy calculations to study the structural
This journal is ß The Royal Society of Chemistry 2012
stability and to establish equilibrium structural parameters. The
generalized gradient approximation (GGA)42–44 includes the
effects of local gradients in the charge density for each point in
the materials and generally gives better equilibrium structural
parameters than the local density approximation (LDA). Hence,
the GGA functional was used for all calculations. The projectoraugmented-wave (PAW)36,45 Perdew, Burke, and Ernzerhof
(PBE)44 pseudo-potentials based on GGA were used to describe
the ion-electron interactions. A criterion of 0.01 meV atom21
was placed on the self-consistent convergence of the total energy
and all calculations were made with plane-wave cutoff of 500 eV,
which guarantees that absolute energies are converged to within
a few meV/f.u. This has been tested to be accurate and reliable
for M-IRMOF-10 systems considered in the present study.
Brillouin-zone integration was performed with a Gaussian
broadening of 0.2 eV during all relaxations. The conjugatedgradient algorithm based on Hellmann-Feynman forces was used
to relax the ions into their instantaneous equilibrium positions.
The forces and the stress tensors were used to determine the
search directions to identify the ground state (i.e., the total
energy is not taken into account). This algorithm is very fast and
efficient when the initial structures are far away from the ground
state. Forces on the ions were calculated using the HellmannFeynman theorem as the partial derivatives of the free electronic
energy with respect to the atomic positions and adjusted using
the Harris-Foulkes correction to the forces. The atoms were
relaxed toward equilibrium until the Hellmann-Feynman forces
were less than 1023 eV Å21.
Because we deal with a rather large system (166 atoms per
primitive cell), the C-point alone is sufficient for sampling the
Brillouin zone during geometry optimization. However, in order
to arrive to an accurate band structure we have used a sufficient
number of k-points for the band structure calculations. The DOS
calculations were performed on the fully optimized structure
with only C-point alone. However, the DOS was calculated in a
fine energy grid (1801 points) due to the narrow band features so
as to visualize DOS correctly.
To gauge the bond strength and character of bonding, we have
analyzed bond overlap population (BOP) values with on the fly
pseudopotential estimated on the basis of the Mulliken population as implemented in the CASTEP code.37 In order to
understand the chemical bonding and interactions between
constituents in the M-IRMOF-10 series, charge density, charge
transfer, and electron localization function (ELF)46–49 analyses
were performed based on the results obtained from the VASP
calculations. We have also calculated the optical properties
including dielectric function, absorption coefficient, reflectivity,
refractive index, optical conductivity, and energy loss function
for the M-IRMOF-10 series with ultrasoft pseudopotential by
using the CASTEP code. In parallel with optical properties
calculations, we also calculated the band structure with ultrasoft
pseudopotential for the whole series with CASTEP, which will
provide some hints and useful information to understand the
electronic structures and optical properties of these materials.
The method used for the calculation of optical properties and
band structures has been proven to be reasonable and compared
favorably with corresponding experimental spectra in previous
contributions from our and other groups.40,41,50–60
RSC Adv., 2012, 2, 1618–1631 | 1619
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III. Results and discussions
A. Structural details
Zn-IRMOF-10 is a member of a series of IRMOFs with oxidecentered Zn4O tetrahedra as nodes linked by organic molecules
and can be synthesized based on the reticular synthesis strategy
proposed by Yaghi and coworkers.4,13,61 In Zn-IRMOF-10 the
organic linker is 4,49-biphenyldicarboxylate (4,49-BPDC).
Zn-IRMOF-10 can be obtained in highly crystalline form with
high specific surface areas of ca. 5000 m2 g21.14,62 Its crystal
structure has 664 atoms (eight formula units of Zn4O(BPDC)3)
in the conventional unit cell with cubic Fm3̄m symmetry (no.
225) and the reported lattice parameter is a = 34.281 Å.13 Its
primitive cell has 166 atoms, including two nodes and six linker
molecules, corresponding to two Zn4O(BPDC)3 formula units.
The computed solid-state structure of Zn-IRMOF-10 is illustrated in Fig. 1. The different crystallographic sites in ZnIRMOF-10 include one type of Zn, two types of O, five types of
C, and two types of H occupying 32f, 8c, 96k, 96k, 48g, 96k, 48g,
48g, 96k, and 96k Wyckoff positions, respectively. The
M-substituted analogues of Zn-IRMOF-10 are readily visualized
by the replacement of Zn+2 ions with M+2 metal ions (i.e., M =
Cd, Be, Mg, Ca, Sr, and Ba). It is assumed that they will have the
same space group and Wyckoff positions as Zn-IRMOF-10, and
the equilibrium structural parameters were estimated from
structural optimization accordingly.
B. Structural optimization of the M-IRMOF-10 series from totalenergy calculations
As commented in the Introduction, the crystals of Zn-IRMOF10 were too small for collection of quality X-ray intensity data
and hence Yaghi and coworkers obtained the structural data
from a simulated structure.13 When the simulated structure data
based on Yaghi’s reported atomic coordinates for Zn-IRMOF10 (p. 70 of Supplementary Information to ref. 13) were
imported in Materials Studio according to the given space
Fig. 1 The crystal structure of the M-IRMOF-10 (M = Zn, Cd, Be, Mg,
Ca, Sr, Ba) series in the cubic Fm3̄m symmetry (no. 225). The atoms with
labels M, O1, O2, C1, C2, C3, C4, C5, H1, and H2 are chemically distinct
sites and will be addressed in the discussion of the chemical bonding and
interpretation of the partial density of states (PDOS).
1620 | RSC Adv., 2012, 2, 1618–1631
group, additional H and C atoms were generated and it was
necessary to ‘‘merge’’ the extra and the original atoms, thus
slightly adjusting the positions, to produce a reasonable input
structure with the visualization tool in Materials Studio.38 The
computed ground-state structure was then obtained from this
input structure by full geometry optimization, i.e. the atom
positions and cell parameters were fully relaxed. This computationally fully optimized structure of Zn-IRMOF-10 then served
as the starting structure for the other M-IRMOF-10 structures
by replacement of the Zn atoms by Cd and the alkaline earth
metal atoms Be, Mg, Ca, Sr, and Ba before new structural
optimization are made.
The structural optimization was achieved by first relaxing the
atomic positions globally using the force-minimization technique, by keeping the lattice constant (a) and cell volume (V) fixed
to the crystallographically determined values. Then the theoretical ground-state volume was determined with optimized atomic
positions by varying the cell volume within ¡10% of the
experimentally determined volume. The calculated total energy
as a function of volume was fitted to the so-called equation of
state (EOS) to calculate the bulk modulus (B0) and its pressure
derivative (B0’). In order to cross-check the calculated B0 and B0’
values, the E–V data were fitted into three different EOS, i.e.
Murnaghan,63 Birch,64 and Universal equation of states
(UEOS).65 The bulk modulus and its pressure derivative (in
parentheses) obtained from the E–V curve using the UEOS are
9.09 GPa (3.12) for M = Zn, 8.30 GPa (2.36) for Cd, 11.49 GPa
(1.28) for Be, 8.74 GPa (7.00) for Mg, 7.32 GPa (3.64) for Ca,
6.57 GPa (9.31) for Sr, and 6.10 GPa (4.23) for Ba in the
M-IRMOF-10 series. The corresponding results derived from the
two other EOSs can be found in Table 1.
It is seen that the B0 and B0’ values estimated from three
different EOS derived from the E–V data are nearly identical,
indicative of the reliability of our results. Moreover, the bulk
moduli decrease monotonically when one moves from Zn to Cd,
and from Be to Ba. On the other hand, there is no clear trend in
their pressure derivatives within these two series, i.e. their
pressure derivatives change randomly. Interestingly, it is
consistently seen that for any given metal M, the values for the
bulk moduli for the M-IRMOF-10 series are 35–41% smaller
than for the recently studied40,41 M-IRMOF-1 series. These
smaller value of the bulk moduli are associated with the linker
lengths. As the compressibility of MOFs at low pressure is
mainly decided by these organic linkers, the longer size of the
linker in IRMOF-10 diminishes the repulsive interaction between
nodes during compression and hence its bulk modulus is
reduced. It may also be noted that the presently calculated B0
values of Zn-IRMOF-10 are larger than the value of 6.00 GPa66
previously obtained by DFTB calculations. The previous data
were calculated from the elastic constants which are obtained
from total energy change after application of a suitable strain.
There are no experimentally measured bulk modulus values
available yet for any of these compounds with which our results
may be compared, and we hope that the present study will
motivate experimentalists to study the mechanical properties of
the M-IRMOF-10 and M-IRMOF-1 series.
The optimized equilibrium atomic positions and lattice
parameters, along with the corresponding experimental values
for IRMOF-10, are listed in Table 2. The lattice parameter of
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Table 1 Optimized equilibrium lattice constant (a/Å), bulk modulus (B0 (GPa)), and its pressure derivative (B0’) for M-IRMOF-10 (M = Zn, Cd, Be,
Mg, Ca, Sr, Ba)
Material M-IRMOF-10
a/Åa
B0 (GPa)b
B0’b
Zn
Cd
Be
Mg
Ca
Sr
Ba
34.831 ,35.348. %34.280&
36.085
33.095
34.877
36.474
37.358
38.288
9.09
8.30
11.49
8.74
7.32
6.57
6.10
3.12
2.36
1.28
7.00
3.64
9.31
4.23
(9.08) [9.09] ,6.00.
(8.30) [8.30]
(11.49) [11.50]
(8.74) [8.74]
(7.32) [7.32]
(6.56) [6.57]
(6.10) [6.10]
(3.09)
(2.38)
(1.26)
(6.96)
(3.64)
(9.27)
(4.20)
[3.11]
[2.44]
[1.20]
[6.99]
[3.65]
[9.29]
[4.22]
a
Data in , . from ref. 66, experimental data in % & from ref. 13. b Data without brackets from Universal EOS; data in ( ) from Murnaghan
EOS; data in [ ] from Birch-Murnaghan 3rd-order EOS; data in , . from theoretical DFTB calculations in ref. 66.
IRMOF-10 in the present work (34.8312 Å) is in good agreement
with the experimental data (34.2807 Å)13 and also with the
available theoretical value obtained from DFTB calculations
(35.348 Å).66 Note that the magnitudes of previously reported
DFTB data are generally somewhat greater than the present
results, which will also be demonstrated in the following
discussion (see Table 3) of bond lengths and angles. The present
results are closer to the experimental data (which were not high
resolution ones, as already commented) than the previously
reported DFTB results.66 The lattice parameters for the whole
series are listed in Table 1. It can be seen that from Zn to Cd, and
from Be to Ba, the optimized equilibrium lattice constants
increase with the atomic number (i.e., aZn , aCd; aBe , aMg ,
aCa , aSr ,aBa) largely as a consequence of the increase in
atomic radii of the central metal atoms. The optimized bond
lengths and angles for the whole series, together with the
experimentally reported values for M = Zn, are listed in Table 3.
From Table 2, it may be noted that there are some
discrepancies in the structural parameters (which can be readily
understood given the fact that the experimental data were
obtained from a simulated structure, as briefly commented
already), but by and large the atomic coordinates of experimental and computational results agree quite well. The bond
lengths and bond angles between the constituents in M-IRMOF10 at the optimized equilibrium volume are given in Table 3. A
comparison of the optimized equilibrium bond lengths (Å) and
bond angles (u) for Zn-IRMOF-10 with the experimental data
reveals that the agreement between experiment and theory is
Table 2 Optimized equilibrium structural parameters for IRMOF-10
Details
PBE-GGA
Expta
Crystal system
Space group
Atoms/cell (fcc)
a/Å
V/Å3
Atom type
Zn1 (32f)
O1 (8c)
O2 (96k)
C1 (96k)
C2 (48g)
C3 (96k)
C4 (48g)
C5 (48g)
H1 (96k)
H2 (96k)
Cubic
Fm3̄m (225)
166
34.8312
42257.64
Atomic positions (x, y, z)
(0.2827, 0.2174, 0.2174)
(1/4, 1/4, 1/4)
(0.2731, 0.2269, 0.1624)
(0.2745, 0.2255, 0.0824)
(1/4, 1/4, 0.1029)
(0.2744, 0.2256, 0.0425)
(1/4, 1/4, 0.1458)
(1/4, 1/4, 0.0213)
(0.2936, 0.2064, 0.0982)
(0.2936, 0.2064, 0.9018)
Cubic
Fm3̄m (225)
166
34.2807
40285.53
a
(0.2828, 0.2172, 0.2172)
(1/4, 1/4, 1/4)
(0.2735, 0.2265, 0.1618)
(0.2747, 0.2253, 0.0822)
(1/4, 1/4, 0.1028)
(0.2747, 0.2248, 0.0413)
(1/4, 1/4, 0.1448)
(1/4, 1/4, 0.0206)
(0.2921, 0.2083, 0.0962)
(0.2916, 0.2073, 0.0275)
Experimental data from p.70 in Supplementary Information to ref. 13.
This journal is ß The Royal Society of Chemistry 2012
quite good for IRMOF-10 (Zn entries in Table 3). The
optimization nicely demonstrates how computations can be an
indispensable tool to resolve the details of solid-state structures
of complex systems when there are ambiguities or uncertainties
in experimentally available structure data. Computational
simulations have made dramatic advances in the past two
decades, and today, accurate prediction of structural properties
of novel molecules and exotic extended structures is possible. It is
therefore reasonable to suggest that poor-resolution experimental data on MOFs should be supplemented with computational
simulations and structure optimizations as a standard tool to
establish more reliably the detailed structures of new MOFs.
C. Energy of formation considerations
Information about formation enthalpies constitute an excellent
means to establish whether theoretically predicted phases are
likely to be stable and such data may serve as a guide to evaluate
possible synthesis routes. Several interesting reports have
appeared in the literature concerning computation of reaction
enthalpies by consideration of electric total energies, zero-point
energy vibrational correction, and thermal contribution (within
the harmonic approximation).67 Of course, kinetic factors can
also play a notable role during synthesis.68 Here, we are
primarily interested to know whether a particular hypothetical
compound is likely to be synthesizable or not on energetic
grounds. We believe that our approach, to be described below,
will give qualitatively sound trends in stabilities, although a
quantitatively accurate prediction of reaction enthalpies cannot
be expected. Further, for the estimation of the vibrational
entropy contribution to the total energy, phonon calculations
within the harmonic approximation should be performed. As the
number of atoms involved in the present calculations is very
large, such computationally intensive phonon calculations are
outside the scope of the present study. It should also be
mentioned that relative stability orders from reaction enthalpies
calculations usually refer to one material having different
structures (phases). Importantly, the IRMOF-10 material
synthesized by Yaghi and coworkers exists (at least so far) as
only one phase.13 This experimentally reported high symmetric
phase attracted much attention from both experiment and
theory. Here, we focused on the viability of synthesizing this
highly symmetric framework phase using alkaline-earth elements
instead of Zn in IRMOF-10. There are several ways to evaluate
the reaction energies; our approach of starting from the elements
is but one. An alternative approach might be to mimic the
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Table 3 Optimized bond lengths (Å) and bond angles (u) for M-IRMOF-1 (M = Zn, Cd, Be, Mg, Ca, Sr, and Ba) at their equilibrium volumes
M
C1–C2
C1–C3
C2–C4
C3–C5
C5–C5
C4–O2
C1–H1
C3–H2
M–O1
M–O2
O1–M–O2
O2–M–O2
Zn
1.402
(1.391)a
1.390
(1.402)
1.411
(1.403)
1.485
(1.413)
1.089
(0.960)
1.390
1.390
1.390
1.390
1.390
1.391
1.411
1.411
1.411
1.411
1.411
1.411
1.485
1.486
1.486
1.486
1.485
1.486
1.090
1.090
1.090
1.090
1.090
1.090
1.089
1.089
1.089
1.089
1.089
1.089
1.970
(1.946)
,2.074.
2.178
1.717
1.988
2.269
2.432
2.606
1.970
(1.953)
,2.088.
2.201
1.635
1.959
2.241
2.405
2.578
111.509
(111.988)
,107.000.
108.469
115.441
110.607
106.315
104.325
102.402
107.359
(106.842)
1.402
1.402
1.402
1.402
1.402
1.402
1.279
(1.280)
,1.319.
1.278
1.275
1.278
1.277
1.277
1.277
1.090
(0.960)
Cd
Be
Mg
Ca
Sr
Ba
1.493
(1.442)
,1.460.b
1.499
1.486
1.491
1.495
1.497
1.500
a
The experimental data in ( ) are from the structure made from the coordinates from the Supplementary Information in ref. 13.
, . are from ref. 66.
experimental synthesis conditions involving the reaction between
Zn4O(OH)6 and the dicarboxylic acid linker.66
In our case, we explore the thermodynamic feasibility of
assembling these M-IRMOF-10 materials from the elements
(eq 1). Thus, as part of this approach we have computed the total
energies for C (R-3m), O2 (P4/mmm), H2 (P4/mmm), Zn (P63/
mmc), Cd (P63/mmc), Be (P63/mmc), Mg (P63/mmc), Ca (Fm3̄m),
Sr (Fm3̄m), and Ba (Im-3m) in their ground state structures with
full geometry optimization. The reaction enthalpies for MOF
formation were calculated from the difference in the total energy
between the products and reactants involved in the reactions
concerned. We focus on the formation enthalpies of the
analogues (M-IRMOF-10, M = Cd, Be, Mg, Ca, Sr, Ba) relative
to the experimentally synthesized Zn-IRMOF-10. Through this
comparison, a general insight can be gained into the relative
stabilities for the whole series when different metals are
substituted into the nodes. The results establish unambiguously
that eqn 1 depicts exothermic reactions for the experimentally
synthesized Zn-IRMOF-10 as well as the analogous, yet
hypothetical, M-IRMOF-10 series.
8M + 13O2 + 84C + 24H2 A M8O26C84H48 (M-IRMOF-10,
M = Zn, Cd, Be, Mg, Ca, Sr, Ba)
(1)
The magnitudes of the calculated formation enthalpies given
in Table 4 (where data for the M-IRMOF-1 series are included
for comparison) show that (1) the stability of Cd-IRMOF-10 is
nearly the same as that of Zn-IRMOF-10, (2) the M-IRMOF-10
(M = Be, Mg, Ca, Sr and Ba) series is more stable than ZnIRMOF-10, and (3) the stabilities (ca. 250 kJ mol21) of the
M-IRMOF-10 (M = Be, Mg, Ca, Sr and Ba) compounds are
very similar since they have comparable formation enthalpies.
The magnitude of the calculated formation enthalpy for ZnIRMOF-10 (235.12 kJ mol21) is somewhat smaller than that for
Zn-IRMOF-1 (246.02 kJ mol21). Nevertheless, the value is
110.455
102.896
108.312
112.434
114.090
115.519
b
The data in
sufficiently large to render Zn-IRMOF-10 stable, which is of
course consistent with the fact that it is readily synthesized.13 For
the alkaline earth metal members of the M-IRMOF-10 series, the
formation enthalpies are consistently ca. 14–16 kJ mol21 less
negative than for the analogous M-IRMOF-1 member.
Nevertheless, the still rather large negative values for the
enthalpies of formation for the M-IRMOF-10 series suggest
that it might be possible to synthesize all these compounds as
stable phases. We eagerly await the experimental synthesis and
investigation of the properties of the predicted M-IRMOF-10
series of compounds.
D. Electronic structure
The data for Zn-IRMOF-10 will serve as a typical example of
electronic structure evaluation for the whole series. The total
electronic density of states (TDOS) and partial density of states
(PDOS) are displayed in separate figures for convenient
visualization and analysis. The TDOS and PDOS at the
equilibrium volume for Zn-IRMOF-10 are displayed in Fig. 2
and 3, respectively. The calculated band gap Eg for Zn-IRMOF10 is 2.925 eV, which is comparable to a recent DFTB
calculation that resulted in 3.07 eV,66 indicating nonmetallic
character. The calculated band gap of IRMOF-10 is substantially smaller than that of IRMOF-1 (MOF-5) at 3.5 eV.15 It
appears that it is the linker rather than the node that primarily
determines the band gap in IRMOF-1 vs. IRMOF-10: The
4,49-biphenyldicarboxylate linker in IRMOF-10 is longer than
the 1,4-benzenedicarboxylate linker in IRMOF-1. TDOS for the
remaining parts of the series will be discussed later.
Unfortunately, there are yet no experimental data on the band
gap value of Zn-IRMOF-10 reported in the literature with which
the calculations can be compared. It should be noted that DFT
calculated band gap values tend to be generally lower than
experimentally determined ones; such an underestimation of the
Table 4 Calculated enthalpies of formation (DH; kJ mol21) for the M-IRMOF-10 and M-IRMOF-1 (M = Cd, Be, Mg, Ca, Sr, Ba) compounds
M-IRMOF-10a
M
DH (kJ mol21)
Zn
235.12
Cd
231.25
Be
247.01
Mg
247.63
Ca
250.67
Sr
249.71
Ba
248.76
Zn
246.02
Cd
240.96
Be
261.69
Mg
262.53
Ca
266.56
Sr
265.34
Ba
264.12
M-IRMOF-1b
M
DH (kJ mol21)
a
This work, according to eqn 1.
b
From ref. 41, based on the analogous reaction to eqn 1.
1622 | RSC Adv., 2012, 2, 1618–1631
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Fig. 2 The calculated total density of states (TDOS) for Zn-IRMOF-10
in the cubic Fm3̄m symmetry (no. 225).
calculated band gaps is an intrinsic feature of the ab initio
method and is related to a DFT limitation in not taking into
account the discontinuity in the exchange–correlation potential.69 To overcome this discrepancy, the so-called scissor
operator,70 D, can be introduced, which effectively eliminates
the difference between the theoretical and experimental gap
values by means of a simple rigid shift of the unoccupied
conduction band with respect to the valence band. In line with
this, for Eg of bulk ZnO, the calculated band gaps are
significantly smaller than the experimental values. (LDA =
0.744/0.573 eV; GGA = 0.804/0.641 eV, LDA + U = 1.988/
1.486 eV, GW = 2.255/2.100 eV, experimental 3.455/3.300 eV for
ZnO–w/ZnO–z, respectively).71 In a recent contribution,40 we
found that the DFT calculations of MOF-5 unexpectedly gave a
band gap value in very good agreement with that obtained from
experimental studies.72,73 It may be of interest to extend this
study to other MOFs that are constructed from various organic
dicarboxylic acid linkers and the Zn4O nodes to understand
more about the role of linkers on the electronic structure and
optical properties of the materials. Metric parameters within the
Zn clusters of IRMOF-10 and MOF-5 closely match those of
bulk ZnO (Zn–O distances are 1.970 Å, 1.936 to 1.948 Å, and
1.974 to 1.983 Å, O–Zn–O angles are 107.366u to 111.502u,
107.7u to 111.2u and 108.3u to 110.7u in IRMOF-10, MOF-5 and
bulk ZnO, respectively). Though the bond distances and angles
are comparable between Zn-IRMOF-10 and ZnO, significant
differences in material properties may arise from the isolated
nature of the oxide nodes which are expected to act like quantum
dots, and also from the perturbation arising from the organic
linker BPDC.
Since the partial density of states (PDOS) is closely relevant to
the chemical bonding, the PDOS of IRMOF-10 (Fig. 3) will be
discussed in more detail in the following subsection dealing with
the characteristics of chemical bonding. The PDOS for the
remaining members (M = Cd, Be, Mg, Ca, Sr and Ba) in the
M-IRMOF-10 series can be found in Figures S7–S12 in the ESI.{
In general, the PDOS for each type of atoms (i.e., C, H and O; all
three types constitute the linker BPDC), except for the metal
atoms, are similar in each material within the series, with
essentially the same characteristic peaks and positions for each
This journal is ß The Royal Society of Chemistry 2012
Fig. 3 The calculated total density of states (TDOS) and partial density of
states (PDOS) for Zn-IRMOF-10 in the cubic Fm3̄m symmetry (no. 225).
type of atoms. Thus, we conclude that there are no discernible
differences between the linker properties in the different
materials within this series.
Figures S7–S12 in the ESI{ show that there are significant
differences in the PDOS when the transition metals (Zn and Cd)
are compared to main-group metals (Be to Ba). Within the maingroup metals, there are also differences, since some (e.g., Ca to
Ba) have d-electrons in the pseudopotential for the calculations,
whereas others (Be and Mg) only have s- and p-electrons.
Differently phrased, the d-states of Zn and Cd atoms are
dominantly contributed in the valence band, whereas both s- and
p-states of Be and Mg atoms are dominantly contributed in both
valence and conduction bands. For Ca, Sr, and Ba atoms, the
p-states are dominantly contributed in the valence bands, while
the d-states are dominantly contributed in the conduction bands.
In order to visualize the effect of changes in the metal ion on
the electronic structure, the total electronic density of states
(TDOS) at the equilibrium volume for the whole M-IRMOF-10
series of compounds is displayed in Fig. 4. The band gap (Eg)
values obtained from the TDOS curves in Fig. 4 are in the range
2.9 to 3.0 eV for all members of the M-IRMOF-10 series,
invariant of the metal. This indicates that all these materials are
nonmetals. The characteristic peaks of TDOS for all these
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Fig. 4 Calculated total density of states (TDOS) for M-IRMOF-10
series (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) in the equilibrium cubic structure
with Fm3̄m symmetry (no. 225).
compounds are quite similar, which implies that the calculated
band gaps within the M-IRMOF-10 series have a common
structural origin that is similar to Zn-IRMOF-10. From the
PDOS of IRMOF-10 in Fig. 3 and the PDOS of the remaining
parts of this series in Figures S7–S12 in the ESI{ we can infer the
origin of Eg for the whole series. It is essentially the p-states of
the C2, C3 and C5 atoms of the linker that determine the band
gap for the whole series. This is in agreement with the
conclusions concerning the PDOS above. Thus, it is the linker,
rather than the node, that determines the Eg in the M-IRMOF10 series. On this basis, it can also be appreciated that the greater
band gap values in the M-IRMOF-1 series, ca. 3.5 eV, is also
invariant to changes in the metal,41 and consistent with the idea
that it is the linker that determines the value of band gap in
isoreticular MOF series. In order to substantiate this finding we
are currently investigating the role of various linkers on band
gap changes in a series of MOF systems.
It is a quite interesting observation that the band gap is
unaffected by the metal replacement in the M-IRMOF-10 series.
This implies that the degree of localization or delocalization of
valence electrons of M(II) ions, or the changes in the bonding
interaction between M and O, will not significantly affect the
band gap value of the M-IRMOF-10 materials. However, a
different case was reported in a recent theoretical study where
1624 | RSC Adv., 2012, 2, 1618–1631
Choi et al. reported74 that it is possible to tune electronic band
gaps from semiconducting to metallic states by substitution of
Zn(II) ions in MOF-5 with Co(II) ions. Such differences in the
electronic properties by cation replacement can be understood as
follows. All the compounds in the M-IRMOF-10 series have the
same linkers and similar nodes. Although the alkaline earth
metals in this series have different atomic numbers and atomic or
ionic radii, they have the same valence shell electron configurations. The replacement of divalent Zn ions in IRMOF-10 with
divalent alkaline-earth metal ions gives similar electronic
structure and bonding behavior. The isoelectronic nature of
the compounds within this series and their isostructural
characteristics contribute to the similar TDOS patterns and the
very similar band gap values. In contrast, the transition metal
ion Co(II) is very different from the main group alkaline earth
metals, as this ion may have different bonding interactions with
the linker oxygen atoms than Zn(II) or the alkaline-earth ions;
this can contribute to the tuning process of the band gap of
MOF-5 and its Co congener. Moreover, Co(II) ions often exhibit
spontaneous magnetic ordering which will also contribute to
metallic behavior. As Co has a highly different valence electron
configuration compared with alkaline-earth metals, the 3d
electrons of Co should play an important role in the band gap
tuning process. Thus, the use of metal atoms with different
electron configurations allows the tuning of the electronic
structure of MOF-5 type materials.
As discussed above, the DFT calculated band gap Eg is
generally smaller than the experimental one, which can be
corrected by a scissor operator. In the following we will briefly
discuss and compare theoretical and experimental band gap
values for Zn-IRMOF-10, and make comparisons with the
calculated data for the hypothetical systems M-IRMOF-10 and
their corresponding bulk binary oxides (Table 5). As mentioned,
calculated band gap values for the M-IRMOF-10 systems are
almost constant, independent of the different cations. In
contrast, the experimental band gap values for the binary oxides
of the corresponding cations are quite different: In particular, the
binary oxides have much higher band gap values than the
corresponding M-IRMOF-10 series. Whereas the band gap
values of ZnO and MOF-5 are almost the same, there is not a
one-to-one correspondence between the band gap values of the
other IRMOFs and their respective binary oxides MO. This
suggests that the origin of band gap formation in MOFs is
different from that in binary oxides, which agrees with the above
conclusion that band gaps in the isoelectronic systems under
investigation originate from the linkers rather than from the
Table 5 Estimated band gap values (Theo. Eg) for the M-IRMOF-10
from CASTEP calculations. Experimental band gap values (Exp. Eg) for
IRMOF-1, ZnO, CdO, and alkaline earth metals oxides (MO)
Theo. Eg (eV)
M-IRMOF-10
Zn-IRMOF-10
Cd-IRMOF-10
Be-IRMOF-10
Mg-IRMOF-10
Ca-IRMOF-10
Sr-IRMOF-10
Ba-IRMOF-10
IRMOF-1 (MOF-5)
2.925
2.942
2.834
2.905
2.912
2.953
2.977
3.4–3.5
40
MO
ZnO-w/-z
CdO
BeO
MgO
CaO
SrO
BaO
Exp. Eg (eV)
71
3.455/3.300 71
2.16 ¡ 0.02 75
10.7 76
7.2 77
6.2 77
5.3 77
4.0 77
3.4–3.5 72,73
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metals. Importantly, if detailed information about the origin of
band gap in MOFs is desired, one should aim at understanding
the electronic structure and chemical bonding in MOFs in some
detail and it is therefore advisable to perform ab initio
calculations.
E. Characteristics of chemical bonding
i. From partial density of states. The distribution of various
electronic states in the valence band and the conduction band
can be characterized from the PDOS of Zn-IRMOF-10. The dand s-states of Zn and H atoms, respectively, contribute
dominantly in the valence band. Both s- and p-states of C and
O atoms also contribute to the VB. The p-states of neighbors (i.e.
C1 and C2, C2 and C4, C1 and C3, C3 and C5) are distributed
energetically in the same range and spatially distributed such as
to effectively overlap to form very strong covalent bonds. The
s-states of H1 and H2 can overlap with the p-states of C1 and C3,
respectively, to form covalent bonds. The p-state of C4 overlaps
with that of O2 to form a directional bond between them. The
d-states of Zn are well localized, and the Zn s electrons are
transferred to the neighboring atoms, leading to ionic Zn–O
bonding. Thus, the picture emerges—as might be anticipated—
that the linker acts as an entity that is covalently bonded
internally and linked to the Zn nodes by a largely ionic
interaction. This is consistent with the following analysis of
charge density and ELF.
An analysis of the PDOS in Figures S7–S12 in the ESI{ leads
to the same conclusion regarding the whole M-IRMOF-10 series.
The main difference in chemical bonding in the series arises from
the relative importance of ionic vs. covalent contributions to M–
O bonding: At the extremes, there is more covalent and less ionic
character in the Be–O bond compared with the Ba–O bond, even
though both bonds are dominated by the ionic components.
ii. From charge density/transfer, ELF and BOP analyses.
Charge density/transfer, ELF,46–49 and bond overlap population
(BOP)/Mulliken population analyses can shed further light on
the bonding situation. The charge density plots in Fig. 5a and
Figures S1a–S6a in the ESI{ show that the organic linker is a
molecule-like subunit with normal covalent C–C, C–H, and C–O
bonds. Charges are spherically distributed at the M and O sites,
characteristic for systems having ionic interactions; this is further
corroborated by the fact that there is no noticeable charge
density distributed between the M and O atoms.
The charge-transfer contour Dr is the self-consistent electron
density in a particular plane, rcomp, from which is subtracted the
electron density of the overlapping free atoms in the same lattice,
ratom, i.e., Dr(r) = rcomp 2 ratom, which allows the visualization
of how electrons are redistributed in a particular plane compared
to free atoms due to the bonding in the compound. Fig. 5b and
Figures S1b–S6b in the ESI{ show charge-transfer plots for all
M-IRMOF-10 species investigated. It is evident that electrons
are transferred from M to O sites, but not entirely in an isotropic
fashion. The anisotropic charge transfer from M to the O sites
indicates iono-covalent bonding between M and O with a
predominant ionic contribution. The nonspherical electron
distributions between neighboring C, H, and O atoms clearly
indicate strong covalent bonding. From Fig. 5c and Figures S1c–
This journal is ß The Royal Society of Chemistry 2012
Fig. 5 Calculated charge density (a), charge transfer (b), and electron
localization function (c) plots for IRMOF-10 in the (110) plane.
S6c in the ESI,{ it can be inferred that the large value of ELF at
the O site indicates strongly paired electrons with local bosonic
character. The negligibly small ELF between M and O, and the
small value of ELF at the M sites (partially due to the presence
of d electrons for the transition metals Zn and Cd) with
spherically symmetric distribution again indicate predominant
ionic bonding between M and O. The ELF distribution at the O
site is polarized towards the M atoms, indicating directional
bonding between M and O. A certain polarized character is
found in the ELF distribution at the H sites in the M-IRMOF-10
series, indicating polar covalent bonding. There is as expected a
maximum in the ELF between the covalently bonded C atoms
and between C and O atoms.
Bond overlap population (BOP) values were calculated on the
basis of a Mulliken population analysis.78 A high BOP value
indicates a strong covalent bond, while a low BOP value
indicates an ionic or nonbonding interaction. The calculated
BOP values for the M–O, C–O, C–C, and C–H bonds are
displayed in Table 6. BOP values for the M–O bonds in the
MOFs are in the range 0.26–0.29 for M = Zn, 0.22–0.23 for Cd,
0.36–0.37 for Be, 0.23 for Mg, 0.14–0.18 for Ca, 0.14–0.17 for Sr,
and 0.11–0.16 for Ba, respectively. The data suggest a
predominant ionic character to the M–O bonding, and the
extent of covalent character decreases down in a group (Zn–O .
Cd–O; Be–O . Mg–O . Ca–O . Sr–O . Ba–O. The high BOP
values for the C–H, C–C, and C–O bonds are consistent with
strong covalent bonds.
We have also calculated the Mulliken effective charges and
bond overlap populations of the corresponding oxides (MO)
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Table 6 Mulliken effective charge (MEC) and bond overlap populations (BOP) and Bader charges (BC) for M-IRMOF-10a
Table 6 (Continued)
Material
Atom site
MEC (e)
BOP
BC (e)
Ba–IRMOF–10
IRMOF-10
Zn
O1
O2
C1
+1.29
21.05
20.65
20.25
+1.3874
21.3197
21.7593
+0.0285
C2
C3
C4
C5
H1
H2
Cd
O1
O2
C1
20.06
20.26
+0.61
20.01
+0.28
+0.27
+1.27
21.02
20.66
20.25
C2
C3
C4
C5
H1
H2
Be
O1
O2
C1
20.06
20.26
+0.63
20.01
+0.28
+0.27
+1.14
20.96
20.63
20.26
C2
C3
C4
C5
H1
H2
Mg
O1
O2
C1
20.05
20.26
+0.60
20.01
+0.31
+0.27
+1.57
21.28
20.71
20.25
C2
C3
C4
C5
H1
H2
Ca
O1
O2
C1
20.07
20.26
+0.60
20.01
+0.28
+0.27
+1.35
21.15
20.70
20.26
C2
C3
C4
C5
H1
H2
Sr
O1
O2
C1
20.06
20.26
+0.65
20.01
+0.31
+0.27
+1.38
21.14
20.70
20.26
C2
C3
C4
C5
H1
H2
20.06
20.26
+0.64
20.01
+0.30
+0.27
0.26–0.29 (Zn–O)
0.26 (O1–Zn)
0.29 (O2–Zn)
1.08 (C1–C2)
1.12 (C1–C3)
0.85 (C2–C4)
1.09 (C3–C5)
0.90 (C4–O2)
0.91 (C5–C5)
0.89 (H1–C1)
0.91 (H2–C3)
0.22–0.23 (Cd–O)
0.22 (O1–Cd)
0.23 (O2–Cd)
1.08 (C1–C2)
1.12 (C1–C3)
0.84 (C2–C4)
1.09 (C3–C5)
0.90 (C4–O2)
0.91 (C5–C5)
0.89 (H1–C1)
0.91 (H2–C3)
0.36–0.37 (Be–O)
0.37 (O1–Be)
0.36 (O2–Be)
1.07 (C1–C2)
1.12 (C1–C3)
0.85 (C2–C4)
1.09 (C3–C5)
0.91 (C4–O2)
0.91 (C5–C5)
0.87 (H1–C1)
0.91 (H2–C3)
0.23 (Mg–O)
0.23 (O1–Mg)
0.23 (O2–Mg)
1.08 (C1–C2)
1.13 (C1–C3)
0.85 (C2–C4)
1.09 (C3–C5)
0.91 (C4–O2)
0.91 (C5–C5)
0.89 (H1–C1)
0.90 (H2–C3)
0.14–0.18 (Ca–O)
0.18 (O1–Ca)
0.14 (O2–Ca)
1.07 (C1–C2)
1.12 (C1–C3)
0.83 (C2–C4)
1.09 (C3–C5)
0.88 (C4–O2)
0.91 (C5–C5)
0.86 (H1–C1)
0.90 (H2–C3)
0.14–0.17 (Sr–O)
0.17 (O1–Sr)
0.14 (O2–Sr)
1.07 (C1–C2)
1.12 (C1–C3)
0.82 (C2–C4)
1.09 (C3–C5)
0.89 (C4–O2)
0.91 (C5–C5)
0.86 (H1–C1)
0.90 (H2–C3)
Cd–IRMOF–10
Be–IRMOF–10
Mg–IRMOF–10
Ca–IRMOF–10
Sr–IRMOF–10
1626 | RSC Adv., 2012, 2, 1618–1631
20.0773
+0.0033
+2.6528
+0.0478
+0.0574
+0.0059
+1.3186
21.2036
21.7435
+0.0411
20.0661
+0.0284
+2.6782
+0.0210
+0.0282
20.0100
+2.0000
22.0057
21.9083
20.0348
+0.0426
+0.0421
+2.6488
20.0817
+0.0803
+0.0164
+2.0000
22.0009
21.9081
+0.0358
20.0738
+0.0095
+2.6625
+0.0396
+0.0426
+0.0062
+1.6187
21.4976
21.8235
+0.0242
20.0336
+0.0308
+2.6887
20.0035
+0.0511
20.0232
+1.6184
21.4708
21.8229
+0.0267
20.0096
20.0154
+2.7104
20.0139
+0.0446
+0.0066
a
Ba
O1
O2
C1
+1.37
21.08
20.70
20.26
0.11–0.16 (Ba–O)
0.16 (O1–Ba)
0.11 (O2–Ba)
1.07 (C1–C2)
1.12 (C1–C3)
C2
20.06
0.82 (C2–C4)
C3
20.26
1.09 (C3–C5)
C4
+0.64
0.89 (C4–O2)
C5
20.01
0.91 (C5–C5)
H1
+0.30
0.86 (H1–C1)
H2
+0.27
0.90 (H2–C3)
The atomic numbering scheme is according to Fig. 1.
+1.6197
21.4326
21.8284
+0.0168
20.0548
+0.0342
+2.7269
20.0146
+0.0536
20.0256
with the same GGA-PBE functional as was used to calculate the
M-IRMOF-10 series. The M–O BOP values within MO are 1.13
(Zn), 1.02 (Cd), 1.44 (Be), 1.33 (Mg), 0.84 (Ca), 0.88 (Sr), and
0.75 (Ba). The MEC values for M in the MO oxides are 0.84
(Zn), 0.82 (Cd), 0.79 (Be), 0.97 (Mg), 1.04 (Ca), 0.97 (Sr), and
0.96 (Ba) |e|. Thus, the general trend of M–O BOP values and
MEC values of M within the MO oxides are similar for the whole
series. We conclude that our computational methods predict
quite well the general trend for the whole series.
In summary, the M–O bonds in the nodes of M-IRMOF-10
series have predominant ionic character similar to that present in
MO, whereas the C–H, C–O and C–C bonds in the linkers have
covalent interactions. The analyses based on charge density/
transfer, ELF, and bond overlap population (BOP)/Mulliken
population analyses give a consistent view of the bonding in the
M-IRMOF-10 series, and agrees with the situation in MOF-540
and the M-IRMOF-1 series,41 as recently described by us.
The calculated Mulliken charges (MEC) are reported in
Table 6. The MEC values are +0.27 to +0.31|e| for H, +1.29|e|
for M = Zn, +1.27|e| for Cd, +1.14|e| for Be, +1.57|e| for Mg,
+1.35|e| for Ca, +1.38|e| for Sr and +1.37|e| for Ba, respectively.
The C1 and C3 atoms connected to H1 and H2 bear negative
charges (20.28 to 20.31|e| and 20.27|e|, respectively). However,
the C2 (which bears the carboxylate group) and C5 (which
connects the phenyl rings in the linker) atoms bear nearly zero
charge (20.05 to 20.07|e| and 20.01|e|, respectively). The
carboxylate C atoms bear positive charges (+0.60 to +0.65|e|).
Finally, the oxygen atom in the M4O node has nearly a single
unit of negative charge (21.05|e| for M = Zn, 21.02|e| for Cd,
20.96 for Be, 21.28 for Mg, 21.15 for Ca, 21.14 for Sr, and
21.08 for Ba), which indicates that the four M atoms together
have transferred a charge corresponding to one electron to the
central O1. The O2 oxygen atoms in the BDC linker bear
negative charges (20.63 to 20.71|e|) indicating that there is
partial electron transfer from M to O2.
iii. Bader topological analysis. Although there is no unique
definition to identify how many electrons are associated with an
atom in a molecule or an atomic group in a solid, it has
nevertheless proved useful in many cases to perform Bader
topological analyses.79–81 In the Bader charge (BC) analysis,
each atom of a compound is surrounded by a surface (called a
Bader region) that runs through minima of the charge density,
and the total charge of an atom is determined by integration of
electrons within the Bader region. The calculated Bader charges
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for the M-IRMOF-10 series are given in Table 6. The BC for M
and O (includes O1 and O2) in the M-IRMOF-10 series
compounds indicate that the interaction between M and O is
almost ionic, as nearly two electrons (+1.39|e| for M = Zn,
+1.32|e| for Cd, +2.00|e| for Be, +2.00|e| for Mg, +1.62|e| for Ca,
+1.62|e| for Sr, and +1.62|e| for Ba) are transferred from M to O.
This finding is consistent with the DOS and charge density
analyses. Within the M4O units, M donates 1.32 to 2.00
electrons, which is slightly smaller than that in a pure ionic
picture. The trend is associated with the noticeable covalency
present between M and O as demonstrated by the ELF and BOP
analyses, discussed above. The results from the BC analysis are
fully consistent with the charge density, charge transfer, ELF,
MEC, and PDOS analyses.
F. Band structure and optical properties
The recent report on the semiconducting behavior of MOFs34
has triggered intense research in this area including the synthesis
and characterization of various semiconducting MOFs with the
aim to develop new materials for optoelectronic applications.
The optical properties for M-IRMOF-10 are here of interest, for
example in view of potential uses of this material in hybrid solar
cell applications as an active material or in the buffer layer
between the electrodes and inorganic active materials. Studies of
optical properties of MOFs will also be of fundamental
importance, since these properties not only depend on the
occupied and unoccupied parts of the electronic structure, but
also carry information about the character of the bands. Insight
into the excited-state electronic properties of M-IRMOF-10 may
also be important for certain applications. It may be noted that
the moisture sensitivity of Zn-IRMOF-10 presents obstacles to
many practical uses of this material.
The central quantity of the optical properties is the dielectric
function e(v), which describes the features of linear response of the
system to electromagnetic radiation, which again governs the
propagation behavior of radiation in the medium. Here e(v) is
connected to the interaction of photons with electrons. Its
imaginary part e2(v) can be derived from interband optical
transitions between the occupied and unoccupied bands including
appropriate momentum matrix elements to take care of the
selection rules, and its real part e1(v) can be derived from e2(v) by
the Kramer-Kronig relationship.50 The real part of e(v) in the limit
of zero energy (or infinite wavelength) is equal to the square of the
refractive index n(v). All the frequency dependent linear optical
properties, such as refractive index n(v), absorption coefficient
a(v), optical conductivity s(v), reflectivity R(v), and electron
energy-loss spectrum L(v) can be deduced from e1(v) and e2(v).
We have conducted CASTEP calculations to estimate the
optical properties of the whole M-IRMOF-10 series (M = Zn,
Cd, Be, Mg, Ca, Sr and Ba), and the results from the optical
calculations for Zn-IRMOF-10 are shown in Fig. 6. The
calculated optical properties of the remaining members of the
series can be found in Figures S13–S18 in the ESI.{ For the
convenience of our discussion, we focus on the properties of ZnIRMOF-10 as a representative case before a comparison is made
within this series.
There are three main peaks in the e2(v) plot (Fig. 6a) of ZnIRMOF-10, located at ca. 4.51, 6.52, and 15.13 eV, the latter
This journal is ß The Royal Society of Chemistry 2012
accompanied by broad shoulders. Figures S13a–S18a in the ESI{
show that characteristic peaks and positions are similar for each
material in the series. The real part of dielectric function, e1(v)
(Fig. 6a and Figures S13a–S18a in ESI{) allows the estimation
the value of the refractive index n(v) at infinite wavelength or
zero energy (i.e., n(0)) at about 1.1651 (Zn), 1.1537 (Cd), 1.1827
(Be), 1.1580 (Mg), 1.1442 (Ca), 1.1373 (Sr), and 1.1318 (Ba).
Thus, n(0) is rather constant in the range 1.13 to 1.18 for the
whole series. At low frequency (0—2.95 eV), the imaginary part
e2(v) is zero below the band gap, which is consistent with the
order of band gaps for the M-IRMOF-10 series.
The reflectivity spectrum (Fig. 6b) of Zn-IRMOF-10 shows
sharp peaks at 4.17, 6.37, and 15.29 eV, the latter accompanied
by shoulders. The two low-frequency peaks mainly arise from
Zn(3d) A C/O(2p) as well as H(1s) A C/O(2p) interband
transitions. A similar situation pertains to the reflectivity curves
for M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba), Fig. S13b–
S18b in the ESI.{ Here, the two sharp low-frequency peaks
mainly arise from the transitions Cd(3d) A C/O(2p) and H(1s)
A C/O(2p) for M = Cd; Be(2s,2p) A C/O(2p) and H(1s) A C/
O(2p) for Be; Mg(3s,3p) A C/O(2p) and H(1s) A C/O(2p) for
Mg; Ca(4p,4d) A C/O(2p) and H(1s) A C/O(2p) for Ca;
Sr(5p,5d) A C/O(2p) and H(1s) A C/O(2p) for Sr; and
Ba(6p,6d) A C/O(2p) and H(1s) A C/O(2p) for Ba. The
reflectivity approaches zero when the energy exceeds 30 eV for
the whole series. The values of reflectivity at infinite wavelength
are 0.005730 (Zn), 0.005015 (Cd), 0.007016 (Be), 0.005332 (Mg),
0.004523 (Ca), 0.004098 (Sr), and 0.003751 (Ba). Thus, passing
from Zn to Cd, and from Be to Ba, the reflectivity consistently
decreases. One general finding here is that the calculated
reflectivity in the whole frequency range is much smaller than
that in typical inorganic solids. This was also seen for
M-IRMOF-1,40,41 and this may prove to be an important
advantage if MOFs are to be used in optoelectronic devices (such
as solar cells and LEDs) where low reflectivity is desired.
Zn-IRMOF-10 has a finite value of the refractive index n(v)
(Fig. 6c) in the range 2.95 to 30 eV. The extinction coefficient
k(v) (the imaginary part of the complex refractive index) shows
three peaks at 4.57, 6.63, and 15.24 eV, the latter with broad
shoulders. The refractive indexes n(v) for M-IRMOF-10 (M =
Cd, Be, Mg, Ca, Sr and Ba) are depicted in Figures S13c–S18c in
the ESI.{ Similar characteristics are seen for the whole series.
The refractive index n(v) at infinite wavelength (i.e., n(0)) has
already been commented in the dielectric function e(v)
paragraph.
The optical conductivity s(v) plot of Zn-IRMOF-10 is shown
in Fig. 6d. The real part of the complex conductivity has its three
main three sharp peaks at 4.57, 6.63, and 15.17 eV. The optical
conductivity s(v) plots of M-IRMOF-10 (M = Cd, Be, Mg, Ca,
Sr and Ba) are depicted in Figures S13d–S18d in the ESI;{ the
characteristics of the main peaks are similar throughout the
whole series.
The electron energy-loss function L(v) (Fig. 6e) is an
important optical parameter describing the energy loss of a fast
electron traversing in a certain material. The peaks in the L(v)
spectra represent the characteristics associated with the plasma
resonance and the corresponding frequency is the so-called
plasma frequency above which the material is a dielectric [e1(v)
. 0] and below which the material behaves like a metallic
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Fig. 6 Calculated optical properties for Zn-IRMOF-10: (a) dielectric function e(v), (b) reflectivity R(v), (c) refractive index n(v); extinction
coefficient k(v), (d) optical conductivity s(v), (e) energy loss function L(v), and (f) absorption a(v).
compound in some sense [e1(v) , 0]. In addition, the peaks of
the L(v) spectra overlap the trailing edges in the reflection
spectra. The peak of L(v) of Zn-IRMOF-10 at 6.93 eV
corresponds to the reduction of R(v). There are five plasma
frequencies at ca. 4.74, 6.93, 8.68, 15.70, and 17.29 eV. In Figures
S13e–S18e in the ESI,{ it is seen that the characteristic main
peaks of M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba) are
quite similar except that the two broad peaks with the strongest
1628 | RSC Adv., 2012, 2, 1618–1631
intensities for Zn, Cd, Be, Mg (at ca. 15.70 and 17.29 eV for M =
Zn) have the appearance of a single sharp peak for Ca, Sr, and
Ba.
Zn-IRMOF-10 has an absorption band (Fig. 6f) ranging from
2.95 to 30 eV, which exhibits three sharp peaks at around 4.63,
6.74, and 15.29 eV. The characteristics of the main peaks are
similar for M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba;
Figures S13f–S18f in the ESI){. The main differences arise from
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the appearance of an additional peak at ca. 25.0–28.0 eV for M =
Ca, Sr and Ba, which is absent for M = Zn, Cd, Be, and Mg.
The calculated optical properties of M-IRMOF-10 series in
this work are similar to that of M-IRMOF-1 in our recent
contributions,40,41 which is consistent with the fact that the
M-IRMOF-10 and M-IRMOF-1 series have similar topological
structures, with common nodes and closely related linkers.
In conjunction with the optical properties calculations we have
also computed the band structures of the whole M-IRMOF-10
(M = Zn, Cd, Be, Mg, Ca, Sr and Ba) series. The calculated band
structure for Zn-IRMOF-10 is shown in Fig. 7. The band
structures of the remaining members of the series are displayed in
Figures S19–S24 in the ESI.{ For the high symmetry directions
in the Brillouin zone sampling, CASTEP automatically chose the
W–L–C–X–W–K path for the face-centered cubic (fcc) symmetry
Brillouin zone of M-IRMOF-10 series. From Fig. 7 and Fig.
S19–S24 it is apparent that the band gap for the whole series is
essentially constant at ca. 2.9–3.0 eV, independent of the central
metal atoms in the framework nodes. The bands in the valence
band as well as in the conduction band are almost parallel and
Fig. 7 The electronic band structure of Zn-IRMOF-10. The Fermi level
is set to zero and placed in the valence band maximum.
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dispersionless. The bands at the VB maximum and CB minimum
for Zn-IRMOF-10 are very flat, which is also the case for the
other members of the series. This appears to be a common
feature for MOF materials.11,82 This flat band behavior makes it
impossible to unequivocally identify whether the band gap is
direct or indirect. However, we still can gain some qualitative
information from the band structures that helps to understand
the electronic structures of MOF materials and provides further
insight into their optical properties. We look forward to future
experimental determination of band structures of the
M-IRMOF-10 series, so that experiment and theory can be
reconciled.
IV. Conclusions
We have presented a detailed investigation on the electronic
structure, chemical bonding behavior, ground-state properties,
and optical properties of the whole M-IRMOF-10 (M = Zn, Cd,
Be, Mg, Ca, Sr and Ba) series using first-principles methods. The
following important conclusions are obtained:
(1) The calculations show that each material in the
M-IRMOF-10 series is soft and ‘‘formed’’ in the high symmetric
face-centered cubic (Fm3̄m, 225) crystal structure; it is demonstrated that computational simulations nicely complement
experiments to accurately determine the equilibrium structural
parameters for complicated MOFs systems.
(2) The large negative formation enthalpy of IRMOF-10 is
consistent with the fact that it has already been synthesized by
experiments. The prediction of a series of hypothetical materials
M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba) with large
negative formation enthalpy hopefully will inspire and guide
synthetic efforts in this direction.
(3) Electronic charge density, charge transfer, ELF, MEC and
BOP analyses shed light on the nature of the M–O, C–O, C–H,
and C–C bonding. The analyses consistently support the notion
that the bonding interaction between M–O is mainly an ionic
interaction, whereas those between C–O, C–H, and C–C are
normal covalent interactions. The ionicity of the M–O bonds
decreases and the covalency increases when passing from Zn to
Cd, and from Be to Ba.
(4) Electronic density of states and band structures study show
that the band gap for the whole M-IRMOF-10 series is ca. 2.9–
3.0 eV, resulting in a nonmetallic character. Until now, there are
no experimental studies available to verify our results, but we
hope to motivate experimentalists to measure the band gap of
this series. Importantly, the band gap of the M-IRMOF-10 series
at 2.9–3.0 eV is independent of the identity of the metal in this
isoelectronic series of structures. Furthermore, the band gap is
substantially lower than the 3.5 eV value found for the analogous
M-IRMOF-1 series. Thus, a systematic variation of the linker
may allow the fine-tuning of band gap values in a given MOF
family. This should influence research in this area and facilitate
the synthesis of semiconducting MOFs with appropriate band
gap values for materials applications in for optoelectronic
devices.
(5) The calculated optical properties of M-IRMOF-10 series
provide useful information for future experimental exploration.
Overall, the peak intensities of the calculated optical spectra for
the M-IRMOF-10 systems are around 30% higher (especially the
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reflectivity and absorption coefficient) than for M-IRMOF-1.
This is associated with the introduction of an additional benzene
structural sub-unit in the M-IRMOF-10 system. However, the
peak positions and distributions are almost the same for both
classes. The observation of very low reflectivity over a wide
energy range show that these materials may have potential uses
in hybrid solar cell applications as an active material or in the
buffer layer between the electrodes and inorganic active
materials. Moreover, potential applications may be found in
organic semiconducting devices such as field-effect transistors,
solar cells, and organic light-emitting devices (OLEDs).
Acknowledgements
We gratefully acknowledge the Research Council of Norway for
financial support and for the computer time at the Norwegian
supercomputer facilities.
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