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Formation of an intermediate band in isoreticular metal–organic framework993 (IRMOF-993) and metal-substituted analogues M-IRMOF-993†
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Published on 12 July 2012 on http://pubs.rsc.org | doi:10.1039/C2JM31360J
Li-Ming Yang,*a Ponniah Ravindran,b Ponniah Vajeestonb and Mats Tilset*a
Received 5th March 2012, Accepted 20th June 2012
DOI: 10.1039/c2jm31360j
Intermediate band (IB) materials are attractive for multiple photon harvesting in solar cells thus
increasing their efficiency beyond the Shockley–Quassier limit. However, it has so far been
demonstrated that this can only be achieved in a few inorganic solids by appropriate doping. Here we
demonstrate that it may be possible to achieve intermediate band materials with the isoreticular metal–
organic framework IRMOF-993 and metal-substituted analogues. The equilibrium crystal structures,
electronic structures, formation enthalpies, chemical bonding, and optical properties of M-IRMOF993 (M ¼ Zn, Cd, Be, Mg, Ca, Sr, Ba) were systematically investigated using density functional theory
methods. The unit cell volume and atomic positions were optimized with the Perdew–Burke–Ernzerhof
(PBE) functional; there was good agreement between the current theoretical equilibrium structural
parameters and previously reported structural data for Zn-IRMOF-993. The calculated bulk moduli
indicate that Zn-IRMOF-993 and its analogues are soft materials. The estimated fundamental bandgap
values from the electronic structure studies for the whole series are ca. 3.5–3.6 eV, indicating a
semiconducting character. The bandgap values estimated from the bottom of the IB to the top of VB
are ca. 1.5–1.6 eV, and those from the top of IB to the bottom of CB are ca. 2.0 eV, suggesting that these
materials may be suitable for enhancing the efficiency of solar cells. As MOFs are considered as
potential materials for photocatalysts, active components in hybrid solar cells, electroluminescence
cells, organic semiconducting devices such as field-effect transistors, and organic light-emitting devices,
the optical properties and chemical bonding of M-IRMOF-993 were also systematically investigated.
I.
Introduction
The porous hybrids known as metal–organic frameworks
(MOFs)1,2 take advantage of the properties of both organic and
inorganic porous materials, and have been recognized as a new
generation of advanced materials. MOFs have received much
attention due to potential applications as materials for gas
storage, gas/vapor separation, catalysis, luminescence, and drug
delivery. Thus, MOFs currently have a huge impact on developments in chemistry, physics, materials science, engineering,
and more.1,2
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, electron localization function (ELF)
plots, the total density of states (TDOS) as well as partial density of
states (PDOS), the band structures and optical properties of
M-IRMOF-993 (M ¼ Cd, Be, Mg, Ca, Sr, Ba). See DOI:
10.1039/c2jm31360j
16324 | J. Mater. Chem., 2012, 22, 16324–16335
In materials science, the concept of intermediate band (IB)
materials3 has received considerable attention. Materials with an
isolated, partially filled intermediate band are of great interest for
harvesting of multiple photons from the solar spectrum and thus
one can go beyond the Shockley–Quasier limit to improve the
efficiency of solar cells. This IB feature has been identified in a
few wide bandgap materials with specific dopants, as seen in
selected theoretical and experimental papers that have been
devoted to exploring intermediate band materials.4–24 The IB
materials are usually formed by introducing an impurity band
between the usual semiconductor valence band (VB) and the
conduction band (CB) in wide bandgap materials. This allows an
electron to be excited from the VB to the IB, and from the IB to
the CB, upon absorption of photons with energy below Eg,
achieving the same total result as with one photon of energy Eg.
Thus, photon energies lower than the Eg can be converted into
electrical energy by using IB materials. Hence, these IB materials
can be used to achieve higher PV efficiencies than those offered
by regular absorbing semiconductors.3
Usually, the search for IB materials has been conducted only
within the traditional semiconductors, especially focused on wide
bandgap semiconductors with transition metal doping. In this
contribution, we predict computationally that IB features are
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possible within the isoreticular MOF structures introduced by
Yaghi and coworkers.25,26 Specifically, the M-IRMOF-993
materials, where M ¼ Zn (as in the original IRMOF-993), Cd,
Be, Mg, Ca, Sr, and Ba, have been investigated via a detailed
DFT computational study through analysis of their solid-state
structures, structural stabilities, electronic structures, chemical
bonding, mechanical, and optical properties using the GGA–
PBE functional as implemented in the VASP code.27–30 The
optical properties were calculated using the CASTEP module31
of the Materials Studio 5.0 program.32 The central feature of this
contribution is the detailed investigation of the electronic structures, and especially the IB and its role in the optical properties
for the M-IRMOF-993 series.
II. Computational details
The Vienna Ab initio Simulation Package (VASP)27–30 was used
for the total-energy calculations to study the structural stability
and to establish equilibrium structural parameters. The calculations were carried out for the primitive cell including all the
crystal symmetries using the periodic DFT code. The generalized
gradient approximation (GGA)33–35 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 projector-augmented-wave
(PAW)36,37 and Perdew, Burke, and Ernzerhof (PBE)35 pseudopotentials were used to describe the ion–electron interactions. A
criterion of 0.01 meV atom1 was placed on the self-consistent
convergence of the total energy, and all calculations were made
with the plane-wave cutoff of 500 eV, which guarantees that
absolute energies are converged to within a few meV per f.u. This
has been tested to be accurate and reliable for our Zn-IRMOF993 system. Brillouin-zone integration was performed with a
Gaussian broadening of 0.2 eV during all relaxations. The
conjugated-gradient algorithm based on Hellmann–Feynman
forces was used to relax the ions into their instantaneous equilibrium positions. The forces and the stress tensor were used to
determine the search directions for locating 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
Hellmann–Feynman 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–
1.
Feynman forces were less than 103 eV A
Because we deal with a rather large system (178 atoms per
primitive cell), the G-point alone was sufficient for sampling the
Brillouin zone during geometry optimization. The DOS calculation was performed on the fully optimized structure.
To gauge the bond strength and character of bonding, bond
overlap population (BOP) values were estimated on the basis of
the Mulliken population as implemented in the CASTEP code.31
Furthermore, charge density, charge transfer, and electron
localization function (ELF)38–41 analyses were also performed.
The optical properties including dielectric function, absorption
coefficient, reflectivity, refractive index, optical conductivity, and
energy loss function for the M-IRMOF-993 series were
This journal is ª The Royal Society of Chemistry 2012
calculated using the CASTEP code. The method used for the
calculation of optical properties has been proven to be reasonable and compared favorably with corresponding experimental
spectra in a series of previous papers from our and other
groups.42–52 The use of computational methods to optimize and
predict MOF structures and evaluate their various properties has
recently become an important supplement to experimental
approaches.53–60
III.
A.
Results and discussions
Structural details
Zn-IRMOF-993 belongs to a member of isoreticular metal–
organic frameworks (IRMOFs) series with oxide-centered Zn4O
tetrahedra as nodes linked by organic dicarboxylates.61 The
structure of Zn-IRMOF-993 may be viewed as being constructed
from discrete semiconductor Zn4O13 quantum dots stabilized
and interconnected by anthracene-9,10-dicarboxylate (ADC)
linkers.
The conventional cell of the Zn-IRMOF-993 crystal structure
has 712 atoms with cubic Fm
3m symmetry (no. 225) and
contains eight formula units of Zn4O(ADC)3. Its primitive cell
has 178 atoms, including two nodes and six linker molecules,
corresponding to two Zn4O(ADC)3 formula units. The solidstate structure of Zn-IRMOF-993 is illustrated in Fig. 1.
Different crystallographic sites in Zn-IRMOF-993 include one
type of Zn, two types of O, five types of C, and two types of H
occupying 32f, 96k, 8c, 96k, 96k, 48g, 48g, 96k, 96k, and 96k
Wyckoff positions, respectively. The M-substituted analogues of
Zn-IRMOF-993 conceptually arise by replacing the Zn ions with
the other divalent main-group metal ions (M ¼ Cd, Be, Mg, Ca,
Sr, Ba). In the present study it is assumed that all these
compounds belong to the same space group and have the same
Wyckoff positions as Zn-IRMOF-993. The equilibrium structural parameters are estimated from structural optimizations
accordingly.
Fig. 1 The crystal structure of M-IRMOF-993 in the cubic Fm3m
symmetry (no. 225). Following the symmetry of this space group, the
different atoms have labels M (Zn, Cd, Be, Mg, Ca, Sr, Ba), O1, O2, C1,
C2, C3, C4, C5, H1, and H2 for the interpretation and understanding of
partial density of states (PDOS) in the following Electronic structure
section.
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B. Structural optimization of M-IRMOF-993 from totalenergy calculation
The input Zn-IRMOF-993 structure was constructed by replacing the BDC (1,4-benzenedicarboxylate) linker of MOF-5 with
ADC (anthracene-9,10-dicarboxylate) while at the same time
keeping the space group and skeleton unchanged, using visualization tools in Materials Studio to generate the starting geometry
for the structural optimization. The theoretical ground-state
structure was obtained from this by full geometry optimization,
i.e. the atom position and cell parameters were fully relaxed. The
fully optimized structure of Zn-IRMOF-993 was then used as the
starting structures for the analogous M-IRMOF-993 via substitution of the Zn atom with Cd and alkaline earth metals, and
subsequent full structural relaxations were then made.
This 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 experimental
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 (B00 ). In order to cross-check the
calculated B0 and B00 values, the E–V data were fitted into three
different EOS, i.e. Murnaghan,62 Birch-Murnaghan,63 and
Universal equation of states.64 The B0 and B00 (in parentheses)
for Zn-IRMOF-993 are 15.85 GPa (6.34), 15.87 GPa (6.45), and
15.87 GPa (6.44) from the above three EOSs, respectively. This
B0 value is much larger than the value of 3.60 GPa (ref. 65) that
was determined using the elastic constants obtained from DFTB
calculations by estimating the total energy change after application of a suitable strain. Note that the B0 of MOF-5 obtained
from the DFTB calculation (8.70 GPa)65 was also found to be
much smaller than that from the present type of calculation
(15.37 GPa), as previously reported by us.66 Our calculated bulk
modulus of MOF-5 is slightly lower than the value of 18.5 GPa
obtained previously by fitting the total energy from VASP
calculations to a cubic polynomial,67 indicating the reliability of
this approach. Thus, we applied the same methodology as in our
recent MOF-5 study66 to obtain the bulk moduli of M-IRMOF993. There are presently no experimental data of B0 available for
Zn-IRMOF-993 for calibration of the data.
For the remaining compounds in the M-IRMOF-993 series,
the B0 and B00 values obtained from the E–V curve using the
UEOS are 12.63 GPa (5.71) for M ¼ Cd, 20.45 GPa (3.22) for Be,
15.15 GPa (3.73) for Mg, 12.11 GPa (2.01) for Ca, 10.58 GPa
(3.03) for Sr, and 9.11 GPa (3.72) for Ba, respectively. The data
derived using the two other EOSs are listed in Table 1. The B0
and B00 values estimated from three different EOS are essentially
identical. Moreover, the B0 values decrease monotonically when
one moves from Zn to Cd, and from Be to Ba, and there appears
to be no systematic change in the B00 values within these series.
For comparison, our calculated B0 value for MOF-5 is 15.37
GPa using either of the three EOSs.66 The bulk moduli for some
members (M ¼ Cd, Ca, Sr, Ba) of the M-IRMOF-993 series are
smaller than that of MOF-5, whereas for M ¼ Be, B0 is greater
than that of MOF-5, and for M ¼ Mg, B0 is nearly identical to
that of MOF-5. The metal dependency may be understood in
light of the systematic changes in the equilibrium volumes (Vo) in
the M-IRMOF-993 series, i.e. the system with the higher value of
Vo has the smaller B0. It has also been shown that B0 depends
significantly on the length of the linker.66,68,69 In general, a longer
linker gives a mechanically less resistant system, thus smaller B0.
However, the lengths of the linkers in the skeleton of MOF-5 and
the M-IRMOF-993 series are similar and hence the slight
differences arise from the different metal atoms in the nodes.
The linkage between the Zn4O group and the organic moieties
results in rather soft materials with relatively small bulk moduli
compared with that of ZnO in the cubic diamond (theo. 441–
457 GPa;70 expt. 443 GPa (ref. 71)), wurtzite (theo. 160 GPa;72
expt. 183 GPa (ref. 73 and 74)), zincblende (theo. 156.8 GPa
(ref. 75)) and rocksalt (theo. 190.3 GPa;75 expt. 194–288 GPa
(ref. 74)) structures. The calculated value of B0 indicates that
Zn-IRMOF-993 is a readily compressible system like the
bulk modulus (B0 (GPa)), and its pressure derivative (B00 ) for M-IRMOF-993 (M ¼ Zn, Cd, Be,
Table 1 Optimized equilibrium lattice constant (a (A)),
Mg, Ca, Sr, Ba)c
Material
Zn-IRMOF-993
Cd-IRMOF-993
Be-IRMOF-993
Mg-IRMOF-993
Ca-IRMOF-993
Sr-IRMOF-993
Ba-IRMOF-993
ZnO
CdO
BeO
MgO
CaO
SrO
BaO
a
a (A)
B0 (GPa)b
B00 b
26.674 h26.926i
27.934
24.938
26.702
28.306
29.189
30.130
15.87 (15.85) [15.87] h3.60i
12.63 (12.62) [12.62]
20.45 (20.44) [20.45]
15.15 (15.14) [15.15]
12.11 (12.11) [12.12]
10.58 (10.58) [10.58]
9.11 (9.10) [9.11]
183 (ref. 74)
148 (ref. 74)
224.4 (ref. 74)
160.3 (ref. 74)
114 (ref. 74)
88 (ref. 74)
61–89 (ref. 74)
6.44 (6.34) [6.45]
5.71 (5.65) [5.70]
3.22 (3.21) [3.23]
3.73 (3.71) [3.73]
2.01 (2.01) [2.05]
3.03 (3.02) [3.05]
3.72 (3.71) [3.73]
a
Computational data hin bracketsi are from ref. 65. b Data without brackets from Universal EOS; data (in parentheses) from Murnaghan EOS; data [in
brackets] from Birch-Murnaghan 3rd-order EOS; data hin bracketsi from ref. 65. c Although there are several reports with somewhat different values for
the bulk moduli of metal oxides MO (M ¼ Zn, Cd, Be, Mg, Ca, Sr, Ba), for the simplicity of our analysis we have listed only the experimental bulk
moduli of metal oxides in Table 1.
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prototypical MOF-5, which remains the best studied system in
this MOF family. Since the inorganic basic system ZnO has a
much larger bulk modulus, the decrease of B0 in the Zn-IRMOF993 is due to the introduction of the organic linker molecules and
the formation of large pores. From the data in Table 1 it is
apparent that the bulk moduli of all members of the M-IRMOF993 series are much smaller than those of corresponding metal
oxides. From this observation one can conclude that the ‘‘hard’’
metal oxides connected by ‘‘soft’’ organic linkers to form MOFs
undergo a dramatic decrease of their bulk moduli, with consequential implications for their mechanical properties.76
The optimized atomic positions and calculated equilibrium
lattice parameters are listed in Table 2. It may be noted that the
equilibrium lattice parameter of Zn-IRMOF-993 in the present
is comparable to that from previous DFTB
work (26.674 A)
65 From Zn to Cd, and from Be to Ba, the
results (26.926 A).
optimized equilibrium lattice constant increases with the atomic
number (i.e., aZn < aCd; aBe < aMg < aCa < aSr < aBa), which is
consistent with the increase in atomic radii of the central metal
atoms. Selected computed bond distances and angles are listed in
Table S1;† there are only slight differences between our data and
previously reported data for M ¼ Zn.65
C. Energy of formation considerations
Data on formation enthalpies constitute an excellent means to
establish whether theoretically predicted phases are likely to be
stable; such data may also serve as a guide to evaluate possible
synthesis routes. The literature offers interesting contributions
concerning the computation of reaction enthalpies by consideration of electric total energies, zero-point energy vibrational
correction and thermal contribution (within the harmonic
approximation).77 Kinetic factors may of course also play a
notable role during preparation.78 Here, we are primarily interested to know whether a particular hypothetical compound is
likely to be synthesizable or not on energetic grounds. We assert
that our approach, to be described below, will give qualitatively, if
not quantitatively, sound trends in stabilities and formation
enthalpies. In order to estimate the vibrational entropy
Table 2 The optimized equilibrium structural parameters for ZnIRMOF-993 obtained from VASP calculations
Property
Crystal system
Space group
Atoms/cell (fcc)
a (A)
3)
V (A
Atom type
Zn1 (32f)
O1 (96k)
O2 (8c)
C1 (96k)
C2 (96k)
C3 (48g)
C4 (48g)
C5 (96k)
H1 (96k)
H2 (96k)
a
PBE–GGA
Cubic
Fm3m (225)
178
26.674 (26.926)a
18 827.47
Atomic positions (x, y, z)
(0.29226, 0.20774, 0.29226)
(0.36397, 0.27953, 0.22047)
(1/4, 1/4, 1/4)
(0.52642, 0.84886, 0.65114)
(0.47247, 0.21703, 0.28297)
(3/4, 0.94503, 3/4)
(3/4, 0.61241, 3/4)
(0.31713, 0.05178, 0.31713)
(0.40774, 0.31790, 0.18210)
(0.45245, 0.37374, 0.12626)
The lattice parameter in parentheses is from ref. 65.
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contribution to total energy one should perform computationally
intensive phonon calculation within the harmonic approximation.
As the number of atoms involved in the present calculations is very
large, the phonon calculation is not within the scope of the present
study. It should be pointed that relative stability orders from
reaction enthalpy calculations usually refer to different structures
(phases) of one given compound. Notably, Yaghi’s IRMOF-993
has only one phase.61 Here, we have focused on the viability of
synthesizing this highly symmetric framework phase using alkaline-earth elements instead of Zn in IRMOF-993. There are several
ways to evaluate the reaction energies; our approach of starting
from the elements is but one. Another approach that has been used
is to roughly mimic the commonly used synthesis conditions, such
as with the hypothetical reaction between preformed Zn4O(OH)6
and the linker in the form of its dicarboxylic acid.65
Here, the thermodynamic feasibility of assembling the MIRMOF-993 materials from the elements is explored. 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 (Fm
3m), Sr (Fm
3m),
and Ba (Im3m) 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 the elements concerned. The results establish
unambiguously that all these compounds might be obtained in a
stable form by synthesis since eqn (1) and (2) describe exothermic
reactions for IRMOF-1 as well as for Yaghi’s Zn-IRMOF-993
and its hypothetical analogues M-IRMOF-993.
8Zn + 13O2 + 48C + 12H2 / Zn8O26C48H24 (IRMOF-1) (1)
8M + 13O2 + 96C + 24H2 / M8O26C96H48 (M-IRMOF-993,
M ¼ Zn, Cd, Be, Mg, Ca, Sr, Ba)
(2)
The formation energy for the prototypical IRMOF-1 (MOF5) obtained from the above approach66 is 46.02 kJ mol1 which
indicates that IRMOF-1 is a thermodynamically stable phase
under ambient conditions. This has of course already been
established by the wealth of experimental and theoretical studies
on IRMOF-1. The magnitude of the calculated formation
enthalpy (26.85 kJ mol1) for Zn-IRMOF-993 is smaller than
that of IRMOF-1. Nevertheless, it is sufficiently negative to
support its availability by synthesis as a compound of high
stability. The formation enthalpy of Zn-IRMOF-993 obtained
from DFTB calculation by Kuc et al.65 was 311 kJ mol1 with
respect to the Zn4O(OH)6 cluster and the linker in the form of its
dicarboxylic acid. Thus, the quantities are not directly comparable as they compare to very different reference states.
Our estimated large negative values of the enthalpy of
formation for all the compounds in the M-IRMOF-993 series
suggest that it might be possible to synthesize all these
compounds as stable phases. The magnitudes of the calculated
formation enthalpies given in Table 3 indicate that: (1) the
stability of Cd-IRMOF-993 is almost the same as that of ZnIRMOF-993, (2) the M-IRMOF-993 (M ¼ Be, Mg, Ca, Sr, Ba)
series is more stable than Zn-IRMOF-993, and (3) the stabilities
(ca. 38 to 46 kJ mol1) of the M-IRMOF-993 (M ¼ Be, Mg,
Ca, Sr, Ba) compounds are similar since they have comparable
formation enthalpies.
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Table 3 Calculated enthalpies of formation (DH; kJ mol1) according to
eqn (2) for Yaghi’s Zn-IRMOF-993 and its analogues M-IRMOF-993
(M ¼ Cd, Be, Mg, Ca, Sr, Ba)
M
Zn
Cd
Be
Mg
Ca
Sr
Ba
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DH (kJ mol1) 26.85 23.25 38.21 38.74 45.93 44.37 44.03
The present enthalpies of formation analysis based on total
energy calculations show that the hypothetical M-IRMOF-993
have negative formation energies, which suggest that they can
exist as stable materials. Of course, under real experimental
conditions it may be possible to form other stable phases, even
ones that may have lower enthalpies of formation than MIRMOF-993, that have not been accessed by our energy minimization procedure which specifically addressed the IRMOF-993
geometry and topology.
D.
Electronic structure
The total electronic density of states (TDOS) and partial density
of states (PDOS) at the equilibrium volume of Zn-IRMOF-993
Fig. 2 (Top): the calculated total density of states (TDOS) for ZnIRMOF-993 in the cubic Fm3m symmetry (no. 225). (Bottom): the
calculated total density of states (TDOS) for Zn-IRMOF-993 is
compared with that of MOF-5, Zn-IRMOF-10, and Zn-IRMOF-14 in
the cubic Fm
3m symmetry (no. 225).
16328 | J. Mater. Chem., 2012, 22, 16324–16335
are displayed in Fig. 2 (top) and 3, respectively, and shows clearly
the intermediate band (IB) and its origin. The calculated
bandgap Eg for Zn-IRMOF-993 is 3.594 eV, indicating a semiconducting character, and is in the range 3.47–3.65 eV for the
entire M-IRMOF-993 series studied here. Our recent computational efforts have established approximate bandgaps of ca.
3.4 eV for the M-IRMOF-1 series,66,68 ca. 3.0 eV for the
M-IRMOF-10 series,69 and ca. 2.5 eV for the M-IRMOF-14
series79 using the same methodology. The cumulated results for
M ¼ Zn are summarized in Scheme 1. It is evident that the
bandgap values are quite dependent on the distance between
the nodes in the MOF materials, these distances being quite
similar for M-IRMOF-1 and M-IRMOF-993. However, the
rather different bandgap values seen for M-IRMOF-10 and
M-IRMOF-14 (which have about the same internodal distances)
suggest that other linker properties, possibly related to the size of
the aromatic p system of the linker, may also play a role. As will
be described in Section F, the band dispersion in the conduction
band minimum and valence band maximum is very narrow and
similar to what is seen in molecular systems. This reduces the
probability of having good semiconducting behavior. However,
the bandgap values are within the limit of wide bandgap materials and hence it may be possible to achieve semiconducting
behavior by appropriate doping.
The 3.59 eV bandgap value determined here for Zn-IRMOF993 is much larger than that reported previously based on DFTB
calculations (2.16 eV)65 where no further details were discussed in
the absence of a DOS plot. Our calculated bandgap for ZnIRMOF-993 is comparable to that of our recent work66 on
Fig. 3 The calculated total density of states (TDOS) and partial
density of states (PDOS) for Zn-IRMOF-993 in the cubic Fm3m
symmetry (no. 225).
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Scheme 1
MOF-5 (3.5 eV). The DFTB band gap for MOF-5 in the FCC
phase is 3.73 eV and that for the simple cubic phase is 3.66 eV.65
Our calculated Eg values for the M-IRMOF-993 series are 3.470
(M ¼ Cd), 3.553 (Be), 3.618 (Mg), 3.593 (Ca), 3.651 (Sr), and
3.537 (Ba) eV, respectively. It is interesting to note that the Eg
value is almost constant (ca. 3.5–3.6 eV) irrespective of the
change in the central metals. A similar behavior has been
observed for the M-IRMOF-1,68 M-IRMOF-10,69 and MIRMOF-14 series.79 The most important finding in the present
investigation is the identification of the IB feature in ZnIRMOF-993; it appears that such a band feature has never before
been observed in MOF systems. The IB bandgap, estimated from
the top of the valence band (VB) to the bottom of the intermediate band, is 1.584 eV for Zn-IRMOF-993. The corresponding
IB bandgap values estimated for the M-IRMOF-993 series are
1.663 (M ¼ Cd), 1.445 (Be), 1.575 (Mg), 1.638 (Ca), 1.698 (Sr),
and 1.734 (Ba) eV (Fig. 4). There are unfortunately no experimental data yet on the bandgaps of the M-IRMOF-993 series
available to compare with.
It should be noted that DFT calculated bandgap values tend to
be generally lower than corresponding experimentally determined values and such an underestimation of the calculated
bandgap is intrinsically related to certain DFT limitations,
namely not taking into account the discontinuity in the exchangecorrelation potential.80 The so-called scissor operator81 D can be
introduced to overcome this discrepancy, as it effectively eliminates the difference between the theoretical and experimental
bandgap values by means of a simple rigid shift of the unoccupied
conduction band with respect to the valence band. This brings the
calculated optical properties in better agreement with experiment. In the case of bulk ZnO, the calculated bandgap values are
significantly smaller than the corresponding experimental values
(LDA ¼ 0.744/0.573 eV; GGA ¼ 0.804/0.641 eV, LDA + U ¼
1.988/1.486 eV, GW ¼ 2.255/2.100 eV, experimental 3.455/
3.300 eV for ZnO-w/-z, respectively).82 However, in our recent
work,66 we found that the Eg estimated from DFT calculations on
MOF-5 is in unexpectedly good agreement with that obtained
from experimental studies.83,84 Thus, we expect that the
This journal is ª The Royal Society of Chemistry 2012
calculated bandgap value of Zn-IRMOF-993 in this work will
also compare well with future experimental results. It will obviously be of interest to extend this study to other MOFs that are
constructed from various organic dicarboxylate linkers and Zn4O
nodes to understand more about the role of various linkers on the
electronic structure and optical properties of these materials.
Though many bond distances and angles are comparable between
Zn-IRMOF-993, Zr-IRMOF-14, Zn-IRMOF-1, and ZnO,
significant differences 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.
In order to shed further light on the predicted unique feature of
IB formation in Zn-IRMOF-993, we have displayed in Fig. 2
(top) the TDOS of Zn-IRMOF-993, and (bottom) the superimposed TDOSs of MOF-5,66 Zn-IRMOF-10,69 Zn-IRMOF14,79 and Zn-IRMOF-993. From Fig. 2 (top) it can be clearly
seen that there is an isolated band located between VB and CB in
the TDOS of Zn-IRMOF-993 and this is the predicted IB. For
MOF-5 and Zn-IRMOF-10, there appears to be an IB just below
the conduction band minimum; this feature is not attractive for
IB solar cell applications. For Zn-IRMOF-14, there is no distinct
IB band feature available at all. The origin of the IB in ZnIRMOF-993 can be identified from the PDOS analysis (Fig. 3). It
is seen that the intermediate band IB mainly arises from the C3
atom with a significant contribution from C4 and smaller, but
noticeable, contributions from C1, C2, C5, and O1. Thus, the
PDOS analysis shows that the main contribution to the IB comes
from carbon atoms. The metal ions are all divalent and hence
their contribution to the formation of IB is essentially invariant.
Fig. 4 Calculated total density of states (TDOS) for M-IRMOF-993
series (M ¼ Zn, Cd, Be, Mg, Ca, Sr, Ba) in the equilibrium cubic structure
with Fm3m symmetry (no. 225). The intermediate bands IB are framed
within the box.
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Apart from the Eg values, other important bandgap parameters in IB materials are the gap between VB maximum and IB
minimum (IMIN; called IE1g) and the gap between IB maximum
(IMAX) and CB minimum (called IE2g). As discussed above,
calculated bandgap values based on DFT tend to be generally
smaller than experimental ones and this should be kept in mind
during the comparison of the bandgap values. In the following
we will briefly discuss and compare theoretical Eg, IE1g, and IE2g
for Zn-IRMOF-993 and make comparisons with the calculated
data for the hypothetical systems M-IRMOF-993 as well as their
corresponding bulk binary oxides. From Table 4, it is seen that
the calculated Eg, IE1g, and IE2g values for the M-IRMOF-993
systems are almost constant, independent of the node metal M.
In contrast, the variation in the experimental Eg values for the
binary oxides is quite different from that of the corresponding
M-IRMOF-993 compounds. Since the Eg values of ZnO and
MOF-5 happen to be nearly the same, one might initially suspect
that there is a one-to-one correspondence between the Eg values
of IRMOFs and those of the corresponding binary oxides.
Indeed, the Eg values of host frameworks M-IRMOF-993 (M ¼
Zn and Ba) are similar to those of their corresponding oxides
MO. However, for M ¼ Be, Mg, Ca, and Sr, the oxides have
much higher bandgap values than the corresponding MIRMOF-993 compounds. Interestingly and unexpectedly, the
bandgap of Cd-IRMOF-993 is much higher than that of the
oxide CdO. These comparisons clearly suggest that there is no
one-to-one relationship after all between the Eg values of MIRMOF-993 compounds and their corresponding binary oxides
MO. This suggests that the origin of Eg in MOFs is different from
that in binary oxides. If detailed knowledge about the electronic
structure and chemical bonding in MOFs is needed, computational efforts are clearly called for.
The IB allows an electron from the VB to be promoted to the
IB, and from the IB to the CB, upon absorption of photons with
energy below Eg. Thus, the same total result is achieved as with
one photon of energy Eg. The use of this material could allow
high PV efficiencies with an ideal limit of as much as 63.1% (if Eg
z 2.0 eV and the IB is optimally placed between the VB and the
CB), while that achievable with one normal absorbing semiconductor (with Eg z 1.1 eV) is 40.7%.3 Currently, the MIRMOF-993 series has an Eg of ca. 3.5–3.6 eV, with the IB
located ca. 1.5–1.7 eV above the Fermi level. The IE1g is slightly
smaller than IE2g, and the IB is located somewhat below the
middle of Eg. This will be an advantage for M-IRMOF-993 if it is
to become a high efficiency IB material for potential solar cell or
other applications.
E. Analysis of chemical bonding
We have recently described in great detail how the bonding
interactions in the M-IRMOF-166,68 and M-IRMOF-1069 series
can be analyzed and understood using a number of different
approaches. Most recently, the M-IRMOF-14 series was subjected to the same scrutiny but in lesser descriptive details.79
Similarly, consistent descriptions of the bonding features of the
M-IRMOF-993 series may be obtained from partial density of
states, charge density/transfer, electron localization function
(ELF),38–41 and bond overlap population (BOP)/Mulliken population analyses. As an example, charge density, charge transfer,
and electron localization function plots for Zn-IRMOF-993 are
depicted in Fig. 5. Further details of these analyses are given in
the ESI – charge density, charge transfer, and ELF plots:
Fig. S1–S6† for all M except Zn; TDOS and PDOS: Fig. S7–S12
and S13–S18,† respectively, for all M except Zn which is given in
Fig. 2 and 3. To summarize the findings, the M-IRMOF-993
systems are constructed from molecular subunits, bonded by
normal C–H, C–C, and C–O covalent or polar covalent bonds.
The bonding between M and O is mainly ionic, but admixed with
partial covalent character. The relative importance of ionic and
covalent contributions leads to slight differences in M–O
bonding. At the extremes, more covalency and less ionicity are
seen in the Be–O bond compared to the Ba–O bond, even though
both are mainly ionic.
The Mulliken population analysis88 provides M–O bond
overlap populations (BOP values, Table S2†) in the range 0.27–
0.30 (M ¼ Zn), 0.22–0.24 (Cd), 0.37–0.39 (Be), 0.24–0.25 (Mg),
0.15–0.18 (Ca), 0.14–0.19 (Sr), and 0.12–0.17 (Ba). High BOP
values indicate strongly covalent bonds, whereas low BOP values
indicate ionic or non-bonding interactions. The covalent
contribution to M–O bonding decreases as Zn–O > Cd–O, and
Be–O > Mg–O > Ca–O > Sr–O > Ba–O, in accord with electronegativity trends within the groups. The calculated BOP
values for the C–O, C–C, and C–H bonds are also listed in Table
S2† and are unexceptional. The calculated Mulliken effective
charges (MEC, Table S2†) for the metal ions are +1.40|e| (M ¼
Zn), +1.37|e| (Cd), +1.14|e| (Be), +1.69|e| (Mg), +1.37|e| (Ca),
+1.42|e| (Sr), +1.41|e| (Ba). The Bader topological analysis89–91
furnished calculated Bader charges (BC) for the M-IRMOF-993
series that are also given in Table S2.† The BC for M and O (the
latter includes O1 and O2) in the series indicate that the interaction between M and O is almost ionic, since nearly two electrons (+1.39|e| for M ¼ Zn, +1.33|e| for Cd, +2.00|e| for Be,
+2.00|e| for Mg, +1.62|e| for Ca, +1.62|e| for Sr, and +1.61|e| for
Table 4 Estimated bandgap values (Theo. Eg, IE1g, IE2g) for the M-IRMOF-993 series (M ¼ Zn, Cd, Be, Mg, Ca, Sr, Ba) and experimental bandgap
values (Exp. Eg) for Zn-IRMOF-1, ZnO, and alkaline earth metal oxides (MO)
M-IRMOF-993
Theo. Eg (eV)
IE1g
IE2g
MO
Exp. Eg (eV)
Zn-IRMOF-993
Cd-IRMOF-993
Be-IRMOF-993
Mg-IRMOF-993
Ca-IRMOF-993
Sr-IRMOF-993
Ba-IRMOF-993
IRMOF-1 (MOF-5)
3.594
3.470
3.553
3.618
3.593
3.651
3.537
3.4–3.5 (ref. 66)
1.584
1.663
1.445
1.575
1.638
1.698
1.734
2.010
1.807
2.108
2.043
1.955
1.953
1.803
ZnO-w/-z82
CdO
BeO
MgO
CaO
SrO
BaO
3.455/3.300 (ref. 82)
2.16 0.02 (ref. 85)
10.7 (ref. 86)
7.2 (ref. 87)
6.2 (ref. 87)
5.3 (ref. 87)
4.0 (ref. 87)
3.4–3.5 (ref. 53 and 54)
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midpoint between VB and CB. This situation is undesirable
because the excitations will in part compete for the same photons
and because of larger non-radiative Shockley, Read and Hall92,93
recombination via a lattice relaxation multiphonon emission
mechanism.94 The latter is important because the IB is quite
localized: as mentioned in the discussion of the structural aspects
of Zr-IRMOF-993, the Zn4O nodes are well isolated and connected by the organic molecular ADC linkers. This well isolated
structural arrangement makes the electronic structure similar to
that of molecules with a localized IB which is the origin for the
dispersionless bands in Zr-IRMOF-993. The bands at the VB
maximum and CB minimum for Zr-IRMOF-993 are flat, which
appears to be a common feature for such MOF materials.95,96
This flat band behavior makes it impossible to unequivocally
identify whether the bandgap is direct or indirect, but some
qualitative information can nevertheless be obtained from the
band structures that helps to understand the electronic and
optical properties of MOF materials. Concerning potential uses
of such materials in solar cell applications, the formation of IB in
these MOFs reduces the bandgap value of the non-IB systems
(ca. 3.5 eV) closer to the optimum value (ca. 1.4 eV) for
conversion of the solar spectrum into electricity.
The optical properties for the M-IRMOF-993 series are of
particular interest, in view of the band structures just discussed
and our prediction that these may in fact be IB materials, with
associated potential uses of these materials in photocatalysis and
Fig. 5 Calculated charge density (a), charge transfer (b), and electron
localization function (c) plots for Zn-IRMOF-993 in the (110) plane.
Ba) are transferred from M to O. These data are in reasonable
agreement with the DOS and charge density analyses. All the
bonding and charge data summarized in this paragraph – absolute values as well as trends – closely resemble those found in
M-IRMOF-1,66,68 M-IRMOF-10,69 and M-IRMOF-14.79
F. Band structure and optical properties
The band structures of the whole M-IRMOF-993 series were also
calculated. The results for the representative example ZnIRMOF-993 are shown in Fig. 6 (the band structures for the
remaining M-IRMOF-993 are given in the ESI†). For the facecentered cubic (FCC) Brillouin zone, CASTEP automatically
chose the W–L–G–X–W–K high symmetry directions for the
band structure plot. The bands in the valence band as well as in
the conduction band are almost parallel and dispersionless.
Moreover, the IB is clearly seen, located at ca. 1.5–1.7 eV above
the Fermi level for the whole series and somewhat below the
This journal is ª The Royal Society of Chemistry 2012
Fig. 6 The electronic band structure of Zn-IRMOF-993. The Fermi
level is set to zero and placed in the valence band maximum.
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optoelectronic applications.97 In-depth studies of optical properties for M-IRMOF-993 are also of fundamental importance, since
these properties involve not only the occupied and unoccupied
parts of the electronic structure, but also carry information about
the character of the IB, and also are related to the excited states of
M-IRMOF-993. In the following discussion, Zn-IRMOF-993 is
selected as a representative example from the M-IRMOF-993
series. Its optical properties will be discussed and compared with
three related MOFs without IB that have been investigated by us,
MOF-5,66 Zn-IRMOF-10,69 and Zn-IRMOF-14.79
The key quantity of the optical properties is the dielectric
function 3(u), which describes the features of the linear response
of the system to electromagnetic radiation, which again governs
the propagation behavior of radiation in a medium. Here 3(u) is
connected with the interaction of photons with electrons. Its
imaginary part 32(u) can be derived from interband optical
transitions by calculating the momentum matrix elements
between the occupied and unoccupied wave functions within the
selection rules, and its real part 31(u) can be derived from 32(u)
by the Kramer–Kronig relationship.42 The real part 31(u) in the
limit of zero energy (or infinite wavelength) is equal to the square
of the refractive index n(u). All the frequency dependent optical
properties, such as refractive index n(u), absorption coefficient
a(u), optical conductivity s(u), reflectivity R(u), and electron
energy-loss spectrum L(u), can be deduced from 31(u) and 32(u).
CASTEP calculations were performed to estimate the optical
properties of Zn-IRMOF-993, and the results from the optical
calculations are shown in Fig. 7. The analogous results for MOF5,66 Zn-IRMOF-10,69 and Zn-IRMOF-1479 are included in the
same plots for easy comparison. The optical properties of the
other members of the M-IRMOF-993 series are quite similar to
those of Zn-IRMOF-993 (see ESI† for details).
Fig. 7 Calculated optical properties for Zn-IRMOF-993: (a) dielectric function 3(u), (b) reflectivity R(u), (c) refractive index n(u); extinction coefficient
k(u), (d) optical conductivity s(u), (e) energy loss function L(u), and (f) absorption a(u). For comparison, the optical properties of MOF-5, ZnIRMOF-10, and Zn-IRMOF-14 are included.
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There are two main peaks in the 32(u) plot of Zn-IRMOF-993
(Fig. 7a), located at ca. 5.30 and 15.37 eV. From the real part of
the dielectric function 31(u) (Fig. 7a) the estimated value of the
refractive index at infinite wavelength for Zn-IRMOF-993 is
1.4225, which is substantially greater than those of MOF-5
(1.25),66 Zn-IRMOF-10 (1.1651),69 and Zn-IRMOF-14 (1.227).79
At low photon energies (0–1.6 eV for Zn-IRMOF-993), (0–3.5 eV
for MOF-5), (0–2.95 eV for Zn-IRMOF-10), and (0–2.5 eV for
Zn-IRMOF-14), the imaginary part 32(u) is zero, the ordering of
which is consistent with the bandgap size.
The reflectivity spectrum (Fig. 7b) of Zn-IRMOF-993 shows
sharp peaks at 3.04 and 5.09 eV. Another set of twin peaks is
located at 15.91 and 16.88 eV with intensities much greater than
the low-energy peaks. Analysis of the two sharp low-frequency
peaks shows that they mainly arise from Zn (3d) / C/O (2p) and
H (1s) / C/O (2p) interband transitions. The reflectivity
approaches zero when the frequency exceeds 40 eV. Moreover,
the values of reflectivity at infinite wavelength, i.e. the R(0)
values, decrease in the order 0.030378 (Zn-IRMOF-993),
0.012264 (MOF-5), 0.010227 (Zn-IRMOF-14), and 0.005730
(Zn-IRMOF-10). The general behavior of the reflectivity of the
MOFs we have considered so far66,68,79 is that they have much
smaller reflectivity values in the visible spectrum range than do
common inorganic solids.
We find that Zn-IRMOF-993 has a refractive index n(u)
(Fig. 7c) in the range 1.6 to 40 eV. The extinction coefficient k(u)
(i.e., the imaginary part of the complex refractive index) of ZnIRMOF-993 (Fig. 7c) shows two closely located peaks at 5.43
and 6.55 eV and a major, broader peak at 15.8 eV. The optical
conductivity s(u) plot of Zn-IRMOF-993 is shown in Fig. 7d.
The real part of the complex conductivity (Re(s)) has two minor
peaks at 5.49 and 6.55 eV, and a major, sharp peak at 15.50 eV.
The electron energy-loss function L(u) (Fig. 7e) is an important optical parameter describing the energy loss of a fast electron traversing in a certain material. The peaks in the L(u)
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 [31(u)
> 0] and below which the material behaves like a metallic
compound in some sense [31(u) < 0]. In addition, the peaks of the
L(u) spectra overlap the trailing edges in the reflection spectra. A
moderately strong peak is found at 7.08 eV, whereas the major,
sharp peak is located at 18.48 eV. Zn-IRMOF-993 has an
absorption band (Fig. 7f) from 1.6 to 40 eV, which has two main
peaks at 6.69 and 16.03 eV.
As a rough approximation, the calculated optical properties of
Zn-IRMOF-993 in this work are relatively similar to those
reported for MOF-5,66 Zn-IRMOF-10,69 and Zn-IRMOF-14,79
which is consistent with the fact that the materials have similar
topologies with identical inorganic building blocks and closely
related dicarboxylate linkers. Nevertheless, there are some
substantial differences between fine structures, in the distribution
of intensities and positions of the peaks. In general, the peak
intensities in the calculated optical properties (3(u), n(u), k(u),
a(u), s(u), R(u), L(u)) for related bands in the different ZnMOFs mostly decrease in the order Zn-IRMOF-993 > MOF-5 >
Zn-IRMOF-14 > Zn-IRMOF-10 for any given optical property
(with few exceptions, some fluctuation of data is apparent). Most
notably, Fig. 7 shows clearly that Re(s), R(u), L(u) and a(u)
This journal is ª The Royal Society of Chemistry 2012
have much greater signal intensities for Zn-IRMOF-993 than for
the other Zn-MOFs included.
The efficiency of the photovoltaic effect will be improved
because the low-energy photons can also create electron–hole
pairs that add up to the pairs created directly by photons whose
energy is higher than the total bandgap between VB and CB. As a
result, the optical absorption will be more efficient. From Fig. 7f,
significant enhancement in absorption due to the IB is seen in ZnIRMOF-993 compared with that of the other Zn-MOFs without
IB. For the Zn-MOFs without IB, only VB / CB excitations
exist, whereas for Zn-IRMOF-993 with IB, VB / IB and IB /
CB excitations may also contribute to the optical absorption
processes if the IB is partially filled by doping and/or by the
VB / IB excitation.
IV.
Conclusions
The following conclusions are obtained in the present work:
(1) By judicious choice of linkers, intermediate band MOFs
may be designed. The present study suggests that by changing the
cations in the nodes of MOFs, the IB position can be slightly
adjusted to different locations between the VB and CB. The IB
effect can enhance the efficiency of the M-IRMOF-993 based
solar cells since multiple photons can be harvested.
(2) The calculations show that each material in the MIRMOF-993 series is soft and exists in the highly symmetric facecentered cubic (Fm
3m, 225) crystal structure. The tetranuclear M
nodes are bridged by dicarboxylate units; the M–O bonding
interactions are mainly ionic.
(3) The electronic structures become particularly complex due
to the introduction of IB in the M-IRMOF-993 series. The band
structure and electronic density of states studies show that the
M-IRMOF-993 materials have bandgaps of ca. 3.5–3.6 eV irrespective of the metal M in the nodes, indicating a semiconductor
character. The IB bandgap, estimated from the top of the valence
band to the bottom of intermediate band, is ca. 1.5–1.7 eV for the
whole series.
To our knowledge this is the first report that predicts the
presence of IB features in MOF systems. We hope that these
findings will stimulate experimentalists to explore this class of
potential IB materials.
Acknowledgements
We gratefully acknowledge the Research Council of Norway for
financial support and for computing resources at the Norwegian
supercomputer facilities.
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