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Physical Chemistry Chemical Physics
Volume 14 | Number 14 | 14 April 2012 | Pages 4661–4992
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Properties of IRMOF-14 and its analogues M-IRMOF-14
(M = Cd, alkaline earth metals): electronic structure, structural
stability, chemical bonding, and optical propertiesw
Li-Ming Yang,*a Ponniah Ravindran,b Ponniah Vajeestonb and Mats Tilset*a
Received 22nd December 2011, Accepted 3rd February 2012
DOI: 10.1039/c2cp24091b
The chemical bonding, electronic structure, and optical properties of the experimentally available
metal–organic framework IRMOF-14 and its metal-substituted analogues M-IRMOF-14
(M = Zn, Cd, Be, Mg, Ca, Sr, Ba), which contain a pyrene-2,7-dicarboxylate linker group, have been
systematically investigated using DFT calculations. The unit cell volume and atomic positions
were optimized with the Perdew–Burke–Ernzerhof (PBE) functional and showed good agreement
between experimental and theoretical equilibrium structural parameters for Zn-IRMOF-14.
The calculated bulk moduli indicate that the whole M-IRMOF-14 series are soft materials. The
estimated band gap from DOS calculations for the M-IRMOF-14 series is ca. 2.5 eV, essentially
independent of the metal ion and indicative of nonmetallic character. The band gap value is
distinctly different from those calculated previously for the M-IRMOF-1 (benzene-1,4-dicarboxylate
linker; ca. 3.5 eV) and M-IRMOF-10 (biphenyl-4,40 -dicarboxylate linker; ca. 3.0 eV) series and this
confirms that the identity of the linker is a key parameter to control band gaps in an isoreticular
series of main-group MOFs. In view of potential uses of MOFs in organic semiconducting devices
such as field-effect transistors, solar cells, and organic light-emitting devices, the linear optical
properties of these materials were also investigated. Comparisons are made with the M-IRMOF-1
and M-IRMOF-10 series.
I.
Introduction
The long-standing challenge of designing and constructing
crystalline solid-state materials from molecular building
blocks is just beginning to be addressed with success. A
conceptual approach, the reticular synthesis1,2 proposed by
Yaghi and coworkers, requires the use of secondary building
units (SBU)3 to direct the assembly of ordered frameworks.
This approach has yielded materials designed to have predetermined structures, compositions, and properties. In particular,
highly porous frameworks with exceptionally large surface areas
and capacity for gas storage are held together by strong
metal–oxygen–carbon bonds, and their pore metrics have
been systematically varied and their organic linkers have
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
w 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 band structures and optical properties of M-IRMOF-14
(M = Cd, Be, Mg, Ca, Sr and Ba). See DOI: 10.1039/c2cp24091b
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been functionalized. Thus, Yaghi and coworkers synthesized a
series of isoreticular metal–organic frameworks, IRMOF-1–16,4
with oxygen-centered Zn4O tetrahedra as nodes linked by different
organic molecules. The pore size and functionality of this series
can be systematically designed and tuned. Scheme 1 shows, in a
highly simplified manner, the key features of three members of the
IRMOF series.
Over the past decades, organic electronics based on polycyclic aromatic hydrocarbons (PAHs) have received intensive
scientific and technological attention because of the tunable
electrical and optical properties that are offered by proper
molecular design, and because of their mechanical flexibility
and capability for large-area processing at low cost with high
performance.5–23 Pyrene-based materials are one member of
PAHs and they have been widely employed as active layers in
organic semiconducting devices such as field-effect transistors,
solar cells, and organic light-emitting devices (OLEDs).24–31
Their performance encourages us to examine from a theoretical
point of view the optical properties and electronic structures
of the pyrene-based material IRMOF-14, which may be a
potential candidate for optoelectronic devices.
Additionally, the change to a future pollutant-free and more
efficient energy exploitation may be aided by the use of hydrogen
as an intermediate medium for storing and transporting energy
Phys. Chem. Chem. Phys., 2012, 14, 4713–4723
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Scheme 1
that is produced from any (preferably renewable) primary
energy source. Among the many materials considered for
hydrogen storage, metal–organic frameworks (MOFs) show
great potential to fulfill many requirements. One possible means
of improving the gravimetric gas storage capacity for this type
of material would be to replace the typically di- or trivalent
transition metal centers of many MOFs with lighter main-group
ions such as Be2+, Mg2+, B3+, Al3+, etc.32–37 As an exciting
example, substitution of the lightest divalent metal, Be2+, for
the Zn2+ ions in MOF-5 would result in ca. 40% increase in
gravimetric surface area and hydrogen storage capacity.38,39
This also is a strong motivation for exploring metal-substituted
analogues of the IRMOF series computationally.
Although IRMOF-14 (in which the tetranuclear Zn nodes are
linked by pyrene-2,7-dicarboxylate (PDC) units) was synthesized
in 2002,4 there appears to exist no comprehensive investigation
of electronic structure, chemical bonding, and optical properties
of IRMOF-14 until now. In contrast, the prototypical MOF-5
(IRMOF-1) has been comprehensively studied by a vast array of
methods, as listed in our recent computational paper on this
particular system.40 Thus, IRMOF-14 deserves more scrutiny by
virtue of its large, planar PAH linker. This material will have
considerable p-electron delocalization and therefore has the
potential to induce charge separation into electrons and holes
upon light absorption, which calls for systematic investigations
into its spectroscopic and optical properties. Moreover, the
presence of inorganic semiconductor quantum entities (such as
dots or wires) in close contact with organic molecules makes the
optical properties of MOFs particularly interesting.
IRMOF-14 has larger pore sizes than MOF-5 which should
motivate its applications in gas absorption and storage. Experimental studies on IRMOF-14 have addressed absorption of light
gases (Ar, CH4, H2),41–46 enhanced H2 storage by Li doping,47,48
adsorption and diffusion of alkane mixtures,49,50 etc. IRMOF-14
can be used in mixed matrix membranes for high efficiency
purification or separation.51–53 The large negative thermal
expansion (NTE) behavior of IRMOF-14 is also of interest.54
One possible reason that IRMOF-14 has not been subjected
to detailed theoretical analyses may be that IRMOF-14 is a
4714
Phys. Chem. Chem. Phys., 2012, 14, 4713–4723
rather large system; first principle calculations will be highly
demanding in computational resources. Another reason is that
it is a rather tedious task to manually construct reasonable
initial solid-state structures for structural optimization of
MOFs. Even though CIF files deposited in the Cambridge
Crystallographic Data Centre (CCDC) may be available, many
of them are of inferior quality when it comes to small details. It
has been pointed out that this problem may at least in part be
caused by disorder imposed by freely rotating organic linkers.55
Thus, experimental atomic positions are often not correctly
identified (especially for hydrogen); the presence of more or less
well-defined guest molecules and atoms dispersed in the pore
also makes experimental structures sometimes intractable for
the computational simulations. Considerable effort is needed to
manually construct sufficiently accurate starting structures for
structure optimization: if the initial structure deviates too far
from the real ground state structure, then the computational
code may optimize the structure to undesired motifs.
Herein, we present optimization of the IRMOF-14 structure
that enables us to address the following:
(1) There is no information yet on the thermodynamic
stability of IRMOF-14, even though it was synthesized as
early as in 2002. 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 for new materials, and help
verify experimentally synthesized materials.
(2) The character of chemical bonding between constituents
in IRMOF-14 remains to be analyzed. The bonding interaction between the constituents is important to understand the
chemical and physical properties of IRMOF-14, including
structural stability and physicochemical properties.
(3) A fundamental understanding of the electronic structure
of IRMOF-14 is an important basis for follow-up investigations.
(4) Detailed information on its optical properties may help
screen it for potential applications in electronic and optical devices.
(5) Metal-substituted analogues of IRMOF-14 are so far
unknown. It is of interest to assess the generality of the
chemistry of IRMOF-14, i.e., whether it is feasible to extend
the IRMOF-14 chemistry to other divalent metal ions, such as
Cd, Be, Mg, Ca, Sr, and Ba.
In the following we describe a detailed computational study
on the crystal structure, phase stability, electronic structure,
chemical bonding, mechanical, and optical properties of
M-IRMOF-14 (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) using DFT
calculations with the GGA-PBE functional implemented in the
Vienna simulation package (VASP) code.56–59 Thus, the calculations were carried out for the primitive cell including all the crystal
symmetries using the periodic DFT code. The optical properties
of IRMOF-14 and its analogues have been calculated using the
CASTEP module60 of the Materials Studio 5.0 program.61
II. Computational details
The VASP56–59 code has been used for the total-energy
calculations to study the structural stability and to establish
equilibrium structural parameters. The generalized gradient
approximation (GGA)62–64 includes the effects of local gradients
in the charge density for each point in the material and generally
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gives better equilibrium structural parameters than the local
density approximation (LDA). Hence, the Perdew, Burke, and
Ernzerhof (PBE)64 GGA functional was used for all calculations.
The projector-augmented-wave (PAW)65,66 pseudo-potentials
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 planewave 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 the IRMOF-14 system. Brillouin-zone
integration was performed with a Gaussian broadening of 0.2 eV
during all relaxations. The highly efficient conjugate-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 finding the equilibrium positions (the total energy was not
taken into account). 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–
Feynman forces were less than 103 eV Å1.
Because we deal with a large system (190 atoms per primitive
cell), the G-point alone is sufficient for sampling the Brillouin
zone during geometry optimization. But, in order to arrive at an
accurate band structure and density of state (DOS), the calculations were performed on the fully optimized structure with a
greater number of k-points. Furthermore, 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, the
bond overlap population (BOP) values were evaluated with
on-the-fly pseudopotential estimated on the basis of the Mulliken
population as implemented in the CASTEP code.60 In order to
understand the chemical bonding and interactions between
constituents in IRMOF-14 and its analogues, charge density,
charge transfer, and electron localization function (ELF)67–70
analyses were performed. The linear optical properties including
dielectric function, absorption coefficient, reflectivity, refractive
index, optical conductivity, and energy loss function were also
calculated for IRMOF-14 and its analogues with ultrasoft
pseudopotential using the CASTEP code. The band structure
was calculated with ultrasoft pseudopotential for the whole
series with CASTEP. The method used for the calculation of
optical properties and band structures has been demonstrated to
be reasonable and compared favorably with corresponding
experimental spectra in a series of previous papers from both
our and other groups.71–81 Others have also demonstrated that
the use of computational methods to optimize and predict MOF
structures and to evaluate their various properties is an important supplement to experimental approaches.82–89
III.
A.
Results and discussions
Structural details
IRMOF-14 is a member of a series of isoreticular metal–organic
frameworks with oxygen-centered Zn4O tetrahedral nodes that are
linked by organic molecules, and is synthesized by the reticular
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Fig. 1 The solid-state structure of M-IRMOF-14 (M = Zn, Cd, Be,
Mg, Ca, Sr, Ba) in the cubic Fm3% m symmetry (no. 225). Following the
symmetry of space group, we distinguish the atoms with labels M, O1,
O2, C1, C2, C3, C4, C5, C6, H1, and H2 for the interpretation and
understanding of partial density of states (PDOS) in the following
electronic structure section.
synthesis approach proposed by Yaghi and coworkers.1,2 The
structure of IRMOF-14 may be viewed as being constructed
from discrete semiconductor Zn4O13 quantum dots stabilized
and interconnected by pyrene dicarboxylate (PDC) linkers; the
PDC units contribute 12 of these 13 oxygen atoms.
IRMOF-14 can be obtained in a crystalline form with high
specific surface area (a theoretical estimate of 4926 m2 g1 90
is considerably higher than the experimentally measured
1453 m2 g1).4 The conventional cell of its crystal structure
has cubic Fm3% m symmetry (no. 225) with the lattice parameter
a = 34.381 Å and contains eight formula units of Zn4O(PDC)3.
Its primitive cell includes two nodes and six linker molecules,
corresponding to two Zn4O(PDC)3 formula units. The solidstate structures of IRMOF-14 and its analogues are illustrated
in Fig. 1. The crystallographically nonequivalent sites in the
M-IRMOF-14 series include one type of M (Zn, Cd, Be, Mg,
Ca, Sr, Ba), two types of O, six types of C, and two types of H,
occupying 32f, 8c, 96k, 96k, 96k, 48g, 48g, 48g, 96k, 96k, and
96k Wyckoff positions, respectively.
B. Structural optimization of M-IRMOF-14 series from totalenergy calculation
For the structural optimization, the experimentally determined
X-ray structure of IRMOF-14 (wherein M = Zn) was used as
the starting geometry. The theoretical ground-state structure of
IRMOF-14 was obtained using full geometry optimization, i.e.
the atom positions and cell parameters were fully relaxed. After
the full optimization of IRMOF-14, the Zn atoms were replaced
by the other divalent metal atoms Cd, Be, Mg, Ca, Sr, and Ba.
These were then used as initial structures for optimization of
the M-IRMOF-14 analogues by full relaxations of the atomic
positions and cell parameters.
The optimization was achieved by first relaxing the atomic
positions globally using the force-minimization technique, i.e. by
initially keeping the lattice constant (a) and cell volume (V) fixed to
the original input values. Then the theoretical ground-state volume
was determined from total energy minimization by varying the cell
Phys. Chem. Chem. Phys., 2012, 14, 4713–4723
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volume within 10% of the experimentally determined volume
where the atom positions were relaxed for each volume step. 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 0 ). In order to cross-check the
calculated B0 and B0 0 values, the E–V data were fitted into three
different EOSs, i.e. the Murnaghan,91 Birch–Murnaghan,92 and
Universal equation of states.93 The bulk moduli and their
pressure derivatives (in parentheses) for Zn-IRMOF-14 are
10.24 GPa (3.62), 10.25 GPa (3.63), and 10.25 GPa (3.64) from
the above three EOSs, respectively. This B0 value is much
larger than the 5.90 GPa value previously obtained by DFTB
calculations,55 where the B0 value was calculated from the elastic
constants obtained from the total energy change after application of a suitable strain. The bulk moduli in GPa and their
pressure derivatives (in parentheses) for the other M-IRMOF-14
members, obtained from the E–V curve using the UEOS, are
8.81 (2.97) for M = Cd, 12.49 (0.59) for Be, 9.98 (3.94) for Mg,
8.24 (11.70) for Ca, 7.65 (2.26) for Sr, and 6.52 (5.55) for Ba. The
results derived from the two other EOSs are listed in Table 1. It
is seen that B0 and B0 0 values estimated from three different
EOSs derived from the E–V data are nearly identical. Moreover,
the bulk modulus decreases monotonically when one moves
from Zn to Cd, and from Be to Ba, but there are no clear trends
in its pressure derivatives within this series. For comparison, the
previously determined bulk moduli in GPa and pressure derivatives (in parentheses) for MOF-540 are 15.37 (5.06), 15.37 (5.13),
and 15.37 (5.17) from the above three EOSs, respectively. The
bulk moduli for the whole M-IRMOF-14 series are consistently
64–71% of the values for the corresponding M-IRMOF-1
members (including MOF-5 (Zn-IRMOF-1)).40,94 Recently, we
also reported95 that the bulk moduli for the M-IRMOF-10 series
showed the same systematic variation with respect to the position in the periodic table and that their values were 59–65% of
the corresponding M-IRMOF-1 values. Thus, it is seen for any
given metal M that the bulk modulus depends significantly on
the linker length. In general, a longer linker gives a mechanically
less resistant system, thus a smaller bulk modulus. As the compressibility of MOFs at low pressure is mainly determined by these
organic linkers, the longer size of the linkers in IRMOF-10 and
IRMOF-14 relative to IRMOF-1 diminishes the repulsive
interaction between nodes during compression and hence their
bulk moduli are reduced when compared to IRMOF-1. In
IRMOF-14, such repulsions are somewhat increased when
compared to IRMOF-10, presumably due to the larger aromatic
linker moiety. Unfortunately, there are no experimental data
available on the bulk modulus value for IRMOF-14.
The linkage between the Zn4O group and the organic
moieties results in rather soft materials with relatively small
bulk moduli. The data may be compared to cubic diamond
(theo. 441–457 GPa;96 expt. 443 GPa97) and the wurtzite
structure (theo. 160 GPa;98 expt. 183 GPa99,100), zinc blende
structure (theo. 156.8 GPa101), and rocksalt structure (theo.
190.3 GPa;101 expt. 194–288 GPa100) of zinc oxide. The data
demonstrate that IRMOF-14 is a readily compressible system
where the lowering of B0 in M-IRMOF-14 compared to the
fundamental inorganic systems ZnO (and the other metal
oxides MO) is caused by the introduction of the flexible
organic linker molecules and the formation of large pores.
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Phys. Chem. Chem. Phys., 2012, 14, 4713–4723
Table 1 Optimized equilibrium lattice constants (a (Å)), bulk moduli
(B0 (GPa)), and their pressure derivatives (B0 0 ) for M-IRMOF-14
(M = Zn, Cd, Be, Mg, Ca, Sr, Ba). Experimental bulk moduli for the
metal oxides MO
Material
aa/Å
B0b/GPa
B0 0 b
IRMOF-14
Cd-IRMOF-14
34.617 h35.386i
hh34.381ii
35.858
Be-IRMOF-14
32.874
Mg-IRMOF-14
34.660
Ca-IRMOF-14
36.257
Sr-IRMOF-14
37.142
Ba-IRMOF-14
38.071
10.25 (10.24)
[10.25] h5.90i
8.81 (8.81)
[8.81]
12.49 (12.49)
[12.50]
9.98 (9.97)
[9.98]
8.24 (8.22)
[8.25]
7.65 (7.65)
[7.65]
6.52 (6.51)
[6.52]
3.64 (3.62)
[3.63]
2.97 (2.96)
[2.98]
0.59 (0.59)
[0.61]
3.94 (3.92)
[3.93]
11.70 (11.52)
[11.91]
2.26 (2.27)
[2.34]
5.55 (5.52)
[5.54]
Experimentalc
18399,100
148100
224.4106
160.3106
114106
88106
61–89106
ZnO
CdO
BeO
MgO
CaO
SrO
BaO
a
Data in braces h i are from ref. 55, experimental data in double
braces hh ii are from ref. 4. b Data without brackets are from
Universal EOS; data in parentheses ( ) are from Murnaghan EOS;
data in brackets [ ] are from Birch–Murnaghan 3rd-order EOS; data in
braces h i are from ref. 55. c Several reports with somewhat differing
values on the bulk moduli of metal oxides MO (M = Zn, Cd, Be, Mg,
Ca, Sr, Ba) are available; for simplicity, only experimental bulk moduli
of metal oxides are listed.
Pertinent theoretical and experimental data are summarized in
Table 1. In conclusion, the connection of ‘‘hard’’ metal oxide
nodes by ‘‘soft’’ organic linkers to form MOFs dramatically
decreases the bulk modulus, an important mechanical parameter
for a material which reflects compressibility and bonding
character in the crystal.102
The optimized atomic positions and calculated equilibrium
lattice parameters of Zn-IRMOF-14, along with the corresponding
experimental values, are listed in Table 2. The metric parameters
for all investigated M-IRMOF-14 materials are listed in Table 3.
From Zn to Cd, and from Be to Ba, the optimized equilibrium
lattice constant increases with the atomic number, which is
consistent with increasing atomic radii of the central metal atoms.
C.
Energy of formation considerations
Data on formation enthalpies may help establish whether
theoretically predicted phases are likely to be stable and such
data may also serve as a guide to evaluate possible synthesis
routes. We use the formation energy of MOF-5 (IRMOF-1) as
a reference with which to compare data for the M-IRMOF-14
series. For the exploration of the thermodynamic feasibility of
accessing these materials from the elements (eqn (1) and (2))
we also computed the total energies for C (R3% m), O2 (P4/mmm),
H2 (P4/mmm), Zn (P63/mmc), Cd (P63/mmc), Be (P63/mmc),
Mg (P63/mmc), Ca (Fm3% m), Sr (Fm3% m), and Ba (Im3% m) in
their ground state structures with full geometry optimization.
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Table 2
Optimized structural parameters for Zn-IRMOF-14
a
Property
PBE-GGA
Expt
Crystal system
Space group
Atoms per cell (fcc)
a/Å
V/Å3
Cubic
Fm3% m (225)
190
34.617
41481.383
Cubic
Fm3% m (225)
190
34.381(13)
40642(26)
Atom type Atomic positions (x, y, z)
Zn1 (32f)
O1 (8c)
O2 (96k)
C1 (96k)
C2 (96k)
C3 (48g)
C4 (48g)
C5 (48g)
C6 (96k)
H1 (96k)
H2 (96k)
a
(0.28280, 0.28280, 0.21720)
(1/4, 1/4, 1/4)
(0.27330, 0.27330, 0.16190)
(0.22520, 0.22520, 0.08180)
(0.22470, 0.22470, 0.04120)
(1/4, 1/4, 0.1019)
(1/4, 1/4, 0.1451)
(1/4, 1/4, 0.0205)
(0.1996, 0.1996, 0.0197)
(0.2061, 0.2061, 0.0980)
(0.1804, 0.1804, 0.0357)
(0.28277, 0.28277, 0.21723)
(1/4, 1/4, 1/4)
(0.27250, 0.27250, 0.16130)
(0.22550, 0.22550, 0.08350)
(0.22670, 0.22670, 0.04280)
(1/4, 1/4, 0.10480)
(1/4, 1/4, 0.14370)
(1/4, 1/4, 0.01920)
(0.20280, 0.20280, 0.02030)
(0.2086, 0.2086, 0.0962)
(0.1859, 0.1859, 0.0331)
Experimental data from the ESI of ref. 4.
The reaction enthalpies for formation of the MOFs were
calculated from the difference in the total energy between
the products and reactants in the reactions concerned. The
results, listed in Table 4, clearly establish that eqn (1) and (2)
express exothermic reactions for both IRMOF-1 and the
M-IRMOF-14 series.
8Zn + 13O2 + 48C + 12H2 - Zn8O26C48H24 (IRMOF-1)
(1)
8M + 13O2 + 108C + 24H2 - M8O26C108H48
(M-IRMOF-14, M = Zn, Cd, Be, Mg, Ca, Sr, Ba)
(2)
The formation energy of IRMOF-1 (MOF-5)40 is
46.02 kJ mol1, indicating that it is a thermodynamically
stable phase under ambient conditions. This has already been
established by a series of experimental and theoretical studies. The
calculated formation enthalpy for IRMOF-14 (30.39 kJ mol1)
is somewhat smaller in magnitude, but still sufficiently large
Table 3
M
D.
Electronic density of states
Improved understanding of the electronic structure and bonding
behavior of the M-IRMOF-14 series may be gained from the
electronic total density of states (TDOS) and partial density of
states (PDOS) at the equilibrium volumes. For Zn-IRMOF-14,
these are displayed in Fig. 2 and 3, respectively. The total
electronic density of states (TDOS) at the equilibrium volume
for the whole M-IRMOF-14 series compounds are displayed in
Fig. 4. The partial density of states (PDOS) for M = Cd, Be,
Mg, Ca, Sr, and Ba are provided in the ESI.w The calculated
band gap value, Eg, for Zn-IRMOF-14 is 2.454 eV, indicative of
semiconductor character, and this is comparable to a previously
reported theoretical value of 2.63 eV.55 The calculated band
gaps through the entire M-IRMOF-14 series are 2.495 (Cd),
2.398 (Be), 2.441 (Mg), 2.454 (Ca), 2.531 (Sr), and 2.564 (Ba)
eV. Thus, the band gap for the whole series is rather constant
at 2.4–2.6 eV and is smaller than that of M-IRMOF-1
(including MOF-5) at 3.4–3.5 eV40,94 and of M-IRMOF-10
at 2.9–3.0 eV.95 It is interesting to note that the band gap is
essentially constant within each of the three series and that the
controlling feature appears to be the identity of the linker, rather
than the cornerstone divalent metal ion. There is only a rather
modest increase in the band gap size as the M-IRMOF-14 series
is traversed from Zn to Cd, and from Be to Ba. Unfortunately,
there are no experimental measurements of the band gap value
for IRMOF-14 available in the literature. It should be noted that
DFT calculated band gap values tend to be generally lower than
Optimized bond length (Å) and bond angles (1) for M-IRMOF-14 (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) at their equilibrium volumes
C1–C2
C1–C3 C3–C4
Zn
1.403
1.401 1.497
(1.401)a (1.398) (1.340)
h1.460ib
Cd 1.403
1.401 1.502
Be 1.402
1.401 1.489
Mg 1.403
1.401 1.495
Ca 1.403
1.401 1.499
Sr 1.403
1.401 1.502
Ba 1.403
1.400 1.504
a
and negative, which is consistent with the fact that it is stable
and experimentally accessible.4
The magnitudes of the calculated formation enthalpies in
Table 4 suggest (1) that the stability of Cd-IRMOF-14 is
almost the same as that of IRMOF-14 (M = Zn), (2) that
the M-IRMOF-14 (M = Be, Mg, Ca, Sr, Ba) series is more
stable than IRMOF-14 (M = Zn), and (3) that the stabilities
of the M-IRMOF-14 (M = Be, Mg, Ca, Sr, Ba) compounds
are quite similar. The data for the series suggest that it might
be possible to synthesize these compounds as stable phases
under suitable experimental conditions.
C2–C5 C2–C6 C5–C5 C6–C6 C4–O2 M–O1
M–O2
C1–C3–C1 C5–C2–C6 O1–M–O2 O2–M–O2
1.431 1.436 1.422 1.366 1.278
(1.393) (1.397) (1.320) (1.400) (1.250)
h1.320i
1.431 1.436 1.422 1.366 1.277
1.432 1.436 1.422 1.365 1.274
1.431 1.436 1.422 1.366 1.277
1.431 1.436 1.422 1.366 1.277
1.431 1.436 1.422 1.366 1.277
1.431 1.436 1.422 1.366 1.276
1.970
(1.990)
h2.089i
2.199
1.635
1.959
2.242
2.405
2.579
120.308
(117.0)
118.724
(111.0)
120.226
120.505
120.285
120.130
120.050
119.978
118.721
118.743
118.712
118.696
118.687
118.650
1.970
(1.950)
h2.067i
2.177
1.716
1.987
2.269
2.432
2.606
Experimental data in parentheses ( ) are for the structure built from the coordinates given in the ESI of ref. 4.
b
111.494
(110.7)
h108i
108.478
115.438
110.611
106.308
104.287
102.394
107.375
(108.2)
110.445
102.900
108.308
112.440
114.120
115.525
Data in braces h i are from ref. 55.
Table 4 Calculated enthalpies of formation (DH, kJ mol1) according to eqn (2) for IRMOF-14 (M = Zn) and the other M-IRMOF-14
(M = Cd, Be, Mg, Ca, Sr, Ba) compounds
M
1
DH/kJ mol
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Zn
Cd
Be
Mg
Ca
Sr
Ba
30.39
27.00
40.77
41.32
43.98
43.15
42.33
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Fig. 2 The calculated total density of states (TDOS) for IRMOF-14
in the cubic Fm3% m symmetry (no. 225).
a simple rigid shift of the unoccupied conduction band with
respect to the valence band. In line with this, the calculated
band gap for bulk ZnO is significantly smaller than the
experimental value (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-wz, respectively).105
In a recent study,40 we demonstrated that the DFT calculated band
gap for MOF-5 agrees quite well with experimental data.106,107
Key metric parameters of ZnO and the Zn-MOFs are quite
similar: the Zn–O bond distances are 1.970 Å, 1.936–1.948 Å,
and 1.974–1.983 Å; the O–Zn–O bond angles are 107.4–111.51,
107.7–111.21 and 108.3-110.71 in IRMOF-14, MOF-5, and
bulk ZnO, respectively. Despite these similarities between
IRMOF-14, MOF-5 and ZnO, significant differences between
the MOFs (IRMOF-14 and MOF-5) and ZnO 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 linkers PDC and BDC.
As mentioned, the band gap values obtained from the
TDOS curves in Fig. 4 are ca. 2.5 eV for all M-IRMOF-14
species studied here, indicating that all these materials are
semiconductors. The characteristic peaks of TDOS for all these
compounds are very similar, which implies that the calculated
bandgaps within the M-IRMOF-14 series have a common
structural origin. A different case was reported by Choi et al.108
Fig. 3 The calculated total density of states (TDOS) and partial density
of states (PDOS) for IRMOF-14 in the cubic Fm3% m symmetry (no. 225).
the experimentally determined ones; this underestimation is an
intrinsic feature of the methods based on DFT, namely not
taking into account the discontinuity in the exchange–correlation
potential.103 To overcome this discrepancy to compare calculated
optical spectra with experiment, the so-called scissor operator,104
D, can be introduced, which effectively eliminates the difference
between the theoretical and experimental gap values by means of
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Fig. 4 Calculated total density of states (TDOS) for the M-IRMOF-14
series (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) in cubic Fm3% m symmetry
(no. 225).
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Table 5 Estimated bandgap values (Theo. Eg) for the M-IRMOF-14
series (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) from CASTEP calculations.
Experimental bandgap values (Exp. Eg) for M-IRMOF-1, M-IRMOF-10,
ZnO, and alkaline earth metal oxides (MO)
M-IRMOF-14
Theo. Eg/eV
Zn-IRMOF-14
Cd-IRMOF-14
Be-IRMOF-14
Mg-IRMOF-14
Ca-IRMOF-14
Sr-IRMOF-14
Ba-IRMOF-14
M-IRMOF-1
M-IRMOF-10
2.454
2.495
2.398
2.441
2.454
2.531
2.564
3.4–3.540,94
2.9–3.095
MO
Exp. Eg/eV
105
ZnO-wz
CdO
BeO
MgO
CaO
SrO
BaO
3.455/3.300105
2.16 0.02110
10.7111
7.2112
6.2112
5.3112
4.0112
3.4–3.5106,107
whose calculations supported tuning of electronic band gaps
from semiconducting to metallic states by substitution of
Zn(II) ions in MOF-5 with Co(II) ions. This difference has
been attributed to the fact that all alkaline-earth M(II) and
Zn(II) have closed shell metal ions and thence quite similar
electronic structures, whereas Co(II) may have a very different
valence state from alkaline-earth and Zn(II) ions.
Comparisons of the calculated data for the hypothetical
systems M-IRMOF-14 and the corresponding bulk binary oxides
are summarized in Table 5. In contrast to the M-IRMOF-14
systems, which have bandgap values essentially independent of
M, the experimental bandgap values for the binary oxides MO
show considerable variation. In particular, the oxides have much
higher bandgap values than do the M-IRMOF-14 series, and the
bandgaps of the oxides show a substantial decrease when going
from Zn to Cd, and from Be to Ba. The data clearly show that
one may not readily extract the properties of MOFs from the
properties of the corresponding oxides that are involved in the
formation of the MOF nodes. If detailed information about and
understanding of electronic structures and chemical bonding in
MOFs is desired, it is highly advisable to perform high-level
computational studies.
Thus far, our computational efforts have established approximate bandgaps of ca. 3.4 eV for the M-IRMOF-1 series59,102
(benzene-1,4-dicarboxylate linker),40,94 ca. 3.0 eV for the
M-IRMOF-10 series95 (biphenyl-4,4 0 -dicarboxylate linker),
ca. 2.5 eV for the M-IRMOF-14 series (pyrene-2,7-dicarboxylate
linker; this work), and ca. 3.5 eV for the M-IRMOF-993 series109
(anthracene-9,10-dicarboxylate linker). It appears that the
bandgap values are mostly 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
differences in values between M-IRMOF-10 and M-IRMOF-14
which have about the same internodal distance suggest that
other linker properties, possibly linked to the size of the
aromatic p system of the linker, also may play a role.
E.
Chemical bonding
We have previously described in high detail how the bonding
interactions in the M-IRMOF-140,94 and M-IRMOF-1095
series can be analyzed and understood using a number of
different approaches. Thus, consistent descriptions of their
bonding features could be obtained from partial density of
states, charge density/transfer, electron localization function
(ELF67–70), and bond overlap population (BOP)/Mulliken
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population analyses. Not surprisingly, the same is found for
the M-IRMOF-14 systems. The details of these findings are
given in the ESIw: charge density, charge transfer, and ELF
(Fig. S1–S7) for all M; PDOS (Fig. S8–S13) for all M except
Zn, which is given in Fig. 3. In summary, the MOFs consist of
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 mixed with some covalency. Slight
differences in chemical bonding arise from the relative importance of ionic and covalent contributions to the M–O bonds.
At the extremes, there is more covalency and less ionicity in
the Be–O bond compared to the Ba–O bond, even though both
have mainly ionic components.
The Mulliken population analysis113 yielded M–O bond
overlap populations (BOP values, Table S1, ESIw) in the range
0.26–0.29 (M = Zn), 0.21–0.23 (Cd), 0.36–0.37 (Be), 0.23 (Mg),
0.14–0.18 (Ca), 0.14–0.17 (Sr), and 0.11–0.16 (Ba). A high BOP
value indicates a strong covalent bond, while a low BOP value
indicates an ionic or non-bonding relationship. The M–O
covalent contribution decreases as Zn–O 4 Cd–O, and
Be–O 4 Mg–O 4 Ca–O 4 Sr–O 4 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 displayed
in Table S1 (ESIw) and are unexceptional. The calculated
Mulliken effective charges (MEC, Table S1, ESIw) for the
metal ions are +1.30|e| (M = Zn), +1.27|e| (Cd), +1.14|e| (Be),
+1.59|e| (Mg), +1.35|e| (Ca), +1.39|e| (Sr), +1.37|e| (Ba).
A Bader topological analysis114–116 led to the calculated Bader
charges (BC) for the M-IRMOF-14 series that are also given in
Table S1 (ESIw). The BC for M and O (includes O1 and O2) in
the M-IRMOF-14 series indicate that the interaction between
M and O is almost ionic, since 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, +1.61|e| for Sr, and +1.61|e| for Ba) are
transferred from M to O. These data are in reasonable
agreement with the DOS and charge density analyses.
F.
Band structures and optical properties
Reports on the semiconducting behavior of MOFs117 have
triggered intense research in this area with the aim to develop
new materials for optoelectronic applications. The investigations of the optical properties of IRMOF-14 are therefore of
interest, as this novel pyrene-based material might find applications in organic semiconducting devices. The optical properties are also of fundamental importance, since these involve
not only 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
IRMOF-14 may also be important for certain applications.
The optical properties of IRMOF-14 (M = Zn) are discussed
in the following. The optical properties of the remaining
members (M = Cd, Be, Mg, Ca, Sr, Ba) of the M-IRMOF-14
series are given as figures in the ESI.w
The fundamental quantity of the optical properties is the
dielectric function e(o), which describes the features of linear
response of the system to electromagnetic radiation. Here e(o)
is connected to the interaction of photons with electrons. Its
imaginary part e2(o) can be derived from interband optical
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Fig. 5 Calculated optical properties of IRMOF-14: (a) dielectric function e(o), (b) reflectivity R(o), (c) refractive index n(o); extinction coefficient
k(o), (d) optical conductivity s(o), (e) energy loss function L(o), and (f) absorption a(o). The plots for IRMOF-1 and IRMOF-10 are included for
comparison.
transitions by calculating the momentum matrix elements
between the occupied and unoccupied wave functions within
the selection rules, and its real part e1(o) can be derived from
e2(o) by the Kramer–Kronig relationship.71 The real part of
e(o) in the limit of zero energy (infinite wavelength) equals the
square of the refractive index n. The other frequency dependent
linear optical properties, such as refractive index n(o), extinction
coefficient k(o), absorption coefficient a(o), optical conductivity
s(o), reflectivity R(o) and electron energy-loss spectrum L(o)
can be deduced from e1(o) and e2(o).71
CASTEP calculations were conducted to determine the
optical properties of IRMOF-14 and the results are shown
in Fig. 5. Previously calculated data for IRMOF-1 (MOF-5)
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and IRMOF-10 are superimposed for facile comparison
between these closely related MOF materials.
There are three main peaks in the e2(o) plot (Fig. 5a) of
IRMOF-14 at ca. 4.45, 6.85, and 15.29 eV. Similar peaks are
seen for the other M-IRMOF-14 members (see ESIw) though
there exist small differences between them. The real part of
dielectric function e1(o) (Fig. 5a and ESIw) allows the estimation
of the value of the refractive index n(o) at infinite wavelength,
n(0), to be 1.227 (M = Zn), 1.210 (Cd), 1.255 (Be), 1.223 (Mg),
1.197 (Ca), 1.185 (Sr), and 1.177 (Ba). Thus, there is a slight
decrease in n(0) from Zn to Cd, and from Be to Ba. At low
frequencies (0–2.5 eV), the imaginary part e2(o) is zero which is
consistent with the bandgap size of the M-IRMOF-14 series.
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The reflectivity spectrum (Fig. 5b) of IRMOF-14 shows two
lower-energy peaks at 4.11 and 6.80 eV. These arise mainly
from Zn (3d) - C/O (2p) as well as H (1s) - C/O (2p)
interband transitions. Another prominent peak is seen
at higher energy at 15.77 eV. Similar features are seen
throughout the M-IRMOF-14 series in ESI.w The reflectivity
approaches zero when the energy exceeds 30 eV for the whole
series. The values of reflectivity are 0.010227 (M = Zn),
0.009044 (Cd), 0.012729 (Be), 0.009962 (Mg), 0.008025 (Ca),
0.007100 (Sr), 0.006594 (Ba). Thus, the reflectivity decreases
uniformly from Zn to Cd, and from Be to Ba. The calculated
reflectivities over the entire frequency range are much smaller
than that in inorganic solids, e.g., the corresponding metal
oxides MO. For example, the reflectivity of IRMOF-14 of
0.010227 is only one tenth that of ZnO, ca. 0.1. This may be an
advantage for use of IRMOFs in optoelectronic devices, such
as solar cells and LEDs, where low reflectivity is desired.
IRMOF-14 has a finite value for the refractive index n(o)
(Fig. 5c) in the range 2.5 to 25 eV, and no refractive index at
energies below 2.5 eV or above 25 eV. The extinction coefficient k(o), i.e. the imaginary part of the complex refractive
index, of IRMOF-14 shows three peaks at around 4.63, 6.94,
and 15.58 eV (Fig. 5c). Similar features are seen for the other
M-IRMOF-14 members in ESI.w
The optical conductivity s(o) plot of IRMOF-14 is shown
in Fig. 5d. The real part of the complex conductivity has three
peaks at 4.57, 6.91, and 15.44 eV. Similar features are seen for
the other M-IRMOF-14 members in ESI.w
The electron energy-loss function L(o) (Fig. 5e) is an
important optical parameter that describes the energy loss of
a fast electron traversing in the material. The peaks in the L(o)
spectra represent the characteristics associated with the plasma
resonance, above which frequency the material is a dielectric
[e1(o) 4 0] and below which the material behaves like a
metallic compound in some sense [e1(o) o 0]. There are three
sharp peaks at 5.02, 7.19, and 17.12 eV; the peak at 7.19 eV
corresponds to the reduction of R(o). In the ESIw, very similar
features are seen for the other M-IRMOF-14 members, one
major difference being that an additional peak is seen at
25.0–28.0 eV for M = Ca, Sr and Ba, which is absent for
Zn, Cd, Be, and Mg.
IRMOF-14 has an absorption band (Fig. 5f) in the range
from 2.5 to 30 eV, with sharp peaks at 4.74, 6.99, and 15.70 eV.
Similar characteristics for the other M-IRMOF-14 members
are seen in the ESIw, a main difference being that an extra
peak is seen at 25.0–28.0 eV for M = Ca, Sr and Ba, which
is absent for Zn, Cd, Be, and Mg. The values of maximum
absorption coefficients are ca. 81 900 (M = Zn), 72 800 (Cd),
94 200 (Be), 77 200 (Mg), 65 900 (Ca), 62 500 (Sr), and
54 200 cm1 (Ba). There is a considerable difference in
the maximum absorption coefficients of the two Zn-based
materials IRMOF-14 (81 900) and ZnO (ca. 2.5 105 cm1),
i.e. the maximum absorption coefficient of the soft, porous
material IRMOF-14 is only ca. 30% of that of the corresponding hard material ZnO.
The overall calculated optical properties of the M-IRMOF-14
series in this work are similar to those of M-IRMOF-1
and M-IRMOF-10 in our recent contributions (see Fig. 5
for comparison),40,94,95 which is consistent with the fact
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that these series are topologically and structurally closely
related.
In conjunction with the optical properties calculations, the
band structures of the whole M-IRMOF-14 series were also
calculated. The results for the only experimentally available
system at present, IRMOF-14 (M = Zn), are shown in Fig. 6,
whereas qualitatively similar figures for the remaining members
are shown in the ESI.w For the face-centered cubic (FCC)
Brillouin zone the CASTEP module automatically chose
the W–L–C–X–W–K high symmetry directions for the band
structure plot. Fig. 6 shows that the bands in the valence band
as well as in the conduction band are almost parallel and
dispersionless, a feature that arises from the fact that the
material consists of well isolated inorganic nodes connected
by molecular PDC organic linkers. This structural arrangement induces an almost molecule-like electronic structure. The
bands at the VB maximum and CB minimum for IRMOF-14
are flat and this appears to be a common feature for these
MOF materials.118 This flat band behavior makes it impossible to unequivocally identify whether the band gap is direct
or indirect. However, the qualitative information from the
band structures may still help to understand the electronic
structures of MOF materials and provides further insight into
their optical properties.
Fig. 6 The electronic band structure of IRMOF-14. The Fermi level
is set to zero and placed in the valence band maximum.
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Conclusions
A detailed investigation on the ground state structure, formation
enthalpies, electronic structure, chemical bonding, and optical
properties of the whole M-IRMOF-14 (M = Zn, Cd, Be, Mg,
Ca, Sr, Ba) series has been conducted using DFT methods. The
following important conclusions are arrived:
(1) The calculations show that each material in the
M-IRMOF-14 series is soft and may exist in the highly symmetric
face-centered cubic (Fm3% m, 225) structure; the optimized atomic
positions and lattice parameters of IRMOF-14 are in good
agreement with the incomplete experimental results. We surmise
that our computational efforts may provide more accurate structural parameters than experiment. All calculated M-IRMOF-14
members have favorable (negative) enthalpies of formation.
(2) Electronic charge density, charge transfer, and ELF
analyses provide a consistent view of the bonding interactions
in the materials studied. The M–O bonding interaction is
mainly ionic, whereas C–O, C–H, and C–C as expected are
covalently bonded. The M–O ionicity increases from Zn to Cd,
and from Be to Ba.
(3) Electronic density of states studies show that the whole
M-IRMOF-14 series has a bandgap of ca. 2.5 eV, resulting in a
semiconducting character, independent of the identity of M.
These results support the notion that in the isoreticular
IRMOF series, the bandgap is governed primarily by the
nature of the organic linker and not by the cornerstone metal,
as long as this metal has a closed-shell electronic configuration.
(4) The calculated optical properties of the whole M-IRMOF-14
series provide useful information for future experimental
exploration. The fact that the reflectivity and maximum absorption coefficient of IRMOF-14 are only 10% and 30% of those of
the corresponding oxide ZnO may have practical consequences
in applications.
(5) The prediction of crystal structure, phase stability,
electronic structure, chemical bonding and optical properties
of M-IRMOF-14 will hopefully trigger further experimentation
in the area.
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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