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Microporous and Mesoporous Materials 175 (2013) 50–58
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Microporous and Mesoporous Materials
journal homepage: www.elsevier.com/locate/micromeso
A quantum mechanically guided view of Cd-MOF-5 from formation energy,
chemical bonding, electronic structure, and optical properties
Li-Ming Yang a,⇑, Ponniah Ravindran b, Ponniah Vajeeston b, Stian Svelle c, Mats Tilset a,⇑
a
Center of Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
Center for Materials Science and Nanotechnology, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
c
inGap Center of Research Based Innovation, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
b
a r t i c l e
i n f o
Article history:
Received 6 November 2012
Received in revised form 14 March 2013
Accepted 17 March 2013
Available online 24 March 2013
Keywords:
Metal-organic framework
DFT calculations
Electronic structure
Chemical bonding
Optical properties
a b s t r a c t
A systematic investigation of the crystal structure, chemical bonding, electronic structure, formation
energy, and optical properties of Cd-MOF-5 via DFT calculations is presented. The calculated bulk modulus (13.4 GPa) indicates that Cd-MOF-5 is a soft material. The estimated band gap for Cd-MOF-5 is
3.6 eV, indicating semiconducting behavior. Moreover, large formation enthalpy (41 kJ mol1) indicates
its high stability and could be synthesizable. The systematic investigation on the optical response properties of Cd-MOF-5 will trigger the experimental efforts in this direction. The detailed chemical bonding
analysis reveals the nature of bonds, i.e., Cd–O having mainly ionic interaction whereas O–C, H–C and C–C
exhibit mainly covalent interactions.
Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction
Metal-organic frameworks (MOFs) [1,2], which exhibit large
surface area and porosity retention upon solvent removal, have attracted considerable attention due to their elegant topology and
potential applications in separation, gas storage, nonlinear optics,
and catalysis [1,2]. A key challenge is the rational design and the
precise control of the formation of a particular network through
the appropriate choice of the constituent metal and bridging organic linkers, which has already been shown in a series of isoreticular metal-organic frameworks (IRMOFs) [3–5] with systematically
designed pore size and functionality and application in methane
storage. By varying the length of the organic backbone of these ligands, many desired MOFs have been successfully built. The further functionalization could be varying the metal ions in the
nodes and substitutions on the ligand. Academic interests as well
as potential industrial applications [6,7] provide driving forces
for the intensified development of new MOFs [8]. The most wellknown example is probably the prototypical MOF-5 (IRMOF-1)
[9], which has been subject to a plethora of investigations from
experimental as well as theoretical perspectives [10]. Investigations have also been conducted to tailor the electronic properties
of MOF-5 [11,12]. Other efforts addressed the electrostatic poten-
⇑ Corresponding authors. Fax: +1 47 22855441 (L. -M. Yang).
E-mail addresses: [email protected] (L.-M. Yang), [email protected]
(M. Tilset).
1387-1811/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.micromeso.2013.03.020
tial and charge density for MOF-5 [13] to gain additional insight
into the interaction of H2 with MOF-5. Mechanical properties of
MOF-5, including bulk moduli and elastic constants, have been
studied [14,15]. Additionally, MOF-5 has attracted attention for
possible use as semiconductor [16] materials. Moreover, numerous
contributions have focused on the spectroscopic properties of
MOF-5. These include X-ray diffraction (XRD) [9,17–21], infrared
spectroscopy (IR) [22,23], ultraviolet/visible spectra (UV/Vis) [21],
nuclear magnetic resonance (NMR) [19,21,24], inelastic neutron
scattering (INS) [25,26], neutron powder diffraction (NPD) [27],
diffuse reflectance infrared spectroscopy (DRIS) [28], single crystal
neutron diffraction (SCND) [29], Raman spectroscopy [30], energy
dispersive X-ray (EDX) [31], terahertz time-domain spectroscopy
(THz TDS) [20], DRIFT [32], X-ray absorption near edge structure
(XANES) [33], X-ray absorption spectroscopy (XAS) [21], transmission electron microscopy (TEM) [21], Extended X-ray absorption
fine structure (EXAFS) [21], photoluminescence [30], and time-resolved diffuse reflectance spectra [16]. Particularly, recent experiments have demonstrated that IRMOFs can be used as efficient
photocatalysts with a tunable band gap [32]. Furthermore, it has
been experimentally demonstrated that ZnO is the origin of the
quantum dot behavior in MOF-5 [30]. 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. More recently, we performed a systematic investigations on the chemical bonding, electronic structure, and optical properties for MOF-5, [34] which might
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
contribute to a much more comprehensive understanding about
this kind of material and shed insight into the synthesis and application of novel and stable MOFs.
In sharp contrast to the prototypical MOF-5, very little attention
has been paid to the heavier congener, Cd-MOF-5, even though
numerous Cd-based MOFs have been experimentally synthesized
so far. One example is the 3D porous MOF, [C6H3 N2O4Cd]NH4,
was constructed from Cd(II) and 2-methylimidazole-4,5-dicarboxylic acid building blocks [35]. Recently, a new CdL2-MOF was
synthesized from an asymmetric Schiff-base ligand LH [36]. Additionally, a series of Cd imidazolate frameworks have been synthesized with polymorphism, high thermal stability, and large surface
areas [37]. The above fruitful experiments on Cd-based MOFs triggered our interest in Cd-MOF-5. Additionally, Srepusharawoot
et al. [38] recently reported that the H2 absorption energies in
Cd-MOF-5 are generally stronger than in MOF-5. Thus, it was suggested that Cd-MOF-5 would be better suited to store hydrogen at
higher temperatures than MOF-5. This is another motivation for
the current detailed investigation on Cd-MOF-5. Moreover, recently, polymeric Cd(II) complexes have been intensively investigated for attractive fluorescence properties and potential
applications as new luminescent materials, such as light-emitting
diodes (LEDs) [39,40]. This is also a good reason to systematically
study Cd-MOF-5 from various aspects.
There appears to be no systematic studies on the Cd-MOF-5 so
far. Among the many questions to be asked are (1) is it possible to
synthesize Cd-MOF-5? (2) if so, what can be said about the stability
of Cd-MOF-5? (3) how does its electronic structure, chemical bonding, and optical properties compare to related MOFs? (4) can the
results be used to identify potential applications of Cd-MOF-5?
(1) Formation enthalpy constitutes 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. Also, these data can confirm the experimentally synthesized materials. Up to now, there is no
systematic investigation on the formation enthalpy for CdMOF-5.
(2) The bonding interaction between the constituents is important to understand the chemical and physical properties of a
system, including structure, stability and physicochemical
properties of Cd-MOF-5, and will help to improve its applications in absorption and separation, catalysis, sensing, and
molecular recognition. Additionally, it will guide the understanding of other MOFs.
(3) The electronic structure is first and foremost important for
the understanding the chemical and physical properties of
any specific materials. This is also the case for Cd-MOF-5.
(4) The detailed information from optical properties will shed
insight onto the potential applications of Cd-MOF-5 as photocatalysts, active components in hybrid solar cells, and electroluminescence cells. Moreover, Cd-MOF-5 may have
potential in the organic semiconducting devices such as
field-effect transistors and OLEDs, etc.
In the present work, Cd-MOF-5 is investigated using DFT calculations with the GGA-PBE functional implemented in the VASP
code [41,42]. The optical properties of Cd-MOF-5 were calculated
using the CASTEP module [43] of the Material Studio 5.0 program
[44].
2. Computational details
The Vienna ab initio simulation package (VASP) [41,42] has been
used for the total-energy calculations to study the structural stabil-
51
ity and to establish equilibrium structural parameters. The generalized gradient approximation (GGA) [45–47] 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-augmentedwave (PAW) [42,48] Perdew, Burke, and Ernzerhof (PBE) [47] 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 plane-wave cutoff of 500 eV, which guarantees that absolute
energies are converged to within a few meV/f.u. This has been
tested to be accurate and reliable for our Cd-MOF-5 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.
Since Cd-MOF-5 has a rather large system size of the primitive
cell (106 atoms), the C-point alone is sufficient for sampling the
Brillouin zone during geometry optimization as previously pointed
out and used by Blomqvist et al. [49]. The band structure and density of state (DOS) calculations were performed on the fully optimized structure with only C-point. 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, bond
overlap population (BOP) values were analyzed with on the fly
pseudopotential estimated on the basis of the Mulliken population
as implemented in the CASTEP code [43]. In order to understand
the chemical bonding and interactions between constituents in
Cd-MOF-5 and its analogues, charge density, charge transfer, and
electron localization function (ELF) [50–53] analyses were performed. Linear optical properties were also calculated, including
dielectric function, absorption coefficient, reflectivity, refractive index, optical conductivity, and energy loss function for Cd-MOF-5
with the use of ultrasoft pseudopotential using the CASTEP code.
In parallel with optical properties calculations, the band structure
was calculated with ultrasoft pseudopotential using CASTEP. This
should provide useful information concerning the electronic structures and optical properties. The method used for the calculation of
optical properties and band structures has been proven to be reasonable, and compares favorably with corresponding experimental
spectra in a series of previous papers from our group [34,54–57].
3. Results and discussion
3.1. Structural and topological details
Cd-MOF-5 has the same topology as MOF-5, also known as IRMOF-1, which is the first member of a series of isoreticular metal-organic frameworks (IRMOFs) with oxide-centered Zn4O
tetrahedra as nodes linked by organic molecules and can be synthesized based on the reticular synthesis chemistry proposed by
Yaghi et al. [5,58]. By replacing Zn with Cd in the nodes, then CdMOF-5 is obtained. Cd-MOF-5 and MOF-5 have the same organic
linker, i.e., benzene-1,4-dicarboxylate (BDC). The conventional cell
of Cd-MOF-5 crystal structure has cubic Fm-3m symmetry
52
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
(no. 225) and contains eight formula units of Cd4O(BDC)3. The
primitive cell includes two nodes and six linker molecules, corresponding to two Cd4O(BDC)3 formula units. The crystal structure
of Cd-MOF-5 is illustrated in Fig. 1. Different crystallographic sites
in Cd-MOF-5 includes one type of Cd, two types of O, three types of
C, and one type of H occupying 32f, 8c, 96k, 48g, 48g, 96k, and 96k
Wyckoff positions, respectively.
3.2. Structural optimization of Cd-MOF-5 from total-energy
calculation
For the structural optimization, the starting geometry by
replacing Zn atom with Cd in MOF-5 was used. The theoretical
ground-state structure was obtained from this by full geometry
optimization, i.e., the atom positions and cell parameters were
fully relaxed.
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 EOSs, i.e., Murnaghan [59], BirchMurnaghan [60], and Universal
equation of states [61]. The bulk moduli and their pressure derivatives (in parentheses) for Cd-MOF-5 are 13.35 GPa (3.41),
13.36 GPa (3.43), and 13.36 GPa (3.43) from the above three EOSs,
respectively. These B0 values are comparable to the value of
14.89 GPa [12] previously obtained by VASP calculations by fitting
the E–V curve to the Birch–Murnaghan EOS. These B0 and B00 values
of Cd-MOF-5 are slightly smaller than that of MOF-5, i.e., they are
15.37 GPa (5.06), 15.37 GPa (5.13), and 15.37 GPa (5.17) for the
above three different EOS, respectively [62]. This is consistent with
the fact that the bigger the lattice parameter, the smaller the bulk
modulus in MOFs of the same topology [34,54–57]. The calculated
bulk moduli for Cd-MOF-5 are awaiting experimental confirmation. The linkage between the Cd4O group and the organic moieties
results in a rather soft material with relatively small bulk modulus
compared with that of CdO in the wurtzite (h-MgO) (theoretical,
103.7 GPa [63]), zincblende (theo., 112.9 GPa [63]) and rocksalt
(theo., 154.4 GPa; [63] experimental, 148 GPa [64]) structures.
The calculated value of B0 indicates that Cd-MOF-5 is a readily
compressible system like the prototypical MOF-5 which is one of
the well studied systems in this family. Since the inorganic basic
system CdO has a much larger bulk modulus, the lowering of B0
in Cd-MOF-5 is caused by the introduction of the organic linker
molecules and the formation of large pores.
The optimized atomic positions, calculated equilibrium lattice
parameter, as well as previously reported calculated lattice parameters are listed in Table 1. The lattice parameter of Cd-MOF-5 obtained by PBE-GGA calculations in the present work (27.3547 Å)
is in good agreement with the previously reported data (27.33 Å)
[38] with the same type of pseudopotential. From Table 1, it can
be seen that different type pseudopotential (GGA vs. LDA) calculations will lead to a slight difference in the lattice parameters (the
GGA values are slightly bigger than that of LDA), but the data are
mutually quite consistent. The lattice parameter of Cd-MOF-5 is
greater than the experimental value for the prototypical MOF-5
(25.8849 Å) [9], which is consistent with the fact that Cd has a larger atomic or ionic radius than Zn. For further structure details of
Cd-MOF-5, some selected bond lengths and angles together with
the previously known results were listed in Table 2. It can be seen
(from Table 2) that the data from different pseudopotential calculations are generally agree well with each other even though the
GGA data are slightly larger than that of LDA.
3.3. Energy of formation considerations
Information about formation enthalpies constitute an excellent
means to establish whether theoretically predicted phases are
likely to be stable and such data may serve as a guide to evaluate
possible synthesis routes. There are several interesting works reported in the literature on the reaction enthalpies by consideration
of electric total energies, zero point energy vibrational correction
and thermal contribution (within the harmonic approximation)
[65]. Moreover, it should also be noted that kinetic factor can play
a notable role during the preparation [66]. Here we are interested
to know whether a particular hypothetical compound is energetically feasible to be synthesizable or not. We believe that such study
will give qualitative trend in the stability though it cannot be used
to quantitatively predict the reaction enthalpies. Further, in order
to estimate the vibrational entropy contribution to total energy
one should perform computationally intensive phonon calculation
Fig. 1. The crystal structure of Cd-MOF-5 in the cubic Fm-3m symmetry (no. 225). The nonequivalent atoms with labels Cd, O1, O2, C1, C2, C3, and H are the basis for the
understanding of the chemical bonding and interpretation of the partial density of states (PDOS).
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
Table 1
The optimized structural parameters as well as previously reported lattice parameters
for Cd-MOF-5.
Property
PBE-GGA
Crystal system
Space group
Atoms/cell (fcc)
a (Å)
Cubic
Fm-3m (225)
106
27.3547 (26.6125 (LDA) [12], 26.83 (LDA) [38],
27.32 (PW91-GGA) [38], 27.33 (PBE-GGA) [38])
Atomic positions (x, y, z)
(0.2960, 0.2960, 0.2960)
(1/4, 1/4, 1/4)
(0.3730, 0.2205, 0.2205)
(1/4, 0.1062, 1/4)
(1/4, 0.0512, 1/4)
(0.4746, 0.7186, 0.7186)
(0.4541, 0.6945, 0.6945)
Atom type
Cd (32f)
O1 (8c)
O2 (96k)
C1 (48g)
C2 (48g)
C3 (96k)
H1 (96k)
within the harmonic approximation. As the number of atoms involved in the present calculations is very large, the phonon calculation is very time consuming and is out of scope of the present
study. It should be pointed that the relative stability order from
reaction enthalpies calculations usually refer to a compound having difference structure (phase). This has been shown in several recent papers [55,57]. It should be pointed out that the MOF-5
synthesized by Yaghi et al. [9] has only one phase with highly cubic
symmetry Fm-3m (no. 225). This experimentally reported high
symmetric phase attracted much attention from both experiment
and theory. Here, we focused on the viability of synthesizing this
highly symmetric framework phase using Cd instead of Zn in
MOF-5. There are several ways to evaluate the reaction energies,
our way is only one among them. Anyway the present approach
give qualitative information about the changes in the formation
enthalpies between Cd- and Zn-MOF-5.
For the exploration of the thermodynamic feasibility of assembling these materials from the elements (Eq. (1)[54]) we have computed the total energies for C (R-3m), O2 (P4/mmm), H2 (P4/mmm),
and Cd (P63/mmc) in their ground state structures with full geometry optimization. The reaction enthalpies for MOF formation were
calculated from the difference in the total energy between the
products and reactants involved in the reaction. The results establish unambiguously that Eq. (1) depicts an exothermic reaction for
the Cd-MOF-5.
8Cd þ 13O2 þ 48C þ 12H2 ! Cd8 O26 C48 H24
53
render Cd-MOF-5 stable, suggesting high possibility of successful
synthesis. We eagerly await the experimental synthesis and investigation of the properties of the predicted Cd-MOF-5.
3.4. Electronic structure
The total electronic density of states (TDOS) and partial density
of states (PDOS) at the equilibrium volumes of Cd-MOF-5 are displayed in Fig. 2. The calculated band gap Eg for Cd-MOF-5 is
3.601 eV, indicative of semiconductor character. This is comparable to the value of 3.4885 eV previously obtained by LDA calculations [12]. The band gap of Cd-MOF-5 is also comparable to that
of MOF-5 (3.4-3.5 eV) [16,30,62]. It should be noted that DFT calculated band gaps tend to be generally lower than experimentally
determined band gaps. This underestimation of the calculated
band gaps is an intrinsic feature of the ab initio method and is related to the DFT limitations, namely not taking into account the
discontinuity in the exchange-correlation potential [67]. To overcome this discrepancy, the so-called scissor operator [68], D, can
be introduced, which effectively eliminates the difference between
the theoretical and experimental gap values by means of a simple
rigid shift of the unoccupied conduction band with respect to the
valence band. Here, we pick up one of the mostly studied oxides,
ZnO, as a comparison and a basis for the discussion on the issue
of band gap predicted by DFT. For Eg of bulk ZnO, the calculated
band gaps are significantly smaller than the experimental values.
(LDA = 0.744/0.573 eV; GGA = 0.804/0.641 eV, LDA + U = 1.988/
1.486 eV, GW = 2.255/2.100 eV, experimental 3.455/3.300 eV for
ZnO-w/-z, respectively) [69]. However, in a recent contribution
[62], it was found that the DFT calculations unexpectedly gave a
ð1Þ
The magnitude of the calculated formation enthalpy of CdMOF-5 (41 kJ mol1) shows that the formation enthalpy is slightly
smaller than that of prototypical MOF-5 (46 kJ mol1) obtained
via the similar scheme from DFT calculations, indicating that the
stability of Cd-MOF-5 is nearly the same as that of experimentally
synthesized MOF-5. The value is certainly sufficiently large to
Table 2
Optimized bond length (Å) and angles (°) for Cd-MOF-5 at the equilibrium volumes.
Atoms in Cd-MOF-5 are numbered according to Fig. 1.
Cd–O1
Cd–O2
C1–O2
C1–C2
C2-C3
C3-C3
2.179
2.200
(2.115)a
Cd–O1–Cd
109.471
1.277
(1.264)
O1–Cd–O2
108.428
1.503
(1.469)
O2–Cd–O2
110.494
(110.010)
1.404
(1.386)
Cd–O2–C1
133.397
1.391
(1.373)
O2–C1–C2
116.561
C3–H
1.089
C1–C2–C3
120.188
a
The data in (parentheses) are from Ref. [12].
Fig. 2. The calculated total density of states (TDOS) and partial density of states
(PDOS) for Cd-MOF-5 in the cubic Fm-3m symmetry (no. 225).
54
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
band gap value in very good agreement with that obtained from
experimental studies for MOF-5 [16,30]. Whereas, for CdO, the
band gap is 2.16 ± 0.02 eV [70], which is much smaller than that
of Cd-MOF-5. This clearly confirms our previous conclusion [62]
that there is no one to one relationship between corresponding
band gaps of the MOF and the corresponding oxide.
3.5. Chemical bonding
3.5.1. Partial density of states
From the PDOS of Cd-MOF-5, the distribution of various electronic states in the valence band and the conduction band can be
characterized. The d- and s-states of Cd and H atoms, respectively,
contribute dominantly to the valence band (VB). Both s- and pstates of C and O atoms also contribute to the VB. The p-states of
C1 and C2 are distributed energetically in the same range and thus
they can effectively overlap and form very strong covalent bonds.
This is consistent with the following analysis of the electron localization function plot, i.e. the ELF values between C1 and C2 are
higher than that between other C-atoms. Furthermore, valence
electrons from both C1 and C2 atoms are also spatially distributed
closer to each other to make strong covalent bonds. The s-states of
H can overlap with the p-states of C3 in the energy range between
7.5 and 2.5 eV and can form covalent bonds. The p-state of C1
can overlap with that of O2 in the energy range between 8.0
and 2.5 eV and form a directional bond between them. Although
the p-state of C1 is energetically degenerate with that of O1, in the
whole valence band, the spatial separation of these two atoms precludes covalent bonding between C1 and O1. The d-state of Cd is
well localized, and also the Cd s electrons are transferred to the
neighboring atoms, which leads to ionic bonding between Cd and
O. This is also consistent with the following analysis of charge density and ELF.
3.5.2. Charge density/transfer, ELF and BOP analyses
In order to further improve the understanding of the bonding
interactions, we turn our attention to charge density/transfer,
ELF, and bond overlap population (BOP)/Mulliken population analyses. From Fig. 3a, it is clear that C, H, and O atoms in the organic
linker form molecule-like O2C-C6H4-CO2 structural subunits. As a
result, the C–C, C–H, and C–O bonding interactions are dominantly
covalent in character. Moreover, there is substantial charge density
distributed between C atoms, and between C and H and O atoms in
the O2C-C6H4-CO2 subunits. This substantiates the presence of
covalent bonding. From Fig. 3a, it can be seen that the charges
are spherically distributed at the Cd and O sites, which is characteristic for systems having ionic interactions. Additionally, there
is no noticeable charge density distributed between Cd and O
atoms, which clearly demonstrates the presence of ionic bonding.
Another convenient and illustrative way to represent and analyze
the bonding effects in the Cd-MOF-5 is to use charge transfer plots.
The charge-transfer contour is the self-consistent electron density
in a particular plane, qcomp, from which is substracted the electron
density of the overlapping free atoms in the same lattice, qatom, i.e.,
Dq(r) = qcompqatom. This allows the visualization of how electrons
are redistributed in a particular plane compared to free atoms due
to the bonding in the compound. From Fig. 3b it is clear that electrons are transferred from Cd to O sites. But the charge transfer
from Cd is not isotropic as clearly seen from Fig. 3a. The anisotropic
charge transfer from Cd to the O sites indicates the presence of
iono-covalent bonding between Cd and O, with a dominant ionic
bonding interaction. Furthermore, electron densities from the C,
O, and H atoms are transferred to the regions in between these
atoms, and the nonspherical electron distribution clearly indicates
the presence of strong covalent bonding. From Fig. 3c, it can be inferred that the large value of ELF at the O site indicates strongly
paired electrons with local bosonic character. The negligibly small
ELF between Cd and O, and the small value of ELF at the Cd site
(partially due to the presence of d electrons) with spherically symmetric distribution indicate that the bonding interaction between
Cd and O is dominated by an ionic interaction. The ELF distribution
at the O site is not spherically symmetric and it is polarized towards Cd atoms, indicating the presence of directional bonding between Cd and O. A certain polarized character is found in the ELF
distribution at the H sites in Cd-MOF-5, indicating the presence
of polar covalent bonding. There is a maximum in the ELF between
the C atoms and between C and O, indicating the covalent bonds.
From the above analyses, one can clearly visualize mixed chemical
bonding in Cd-MOF-5.
In order to give a better understanding about the interaction between the constituents, the bond overlap population (BOP) values
were calculated on the basis of the Mulliken population analysis
[71]. The BOP can provide useful information about the bonding
property between the two atoms. A high BOP value indicates a
strong covalent bond, while a low BOP value indicates an ionic/
nonbonding interaction. The calculated BOP values for the Cd–O,
C–O, C–C, and C–H bonds are displayed in Table 2. From Table 2
it can be seen that the BOP values for the Cd–O bonds in the crystal
fall in the range 0.21–0.22, which indicates a dominantly ionic
character. Similarly, the calculated BOP value for the C–O bond is
0.91, which is very close to a covalent C–O single bond. The BOP value for C–H is 0.89, indicative of the predominant covalent character. For the C–C bonds, the calculated BOP values vary between
0.83 and 1.10, the latter of which is almost equal to the covalent
C–C bond in diamond (1.08), and therefore, the C–C bonds are
strong covalent bonds. It should be noted that the order of BOP values is Cd–O < C–H C–O < C–C. Therefore, the Cd–O bonds in the
nodes of Cd-MOF-5 have predominant ionic character similar to
that present in CdO, whereas the C–H, C–O and C–C bonds in the
linkers of Cd-MOF-5 have covalent interactions such as those in
regular organic molecules.
The above discussions demonstrated that analyses based on
charge density/transfer, ELF, and bond overlap population (BOP)/
Mulliken population analyses give a consistent view of the bonding
in Cd-MOF-5.
The calculated Mulliken charges and electron configuration of
atoms for Cd-MOF-5 are presented in Tables 3 and 4, respectively.
The corresponding Mulliken effective charges (MEC) (in Table 3)
values for H and Cd are +0.29|e| and +1.28|e|, respectively. The
unsubstituted aromatic C atoms bear negative charges (0.27|e|).
While, the carboxylate-bearing aromatic C atoms bear nearly zero
charge (0.06|e|). The carboxylate group C atoms bear positive
charges (+0.59|e|). Finally, the central O in the Cd4O node has a single unit of negative charge (1.02|e|), which indicates that the four
Cd atoms together have transferred a charge corresponding to
one electron to the central O. The carboxylate O atoms in the
BDC linker bear negative charges (0.63|e|) indicating that there is
partial electron transfer from Cd to O. From the Mulliken population analysis we can also identify the distribution of electrons in
different orbitals in Table 4. As might be intuitively predicted, for
H, the electron is only located at the s orbital; for C and O, electrons
are located at both s and p orbitals; and for Cd, electrons are located at s, p and d orbitals.
3.5.3. Bader topological analysis
In an effort to quantify the bonding and estimate the electron
distribution at and between participating atoms we have also
made Bader topological analysis. Although there is no unique definition to identify how many electrons are associated with an atom
in a molecule or an atomic group in a solid, it has nevertheless
proved useful in many cases to perform Bader analyses [72–73].
In the Bader charge (BC) analysis, each atom of a compound is
55
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
Fig. 3. Calculated charge density (a), charge transfer (b), and electron localization function (c) plots for Cd-MOF-5 in the (1 1 0) plane.
Table 3
The calculated Mulliken effective charge (MEC; given in terms of e), bond overlap
populations (BOP) and Bader charges (BC; given in terms of e) for Cd-MOF-5. Atoms in
Cd-MOF-5 are numbered according to Fig. 1.
Atom
MEC (e)
BOP
BC (e)
H
C1
+0.29
+0.59
+0.0571
+2.7281
C2
C3
O1
O2
Cd
0.06
0.27
1.02
0.63
+1.28
0.89 (H–C3)
0.91 (C1–O2)
0.83 (C1–C2)
1.08 (C2–C3)
1.10 (C3–C3)
0.21 (O1–Cd)
0.22 (O2–Cd)
0.21–0.22 (Cd–O)
0.0057
0.0021
1.2144
1.7548
+1.3192
surrounded by a surface (called Bader regions) that run through
minima of the charge density. The total charge of an atom is determined by integration of electrons within the Bader region. The calculated Bader charges for Cd-MOF-5 are given in Table 2. The BC for
Cd and O (includes O1 and O2) in the Cd-MOF-5 compound indicate that the interaction between Cd and O is partially ionic
(+1.3192|e| are transferred from Cd to O). This finding is consistent
with the DOS and charge density analyses. Within the Cd4O units,
Table 4
The electron configuration of atoms for Cd-MOF-5 from atomic populations
(Mulliken).
Atom
s
p
d
f
Total
Charge (e)
H
C1
C2
C3
O1
O2
Cd
0.71
0.94
1.09
1.18
1.91
1.80
0.42
0.00
2.47
2.96
3.09
5.12
4.83
0.32
0.00
0.00
0.00
0.00
0.00
0.00
9.98
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.71
3.41
4.06
4.27
7.02
6.63
10.72
0.29
0.59
0.06
0.27
1.02
0.63
1.28
Cd donates nearly 1.32 electrons, which is somewhat smaller than
expected in a purely ionic picture. This discrepancy is associated
with the noticeable covalency also present between Cd and O as
demonstrated in Section 3.5.2. Yet, the effect may also be caused
by artifacts when making boundaries to integrate charges in each
atomic basin using Bader’s ‘‘atoms in molecule’’ approach. Anyway,
the results from the BC analysis is consistent with the charge density, charge transfer, ELF, and PDOS analysis, i.e., Cd atoms donate
electrons to the O sites.
56
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
3.6. Band structure and optical properties
The coordination polymeric systems usually display different
optical properties as compared to the free ligands, such as fluorescent excitation/emission wavelength, intensity, lifetime, and so on.
This provides an effective way to produce functional materials
with desired properties. Nevertheless, up to now, rational design
and synthesis of desired coordination polymers is still a challenge.
Hopefully, the computational simulations will be an indispensible
tool in this direction. The studies of the optical properties for CdMOF-5 are of interest for example in view of potential uses of this
material in hybrid solar cell applications as an active material or in
the buffer layer between the electrodes and inorganic active materials. Optical properties studies for Cd-MOF-5 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. Moreover, it is also
related to the excited states of Cd-MOF-5, from which one can gain
insight into the excited electronic properties of Cd-MOF-5 which
may also be important for certain applications.
The central quantity of the optical properties is the dielectric
function e(x), which describes the features of linear response of
the system to an electromagnetic radiation, which again governs
the propagation behavior of radiation in a medium. Here e(x) is
connected with the interaction of photons with electrons. Its imaginary part e2(x) 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 e1(x) can be derived from e2(x) by the Kramer–
Kronig relationship [75]. The real part of e(x) in the limit of zero
energy (or infinite wavelength) is equal to the square of the refractive index n(x). All the frequency dependent optical properties,
such as refractive index n(x), extinction coefficient k(x), absorption coefficient a(x), optical conductivity r(x), reflectivity R(x)
and electron energy-loss spectrum L(x) can be deduced from
e1(x) and e2(x) [75].
CASTEP calculations have been performed to estimate the optical properties of Cd-MOF-5, and the results are shown in Fig. 4. As a
comparison, the optical properties of MOF-5 are also superimposed
in Fig. 4. Even though there are some differences in the optical
properties between Cd-MOF-5 and MOF-5, the global shape of
the optical properties for both Cd-MOF-5 and MOF-5 are similar.
In the following sections, we will focus on the discussion and analysis on the optical properties of Cd-MOF-5.
There are three main peaks in the e2(x) plot (Fig. 4a) of CdMOF-5. Two are located at ca. 5.27 and 6.55 eV, and the third at
higher energy, ca. 15.07 eV. The real part of dielectric function
e1(x) (Fig. 4a) allows us to estimate the value of the refractive index at infinite wavelength is 1.2229. At the low frequency (0–
3.6 eV), the imaginary part e2(x) is zero below the bandgap, which
is consistent with the order of bandgap of Cd-MOF-5.
The reflectivity spectrum (Fig. 4b) of Cd-MOF-5 shows major
peaks at ca. 5.03 (very strong and sharp) and 6.49 eV. The reflectivity at infinite wavelength is ca. 0.01. These two major peaks mainly
arise from the Cd (3d) ? O (2p) interband transitions. This is consistent with the order of bandgap of Cd-MOF-5. Another strong and
Fig. 4. Calculated optical properties for Cd-MOF-5 and MOF-5: (a) dielectric function e(x), (b) reflectivity R(x), (c) refractive index n(x); extinction coefficient k(x), (d)
optical conductivity r(x), (e) energy loss function L(x), and (f) absorption a(x).
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
sharp peak located at around 15.24 eV together with two shallow
shoulders on the left (ca. 13.15 eV) and right (ca. 16.25 eV) sides,
respectively. Cd-MOF-5 has a finite value for the reflectivity R(x)
(Fig. 4b) in the range 3.6–40 eV, and no reflectivity at energies below 3.6 eV or above 40 eV.
The Cd-MOF-5 has a extinction coefficient k(x) (the imaginary
part of the complex refractive index) (Fig. 4c) in the range 3.6–
35 eV, and no extinction coefficient k(x) in the energy regions lower than 3.6 eV or higher than 35 eV. The extinction coefficient k(x)
(Fig. 4c) of Cd-MOF-5 shows three peaks at ca. 5.38, 6.67, and
15.25 eV, respectively.
The optical conductivity r(x) plot of Cd-MOF-5 is shown in
Fig. 4d. The real part of the complex conductivity has three peaks
at ca. 5.37, 6.67, and 15.18 eV, respectively.
The electron energy-loss function L(x) (Fig. 4e) is an important
optical parameter describing the energy loss of a fast electron traversing in a certain material. The peaks in the L(x) spectra represent the characteristics associated with the plasma resonance
and the corresponding frequency is the so-called plasma frequency
above which the material is a dielectric [e1(x) > 0] and below
which the material behaves like a metallic compound in some
sense [e1(x) < 0]. In addition, the peaks of the L(x) spectra overlap
the trailing edges in the reflection spectra. There are two peaks of
57
L(x) of Cd-MOF-5 at around 5.67 and 6.95 eV, which corresponds
to the reduction of R(x). Another very strong and very sharp located at around 16.70 eV.
The Cd-MOF-5 has an absorption band (Fig. 4f) from 3.6 to
40 eV, which contains two sharp peaks at around 5.49 and
6.73 eV. Another strong broad peak (similar to twin peaks) centrally located at ca. 15.35 and 16.18 eV, together with a broad
shoulder at ca. 22.21 eV from the right side.
In general, it can be seen (from Fig. 4) that the optical response
of Cd-MOF-5 is as strong as that of MOF-5 even though there exist
somewhat small difference of peaks and positions between them.
This could be understandable from the fact that they (Cd-MOF-5
and MOF-5) both have the same topology and belong to the same
IRMOFs series.
In parallel with the optical properties calculations, the band
structure of Cd-MOF-5, which is similar to that of MOF-5, was also
calculated. The result for Cd-MOF-5 is shown in Fig. 5. For the facecentered cubic (FCC) Brillouin zone the CASTEP automatically
chose the W–L–C–X–W–K high symmetry directions for the band
structure plot. From Fig. 5 one can see that the bands in the valence
band as well as in the conduction band are very flat, almost parallel
and dispersionless. As discussed in Section 3.1 about the structural
aspects of Cd-MOF-5, the Cd4O nodes are well isolated and connected by BDC organic molecular linkers. This well isolated structural arrangement makes a molecule-like electronic structure and
this is the origin for the dispersionless bands in Cd-MOF-5. The
bands at the VB maximum and CB minimum for Cd-MOF-5 are flat
and this is a common feature for these MOFs materials [12]. This
flat band behavior makes it impossible to unequivocally identify
whether the band gap is direct or indirect. But, we still can gain
some qualitative information from the band structures that helps
to understand the electronic structures of MOF materials and provides further insight into their optical properties.
4. Conclusions
We have performed a systematic study of the solid-state structure, electronic structure, chemical bonding, and optical properties
of Cd-MOF-5 by DFT calculations. The main conclusions are as
follows:
Fig. 5. The calculated electronic band structure of Cd-MOF-5. The Fermi level is set
to zero and placed in the valence band maximum.
(1) The calculations show that Cd-MOF-5 exists in the same
cubic (Fm-3m, 225) structure as that of MOF-5; the lattice
parameter is in very good agreement with recent theoretical
results. The estimated bulk modulus indicates that Cd-MOF5 is a soft material. Moreover, the large negative formation
enthalpy indicates Cd-MOF-5 is thermodynamically as stable as that of prototypical MOF-5 and very likely to be synthesized under proper conditions.
(2) Electronic charge density, charge transfer, ELF, BOP and Bader Charge analyses shed light on the nature of the Cd–O, C–O,
C–H, and C–C bonds. The analyses consistently support the
notion that the bonding interaction between Cd–O is mainly
an ionic interaction, whereas those between C–O, C–H, and
C–C are mainly covalent interactions.
(3) Electronic density of states and band structure studies show
that Cd-MOF-5 has a band gap of ca. 3.6 eV, indicating semiconductor character.
(4) The calculated optical properties of Cd-MOF-5 provide useful
information for future experimental investigations. Moreover, Cd-MOF-5 might be used as a new semiconducting
material and have potential applications in semiconducting
devices such as field-effect transistors, solar cells, and organic
light-emitting devices (OLEDs). Additionally, Cd-MOF-5 may
also have the potential applications in catalysis since there
are myriad reports on MOFs as catalysts so far.
58
L.-M. Yang et al. / Microporous and Mesoporous Materials 175 (2013) 50–58
(5) The prediction of crystal structure, phase stability, electronic
structure, chemical bonding and optical properties of CdMOF-5 will hopefully trigger further experimentation in this
direction.
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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