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Ab initio investigations on the crystal structure, formation enthalpy,electronic structure, chemical bonding, and optical properties ofexperimentally synthesized isoreticular metal–organic framework-10 and itsanalogues: M-IRMOF-10 (M = Zn, Cd, Be, Mg, Ca, Sr and Ba){

Li-Ming Yang,*a Ponniah Ravindran,b Ponniah Vajeestonb and Mats Tilset*a

Received 20th May 2011, Accepted 31st October 2011

DOI: 10.1039/c1ra00187f

The equilibrium solid-state structure, electronic structure, formation enthalpy, chemical bonding, and

optical properties of IRMOF-10 and its alkaline earth metal analogues M-IRMOF-10 (M = Cd, Be,

Mg, Ca, Sr, Ba) have been investigated with density functional calculations. The unit cell volume and

atomic positions were fully optimized with the GGA functional. This supplements the incomplete

experimental structural parameters available for Zn-IRMOF-10. The calculated bulk moduli decrease

monotonically from Zn to Cd, and from Be to Ba, and indicate that Zn-IRMOF-10 and its analogues

are relatively soft materials. The estimated bandgap values are in the range 2.9 to 3.0 eV, indicating

nonmetallic character. Importantly, the bandgaps within the M-IRMOF-10 series (containing a

rather long 4,49-biphenyldicarboxylate linker) are smaller than those within the M-IRMOF-1 series

(shorter benzene dicarboxylate linker). The optical properties (dielectric function e(v), refractive

index n(v), absorption coefficient a(v), optical conductivity s(v), reflectivity R(v), and electron

energy-loss spectrum L(v)) of the M-IRMOF-10 series were computed. The observation of very small

reflectivities over a wide energy range suggests possible uses in hybrid solar cell applications. The

main characteristics of the optical properties are similar for the whole series although differences are

seen in the details. An analysis of chemical bonding in the M-IRMOF-10 series reveals as might be

anticipated that M–O bonds are largely ionic whereas C–O, C–H and C–C exhibit mainly covalent

interactions. The BOP values of M–O decrease through the series when going from Zn to Cd, and

from Be to Ba, i.e. the ionicity increases and the covalency decreases for the M–O bonds.

I. Introduction

MOFs constitute a rather new class of porous materials that are

considered for many applications, including catalysis, petro-

chemistry, gas adsorption and storage (e.g., H2, CH4, CO2, etc.),

selective separation, sensing, molecular recognition, and much

more.1 Within the huge MOF family of structures, the series of

isoreticular metal–organic frameworks (IRMOF-1–16), prepared

by Yaghi and coworkers,2–4 may have attracted most attention.

Systematic changes in linker size and linker functionalization

affects the adsorptive and diffusive properties of the material.

Interestingly, MOFs have been recently considered as suitable

preconcentrators for detection of explosive compounds,5 i.e.

detection at parts per trillion levels.6 In this respect, several

MOFs have shown effective selective preconcentration proper-

ties, i.e., IRMOF-1,7–10 IRMOF-3,8 IRMOF-8,11 and IRMOF-

10.8,12 A predictive understanding of the relationship between

MOF structure and its corresponding physicochemical proper-

ties will help match MOFs to a particular application. Optical

and electronic properties may be of relevance concerning the

suitability of MOFs to act as sensors when exposed to adsorbing

species. Currently, limited experimental or computational

techniques are used to establish structure/property relationships,

mostly on a case-by-case basis.

Compared to the ‘‘prototypical’’ IRMOF-1 (also known as

MOF-5) in which tetranuclear Zn clusters are linked by a

benzene-1,4-dicarboxylate unit, IRMOF-1013 with its longer

4,49-biphenyldicarboxylate linker has received much less atten-

tion concerning its physicochemical properties. IRMOF-10 was

first synthesized by Yaghi and coworkers.2–4,13 The higher

surface area and pore sizes of IRMOF-1014 is a key feature for its

use for gas absorption and separation and hydrogen storage.15–23

aCenter of Theoretical and Computational Chemistry, Department ofChemistry, University of Oslo, P.O.Box 1033 Blindern, N-0315, Oslo,Norway. E-mail: [email protected]; [email protected];Fax: +47 22855441bCenter for Materials Science and Nanotechnology, Department ofChemistry, University of Oslo, P.O.Box 1033, Blindern, N-0315, Oslo,Norway{ Electronic supplementary information (ESI) available: The calculatedcharge density, charge transfer, and electron localization function (ELF)plots, the total density of states (TDOS) and partial density of states(PDOS), the optical properties and band structures for M-IRMOF-10(M = Cd, Be, Mg, Ca, Sr and Ba). See DOI: 10.1039/c1ra00187f

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Interestingly, exceptional negative thermal expansion has been

reported for Zn-IRMOF-10.24 Other than adsorption and separa-

tion properties, scarce attention has been paid to other properties

of IRMOF-10, e.g., structural stability, mechanical properties,

chemical bonding, optical properties, etc. Interestingly, even its

solid-state structure remains to be well characterized: The crystals

of Zn-IRMOF-10 were too small for collection of quality X-ray

intensity data and instead, the structure was assigned by a simple

simulation (see ref. 13, supplementary info p.70): The unit cell

constants and space group information of a related IRMOF-12

was used to build the IRMOF-10 structure. The simulated powder

diffraction pattern of the predicted structure was in reasonable, but

far from perfect, agreement with the measured PXRD patterns of

IRMOF-10 and IRMOF-12. Under such circumstances, structural

optimization based on computational calculations should be an

indispensable tool to determine and/or confirm the solid-state

structure since many experimentally determined MOF structures

are relatively coarse. In this respect, the contributions from Mellot-

Draznieks and coworkers to predict structures by computational

tools are particularly noteworthy.25–32

Recent reports on MOFs as semiconductors33,34 have trig-

gered intense research in this area and is a motivation for

studying their electronic and optical properties. The quantum

confinement of inorganic semiconductor entities (such as dots or

wires) in close contact with organic molecules makes the optical

properties of MOFs particularly interesting. To our knowledge,

there are until now no detailed theoretical reports on these

aspects of M-IRMOF-10 available.

Herein, we present a comprehensive computational study on the

solid-state structure, stability, electronic structure, formation

energy, chemical bonding, and mechanical properties of the

experimentally known Zn-IRMOF-10 using DFT calculations

with the GGA-PBE functional as implemented in the VASP

code.35,36 Moreover, analogues of Zn-IRMOF-10, i.e.,

M-IRMOF-10 with M = Cd, Be, Mg, Ca, Sr, and Ba are studied

systematically. The optical properties of this whole M-IRMOF-10

series were calculated using the CASTEP module37 of the Material

Studio 5.0 program.38 The acquired insight should be valuable for

future uses of the M-IRMOF-10 series of materials as photo-

catalysts, photoactive materials for photovoltaic cells, and

components for electroluminescence devices.

Computational details are provided in the following section.

The details of the results and discussions are then described,

including structural details, formation energies, electronic

structures, chemical bonding, calculated band structures, and

finally optical properties. In order to conveniently present the

comprehensive results in this work, we use the experimentally

synthesized, Zn-based IRMOF-10 as the main line for the

discussion and analysis for the whole series. Moreover, we

compare and discuss the analogues (i.e., M-IRMOF-10, with M

? Zn) with IRMOF-10 (M = Zn)39 and try to elucidate

systematic trends in the properties for the whole series. The

findings for M-IRMOF-10 will also be compared with data for

the M-IRMOF-1 analogues, recently published by us.40,41

II. Computational details

The Vienna ab initio simulation package (VASP)35,36 has been

used for the total-energy calculations to study the structural

stability and to establish equilibrium structural parameters. The

generalized gradient approximation (GGA)42–44 includes the

effects of local gradients in the charge density for each point in

the materials and generally gives better equilibrium structural

parameters than the local density approximation (LDA). Hence,

the GGA functional was used for all calculations. The projector-

augmented-wave (PAW)36,45 Perdew, Burke, and Ernzerhof

(PBE)44 pseudo-potentials based on GGA were used to describe

the ion-electron interactions. A criterion of 0.01 meV atom21

was placed on the self-consistent convergence of the total energy

and all calculations were made with plane-wave cutoff of 500 eV,

which guarantees that absolute energies are converged to within

a few meV/f.u. This has been tested to be accurate and reliable

for M-IRMOF-10 systems considered in the present study.

Brillouin-zone integration was performed with a Gaussian

broadening of 0.2 eV during all relaxations. The conjugated-

gradient algorithm based on Hellmann-Feynman forces was used

to relax the ions into their instantaneous equilibrium positions.

The forces and the stress tensors were used to determine the

search directions to identify the ground state (i.e., the total

energy is not taken into account). This algorithm is very fast and

efficient when the initial structures are far away from the ground

state. Forces on the ions were calculated using the 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 1023 eV A21.

Because we deal with a rather large system (166 atoms per

primitive cell), the C-point alone is sufficient for sampling the

Brillouin zone during geometry optimization. However, in order

to arrive to an accurate band structure we have used a sufficient

number of k-points for the band structure calculations. The DOS

calculations were performed on the fully optimized structure

with only C-point alone. However, the DOS was calculated in a

fine energy grid (1801 points) due to the narrow band features so

as to visualize DOS correctly.

To gauge the bond strength and character of bonding, we have

analyzed bond overlap population (BOP) values with on the fly

pseudopotential estimated on the basis of the Mulliken popula-

tion as implemented in the CASTEP code.37 In order to

understand the chemical bonding and interactions between

constituents in the M-IRMOF-10 series, charge density, charge

transfer, and electron localization function (ELF)46–49 analyses

were performed based on the results obtained from the VASP

calculations. We have also calculated the optical properties

including dielectric function, absorption coefficient, reflectivity,

refractive index, optical conductivity, and energy loss function

for the M-IRMOF-10 series with ultrasoft pseudopotential by

using the CASTEP code. In parallel with optical properties

calculations, we also calculated the band structure with ultrasoft

pseudopotential for the whole series with CASTEP, which will

provide some hints and useful information to understand the

electronic structures and optical properties of these materials.

The method used for the calculation of optical properties and

band structures has been proven to be reasonable and compared

favorably with corresponding experimental spectra in previous

contributions from our and other groups.40,41,50–60

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III. Results and discussions

A. Structural details

Zn-IRMOF-10 is a member of a series of IRMOFs with oxide-

centered Zn4O tetrahedra as nodes linked by organic molecules

and can be synthesized based on the reticular synthesis strategy

proposed by Yaghi and coworkers.4,13,61 In Zn-IRMOF-10 the

organic linker is 4,49-biphenyldicarboxylate (4,49-BPDC).

Zn-IRMOF-10 can be obtained in highly crystalline form with

high specific surface areas of ca. 5000 m2 g21.14,62 Its crystal

structure has 664 atoms (eight formula units of Zn4O(BPDC)3)

in the conventional unit cell with cubic Fm3m symmetry (no.

225) and the reported lattice parameter is a = 34.281 A.13 Its

primitive cell has 166 atoms, including two nodes and six linker

molecules, corresponding to two Zn4O(BPDC)3 formula units.

The computed solid-state structure of Zn-IRMOF-10 is illu-

strated in Fig. 1. The different crystallographic sites in Zn-

IRMOF-10 include one type of Zn, two types of O, five types of

C, and two types of H occupying 32f, 8c, 96k, 96k, 48g, 96k, 48g,

48g, 96k, and 96k Wyckoff positions, respectively. The

M-substituted analogues of Zn-IRMOF-10 are readily visualized

by the replacement of Zn+2 ions with M+2 metal ions (i.e., M =

Cd, Be, Mg, Ca, Sr, and Ba). It is assumed that they will have the

same space group and Wyckoff positions as Zn-IRMOF-10, and

the equilibrium structural parameters were estimated from

structural optimization accordingly.

B. Structural optimization of the M-IRMOF-10 series from total-

energy calculations

As commented in the Introduction, the crystals of Zn-IRMOF-

10 were too small for collection of quality X-ray intensity data

and hence Yaghi and coworkers obtained the structural data

from a simulated structure.13 When the simulated structure data

based on Yaghi’s reported atomic coordinates for Zn-IRMOF-

10 (p. 70 of Supplementary Information to ref. 13) were

imported in Materials Studio according to the given space

group, additional H and C atoms were generated and it was

necessary to ‘‘merge’’ the extra and the original atoms, thus

slightly adjusting the positions, to produce a reasonable input

structure with the visualization tool in Materials Studio.38 The

computed ground-state structure was then obtained from this

input structure by full geometry optimization, i.e. the atom

positions and cell parameters were fully relaxed. This computa-

tionally fully optimized structure of Zn-IRMOF-10 then served

as the starting structure for the other M-IRMOF-10 structures

by replacement of the Zn atoms by Cd and the alkaline earth

metal atoms Be, Mg, Ca, Sr, and Ba before new structural

optimization are made.

The structural optimization was achieved by first relaxing the

atomic positions globally using the force-minimization techni-

que, by keeping the lattice constant (a) and cell volume (V) fixed

to the crystallographically determined values. Then the theore-

tical ground-state volume was determined with optimized atomic

positions by varying the cell volume within ¡10% of the

experimentally determined volume. The calculated total energy

as a function of volume was fitted to the so-called equation of

state (EOS) to calculate the bulk modulus (B0) and its pressure

derivative (B0’). In order to cross-check the calculated B0 and B0’

values, the E–V data were fitted into three different EOS, i.e.

Murnaghan,63 Birch,64 and Universal equation of states

(UEOS).65 The bulk modulus and its pressure derivative (in

parentheses) obtained from the E–V curve using the UEOS are

9.09 GPa (3.12) for M = Zn, 8.30 GPa (2.36) for Cd, 11.49 GPa

(1.28) for Be, 8.74 GPa (7.00) for Mg, 7.32 GPa (3.64) for Ca,

6.57 GPa (9.31) for Sr, and 6.10 GPa (4.23) for Ba in the

M-IRMOF-10 series. The corresponding results derived from the

two other EOSs can be found in Table 1.

It is seen that the B0 and B0’ values estimated from three

different EOS derived from the E–V data are nearly identical,

indicative of the reliability of our results. Moreover, the bulk

moduli decrease monotonically when one moves from Zn to Cd,

and from Be to Ba. On the other hand, there is no clear trend in

their pressure derivatives within these two series, i.e. their

pressure derivatives change randomly. Interestingly, it is

consistently seen that for any given metal M, the values for the

bulk moduli for the M-IRMOF-10 series are 35–41% smaller

than for the recently studied40,41 M-IRMOF-1 series. These

smaller value of the bulk moduli are associated with the linker

lengths. As the compressibility of MOFs at low pressure is

mainly decided by these organic linkers, the longer size of the

linker in IRMOF-10 diminishes the repulsive interaction between

nodes during compression and hence its bulk modulus is

reduced. It may also be noted that the presently calculated B0

values of Zn-IRMOF-10 are larger than the value of 6.00 GPa66

previously obtained by DFTB calculations. The previous data

were calculated from the elastic constants which are obtained

from total energy change after application of a suitable strain.

There are no experimentally measured bulk modulus values

available yet for any of these compounds with which our results

may be compared, and we hope that the present study will

motivate experimentalists to study the mechanical properties of

the M-IRMOF-10 and M-IRMOF-1 series.

The optimized equilibrium atomic positions and lattice

parameters, along with the corresponding experimental values

for IRMOF-10, are listed in Table 2. The lattice parameter of

Fig. 1 The crystal structure of the M-IRMOF-10 (M = Zn, Cd, Be, Mg,

Ca, Sr, Ba) series in the cubic Fm3m symmetry (no. 225). The atoms with

labels M, O1, O2, C1, C2, C3, C4, C5, H1, and H2 are chemically distinct

sites and will be addressed in the discussion of the chemical bonding and

interpretation of the partial density of states (PDOS).


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IRMOF-10 in the present work (34.8312 A) is in good agreement

with the experimental data (34.2807 A)13 and also with the

available theoretical value obtained from DFTB calculations

(35.348 A).66 Note that the magnitudes of previously reported

DFTB data are generally somewhat greater than the present

results, which will also be demonstrated in the following

discussion (see Table 3) of bond lengths and angles. The present

results are closer to the experimental data (which were not high

resolution ones, as already commented) than the previously

reported DFTB results.66 The lattice parameters for the whole

series are listed in Table 1. It can be seen that from Zn to Cd, and

from Be to Ba, the optimized equilibrium lattice constants

increase with the atomic number (i.e., aZn , aCd; aBe , aMg ,

aCa , aSr ,aBa) largely as a consequence of the increase in

atomic radii of the central metal atoms. The optimized bond

lengths and angles for the whole series, together with the

experimentally reported values for M = Zn, are listed in Table 3.

From Table 2, it may be noted that there are some

discrepancies in the structural parameters (which can be readily

understood given the fact that the experimental data were

obtained from a simulated structure, as briefly commented

already), but by and large the atomic coordinates of experi-

mental and computational results agree quite well. The bond

lengths and bond angles between the constituents in M-IRMOF-

10 at the optimized equilibrium volume are given in Table 3. A

comparison of the optimized equilibrium bond lengths (A) and

bond angles (u) for Zn-IRMOF-10 with the experimental data

reveals that the agreement between experiment and theory is

quite good for IRMOF-10 (Zn entries in Table 3). The

optimization nicely demonstrates how computations can be an

indispensable tool to resolve the details of solid-state structures

of complex systems when there are ambiguities or uncertainties

in experimentally available structure data. Computational

simulations have made dramatic advances in the past two

decades, and today, accurate prediction of structural properties

of novel molecules and exotic extended structures is possible. It is

therefore reasonable to suggest that poor-resolution experimen-

tal data on MOFs should be supplemented with computational

simulations and structure optimizations as a standard tool to

establish more reliably the detailed structures of new MOFs.

C. Energy of formation considerations

Information about formation enthalpies constitute an excellent

means to establish whether theoretically predicted phases are

likely to be stable and such data may serve as a guide to evaluate

possible synthesis routes. Several interesting reports have

appeared in the literature concerning computation of reaction

enthalpies by consideration of electric total energies, zero-point

energy vibrational correction, and thermal contribution (within

the harmonic approximation).67 Of course, kinetic factors can

also play a notable role during synthesis.68 Here, we are

primarily interested to know whether a particular hypothetical

compound is likely to be synthesizable or not on energetic

grounds. We believe that our approach, to be described below,

will give qualitatively sound trends in stabilities, although a

quantitatively accurate prediction of reaction enthalpies cannot

be expected. Further, for the estimation of the vibrational

entropy contribution to the total energy, phonon calculations

within the harmonic approximation should be performed. As the

number of atoms involved in the present calculations is very

large, such computationally intensive phonon calculations are

outside the scope of the present study. It should also be

mentioned that relative stability orders from reaction enthalpies

calculations usually refer to one material having different

structures (phases). Importantly, the IRMOF-10 material

synthesized by Yaghi and coworkers exists (at least so far) as

only one phase.13 This experimentally reported high symmetric

phase attracted much attention from both experiment and

theory. Here, we focused on the viability of synthesizing this

highly symmetric framework phase using alkaline-earth elements

instead of Zn in IRMOF-10. There are several ways to evaluate

the reaction energies; our approach of starting from the elements

is but one. An alternative approach might be to mimic the

Table 1 Optimized equilibrium lattice constant (a/A), bulk modulus (B0 (GPa)), and its pressure derivative (B0’) for M-IRMOF-10 (M = Zn, Cd, Be,Mg, Ca, Sr, Ba)

Material M-IRMOF-10 a/Aa B0 (GPa)b B0’b

Zn 34.831 ,35.348. %34.280& 9.09 (9.08) [9.09] ,6.00. 3.12 (3.09) [3.11]Cd 36.085 8.30 (8.30) [8.30] 2.36 (2.38) [2.44]Be 33.095 11.49 (11.49) [11.50] 1.28 (1.26) [1.20]Mg 34.877 8.74 (8.74) [8.74] 7.00 (6.96) [6.99]Ca 36.474 7.32 (7.32) [7.32] 3.64 (3.64) [3.65]Sr 37.358 6.57 (6.56) [6.57] 9.31 (9.27) [9.29]Ba 38.288 6.10 (6.10) [6.10] 4.23 (4.20) [4.22]a Data in , . from ref. 66, experimental data in % & from ref. 13. b Data without brackets from Universal EOS; data in ( ) from MurnaghanEOS; data in [ ] from Birch-Murnaghan 3rd-order EOS; data in , . from theoretical DFTB calculations in ref. 66.

Table 2 Optimized equilibrium structural parameters for IRMOF-10

Details PBE-GGA Expta

Crystal system Cubic CubicSpace group Fm3m (225) Fm3m (225)Atoms/cell (fcc) 166 166a/A 34.8312 34.2807V/A3 42257.64 40285.53Atom type Atomic positions (x, y, z)Zn1 (32f) (0.2827, 0.2174, 0.2174) (0.2828, 0.2172, 0.2172)O1 (8c) (1/4, 1/4, 1/4) (1/4, 1/4, 1/4)O2 (96k) (0.2731, 0.2269, 0.1624) (0.2735, 0.2265, 0.1618)C1 (96k) (0.2745, 0.2255, 0.0824) (0.2747, 0.2253, 0.0822)C2 (48g) (1/4, 1/4, 0.1029) (1/4, 1/4, 0.1028)C3 (96k) (0.2744, 0.2256, 0.0425) (0.2747, 0.2248, 0.0413)C4 (48g) (1/4, 1/4, 0.1458) (1/4, 1/4, 0.1448)C5 (48g) (1/4, 1/4, 0.0213) (1/4, 1/4, 0.0206)H1 (96k) (0.2936, 0.2064, 0.0982) (0.2921, 0.2083, 0.0962)H2 (96k) (0.2936, 0.2064, 0.9018) (0.2916, 0.2073, 0.0275)a Experimental data from p.70 in Supplementary Information to ref. 13.


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experimental synthesis conditions involving the reaction between

Zn4O(OH)6 and the dicarboxylic acid linker.66

In our case, we explore the thermodynamic feasibility of

assembling these M-IRMOF-10 materials from the elements

(eq 1). Thus, as part of this approach we have computed the total

energies for C (R-3m), O2 (P4/mmm), H2 (P4/mmm), Zn (P63/

mmc), Cd (P63/mmc), Be (P63/mmc), Mg (P63/mmc), Ca (Fm3m),

Sr (Fm3m), and Ba (Im-3m) in their ground state structures with

full geometry optimization. The reaction enthalpies for MOF

formation were calculated from the difference in the total energy

between the products and reactants involved in the reactions

concerned. We focus on the formation enthalpies of the

analogues (M-IRMOF-10, M = Cd, Be, Mg, Ca, Sr, Ba) relative

to the experimentally synthesized Zn-IRMOF-10. Through this

comparison, a general insight can be gained into the relative

stabilities for the whole series when different metals are

substituted into the nodes. The results establish unambiguously

that eqn 1 depicts exothermic reactions for the experimentally

synthesized Zn-IRMOF-10 as well as the analogous, yet

hypothetical, M-IRMOF-10 series.

8M + 13O2 + 84C + 24H2 A M8O26C84H48 (M-IRMOF-10,M = Zn, Cd, Be, Mg, Ca, Sr, Ba) (1)

The magnitudes of the calculated formation enthalpies given

in Table 4 (where data for the M-IRMOF-1 series are included

for comparison) show that (1) the stability of Cd-IRMOF-10 is

nearly the same as that of Zn-IRMOF-10, (2) the M-IRMOF-10

(M = Be, Mg, Ca, Sr and Ba) series is more stable than Zn-

IRMOF-10, and (3) the stabilities (ca. 250 kJ mol21) of the

M-IRMOF-10 (M = Be, Mg, Ca, Sr and Ba) compounds are

very similar since they have comparable formation enthalpies.

The magnitude of the calculated formation enthalpy for Zn-

IRMOF-10 (235.12 kJ mol21) is somewhat smaller than that for

Zn-IRMOF-1 (246.02 kJ mol21). Nevertheless, the value is

sufficiently large to render Zn-IRMOF-10 stable, which is of

course consistent with the fact that it is readily synthesized.13 For

the alkaline earth metal members of the M-IRMOF-10 series, the

formation enthalpies are consistently ca. 14–16 kJ mol21 less

negative than for the analogous M-IRMOF-1 member.

Nevertheless, the still rather large negative values for the

enthalpies of formation for the M-IRMOF-10 series suggest

that it might be possible to synthesize all these compounds as

stable phases. We eagerly await the experimental synthesis and

investigation of the properties of the predicted M-IRMOF-10

series of compounds.

D. Electronic structure

The data for Zn-IRMOF-10 will serve as a typical example of

electronic structure evaluation for the whole series. The total

electronic density of states (TDOS) and partial density of states

(PDOS) are displayed in separate figures for convenient

visualization and analysis. The TDOS and PDOS at the

equilibrium volume for Zn-IRMOF-10 are displayed in Fig. 2

and 3, respectively. The calculated band gap Eg for Zn-IRMOF-

10 is 2.925 eV, which is comparable to a recent DFTB

calculation that resulted in 3.07 eV,66 indicating nonmetallic

character. The calculated band gap of IRMOF-10 is substan-

tially smaller than that of IRMOF-1 (MOF-5) at 3.5 eV.15 It

appears that it is the linker rather than the node that primarily

determines the band gap in IRMOF-1 vs. IRMOF-10: The

4,49-biphenyldicarboxylate linker in IRMOF-10 is longer than

the 1,4-benzenedicarboxylate linker in IRMOF-1. TDOS for the

remaining parts of the series will be discussed later.

Unfortunately, there are yet no experimental data on the band

gap value of Zn-IRMOF-10 reported in the literature with which

the calculations can be compared. It should be noted that DFT

calculated band gap values tend to be generally lower than

experimentally determined ones; such an underestimation of the

Table 3 Optimized bond lengths (A) and bond angles (u) for M-IRMOF-1 (M = Zn, Cd, Be, Mg, Ca, Sr, and Ba) at their equilibrium volumes

M C1–C2 C1–C3 C2–C4 C3–C5 C5–C5 C4–O2 C1–H1 C3–H2 M–O1 M–O2 O1–M–O2 O2–M–O2

Zn 1.402 1.390 1.493 1.411 1.485 1.279 1.090 1.089 1.970 1.970 111.509 107.359(1.391)a (1.402) (1.442) (1.403) (1.413) (1.280) (0.960) (0.960) (1.946) (1.953) (111.988) (106.842)

,1.460.b ,1.319. ,2.074. ,2.088. ,107.000.

Cd 1.402 1.390 1.499 1.411 1.485 1.278 1.090 1.089 2.178 2.201 108.469 110.455Be 1.402 1.390 1.486 1.411 1.486 1.275 1.090 1.089 1.717 1.635 115.441 102.896Mg 1.402 1.390 1.491 1.411 1.486 1.278 1.090 1.089 1.988 1.959 110.607 108.312Ca 1.402 1.390 1.495 1.411 1.486 1.277 1.090 1.089 2.269 2.241 106.315 112.434Sr 1.402 1.390 1.497 1.411 1.485 1.277 1.090 1.089 2.432 2.405 104.325 114.090Ba 1.402 1.391 1.500 1.411 1.486 1.277 1.090 1.089 2.606 2.578 102.402 115.519a The experimental data in ( ) are from the structure made from the coordinates from the Supplementary Information in ref. 13. b The data in, . are from ref. 66.

Table 4 Calculated enthalpies of formation (DH; kJ mol21) for the M-IRMOF-10 and M-IRMOF-1 (M = Cd, Be, Mg, Ca, Sr, Ba) compounds

M-IRMOF-10a

M Zn Cd Be Mg Ca Sr BaDH (kJ mol21) 235.12 231.25 247.01 247.63 250.67 249.71 248.76

M-IRMOF-1b

M Zn Cd Be Mg Ca Sr BaDH (kJ mol21) 246.02 240.96 261.69 262.53 266.56 265.34 264.12a This work, according to eqn 1. b From ref. 41, based on the analogous reaction to eqn 1.


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calculated band gaps is an intrinsic feature of the ab initio

method and is related to a DFT limitation in not taking into

account the discontinuity in the exchange–correlation poten-

tial.69 To overcome this discrepancy, the so-called scissor

operator,70 D, can be introduced, which effectively eliminates

the difference between the theoretical and experimental gap

values by means of a simple rigid shift of the unoccupied

conduction band with respect to the valence band. In line with

this, for Eg of bulk ZnO, the calculated band gaps are

significantly smaller than the experimental values. (LDA =

0.744/0.573 eV; GGA = 0.804/0.641 eV, LDA + U = 1.988/

1.486 eV, GW = 2.255/2.100 eV, experimental 3.455/3.300 eV for

ZnO–w/ZnO–z, respectively).71 In a recent contribution,40 we

found that the DFT calculations of MOF-5 unexpectedly gave a

band gap value in very good agreement with that obtained from

experimental studies.72,73 It may be of interest to extend this

study to other MOFs that are constructed from various organic

dicarboxylic acid linkers and the Zn4O nodes to understand

more about the role of linkers on the electronic structure and

optical properties of the materials. Metric parameters within the

Zn clusters of IRMOF-10 and MOF-5 closely match those of

bulk ZnO (Zn–O distances are 1.970 A, 1.936 to 1.948 A, and

1.974 to 1.983 A, O–Zn–O angles are 107.366u to 111.502u,107.7u to 111.2u and 108.3u to 110.7u in IRMOF-10, MOF-5 and

bulk ZnO, respectively). Though the bond distances and angles

are comparable between Zn-IRMOF-10 and ZnO, significant

differences in material properties may arise from the isolated

nature of the oxide nodes which are expected to act like quantum

dots, and also from the perturbation arising from the organic

linker BPDC.

Since the partial density of states (PDOS) is closely relevant to

the chemical bonding, the PDOS of IRMOF-10 (Fig. 3) will be

discussed in more detail in the following subsection dealing with

the characteristics of chemical bonding. The PDOS for the

remaining members (M = Cd, Be, Mg, Ca, Sr and Ba) in the

M-IRMOF-10 series can be found in Figures S7–S12 in the ESI.{In general, the PDOS for each type of atoms (i.e., C, H and O; all

three types constitute the linker BPDC), except for the metal

atoms, are similar in each material within the series, with

essentially the same characteristic peaks and positions for each

type of atoms. Thus, we conclude that there are no discernible

differences between the linker properties in the different

materials within this series.

Figures S7–S12 in the ESI{ show that there are significant

differences in the PDOS when the transition metals (Zn and Cd)

are compared to main-group metals (Be to Ba). Within the main-

group metals, there are also differences, since some (e.g., Ca to

Ba) have d-electrons in the pseudopotential for the calculations,

whereas others (Be and Mg) only have s- and p-electrons.

Differently phrased, the d-states of Zn and Cd atoms are

dominantly contributed in the valence band, whereas both s- and

p-states of Be and Mg atoms are dominantly contributed in both

valence and conduction bands. For Ca, Sr, and Ba atoms, the

p-states are dominantly contributed in the valence bands, while

the d-states are dominantly contributed in the conduction bands.

In order to visualize the effect of changes in the metal ion on

the electronic structure, the total electronic density of states

(TDOS) at the equilibrium volume for the whole M-IRMOF-10

series of compounds is displayed in Fig. 4. The band gap (Eg)

values obtained from the TDOS curves in Fig. 4 are in the range

2.9 to 3.0 eV for all members of the M-IRMOF-10 series,

invariant of the metal. This indicates that all these materials are

nonmetals. The characteristic peaks of TDOS for all these

Fig. 3 The calculated total density of states (TDOS) and partial density of

states (PDOS) for Zn-IRMOF-10 in the cubic Fm3m symmetry (no. 225).

Fig. 2 The calculated total density of states (TDOS) for Zn-IRMOF-10

in the cubic Fm3m symmetry (no. 225).


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compounds are quite similar, which implies that the calculated

band gaps within the M-IRMOF-10 series have a common

structural origin that is similar to Zn-IRMOF-10. From the

PDOS of IRMOF-10 in Fig. 3 and the PDOS of the remaining

parts of this series in Figures S7–S12 in the ESI{ we can infer the

origin of Eg for the whole series. It is essentially the p-states of

the C2, C3 and C5 atoms of the linker that determine the band

gap for the whole series. This is in agreement with the

conclusions concerning the PDOS above. Thus, it is the linker,

rather than the node, that determines the Eg in the M-IRMOF-

10 series. On this basis, it can also be appreciated that the greater

band gap values in the M-IRMOF-1 series, ca. 3.5 eV, is also

invariant to changes in the metal,41 and consistent with the idea

that it is the linker that determines the value of band gap in

isoreticular MOF series. In order to substantiate this finding we

are currently investigating the role of various linkers on band

gap changes in a series of MOF systems.

It is a quite interesting observation that the band gap is

unaffected by the metal replacement in the M-IRMOF-10 series.

This implies that the degree of localization or delocalization of

valence electrons of M(II) ions, or the changes in the bonding

interaction between M and O, will not significantly affect the

band gap value of the M-IRMOF-10 materials. However, a

different case was reported in a recent theoretical study where

Choi et al. reported74 that it is possible to tune electronic band

gaps from semiconducting to metallic states by substitution of

Zn(II) ions in MOF-5 with Co(II) ions. Such differences in the

electronic properties by cation replacement can be understood as

follows. All the compounds in the M-IRMOF-10 series have the

same linkers and similar nodes. Although the alkaline earth

metals in this series have different atomic numbers and atomic or

ionic radii, they have the same valence shell electron configura-

tions. The replacement of divalent Zn ions in IRMOF-10 with

divalent alkaline-earth metal ions gives similar electronic

structure and bonding behavior. The isoelectronic nature of

the compounds within this series and their isostructural

characteristics contribute to the similar TDOS patterns and the

very similar band gap values. In contrast, the transition metal

ion Co(II) is very different from the main group alkaline earth

metals, as this ion may have different bonding interactions with

the linker oxygen atoms than Zn(II) or the alkaline-earth ions;

this can contribute to the tuning process of the band gap of

MOF-5 and its Co congener. Moreover, Co(II) ions often exhibit

spontaneous magnetic ordering which will also contribute to

metallic behavior. As Co has a highly different valence electron

configuration compared with alkaline-earth metals, the 3d

electrons of Co should play an important role in the band gap

tuning process. Thus, the use of metal atoms with different

electron configurations allows the tuning of the electronic

structure of MOF-5 type materials.

As discussed above, the DFT calculated band gap Eg is

generally smaller than the experimental one, which can be

corrected by a scissor operator. In the following we will briefly

discuss and compare theoretical and experimental band gap

values for Zn-IRMOF-10, and make comparisons with the

calculated data for the hypothetical systems M-IRMOF-10 and

their corresponding bulk binary oxides (Table 5). As mentioned,

calculated band gap values for the M-IRMOF-10 systems are

almost constant, independent of the different cations. In

contrast, the experimental band gap values for the binary oxides

of the corresponding cations are quite different: In particular, the

binary oxides have much higher band gap values than the

corresponding M-IRMOF-10 series. Whereas the band gap

values of ZnO and MOF-5 are almost the same, there is not a

one-to-one correspondence between the band gap values of the

other IRMOFs and their respective binary oxides MO. This

suggests that the origin of band gap formation in MOFs is

different from that in binary oxides, which agrees with the above

conclusion that band gaps in the isoelectronic systems under

investigation originate from the linkers rather than from the

Fig. 4 Calculated total density of states (TDOS) for M-IRMOF-10

series (M = Zn, Cd, Be, Mg, Ca, Sr, Ba) in the equilibrium cubic structure

with Fm3m symmetry (no. 225).

Table 5 Estimated band gap values (Theo. Eg) for the M-IRMOF-10from CASTEP calculations. Experimental band gap values (Exp. Eg) forIRMOF-1, ZnO, CdO, and alkaline earth metals oxides (MO)

M-IRMOF-10 Theo. Eg (eV) MO Exp. Eg (eV)

Zn-IRMOF-10 2.925 ZnO-w/-z 71 3.455/3.300 71

Cd-IRMOF-10 2.942 CdO 2.16 ¡ 0.02 75

Be-IRMOF-10 2.834 BeO 10.7 76

Mg-IRMOF-10 2.905 MgO 7.2 77

Ca-IRMOF-10 2.912 CaO 6.2 77

Sr-IRMOF-10 2.953 SrO 5.3 77

Ba-IRMOF-10 2.977 BaO 4.0 77

IRMOF-1 (MOF-5) 3.4–3.5 40 3.4–3.5 72,73


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metals. Importantly, if detailed information about the origin of

band gap in MOFs is desired, one should aim at understanding

the electronic structure and chemical bonding in MOFs in some

detail and it is therefore advisable to perform ab initio

calculations.

E. Characteristics of chemical bonding

i. From partial density of states. The distribution of various

electronic states in the valence band and the conduction band

can be characterized from the PDOS of Zn-IRMOF-10. The d-

and s-states of Zn and H atoms, respectively, contribute

dominantly in the valence band. Both s- and p-states of C and

O atoms also contribute to the VB. The p-states of neighbors (i.e.

C1 and C2, C2 and C4, C1 and C3, C3 and C5) are distributed

energetically in the same range and spatially distributed such as

to effectively overlap to form very strong covalent bonds. The

s-states of H1 and H2 can overlap with the p-states of C1 and C3,

respectively, to form covalent bonds. The p-state of C4 overlaps

with that of O2 to form a directional bond between them. The

d-states of Zn are well localized, and the Zn s electrons are

transferred to the neighboring atoms, leading to ionic Zn–O

bonding. Thus, the picture emerges—as might be anticipated—

that the linker acts as an entity that is covalently bonded

internally and linked to the Zn nodes by a largely ionic

interaction. This is consistent with the following analysis of

charge density and ELF.

An analysis of the PDOS in Figures S7–S12 in the ESI{ leads

to the same conclusion regarding the whole M-IRMOF-10 series.

The main difference in chemical bonding in the series arises from

the relative importance of ionic vs. covalent contributions to M–

O bonding: At the extremes, there is more covalent and less ionic

character in the Be–O bond compared with the Ba–O bond, even

though both bonds are dominated by the ionic components.

ii. From charge density/transfer, ELF and BOP analyses.

Charge density/transfer, ELF,46–49 and bond overlap population

(BOP)/Mulliken population analyses can shed further light on

the bonding situation. The charge density plots in Fig. 5a and

Figures S1a–S6a in the ESI{ show that the organic linker is a

molecule-like subunit with normal covalent C–C, C–H, and C–O

bonds. Charges are spherically distributed at the M and O sites,

characteristic for systems having ionic interactions; this is further

corroborated by the fact that there is no noticeable charge

density distributed between the M and O atoms.

The charge-transfer contour Dr is the self-consistent electron

density in a particular plane, rcomp, from which is subtracted the

electron density of the overlapping free atoms in the same lattice,

ratom, i.e., Dr(r) = rcomp 2 ratom, which allows the visualization

of how electrons are redistributed in a particular plane compared

to free atoms due to the bonding in the compound. Fig. 5b and

Figures S1b–S6b in the ESI{ show charge-transfer plots for all

M-IRMOF-10 species investigated. It is evident that electrons

are transferred from M to O sites, but not entirely in an isotropic

fashion. The anisotropic charge transfer from M to the O sites

indicates iono-covalent bonding between M and O with a

predominant ionic contribution. The nonspherical electron

distributions between neighboring C, H, and O atoms clearly

indicate strong covalent bonding. From Fig. 5c and Figures S1c–

S6c in the ESI,{ it can be inferred that the large value of ELF at

the O site indicates strongly paired electrons with local bosonic

character. The negligibly small ELF between M and O, and the

small value of ELF at the M sites (partially due to the presence

of d electrons for the transition metals Zn and Cd) with

spherically symmetric distribution again indicate predominant

ionic bonding between M and O. The ELF distribution at the O

site is polarized towards the M atoms, indicating directional

bonding between M and O. A certain polarized character is

found in the ELF distribution at the H sites in the M-IRMOF-10

series, indicating polar covalent bonding. There is as expected a

maximum in the ELF between the covalently bonded C atoms

and between C and O atoms.

Bond overlap population (BOP) values were calculated on the

basis of a Mulliken population analysis.78 A high BOP value

indicates a strong covalent bond, while a low BOP value

indicates an ionic or nonbonding interaction. The calculated

BOP values for the M–O, C–O, C–C, and C–H bonds are

displayed in Table 6. BOP values for the M–O bonds in the

MOFs are in the range 0.26–0.29 for M = Zn, 0.22–0.23 for Cd,

0.36–0.37 for Be, 0.23 for Mg, 0.14–0.18 for Ca, 0.14–0.17 for Sr,

and 0.11–0.16 for Ba, respectively. The data suggest a

predominant ionic character to the M–O bonding, and the

extent of covalent character decreases down in a group (Zn–O .

Cd–O; Be–O . Mg–O . Ca–O . Sr–O . Ba–O. The high BOP

values for the C–H, C–C, and C–O bonds are consistent with

strong covalent bonds.

We have also calculated the Mulliken effective charges and

bond overlap populations of the corresponding oxides (MO)

Fig. 5 Calculated charge density (a), charge transfer (b), and electron

localization function (c) plots for IRMOF-10 in the (110) plane.


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with the same GGA-PBE functional as was used to calculate the

M-IRMOF-10 series. The M–O BOP values within MO are 1.13

(Zn), 1.02 (Cd), 1.44 (Be), 1.33 (Mg), 0.84 (Ca), 0.88 (Sr), and

0.75 (Ba). The MEC values for M in the MO oxides are 0.84

(Zn), 0.82 (Cd), 0.79 (Be), 0.97 (Mg), 1.04 (Ca), 0.97 (Sr), and

0.96 (Ba) |e|. Thus, the general trend of M–O BOP values and

MEC values of M within the MO oxides are similar for the whole

series. We conclude that our computational methods predict

quite well the general trend for the whole series.

In summary, the M–O bonds in the nodes of M-IRMOF-10

series have predominant ionic character similar to that present in

MO, whereas the C–H, C–O and C–C bonds in the linkers have

covalent interactions. The analyses based on charge density/

transfer, ELF, and bond overlap population (BOP)/Mulliken

population analyses give a consistent view of the bonding in the

M-IRMOF-10 series, and agrees with the situation in MOF-540

and the M-IRMOF-1 series,41 as recently described by us.

The calculated Mulliken charges (MEC) are reported in

Table 6. The MEC values are +0.27 to +0.31|e| for H, +1.29|e|

for M = Zn, +1.27|e| for Cd, +1.14|e| for Be, +1.57|e| for Mg,

+1.35|e| for Ca, +1.38|e| for Sr and +1.37|e| for Ba, respectively.

The C1 and C3 atoms connected to H1 and H2 bear negative

charges (20.28 to 20.31|e| and 20.27|e|, respectively). However,

the C2 (which bears the carboxylate group) and C5 (which

connects the phenyl rings in the linker) atoms bear nearly zero

charge (20.05 to 20.07|e| and 20.01|e|, respectively). The

carboxylate C atoms bear positive charges (+0.60 to +0.65|e|).

Finally, the oxygen atom in the M4O node has nearly a single

unit of negative charge (21.05|e| for M = Zn, 21.02|e| for Cd,

20.96 for Be, 21.28 for Mg, 21.15 for Ca, 21.14 for Sr, and

21.08 for Ba), which indicates that the four M atoms together

have transferred a charge corresponding to one electron to the

central O1. The O2 oxygen atoms in the BDC linker bear

negative charges (20.63 to 20.71|e|) indicating that there is

partial electron transfer from M to O2.

iii. Bader topological analysis. Although there is no unique

definition to identify how many electrons are associated with an

atom in a molecule or an atomic group in a solid, it has

nevertheless proved useful in many cases to perform Bader

topological analyses.79–81 In the Bader charge (BC) analysis,

each atom of a compound is surrounded by a surface (called a

Bader region) that runs through minima of the charge density,

and the total charge of an atom is determined by integration of

electrons within the Bader region. The calculated Bader charges

Table 6 Mulliken effective charge (MEC) and bond overlap popula-tions (BOP) and Bader charges (BC) for M-IRMOF-10a

Material Atom site MEC (e) BOP BC (e)

IRMOF-10 Zn +1.29 0.26–0.29 (Zn–O) +1.3874O1 21.05 0.26 (O1–Zn) 21.3197O2 20.65 0.29 (O2–Zn) 21.7593C1 20.25 1.08 (C1–C2) +0.0285

1.12 (C1–C3)C2 20.06 0.85 (C2–C4) 20.0773C3 20.26 1.09 (C3–C5) +0.0033C4 +0.61 0.90 (C4–O2) +2.6528C5 20.01 0.91 (C5–C5) +0.0478H1 +0.28 0.89 (H1–C1) +0.0574H2 +0.27 0.91 (H2–C3) +0.0059

Cd–IRMOF–10 Cd +1.27 0.22–0.23 (Cd–O) +1.3186O1 21.02 0.22 (O1–Cd) 21.2036O2 20.66 0.23 (O2–Cd) 21.7435C1 20.25 1.08 (C1–C2) +0.0411

1.12 (C1–C3)C2 20.06 0.84 (C2–C4) 20.0661C3 20.26 1.09 (C3–C5) +0.0284C4 +0.63 0.90 (C4–O2) +2.6782C5 20.01 0.91 (C5–C5) +0.0210H1 +0.28 0.89 (H1–C1) +0.0282H2 +0.27 0.91 (H2–C3) 20.0100

Be–IRMOF–10 Be +1.14 0.36–0.37 (Be–O) +2.0000O1 20.96 0.37 (O1–Be) 22.0057O2 20.63 0.36 (O2–Be) 21.9083C1 20.26 1.07 (C1–C2) 20.0348

1.12 (C1–C3)C2 20.05 0.85 (C2–C4) +0.0426C3 20.26 1.09 (C3–C5) +0.0421C4 +0.60 0.91 (C4–O2) +2.6488C5 20.01 0.91 (C5–C5) 20.0817H1 +0.31 0.87 (H1–C1) +0.0803H2 +0.27 0.91 (H2–C3) +0.0164

Mg–IRMOF–10 Mg +1.57 0.23 (Mg–O) +2.0000O1 21.28 0.23 (O1–Mg) 22.0009O2 20.71 0.23 (O2–Mg) 21.9081C1 20.25 1.08 (C1–C2) +0.0358

1.13 (C1–C3)C2 20.07 0.85 (C2–C4) 20.0738C3 20.26 1.09 (C3–C5) +0.0095C4 +0.60 0.91 (C4–O2) +2.6625C5 20.01 0.91 (C5–C5) +0.0396H1 +0.28 0.89 (H1–C1) +0.0426H2 +0.27 0.90 (H2–C3) +0.0062

Ca–IRMOF–10 Ca +1.35 0.14–0.18 (Ca–O) +1.6187O1 21.15 0.18 (O1–Ca) 21.4976O2 20.70 0.14 (O2–Ca) 21.8235C1 20.26 1.07 (C1–C2) +0.0242

1.12 (C1–C3)C2 20.06 0.83 (C2–C4) 20.0336C3 20.26 1.09 (C3–C5) +0.0308C4 +0.65 0.88 (C4–O2) +2.6887C5 20.01 0.91 (C5–C5) 20.0035H1 +0.31 0.86 (H1–C1) +0.0511H2 +0.27 0.90 (H2–C3) 20.0232

Sr–IRMOF–10 Sr +1.38 0.14–0.17 (Sr–O) +1.6184O1 21.14 0.17 (O1–Sr) 21.4708O2 20.70 0.14 (O2–Sr) 21.8229C1 20.26 1.07 (C1–C2) +0.0267

1.12 (C1–C3)C2 20.06 0.82 (C2–C4) 20.0096C3 20.26 1.09 (C3–C5) 20.0154C4 +0.64 0.89 (C4–O2) +2.7104C5 20.01 0.91 (C5–C5) 20.0139H1 +0.30 0.86 (H1–C1) +0.0446H2 +0.27 0.90 (H2–C3) +0.0066

Table 6 (Continued)

Ba–IRMOF–10 Ba +1.37 0.11–0.16 (Ba–O) +1.6197O1 21.08 0.16 (O1–Ba) 21.4326O2 20.70 0.11 (O2–Ba) 21.8284C1 20.26 1.07 (C1–C2) +0.0168

1.12 (C1–C3)C2 20.06 0.82 (C2–C4) 20.0548C3 20.26 1.09 (C3–C5) +0.0342C4 +0.64 0.89 (C4–O2) +2.7269C5 20.01 0.91 (C5–C5) 20.0146H1 +0.30 0.86 (H1–C1) +0.0536H2 +0.27 0.90 (H2–C3) 20.0256

a The atomic numbering scheme is according to Fig. 1.


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for the M-IRMOF-10 series are given in Table 6. The BC for M

and O (includes O1 and O2) in the M-IRMOF-10 series

compounds indicate that the interaction between M and O is

almost ionic, as nearly two electrons (+1.39|e| for M = Zn,

+1.32|e| for Cd, +2.00|e| for Be, +2.00|e| for Mg, +1.62|e| for Ca,

+1.62|e| for Sr, and +1.62|e| for Ba) are transferred from M to O.

This finding is consistent with the DOS and charge density

analyses. Within the M4O units, M donates 1.32 to 2.00

electrons, which is slightly smaller than that in a pure ionic

picture. The trend is associated with the noticeable covalency

present between M and O as demonstrated by the ELF and BOP

analyses, discussed above. The results from the BC analysis are

fully consistent with the charge density, charge transfer, ELF,

MEC, and PDOS analyses.

F. Band structure and optical properties

The recent report on the semiconducting behavior of MOFs34

has triggered intense research in this area including the synthesis

and characterization of various semiconducting MOFs with the

aim to develop new materials for optoelectronic applications.

The optical properties for M-IRMOF-10 are here of interest, for

example in view of potential uses of this material in hybrid solar

cell applications as an active material or in the buffer layer

between the electrodes and inorganic active materials. Studies of

optical properties of MOFs will also be of fundamental

importance, since these properties not only depend on the

occupied and unoccupied parts of the electronic structure, but

also carry information about the character of the bands. Insight

into the excited-state electronic properties of M-IRMOF-10 may

also be important for certain applications. It may be noted that

the moisture sensitivity of Zn-IRMOF-10 presents obstacles to

many practical uses of this material.

The central quantity of the optical properties is the dielectric

function e(v), which describes the features of linear response of the

system to electromagnetic radiation, which again governs the

propagation behavior of radiation in the medium. Here e(v) is

connected to the interaction of photons with electrons. Its

imaginary part e2(v) can be derived from interband optical

transitions between the occupied and unoccupied bands including

appropriate momentum matrix elements to take care of the

selection rules, and its real part e1(v) can be derived from e2(v) by

the Kramer-Kronig relationship.50 The real part of e(v) in the limit

of zero energy (or infinite wavelength) is equal to the square of the

refractive index n(v). All the frequency dependent linear optical

properties, such as refractive index n(v), absorption coefficient

a(v), optical conductivity s(v), reflectivity R(v), and electron

energy-loss spectrum L(v) can be deduced from e1(v) and e2(v).

We have conducted CASTEP calculations to estimate the

optical properties of the whole M-IRMOF-10 series (M = Zn,

Cd, Be, Mg, Ca, Sr and Ba), and the results from the optical

calculations for Zn-IRMOF-10 are shown in Fig. 6. The

calculated optical properties of the remaining members of the

series can be found in Figures S13–S18 in the ESI.{ For the

convenience of our discussion, we focus on the properties of Zn-

IRMOF-10 as a representative case before a comparison is made

within this series.

There are three main peaks in the e2(v) plot (Fig. 6a) of Zn-

IRMOF-10, located at ca. 4.51, 6.52, and 15.13 eV, the latter

accompanied by broad shoulders. Figures S13a–S18a in the ESI{show that characteristic peaks and positions are similar for each

material in the series. The real part of dielectric function, e1(v)

(Fig. 6a and Figures S13a–S18a in ESI{) allows the estimation

the value of the refractive index n(v) at infinite wavelength or

zero energy (i.e., n(0)) at about 1.1651 (Zn), 1.1537 (Cd), 1.1827

(Be), 1.1580 (Mg), 1.1442 (Ca), 1.1373 (Sr), and 1.1318 (Ba).

Thus, n(0) is rather constant in the range 1.13 to 1.18 for the

whole series. At low frequency (0—2.95 eV), the imaginary part

e2(v) is zero below the band gap, which is consistent with the

order of band gaps for the M-IRMOF-10 series.

The reflectivity spectrum (Fig. 6b) of Zn-IRMOF-10 shows

sharp peaks at 4.17, 6.37, and 15.29 eV, the latter accompanied

by shoulders. The two low-frequency peaks mainly arise from

Zn(3d) A C/O(2p) as well as H(1s) A C/O(2p) interband

transitions. A similar situation pertains to the reflectivity curves

for M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba), Fig. S13b–

S18b in the ESI.{ Here, the two sharp low-frequency peaks

mainly arise from the transitions Cd(3d) A C/O(2p) and H(1s)

A C/O(2p) for M = Cd; Be(2s,2p) A C/O(2p) and H(1s) A C/

O(2p) for Be; Mg(3s,3p) A C/O(2p) and H(1s) A C/O(2p) for

Mg; Ca(4p,4d) A C/O(2p) and H(1s) A C/O(2p) for Ca;

Sr(5p,5d) A C/O(2p) and H(1s) A C/O(2p) for Sr; and

Ba(6p,6d) A C/O(2p) and H(1s) A C/O(2p) for Ba. The

reflectivity approaches zero when the energy exceeds 30 eV for

the whole series. The values of reflectivity at infinite wavelength

are 0.005730 (Zn), 0.005015 (Cd), 0.007016 (Be), 0.005332 (Mg),

0.004523 (Ca), 0.004098 (Sr), and 0.003751 (Ba). Thus, passing

from Zn to Cd, and from Be to Ba, the reflectivity consistently

decreases. One general finding here is that the calculated

reflectivity in the whole frequency range is much smaller than

that in typical inorganic solids. This was also seen for

M-IRMOF-1,40,41 and this may prove to be an important

advantage if MOFs are to be used in optoelectronic devices (such

as solar cells and LEDs) where low reflectivity is desired.

Zn-IRMOF-10 has a finite value of the refractive index n(v)

(Fig. 6c) in the range 2.95 to 30 eV. The extinction coefficient

k(v) (the imaginary part of the complex refractive index) shows

three peaks at 4.57, 6.63, and 15.24 eV, the latter with broad

shoulders. The refractive indexes n(v) for M-IRMOF-10 (M =

Cd, Be, Mg, Ca, Sr and Ba) are depicted in Figures S13c–S18c in

the ESI.{ Similar characteristics are seen for the whole series.

The refractive index n(v) at infinite wavelength (i.e., n(0)) has

already been commented in the dielectric function e(v)

paragraph.

The optical conductivity s(v) plot of Zn-IRMOF-10 is shown

in Fig. 6d. The real part of the complex conductivity has its three

main three sharp peaks at 4.57, 6.63, and 15.17 eV. The optical

conductivity s(v) plots of M-IRMOF-10 (M = Cd, Be, Mg, Ca,

Sr and Ba) are depicted in Figures S13d–S18d in the ESI;{ the

characteristics of the main peaks are similar throughout the

whole series.

The electron energy-loss function L(v) (Fig. 6e) is an

important optical parameter describing the energy loss of a fast

electron traversing in a certain material. The peaks in the L(v)

spectra represent the characteristics associated with the plasma

resonance and the corresponding frequency is the so-called

plasma frequency above which the material is a dielectric [e1(v)

. 0] and below which the material behaves like a metallic


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compound in some sense [e1(v) , 0]. In addition, the peaks of

the L(v) spectra overlap the trailing edges in the reflection

spectra. The peak of L(v) of Zn-IRMOF-10 at 6.93 eV

corresponds to the reduction of R(v). There are five plasma

frequencies at ca. 4.74, 6.93, 8.68, 15.70, and 17.29 eV. In Figures

S13e–S18e in the ESI,{ it is seen that the characteristic main

peaks of M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba) are

quite similar except that the two broad peaks with the strongest

intensities for Zn, Cd, Be, Mg (at ca. 15.70 and 17.29 eV for M =

Zn) have the appearance of a single sharp peak for Ca, Sr, and

Ba.

Zn-IRMOF-10 has an absorption band (Fig. 6f) ranging from

2.95 to 30 eV, which exhibits three sharp peaks at around 4.63,

6.74, and 15.29 eV. The characteristics of the main peaks are

similar for M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba;

Figures S13f–S18f in the ESI){. The main differences arise from

Fig. 6 Calculated optical properties for Zn-IRMOF-10: (a) dielectric function e(v), (b) reflectivity R(v), (c) refractive index n(v); extinction

coefficient k(v), (d) optical conductivity s(v), (e) energy loss function L(v), and (f) absorption a(v).


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the appearance of an additional peak at ca. 25.0–28.0 eV for M =

Ca, Sr and Ba, which is absent for M = Zn, Cd, Be, and Mg.

The calculated optical properties of M-IRMOF-10 series in

this work are similar to that of M-IRMOF-1 in our recent

contributions,40,41 which is consistent with the fact that the

M-IRMOF-10 and M-IRMOF-1 series have similar topological

structures, with common nodes and closely related linkers.

In conjunction with the optical properties calculations we have

also computed the band structures of the whole M-IRMOF-10

(M = Zn, Cd, Be, Mg, Ca, Sr and Ba) series. The calculated band

structure for Zn-IRMOF-10 is shown in Fig. 7. The band

structures of the remaining members of the series are displayed in

Figures S19–S24 in the ESI.{ For the high symmetry directions

in the Brillouin zone sampling, CASTEP automatically chose the

W–L–C–X–W–K path for the face-centered cubic (fcc) symmetry

Brillouin zone of M-IRMOF-10 series. From Fig. 7 and Fig.

S19–S24 it is apparent that the band gap for the whole series is

essentially constant at ca. 2.9–3.0 eV, independent of the central

metal atoms in the framework nodes. The bands in the valence

band as well as in the conduction band are almost parallel and

dispersionless. The bands at the VB maximum and CB minimum

for Zn-IRMOF-10 are very flat, which is also the case for the

other members of the series. This appears to be a common

feature for MOF materials.11,82 This flat band behavior makes it

impossible to unequivocally identify whether the band gap is

direct or indirect. However, we still can gain some qualitative

information from the band structures that helps to understand

the electronic structures of MOF materials and provides further

insight into their optical properties. We look forward to future

experimental determination of band structures of the

M-IRMOF-10 series, so that experiment and theory can be

reconciled.

IV. Conclusions

We have presented a detailed investigation on the electronic

structure, chemical bonding behavior, ground-state properties,

and optical properties of the whole M-IRMOF-10 (M = Zn, Cd,

Be, Mg, Ca, Sr and Ba) series using first-principles methods. The

following important conclusions are obtained:

(1) The calculations show that each material in the

M-IRMOF-10 series is soft and ‘‘formed’’ in the high symmetric

face-centered cubic (Fm3m, 225) crystal structure; it is demon-

strated that computational simulations nicely complement

experiments to accurately determine the equilibrium structural

parameters for complicated MOFs systems.

(2) The large negative formation enthalpy of IRMOF-10 is

consistent with the fact that it has already been synthesized by

experiments. The prediction of a series of hypothetical materials

M-IRMOF-10 (M = Cd, Be, Mg, Ca, Sr and Ba) with large

negative formation enthalpy hopefully will inspire and guide

synthetic efforts in this direction.

(3) Electronic charge density, charge transfer, ELF, MEC and

BOP analyses shed light on the nature of the M–O, C–O, C–H,

and C–C bonding. The analyses consistently support the notion

that the bonding interaction between M–O is mainly an ionic

interaction, whereas those between C–O, C–H, and C–C are

normal covalent interactions. The ionicity of the M–O bonds

decreases and the covalency increases when passing from Zn to

Cd, and from Be to Ba.

(4) Electronic density of states and band structures study show

that the band gap for the whole M-IRMOF-10 series is ca. 2.9–

3.0 eV, resulting in a nonmetallic character. Until now, there are

no experimental studies available to verify our results, but we

hope to motivate experimentalists to measure the band gap of

this series. Importantly, the band gap of the M-IRMOF-10 series

at 2.9–3.0 eV is independent of the identity of the metal in this

isoelectronic series of structures. Furthermore, the band gap is

substantially lower than the 3.5 eV value found for the analogous

M-IRMOF-1 series. Thus, a systematic variation of the linker

may allow the fine-tuning of band gap values in a given MOF

family. This should influence research in this area and facilitate

the synthesis of semiconducting MOFs with appropriate band

gap values for materials applications in for optoelectronic

devices.

(5) The calculated optical properties of M-IRMOF-10 series

provide useful information for future experimental exploration.

Overall, the peak intensities of the calculated optical spectra for

the M-IRMOF-10 systems are around 30% higher (especially the

Fig. 7 The electronic band structure of Zn-IRMOF-10. The Fermi level

is set to zero and placed in the valence band maximum.


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reflectivity and absorption coefficient) than for M-IRMOF-1.

This is associated with the introduction of an additional benzene

structural sub-unit in the M-IRMOF-10 system. However, the

peak positions and distributions are almost the same for both

classes. The observation of very low reflectivity over a wide

energy range show that these materials may have potential uses

in hybrid solar cell applications as an active material or in the

buffer layer between the electrodes and inorganic active

materials. Moreover, potential applications may be found in

organic semiconducting devices such as field-effect transistors,

solar cells, and organic light-emitting devices (OLEDs).

Acknowledgements

We gratefully acknowledge the Research Council of Norway for

financial support and for the computer time at the Norwegian

supercomputer facilities.

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