J. Phys. Chem. B 2007, 111, 8179-8186
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Metal-Organic Frameworks: Structural, Energetic, Electronic, and Mechanical Properties A. Kuc, A. Enyashin, and G. Seifert* Physikalische Chemie, Technische UniVersitaet Dresden, D-01062 Dresden, Germany ReceiVed: March 15, 2007; In Final Form: April 27, 2007
The structural, energetic, electronic, and mechanical properties of a series of metal-organic framework (MOF) materials have been systematically studied with the density functional based tight-binding method. The cubic array of Zn4O(CO2)6 units (connectors) connected by different types of organic secondary building blocks (linkers) was considered. The results show that these materials are stable with bulk moduli ranging from 0.5 to 24 GPa with decreasing size of the linker. All MOFs are semiconductors or insulators with band gaps between 1.0 and 5.5 eV, mainly determined by highest occupied molecular orbital-lowest unoccupied molecular orbital gaps of the linker molecules. The atomic charges are nearly the same for free building blocks and the solid MOFs.
1. Introduction The assembly of new materials with tailored properties from well-defined molecular building blocks1 is nowadays of great interest. Copolymerization of a wide range of organic molecules with polynuclear complexes can result in the formation of metal-organic frameworks (MOFs)2-6 that are considered a new class of coordination polymers. MOFs with their inorganic connecting units (based on a transition metal complex or cluster) and the manifold of organic linker molecules are promising materials with uniform and monodisperse pore sizes in the nanometer region. A linker and a connector are both designed to assemble three-dimensional (3D) open frameworks. Dicarboxylate organic linkers form rigid metal carboxylate clusters that act as secondary building units in the extended solid. The way of connection between the building blocks in an MOF is as important as the molecular units themselves.2,7,8 For a given topology of a connector, for example, an octahedral Zn4O(CO2)6 cluster, one can obtain an isoreticular series of MOFs. Such materials with zinc carboxylate clusters have been successfully synthesized by Eddaoudi et al. using a strategy based on reticulating metal ions and organic carboxylate linkers into extended periodic structures. They have obtained 16 different metal-organic frameworks, so-called isoreticular MOFs (IRMOFs). Novel strategies of synthesis allow a systematic variation of the pore size using different organic linkers without changing the cubic topology of the whole framework. The framework topologies can be predicted by consideration of the geometry and conformational informations of secondary building units. As an example, the structure of IRMOF-1 (MOF5) is shown in Figure 1a. This system can be considered as being composed of two distinct structural units: the zinc oxidebased connector (shown in Figure 1b) and the benzene-based linker (shown in Figure 1c), resulting in a 3D cubic porous network. The synthesis of crystalline MOFs is simple and based on mixing together a solution of the acid form of the linker with a simple metal salt in the desired stoichiometry, as described in literature.7 MOFs have a high potential in a variety of practical applications: catalysis, gas separation, molecular sensors, and * Corresponding author.
so forth.8-13 Large surface areas and controlled pore size, as well as easy functionalization of the organic part, allow these crystalline compounds to be excellent systems for molecular sorption applications. MOFs exhibit unique framework properties such as interpenetration, dynamical crystal-to-crystal transformations, and chirality. Other properties of MOFs, such as cavity radius, density, and free volume, can be widely varied, leading to the lowest known densities for a crystalline material.8 The properties of such systems can be modified by the following three approaches: exchange of the benzene linker (MOF-5) by other organic molecules; substitution of the connector, changing the metal atoms in it; and exchange of both the linker and the connector. Theoretical investigations of very few MOF structures have been already reported in the literature.14-17 The exchange of the transition metal (Zn on Cd, Be, Mg, and Ca) in the IRMOF-1 has been studied theoretically for example by Fuentes-Cabera et al.14 Local density approximation density functional theory (LDA DFT) calculations using periodic boundary conditions (PBC) of the geometric, electronic, and mechanical properties were performed for IRMOF-1 by Mattesini et al.16 Kim et al.17 have employed generalized gradient approximation (GGA) DFT with PBC in their calculations of the IRMOF-n (n ) 1, 3, 18) structures. These structures are derived from IRMOF-1 by substitution of hydrogens in the benzene ring by an -NH2 group (IRMOF-3) or a -CH3 group (IRMOF-18). For these materials, the authors have mainly investigated the electronic structure. Semiempirical, Hartree-Fock (HF), and DFT calculations were also employed by Braga et al.15 to study the structure of IRMOF1. They used different model systems to represent the properties of the crystal structure, starting from Zn4O(CH3COO)6, through Zn4O(PhCOO)6, and up to the enlarged system of (CH3COO)5(Zn4O)(OOC-C6H4-COO)(Zn4O)(CH3COO)5. In this paper, we present the results of a systematic study and give an overview of the properties of a wide range of IRMOFs. We have focused our interest on the role of the organic linker nature in MOFs. Density functional based tight-binding (DFTB) calculations18-20 using PBC were performed. The structures considered can be represented as an octahedral array of dicarboxylate organic bridges connected to a transition metal complex of tetrahedral moieties (OZn4)6+. The (OZn4)6+
10.1021/jp072085x CCC: $37.00 © 2007 American Chemical Society Published on Web 06/22/2007
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Figure 1. Structure of IRMOF-1 (MOF-5) consists of cubic fragments (a). Each corner of the cubes is made up of a connector (b). The connectors are linked by organic molecules (linkers (c), here, 1,4-benzenedicarboxylate), which form the edges of the cube. The connector can be described as four distorted tetrahedra Zn(O1)3O2 connected by a central O2.
Figure 2. Reference structure IRMOF-M0. The system is built up from connectors and includes no organic linker: black, C; gray, Zn; and white, oxygen.
connectors linked by different organic molecules form highly porous materials. We have studied well-known MOF structures and also hypothetical systems that may exhibit interesting properties. As a reference system, we have chosen a hypothetical structure with no organic linker (see Figure 2; IRMOF-M0). We discuss here the electronic, structural, and mechanical characteristics of IRMOFs with a large variety of linker molecules (see Figure 3). They are either polycyclic hydrocarbons (PHs) or carbon cages. In this way, IRMOFs with a wide range of pore sizes were studied. The aim of this paper is a theoretical search of new stable systems of high porosity. The systematic theoretical investigations may provide general and specific clues to enhance for example the sorption properties of MOFs and may play a helpful role in the design of new and interesting MOF-like systems. 2. Methods and Computational Details The DFTB method was used to determine the geometry, stability, and electronic structure of isoreticular Zn-based MOFs containing different organic linkers. Some of the initial structure models of IRMOFs were built from the reported crystal structure data,9,21 and PBC were used to represent the framework of the crystalline solid state.
The lattice parameters as well as the structures were fully optimized. The number of k points was determined by reaching convergence for the total energy, as a function of the number of k points. The results were compared with available experimental data. We have considered MOFs with face-centered cubic (FCC), simple cubic (SC), or body-centered cubic (BCC, see example in Figure 4) crystal structures. We have analyzed the electronic properties (Mulliken atomic charges and density of states, DOS) of MOFs with FCC unit cells. The mechanical properties were investigated by the calculation of the total energy change after application of a suitable strain. The determined elastic constants were used to calculate the bulk moduli (B) of these systems. Furthermore, we have employed molecular dynamics (MD) simulations to check the thermal stability of the MOFs. The linkers have been divided into four groups: symmetric (IRMOF-1, IRMOF-993, IRMOF-13/14, etc.) with O2-C1C1-O2 atoms in the same line coinciding with the linkage axis (see Figure 5a); asymmetric relative to the linkage axis (IRMOF7, IRMOF-M4a, IRMOF-M5, etc.) but with O2-C1-C1-O2 atoms in the same line; symmetric (IRMOF-8, IRMOF-M1b, IRMOF-M6b, etc.) with O2-C1-C1-O2 atoms not in the same line (see Figure 5b); and asymmetric (IRMOF-M4b, IRMOFM3d, IRMOF-M6a, etc.) with O2--C1-C1-O2 atoms not in the same line. The connector is a complex consisting of four Zn(O1)3O2 distorted tetrahedra which are connected by a central O2, forming a (Zn)4(O2) tetrahedron. Such an arrangement creates six inorganic (zinc-oxo carboxylato) and six organic (for example, benzene) rings per corner (see Figure 5). 3. Results and Discussion 3.1. Geometry. The calculated equilibrium distances of selected bonds in the studied MOFs are summarized in Table 1. The results are compared with the available experimental data (values in parenthesis). The last column gives information how the organic and inorganic rings are oriented to each other. Table 1 reveals that the bond lengths in the zinc-oxo carboxylato ring are almost unchanged for different organic linkers comparing with the reference system of IRMOF-M0. The calculated C-C bond lengths agree very well with the corresponding measured distances (∆R < 2%). The agreement between calculated and experimental O-C distances is also good (∆R ∼ 2-3%), however, the O-C distances in IRMOF-
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Figure 3. Organic linkers considered in the present work. For clarity, hydrogen atoms are not shown. Notation: IRMOF-x, where x is corresponding to the name given in the literature for experimentally known MOFs or IRMOF-Mn denoting the marks of the proposed linkers for hypothetical MOFs studied here (a, b, c, etc. indicate different isomers for a given linker).
7, -8, and -14 are somewhat larger than the experimental findings. Also, the Zn-O distances are calculated slightly larger than measured ones, but this overestimation is uniform for all systems, where experimental data were available. Theoretical and experimental investigations agree in the fact that the O1-Zn bond length is a bit larger than that of O2-Zn in most of the cases. This tendency can also be seen for hypothetical IRMOFs. Furthermore, it can be noticed that the O1-C1 distances correspond to values between those for the typical single (1.42 Å) and double (1.22 Å) O-C bond, while C1-C2 bond lengths are close to the typical single sp2-sp2 C-C bond (∼1.46 Å).
In the case of BCC lattices, two kinds of O1-C1 and C1C2 bonds were obtained, depending on the orientation of organic and inorganic rings (see discussion below). Generally, the equilibrium bond lengths, shown in Table 1, are shorter for the BCC than for corresponding FCC crystals. We find, however, that the orientation of organic and inorganic rings (see Figure 5) changes significantly for different types of organic linkers, going from the in-plane orientation to the perpendicular to each other and with twisted forms in between. If the connector is not distorted, then the O1-C1C2-C3 torsion angle is in the plane and has one fixed O1Zn-O1 angle. This is typical for the group 1 of the organic
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Figure 4. Structure of IRMOF-14 in simple cubic (a) and body centered cubic (b; IRMOF-13) representations.
Figure 5. Zinc-oxo carboxylato ring connected with the organic ring in the in-plane orientation in IRMOF-1 (a) and IRMOF-8 (b) and the atomic labels. The hydrogen atoms are not shown for clarity.
linkers. For linkers from group 3, the zinc-oxo carboxylato ring can be slightly distorted. In this case, the O1-Zn-O1 angles vary in a small range, and both rings can be either in the plane or orthogonal to each other. A wide range of values for the O1-Zn-O1 angle and twisted O1-C1-C2-C3 torsion angle is typical for a large distortion of the inorganic part (groups 2 and 4). Thus, both rings are in the same plane when the linker is symmetric and not extended into the inner space of a MOF crystal, like in IRMOF-1, IRMOF-8, IRMOF-14, IRMOF-M1b, and so forth. In the case of symmetric and functionalized linkers, both rings are perpendicular to each other (IRMOF-18). Asymmetric linkers and big symmetric ones cause distortion of the connector and a large variation of the O1-Zn-O1 angle, depending on the size of the linker (IRMOF-M6a, IRMOF-M1a, IRMOF-M9, etc.). Moreover, if both rings are in the same plane, then the angle O1-Zn-O1 is fixed with ∼109° or slightly distorted (∼109113°). The facts mentioned above show that the distortions of a connector (caused by some linkers) may lead to the lowering of the crystal symmetry. These systems can crystallize in other than cubic structures (e.g. IRMOF-1). In the case of IRMOF-9/10 (group 1), the benzene rings of the biphenyl linker might give different conformers. This may lead to a distortion of the inorganic part. However, benzene rings in these systems can be stacked; for example, in the case of IRMOF-13/14, such materials have the properties of group 1 (no distortion). A similar situation can be seen in the case of IRMOF-15/16. BCC structures were found to have three of the rings (organic and inorganic) in plane and three perpendicular to each other. This gives two different bond lengths: orientation in plane has shorter O1-C1 and longer C1-C2 bonds, compared with the perpendicular orientation.
The calculated equilibrium lattice constants (a) for all compounds studied here are given in Table 2. We have found experimental data only for some of the IRMOFs, and they are given in parenthesis. The calculated lattice parameters (a) were found to be in all cases a bit larger than those of experiment. The error for a value is in the range 2-4%. Table 2 also includes the highest occupied molecular orbitallowest unoccupied molecular orbital (HOMO-LUMO) gaps, bulk moduli (B), densities, and energies of formation that will be discussed in the next sections. These highly porous structures have the lowest known mass densities for a crystalline material (third column in Table 1). Besides the IRMOF-M0 structure, in many cases, the densities are considerably smaller than 1 g/cm3. 3.2. Energetic and Mechanical Properties. We estimated a kind of formation energy (∆E) as the difference in total energies of the products and reactants, according to the following reaction:
Zn4O(OH)6 + 3R(COOH)2 f Zn4OR3(COO)6 + 6H2O (1) The calculated formation energies are shown in the Table 2 (last column). All values are negative suggesting that energetically a formation of these structures is favorable. The most stable structure, concerning ∆E, is IRMOF-18 which contains the organic linker functionalized by four methyl groups that are arranged in a conformation where the steric repulsion between both rings is minimized. This suggests that the functionalization of the linker is one of the factors that can stabilize the system. The results show that the BCC structures are only more stable than the corresponding FCC structures for longer linkers because of steric hindrance effects.
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TABLE 1: Selected Bond Distances [angstrom] and the O1-Zn-O1 Angle [degree] of the Zinc-Oxo Carboxylato Ringa link
O2-Zn
O1-C1
C1-C2
IRMOF-7 IRMOF-8 IRMOF-993 IRMOF-M1a IRMOF-M1b IRMOF-M4a IRMOF-M4b IRMOF-M2a IRMOF-M2b IRMOF-M2c IRMOF-M3a IRMOF-M3b IRMOF-M3c IRMOF-M3d IRMOF-M6a IRMOF-M6b IRMOF-14 IRMOF-13
2.088 SC 2.092 2.092 (1.941) SC 2.085 (1.941) BCC 2.084 2.069 (2.000) 2.080 (-) 2.082 2.119 2.085 2.091 2.069 2.074 2.097 2.086 2.080 2.070 2.107 2.088 2.095 2.080 2.089 (1.990) BCC 1.995
2.072 2.065 2.072 (1.922) 2.092 (1.922) 2.095 2.067 (1.938) 2.062 (1.938) 2.060 2.082 2.081 2.097 2.082 2.066 2.083 2.096 2.091 2.069 2.118 2.090 2.098 2.098 2.067 (1.950) 2.000
IRMOF-M7 IRMOF-M5 IRMOF-6 IRMOF-10 IRMOF-9
2.060 2.094 2.085 (1.949) 2.088 (1.936) BCC 1.980 (1.923)
2.085 2.094 2.065 (1.939) 2.074 (1.928) 1.990 (1.928)
IRMOF-16 IRMOF-15
2.093 (1.926) BCC 2.014 (1.926)
2.065 (1.935) 2.012 (1.935)
IRMOF-18 IRMOF-M8 IRMOF-M9 IRMOF-M10 IRMOF-M11 IRMOF-M13 IRMOF-M12a IRMOF-M12b
2.084 (1.926) 2.075 2.081 2.081 2.082 2.099 2.062 2.105
2.074 (1.941) 2.086 2.087 2.078 2.066 2.076 2.216 2.184
1.307 1.302 1.316 (1.301) 1.319 (1.301) 1.319 1.305 (1.250) 1.315 (1.234) 1.312 1.315 1.316 1.318 1.310 1.310 1.313 1.321 1.315 1.313 1.337 1.310 1.307 1.320 1.320 (1.250) 1.293 1.304 1.316 1.320 1.315 (1.275) 1.319 (1.283) 1.293 (1.267) 1.303 1.310 (1.306) 1.298 (1.306) 1.308 1.312 (1.248) 1.319 1.317 1.310 1.312 1.312 1.313 1.314
1.464 (1.486) 1.460 (1.486) 1.460 1.462 (1.460) 1.455 (1.482) 1.470 1.466 1.460 1.460 1.456 1.468 1.464 1.459 1.463 1.455 1.450 1.456 1.455 1.459 1.460 (-) 1.456 1.436 1.451 1.460 1.408 (1.440) 1.460 (1.444) 1.448 (1.444) 1.432 1.480 (1.45) 1.460 (1.450) 1.440 1.480 (1.483) 1.460 1.460 1.494 1.468 1.496 1.490 1.489
IRMOF-M0 (non linker) IRMOF-1
O1-Zn
O1-Zn-O1
109 115 112-114 105-115 108-113 109 99-119 109-113 113-115 110-118 97-120 97-119 108-113 93-126 109-112 109-122 106-120 108-124 110-116 108 108 108 109-113 112-114 109 107 107 107 108 108 108 110-111 108-114 105-116 109-112 109 109 114-129 115-122
O1-C1-C2-C3
in plane in plane ∼16° ∼20° in plane ∼50° ∼38° in plane ∼13° ∼11° ∼65° ∼30° in plane ∼38° in plane ∼30° ∼17° ∼20° ∼16° in plane in plane (half) normal to plane (half) in plane ∼12° in plane in plane in plane (half) normal to plane (half) in plane in plane (half) normal to plane (half) normal to plane ∼18°
a The atoms are numbered according to the crystallographic positions (see Figure 5). In parenthesis are given experimental values. SC, simple cubic; BCC, body centered cubic; otherwise FCC lattice.
Moreover, it can be noticed that different isomers of the same linker have similar ∆E (e.g., IRMOF-M4a and -M4b). Generally, the formation energy depends strongly on the size and the shape of the organic linker. We have also investigated the mechanical properties of IRMOFs. The results are given in Table 2. The structures held together by strong Zn-O-C bonds. The linkage between the Zn4O group and the organic moieties results in rather soft materials with relatively small bulk moduli, compared with cubic diamond (theory, 441-457 GPa;22 expt, 443 GPa23) and the wurtzite structure of zinc oxide (theory, 160 GPa;24 expt, 183 GPa25). The calculated values of B indicate that IRMOFs are easily compressible systems. Since the inorganic basic system ZnO has a much larger bulk modulus, the lowering of B in the MOFs is caused by the introduction of the organic linker molecules. The most rigid system is therefore the reference system IRMOF-M0. It can also be shown that the bulk moduli depend significantly on the length of the linker. A longer linker gives a mechanically less resistant system. The largest values of B belong to IRMOFs with hypothetical linkers based on the cagelike structures. The BCC structures also have larger bulk moduli than the FCC systems. The organic linkers can rotate freely in the solid MOF at ambient conditions. We have calculated the energy barrier of a
linker rotation along the connection axis. The rotation of the linker (e.g., rotation barrier for IRMOF-1 ∆Erot ) ∼0.35 eV) can be thermally activated, which is also observed in MD simulations. We have performed molecular dynamics (MD) simulations within NVT ensembles (the canonical ensemble, where number of atoms (N), volume (V), and temperature (T) are conserved during the simulation) at 300 and 1200 K. The nearly free rotation of the linker was observed already at 300 K. These simulations also indicate good thermal stability of MOFs at 1200 K. 3.3. Electronic Structure. 3.3.1. Charge Distribution. In order to study the electronic properties of MOFs, we have analyzed their charge distribution. We have compared results of extended crystals with those for free building blocks. The calculated Mulliken atomic charges (q) of the MOF systems are summarized in Table 3. The results show that MOFs have in all cases an almost unchanged charge distribution, comparing different organic linkers. Moreover, the solid structures keep nearly the same charges as free linkers and free connector (see discussion below). The Zn atoms are positively charged (q ∼ +0.92). This value varies between 1.09 and 0.82, which corresponds to the charges of the Zn atom in the free Zn-O skeleton (free connector; see Figure 6) and the bulk ZnO (wurtzite) structure, respectively.
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TABLE 2: Calculated Equilibrium Lattice Parameter, Band Gap, Bulk Modulus, and Energy of Formation of Several (OZn4)6+-Based IRMOFs with Different Linkersa a/2 [Å]
d [g/cm3]
Gap [eV]
B [GPa]
∆E [kJ/mol]
9.152 SC 9.157 13.440 (12.916) SC 13.197 BCC 13.213 13.343 (12.914) 15.348 (15.046) 13.463 13.285 17.761 17.550 15.318 13.329 13.279 19.974 13.202 19.767 15.283 17.740 15.370 15.591 17.693 (17.190) BCC 17.661 19.653 17.601 13.516 (12.921) 17.674 (17.140) BCC 17.486 22.012 (21.490) BCC 22.024 (21.459) 13.382 (12.807) 16.814 17.857 13.252 13.334 15.078 18.717 18.717
1.182 1.172 0.527 0.556
4.17 5.56 3.73 3.66
24.3 22.3 8.70 6.33
-313.779 -303.731 -309.506 -294.140
0.643 0.423 0.728 0.758 0.317 0.329 0.495 0.856 0.865 0.254 0.881 0.262 0.568 0.363 0.522 0.501 0.342 0.689 0.267 0.372 0.570 0.300 0.620 0.191 0.382 0.650 0.267 0.419 0.927 0.594 0.638 0.781 0.768
2.77 2.83 2.16 2.04 2.13 2.89 2.67 1.50 1.56 1.61 2.15 2.39 2.22 2.25 2.11 2.28 2.63 2.62 2.65 2.90 3.35 3.07 3.15 3.06 2.94 4.28 2.66 2.38 4.56 4.91 5.49 1.32 1.31
3.70 2.40 3.60 4.50 3.20 3.40 1.50 2.41 6.90 2.00 5.10 2.60 3.00 1.10 1.70 3.40 5.90 9.70 0.30 4.20 12.41 6.00 9.80 7.50 7.90 5.00 3.50 4.40 9.20 12.6 9.00
-299.530 -299.768 -311.000 -291.361 -276.777 -296.877 -298.297 -295.186 -291.984 -303.469 -287.275 -305.003 -292.456 -263.769 -293.214 -301.428 -308.395 -254.333 -300.142 -297.322 -304.097 -306.048 -287.373 -283.098 -306.582 -338.050 -297.809 -297.644 -314.160 -313.601 -309.196 -233.291 -289.234
Link (COOH)2 IRMOF-1 IRMOF-7 IRMOF-8 IRMOF-993 IRMOF-M1a IRMOF-M1b IRMOF-M4a IRMOF-M4b IRMOF-M2a IRMOF-M2b IRMOF-M2c IRMOF-M3a IRMOF-M3b IRMOF-M3c IRMOF-M3d IRMOF-M6a IRMOF-M6b IRMOF-14 IRMOF-13 IRMOF-M7 IRMOF-M5 IRMOF-6 IRMOF-10 IRMOF-9 IRMOF-16 IRMOF-15 IRMOF-18 IRMOF-M8 IRMOF-M9 IRMOF-M10 IRMOF-M11 IRMOF-M13 IRMOF-M12a IRMOF-M12b
a Experimental values are given in parentheses. The energy of formation was calculated according to reaction 1; see text. SC, simple cubic; BCC, body centered cubic; otherwise FCC lattice.
TABLE 3: Calculated Atomic Charges (q, e) of the Linkers and the Connector Atoms for Selected MOFsa structure IRMOF-M0 IRMOF-1 IRMOF-7 IRMOF-8 IRMOF-993 IRMOF-M1a IRMOF-M1b IRMOF-M2c IRMOF-18 IRMOF-M8 IRMOF-M9 IRMOF-M11
C(-H) -0.08 -0.12; -0.07 -0.10; -0.07 -0.11 -0.12; -0.07 -0.11; -0.06 -0.11; -0.06 -0.10; -0.05 -0.12; -0.08 -0.11; -0.08
C2 0.01 0-0.009 -0.01 -0.01 0.008; 0.003 -0.03 -0.02 -0.05 -0.02 -0.03 -0.01
C(-CH)
0.04 0.04 0.04 0.04 0.04 0.03 0.04 0.03
Zn
O1
O2
C1
0.92 0.93 0.92 0.92 0.91 0.94 0.92 0.92 0.92 0.93 0.92 0.91
-0.70 -0.73 -0.75 -0.75 -0.72 -0.75 -0.74 -0.74 -0.72 -0.77 -0.75 -0.72
-0.88 -0.88 -0.90 -0.93 -0.88 -0.94 -0.93 -0.96 -0.91 -0.91 -0.97 -0.88
0.92 0.92 0.92 0.92 0.93 0.92 0.92 0.92 0.95 0.92 0.92 0.93
a C(-H) indicates the carbon atoms of the linker that are saturated by H atoms. C(-CH) denotes the carbon atoms of the linker that are connected to C(-H) carbon atoms (as an example, see carbon C4 in Figure 5b).
The oxygen atoms O1 and O2 are both negatively charged with q ) -0.70 to -0.77 and q ) -0.88 to -0.97, respectively. In the free connector, we have found the O1 and O2 atoms charged with q ) -0.92 and q ) -1.26, respectively. Both values are larger than the corresponding charges in the MOF crystal. On the other hand, the charge of -0.82 for oxygen atoms in ZnO bulk system is slightly smaller than that for the equivalent O2 atom in MOFs. In the free linker (dicarboxylate form of the linker; see Figure 6), we can distinguish between the O1 atoms connected to the C1 atoms with a double bond and the O1 atoms from the -OH group. The charge of O1 in
the first case is -1.02, and that in the other one is -0.35. Thus, in the MOF crystal, the charge of the O1 atom is an average of both values in the free linker. The C1 atoms, which bind the linker and the connector together, are positively charged with q ) +0.92, and this value does not change for structures with different linkers. Carbon atoms bound to hydrogen atoms (C(-H)) are slightly negatively charged with q ) -0.11 and q ) -0.07. The C2 carbon atoms have charges close to zero in all cases. Generally, the carbon atoms in the free linker and the MOF crystal have the same charge distribution.
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Figure 6. Structures of free building blocks: (a) the connector and (b) the example linker of IRMOF-M7. Gray, Zn; big white, O; small white, H; black, C.
Figure 7. PDOS of the bulk wurtzite ZnO system in comparison with the skeleton in IRMOF-1. For clarity, only Zn and O2 states are shown for IRMOF-1 (see Figure 1). The Fermi level is indicated by the dotted line. DOS is given in number of states per H atom.
3.3.2. Density of States. We have investigated the partial density of states (PDOS) and the total DOS for the free linkers and the free connector in comparison with all IRMOF crystals studied in this paper. The results show that PDOS (on carbon atoms) of a free linker and the MOF system do not nearly change between each other. On the other hand, the PDOS of oxygen atoms differ in both cases since in an MOF we have one type of O1 and in the free linker we have two types of O1 (see above, section 3.3.1). Considering the free connector, we find the PDOS for zinc atoms to be very similar to the MOF systems and bulk ZnO. The overall electronic properties of IRMOFs are basically characterized by (Zn1)4(O2) clusters that bring to the systems the character of a wide band gap semiconductor (ZnO) (see Figure 7). On the other hand, the organic linkers (especially PAHs) reduce the gap size (see Figure 8). IRMOF-M0 (no linker) was chosen as the reference system to analyze the differences in electronic properties for IRMOFs with different organic linkers. The PDOS graphs of the example structures (described below) are compared with the PDOS of IRMOF-M0. The IRMOF-M0 PDOS (for different states of a given atom) show that the valence band is composed of the Zn 3d states, the O 2p (similarly to the bulk ZnO system), and the C 2p states. The unoccupied band is determined by s and p orbitals of zinc
Figure 8. PDOS of carbon atoms in example IRMOFs. The Fermi level is indicated by the dotted line. For clarity, the atoms of carbon higher than 2 (crystallographic position) are presented together. DOS is given in number of states per H atom.
atoms and the p orbitals of oxygen and carbon. Similar electronic properties are found for IRMOF-1. That is also in agreement with earlier work of Fuantes-Cabrera et al.14 The values of the band gap (HOMO-LUMO gap), shown in the Table 2, depend on the size of the linker. Smaller band gaps are observed for linkers with a larger number of conjugated carbon atoms. MOFs have the HOMO-LUMO gaps range from 1.0 to 5.5 eV. That means they cross the borderline between insulating and semiconducting materials. The largest numbers belong to the structures with linkers that do not contain conjugated sp2 carbon atoms, for example, IRMOF-M0, IRMOF-M11, or IRMOF-M13 (see description below). Figures 8 and 9 show the PDOS of some structures with different sizes of the PH molecule. The results are compared with the DOS of the reference system and the IRMOF-M11 (cage-like linker). The results of PDOS show that the HOMO-LUMO gap is dominated by the π states of sp2 carbon atoms within linkers. It can be noticed in Figure 8 that with increasing the number of the sp2 carbon atoms in the linker the band gap is decreased. This is due to the larger contribution of π states. That means the top of the valence band is dominated by π states of the C3, C4, and so forth atoms (see Figure 5 for numbering). A similar tendency is observed for unoccupied bands, where a big influence of π states of C1 is observed for structures with a small number of sp2 C atoms (e.g., IRMOF-M0 and IRMOF-
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Kuc et al. properties of these materials reveal a wide range of the band gap. Thus, all systems studied here can be classified as semiconductors or insulators. The HOMO-LUMO bands, near the Fermi level, are dominated by C sp2 states of the organic linkers. The PDOS of carbon and zinc atoms are kept almost unchanged when going from the building blocks to the extended MOF crystals. We have only found differences for the oxygen atoms, what was already shown with the charge distribution. The electronic properties are the same for both building units and MOF crystals. The knowledge of this fact gives an opportunity to create proper materials for hydrogen storage, optical applications, and so forth. Longer linkers offer smaller band gaps, but on the other hand, such systems loose their stiffness. Our investigation may be helpful in the synthesis of new MOF materials and in choosing systems of interesting properties for a wide range of applications.
Figure 9. PDOS of zinc atoms in example IRMOFs. The p states of the O1 atoms are shown as well. The dotted line denotes the Fermi level. The dashed line shows the position of the Zn d states in the valence and conduction bands of the reference system. DOS is given in number of states per H atom.
Acknowledgment. Support of this research is acknowledged to Stiftung Energieforschung BW. The authors also thank Dr. T. Heine and A. F. Oliveira for interesting discussions and thank K. Vietze for computational assistance. References and Notes
M11). In the systems with cage-like linkers (e.g., IRMOF-M11 or IRMOF-M13), the band gap is larger because of the lack of sp2 carbon atoms. In all cases, adding the organic linker causes a shift of the O1 p states compared with the reference system (see Figure 9). The peak is shifted to the lower energies relative to Fermi level (EF). The central atom of the connector (O2) has, on the other hand, an unchanged DOS comparing different linkers. These differences in the feature of electronic structures of O1 and O2 might be explained with the fact that atom O1 is involved in a sp2-like bonding with atom C1, while O2 forms pure sp3 hybridization with the surrounding Zn atoms. Figure 9 shows the behavior of 3d states of zinc atoms: similar to oxygen, peaks of these states are shifted to the lower energies comparing different linkers. The dashed lines indicate the positions of Zn 3d states in the reference system. 4. Conclusions We have investigated so-called IFMOFs keeping the cubic topology of all structures. The inorganic part was based on the tetrahedral moieties (OZn4)6+ linked by a wide range of different organic molecules. In this work, over 30 structures have been investigated with respect to their stability, geometry, and electronic properties. The MOF systems were found to be energetically stable. All energies of formation are negative and strongly dependent on the size and shape of the linker. We have found some trends in the relations between the distortions in the zinc-oxo carboxylato rings and topology of a linker. Symmetric linkers seem to have little or no influence on the geometry of the inorganic part, independent from the size. However, asymmetric organic parts cause remarkable distortions of the connector and a possibility for the MOFs existing in a noncubic lattice. Organic linkers may also rotate freely. The free rotation of the linker can be thermally activated (energy barrier of rotation), which was observed in the MD simulations already at 300 K. MOFs lattices have small values of bulk moduli and are easily compressible. However, we also proposed the hypothetical linkers, based on carbon cages, with larger bulk moduli. MOFs have a charge distribution which is kept unchanged compared with the building units. The only change is found for atomic charges of linking oxygen atoms since they are changed, going from the free linker to the MOF. The electronic
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