Theoretical Investigation of Charge Transfer in Metal Organic

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Theoretical Investigation of Charge Transfer in Metal Organic Frameworks (MOFs) For Electrochemical Device Applications Sameer Patwardhan, and George C. Schatz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06065 • Publication Date (Web): 12 Oct 2015 Downloaded from http://pubs.acs.org on October 13, 2015

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The Journal of Physical Chemistry

Theoretical Investigation of Charge Transfer in Metal Organic Frameworks (MOFs) For Electrochemical Device Applications Sameer Patwardhan* and George C. Schatz* Argonne-Northwestern Solar Energy Research (ANSER) Center and Department of Chemistry, Northwestern University, Evanston, IL 60208-3113

*corresponding authors: [email protected] (847-491-2793) [email protected] (847-491-5657)

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Abstract For electrochemical device applications metal organic frameworks (MOFs) must exhibit suitable conduction properties. To this end, we have performed computational studies of intermolecular charge transfer in MOFs consisting of hexa-ZrIV nodes and tetratopic carboxylate linkers. This includes an examination of the electronic structure of linkers that are derived from tetraphenyl benzene 1, tetraphenyl pyrene 2 and tetraphenyl porphyrin 3 molecules. These results are used to determine charge transfer propensities in MOFs, within the framework of Marcus theory, including an analysis of the key parameters (charge transfer integral t, reorganization energy λ and free energy change ∆G0), and evaluation of figures of merit for charge transfer based on the chemical structures of the linkers. This qualitative analysis indicates that delocalization of the HOMO/LUMO on terminal substituents increases t and decreases λ, while weaker binding to counterions decreases ∆G0, leading to better charge transfer propensity. Subsequently, we study hole transfer in the linker 2 containing MOFs, NU-901 and NU-1000, in detail and describe mechanisms (hopping and superexchange) that may be operative under different electrochemical conditions. Comparisons with experiment are provided where available. Based on the redox and catalytic activity of nodes and linkers, we propose three possible schemes for constructing electrochemical devices for catalysis. We believe that the results of this study will lay the foundation for future experimental work on this topic.


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1. Introduction Metal Organic Frameworks (MOFs) are crystalline materials consisting of metal ions (or nodes) coordinated to rigid organic linkers in a 3D network.1-3 They are chemically and structurally diverse materials (~20000 known compounds), and may exhibit unusually high porosities and internal surface areas. Surprisingly, only a few dozen have the thermal and chemical stability desired for certain applications, such as catalysis in harsh environments.4-7 Examples of these include MOFs constructed from hexa-ZrIV nodes and carboxylate-terminated linkers.4,8 Due to their structural design, MOFs have been extensively studied for chemical separation,9 gas storage10,11 and chemical catalysis.12,13 More recently, MOFs are being investigated for electrochemical device applications,14 including electrochemical catalysis,15 batteries,16 supercapacitors17 and electrochromic devices.18 These new applications require intrinsic charge transport within the MOF framework, a property that has not been fully explored.19 Moreover, charge transport may have to be strongly coupled to ions in solution to minimize repulsion due to high charge concentration. This requirement will be stricter for electrochromic and energy storage devices, since all linker molecules have to be oxidized/reduced for optimum performance. For electrochemical catalysis, the requirement could be relaxed, provided consumption of charge due to catalysis is comparable to supply of charge from the electrode. The coupling of charge and ion transport makes charge transport processes in MOFs distinct from traditional semiconductors. Charge transport in molecular materials requires an electronic coupling element, or charge transfer integral t,20 between adjacent molecules. t depends on the spatial overlap between frontier orbitals, which falls off exponentially with intermolecular distance. In organic semiconductors, such as conjugated polymers,21 molecular crystals,22 columnar liquid crystals



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(CLCs),23-25 self-assembling materials26,27 and covalent organic frameworks (COFs),28 the piconjugated building blocks are in close proximity. As a result, the charge transfer integrals are reasonably large (~0.1 eV); charge carriers are at least partially delocalized; and intrinsic carrier mobilities are often 0.01-1.00 cm2V-1s-1. On the contrary, the adjacent linkers in MOFs are typically spatially well separated. Consequently, the overlap between frontier orbitals on adjacent linkers, and therefore the electronic coupling, is small. In addition, coupling to ions increases the activation energy for charge transfer substantially. Thus, MOFs exhibit poor charge transport properties that may be described as diffusive motion of localized charge carriers.29-31 In recent years, different design strategies have been adopted to construct conducting MOFs, for example, using pi-stacking in aromatic linkers,30,32,33 the formation of 1-D chains of alternating metal-sulfur or metal-oxygen atoms,34,35 and infiltration with guest molecules or nanocrystals.36,37 In these MOFs, the porosity (needed for motion of ions) and chemical stability (needed during catalysis) are compromised. As a result, these MOFs are not suitable for electrochemical devices. On the contrary, MOFs constructed from hexa-ZrIV nodes and tetratopic 1,3,6,8-tetrakis(p-benzoic-acid)pyrene linkers, i.e. polymorphs NU-901 and NU-1000, exhibit high porosity, chemical stability and conductivity, simultaneously, making these suitable for electrochemical device applications.8,18,38-40 Depending on the application, additional material requirements besides charge transport include energy transport,41-43 optical response44-46 and catalytic activity.13 The catalytic activity of MOFs has been studied for a variety of reactions, including oxidation, hydrogenation and condensation reactions.13 Usually, the catalytically active centers are transition metal ions on the organic linkers or on undercoordinated nodes.


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In this study, we investigate intermolecular charge transfer in MOFs containing hexa-ZrIV nodes and tetratopic linkers derived from tetraphenyl benzene 1, tetraphenyl pyrene 2 and tetraphenyl porphyrin 3 (Figure 1). The first part of the manuscript (Sections 4.1-4.3) describes charge transfer in relation to linker structure. The key parameters determining charge transport, i.e. charge transfer integrals, reorganization energies and free energy change, are analyzed, including effects of counter ion coupling. Subsequently (Sections 4.4-4.5), we consider the 2 containing MOFs, NU-901 and NU-1000, in detail, providing comparisons with experiment where possible. We calculate hole transfer rates along different crystallographic directions and describe different mechanisms that may be operative under different electrochemical conditions. Lastly (Section 4.6), we use the results of this study to propose three different schemes for employing MOFs in electrochemical device applications.



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Figure 1. Chemical structures of the three tetratopic linkers (derivatives of tetraphenyl benzene 1, tetraphenyl pyrene 2, tetraphenyl porphyrin 3). Also plotted are the hexa-ZrIV node, and the crystal structure of NU-1000 MOF containing linker 2.

2. Theory In a weakly coupled supramolecular system, such as the adjacent linkers in MOFs, the Marcus equation20,47 can be used to describe the rate of intermolecular hole/electron transfer (kh/e) as follows 2  0 λ + ∆G ( ) 2π 2 1 h/e  kh/e = th/e exp −  h 4 λh/e kbT  4πλh/e kbT  

1

where t is the electronic coupling between the initial and final states, called the charge transfer integral. It is defined as

th/e = Ψ D±A0 VDA Ψ D0A± .

2

Here, Ψ D±A0 and Ψ D0A± are the wavefunctions of the initial and final states with hole/electron localized on donor and acceptor molecules, respectively. VDA is the coulomb interaction term. The reorganization energy λ is the energy required to conform bonding and solvent conditions of the system before electron transfer to the final state of the system. λ can be decomposed into internal and solvent energy terms, the former (λint) is the energy change associated with structural deformation of the molecules while the later (λsolv) is the energy change associated with solvent reorganization in the charge transfer process. λint can be defined as int λh/e =  E ± ( g 0 ) − E ± ( g± ) +  E 0 ( g± ) − E 0 ( g 0 )

3


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( )

± 0 where E g is the energy of the monomer with the excess charge q=±1, while the nuclear

geometry g0 corresponds to that for the neutral monomer unit in equilibrium, etc. λsolv can be defined as48

λ

solv

e 2  1 1  1 1 1  =  −  + −  8π  ε∞ ε0  2RD 2RA RAD 

4

where ε∞ and ε0 are the high frequency and static dielectric constants of the solvent, respectively. RD/A is the radius of the pi-electron cloud associated with excess charge on the donor/acceptor, whereas RAD is the interlinker distance. Even if the donor and acceptor linkers have identical chemical structures in MOFs, an energy difference between the Ψ D±A0 and Ψ D0A± states (∆G0) may arise due to different binding states of the counterions to the donor and acceptor molecules during the charge transfer process. If the electronic coupling between donor and acceptor states is negligible, the charge may tunnel using the virtual states of bridging molecules, i.e. superexchange mechanism.48,49 For instance, charge transfer across redox active nodes in MOFs may occur through virtual states of the bridging linker units, where the bridging units may not be redox active.39 In this case, a rate expression, similar to Equation 1, can be derived, where the effective charge transfer integral is defined by teff=tDBtBA/(ED-EB).

5

Here tDB and tBA are charge transfer integrals between donor-node/bridging-linker and bridginglinker/acceptor-node states, respectively. ED-EB is the energy difference between node and linker states, respectively.



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3. Computational Details Density functional theory (DFT) calculations have been performed on chemically relevant fragments taken from the crystal structure using the ADF software.50,51 The M06-2X (M06-L52 if iron is involved) exchange correlation functional with a TZP all electron basis set is used. The carboxylic acid groups have been removed from linkers for the qualitative studies in Sections 4.1-4.3, while they were included in the quantitative calculations in Section 4.4. The contributions of phenyl substituents to the frontier orbitals of the molecules, i.e. highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), are determined using the fragment orbital approach, implemented in ADF.51 The reorganization energies are determined by calculating the four terms in Equation 3. The charge transfer integrals are calculated between adjacent linkers in NU-901 and NU-1000, taken from the crystal structure along different crystallographic directions (coordinates provided in the SI). Charge transfer integrals were calculated using a fragment-based approach implemented in the ADF program.49,53 Interaction energies were calculated by the supramolecular approach, i.e., by subtracting energies of the isolated donor/acceptor species and counterion ( PF6− ) from that of complex.54 Basis set superposition energy corrections were taken into account. 4. Results and Discussion In Sections 4.1-4.3, we study charge transfer in hypothetical MOFs in relation to the properties of constituent linkers, disregarding identity of the node and crystal structure of the MOF. The broader objective of this qualitative analysis is to provide guidelines for designing linkers for optimum charge transport in hypothetical MOFs. According to the Marcus equation, the charge transfer rate depends on charge transfer integrals t, reorganization energies λ, and the free energy term ∆G0. In Section 4.1 and Section 4.2, we discuss the contributions of the t, λ and


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∆G0 terms to the charge transfer rates. In Section 4.3, we discuss the overall charge transfer propensities in these MOFs. In Section 4.4 and Section 4.5, we take up the example of NU-901/NU-1000, containing linker 2 and the hexa-ZrIV node, and discuss hole transport in detail. While carboxylate groups were not included in the calculations above, they have been included in these explicit calculations. We compare incoherent hopping v/s superexchange mechanisms, and provide electrochemical conditions under which these operate. Lastly, in Section 4.6, we propose different schemes for employing MOFs in electrochemical devices. 4.1 Charge Transfer Integrals t Based on the energy of frontier orbitals (Figure S1), the linkers can be divided into two fragments: the core of the linkers and the phenyl substituents. Adjacent linkers are connected at hexa-ZrIV nodes at terminal end of the linker. Therefore, for larger electronic coupling and charge transport, it is beneficial to have larger delocalization of the frontier orbitals on the substituents. In Figure 2, we plot isosurfaces of the frontier orbitals of the linkers (core+phenyl). We obtain substantial delocalization of the orbitals on phenyl substituents on linker 1 compared to 2 and 3. These results can be understood by comparing the orbital energies of the cores (benzene, pyrene, porphyrin) to the substituent (benzene) (Figure S1). As we go down in the series, benzene/pyrene/porphyrin, their HOMO-LUMO gap reduces, moving the frontier orbital energies away from that of the benzene substituent. As a result, the frontier orbitals in 2 and 3 are primarily composed of the pyrene and porphyrin cores, while they are substantially delocalized in 1. In Table 1, we provide the fractional contributions of the phenyl substituents (χh/e) to the frontier orbitals of the linkers. The charge transfer integral t, which depends on orbital overlap, is proportional to χ2. We obtain relative values by normalizing χ2 to the minimum value in the data



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4 4 2 2 set, i.e. χ h/e . The Marcus rate is proportional to t2, therefore we provide t χ2 ,h/e = χ h/e / χ min / χ min

as a relevant parameter to access relative charge transfer rates. As expected, the values of t χ2 are substantially larger for 1 (>1100) than 2 and 3 (1-10). Moreover, t χ2 ,h > t χ2 ,e for 1, while t χ2 ,e = 2t χ2 ,h for 2 and 3. The results indicate faster charge transport in 1-based MOFs compared to those based on 2 and 3.

Table 1: Fractional contribution of phenyl substituents to the frontier orbitals (HOMO/LUMO) 4 χ, and relative charge transfer integrals in MOFs ( t χ2 = χ e4 / χ min ). Optimized geometries of the

linkers, without the carboxylate groups, were used for these calculations. Molecule

χh

4 t χ2 ,h = χ h4 / χ min

χe

4 t χ2 ,e = χ e4 / χ min

1

0.59

1212

0.58

1132

2

0.15

5

0.18

10

3

0.10 (χmin)

1

0.12

2


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Figure 2. HOMO/LUMO orbital isosurfaces (at 0.15 a.u.) for linkers 1, 2 and 3 in gas phase (M06-2X xc-functional, TZP all electron basis set). Crystal structures of the MOFs, determined by X-ray diffraction and molecular modeling studies, are not resolved to atomic detail. Although approximate positions of the organic linkers and nodes can be determined, their structural configurations are largely unknown. Therefore, the effect of changes in structural configuration on charge transfer needs to be investigated. In Figure 3, we provide the relative potential energy E(θ)-E(0°) and the relative charge transfer integrals t2(θ)/t2(0°) as a function of phenyl rotation for the pyrene linker. Here, 0° refers to the rotation angle between phenyl substituent and pyrene ring at the optimized geometry (~54.9°); and θ refers to the angle by which the four phenyl rings are simultaneously and symmetrically rotated from the equilibrium angle. Within 60° rotations around the equilibrium angle, the energy change is a mere 0.5 eV. In comparison, the energy associated with linker binding to nodes in the crystal is >5 eV (strong ionic bonds between the four carboxylate groups and nodes). Therefore, we anticipate that the equilibrium phenyl rotation angle will vary from one MOF to the other, depending on the constraints imposed by their crystal structures. Suitable examples in the present context are MOF-525 with a box-structure55 and PCN-222 with hexagonal structure,56 both of which are constructed from linker 3 and hexa-ZrIV nodes. Based on the analysis of crystal structures, the phenyl groups are expected to be closer to coplanar in MOF-525 and ~55° in PCN-222. Interestingly, the charge transfer integrals vary by three orders of magnitude (9.278 at 30° to 0.005 at -30°) within the 60° rotations, indicating the importance of phenyl rotation for describing charge transfer. This shows that having suitable chemical structures of the linkers (discussed in Sections 4.1-4.3) is not sufficient to guarantee efficient charge transport in the 11 ACS Paragon Plus Environment


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resulting MOFs. Also, charge transfer rates are expected to be significantly higher in MOF-525 than PCN-222, even with the same redox active linker. Indeed, it has been shown that MOF-525 is electroactive for nitrite oxidation in a recent study.40 Similarly, structural dynamics may also influence the charge transfer process. The extent of the rotation of a single phenyl group due to thermal fluctuations can be determined by comparing the energy required for rotating this phenyl group (approx. 1/4th of the E(θ)-E(0°) value) to the energy associated with thermal fluctuations (0.025 eV). This means that within the 30°-window (E(θ)-E(0°)~0.1 eV at ±15°) accessible by thermal fluctuations, charge transfer propensities (t2=3.47 at -15° and 0.13 at 15°) will differ up to a factor of 30.

Figure 3: Effects of rotation of the four phenyl rings on the potential energy E(θ)-E(0°) (red) and charge transfer integral t2(θ)/t2(0°)= χ4(θ)/χ4(0°) (blue) 0° corresponds to the 54.9° equilibrium geometry in the gas phase. The reorganization energy λ(θ) doesn’t change significantly (see Table S1). The potential energy surface (red) is asymmetric due to impending steric hindrance at lower angles, which steeply increases the potential energy for negative angles. 12 ACS Paragon Plus Environment

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4.2 Reorganization Energy λ and Free Energy ∆G0 In Table 2, we provide the reorganization energies λint and λsolv, which are associated with structural changes and solvation, respectively. To compute λsolv (Equation 4), we need to determine the size of the pi-electron cloud 2RD/A and interlinker distance RAD. Following the results for frontier orbital delocalization (Figure 2), 2RD/A is taken as the size of the pyrene core for 2 (0.7 nm) and porphyrin core for 3 (0.86 nm), and phenyl core + substituents for 1 (1.14 nm). The interlinker distance RAD for linker 2 is taken as 1.6 nm (interlinker distance in NU1000 along the c-axis, calculated between the geometrical centers of adjacent linkers). For 1 and 3, the RAD value of 1.6 nm is scaled to the linker size, to obtain 1.33 nm and 1.8 nm, respectively. Acetonitrile (ε∞=1.8, ε0=37.5)57, which has been used in experimental studies, is considered for the solvent. The variation in λsolv is larger and contributes more to the reorganization energy than λint. This will become more prominent if water is used as a solvent, as this has a higher dielectric constant. A smaller λsolv is desired for higher charge transfer propensities. In this regard, extended delocalization of the frontier orbitals would not only reduce λsolv, by increase RD/A, but may also increase the charge transfer integrals, as described previously. Thus, we see over an order of magnitude higher hole transfer propensity in 1 compared to 2 and 3. Similarly, we obtain a higher value for electron transfer in 1, although higher λint compensates for smaller λsolv. The values of electron and hole transfer propensities are higher for 3 than 2.



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Table 2: Internal reorganization energy of electron (λe) and hole (λh), solvent reorganization energy λsolv, and relative charge transfer propensity exp[-(λh/e- λmax)/4kbT]. Here, λ=λint+λsolv and kbT =0.025 eV at room temperature. Molecule

λsolv (eV)

λhint (eV)

λeint (eV)

1 2 3

0.38 0.86 0.67

0.32 0.28 0.38

0.53 0.39 0.29

exp[-(λhλmax)/4kbT] 81.5 1 2.5

exp[-(λeλmax)/4kbT] 10 0.3 6

In MOFs, charge transfer is commonly coupled to the movement of counterions in solvent to neutralize the excess charge, such as in electrochromic and energy storage devices, as discussed above. Thus, counterion diffusion may strongly influence long-range motion of the charge carriers. Different design strategies can be adopted to improve counterion accessibility. For instance, a counterion concentration comparable or higher than the concentration of linkers may give one counterion in the vicinity of every linker. On the contrary, at very low concentrations the counterions have to move from donor to acceptor, which is a slower process. The chemical structure of the linkers can be tuned to increase affinity of counterions towards the MOF framework, such as by increasing polarizability. The interaction of counterions with linkers may have to be considered, especially in low dielectric solvents. The studied MOFs have two distinct regions: the hydrophilic node region consists of polar hexa-ZrIV particles coordinated to carboxylate groups of the linkers, and the hydrophobic surface of the linkers. In this regard, an oxidized or reduced linker will be highly polar due to excess charge. Thus, the affinity of counterions, and that of solvent molecules, will be significantly higher for the charged linker compared to neutral linker. If the electron transfer rate is faster than structural reorganization of the counterions, this difference in binding 14 ACS Paragon Plus Environment

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properties will contribute to the ∆G0 term in Equation 1. Without considering the identity of the counterions and organic linkers at this point, we take ∆G0=0.1 eV to compute rates (see Table 3). This approximate analysis is motivated by atomistic calculations that we present later (Section 4.4). The relative charge transfer rates don’t change significantly due to the ∆G0 contribution, although the absolute values go down by a factor of 8. Interestingly, donor to acceptor forward transfer is slower than back transfer by a factor of 55 [kbck/kfwd=exp(∆G0/kbT)], which is detrimental to long range transport across multiple linkers.

Table 3: Charge transfer propensities exp[-(λ+∆G0)2/4λkbT], relative to the lowest value in the series, i.e. electron transfer for 2. The reorganization energy values are taken from Table 2 and ∆G0=0.1. (kbT =0.025 eV at room temperature) Molecule

exp[-(λh+ ∆G0)2/4λkbT] exp[-(λe+∆G0)2/4λkbT]

1

230

29

2

3

1

3

7

18

Table 4: Relative rates of electron/hole transfer in MOFs, obtained by multiplying corresponding entries for t2 and exp[-(λh/e+∆G0)2/4λh/ekbT] from Tables 1 and 3. Linker

kh

ke

1

~105

~104

2

15

10

3

7

35

4.3 Charge Transfer Rates



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The relative charge transfer propensities (kh/e) in MOFs are obtained by multiplying the corresponding values of t2 and exp[-(λh/e+∆G0)2/4λh/ekbT] from Tables 1 and 3 (see Table 4). Electron and hole transport in the 1-based MOF is orders of magnitude faster than the others, due to favorable contribution from both t and λ. The values are comparable for linkers 2 and 3, with electron transfer slightly faster in 3 and hole transfer slightly faster in 2. The analysis indicates that fast charge transport in MOFs requires linkers with maximum HOMO/LUMO densities on the terminal groups (t and λ terms) and weaker binding to counterions (∆G0 term). In addition to the intrinsic charge transport properties of MOFs, it is crucial to have the right energy level alignment of the MOF with other components of the device, such as solvent, catalyst and contacts. The solvent requirement is related to stability; on a catalyst it is related to overpotential during electrochemical catalysis, and on contacts it is related to charge injection/extraction. Although, it is an efficient charge transporter, linker 1 has shallow LUMO and deep HOMO energy levels (Figure S2). As a result, the injected electrons and holes will easily transfer to (polar) solvent molecules instead of getting transported along the MOF framework. In addition, hole injection will require higher applied potentials; and linkers will be chemically unstable. As a result of this, it will be hard to perform successful device measurements on 1-based MOFs. Moreover, the large HOMO-LUMO gap in 1 will yield a wide band gap MOF material that will only absorb in far UV, so it will not be suitable for optoelectronic applications. Contrary to 1, in 2 and 3, the orbital energies are more favorable for charge injection from contacts, especially for holes, and from the standpoint of stability in a suitable solvent environment. Thus, the redox properties are more suitable for applications in going from 1 to 3, i.e. HOMO energies vary as 13 (Figure S2), albeit at


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the expense of poorer intrinsic charge transport properties in the resulting MOFs. Amongst the studied MOFs, 2 and 3 are appropriate for practical applications. Indeed, it has been demonstrated experimentally that the two known polymorphs, NU-901 and NU-1000, both of which contain 2, are electroactive,18,38 although hole transport properties have not been investigated. In the following section, we will study hole transport in these materials in detail.

4.4 Linker Activated Hole Transfer in NU-901 and NU-1000 The crystal structure of NU-901 is composed of diamond-shaped channels, while that of NU-1000 contains hexagonal and triangular channels (Figure 4). In both cases, the channels can transport counterions as large as tetrabutylammonium (9.9 Å) and hexafluorophosphate (5.5 Å),18 making these materials suitable for charge transport, and therefore, for electrochemical device applications. NU-1000 can be considered as a reconstructed structure of NU-901, as shown by highlighted black lines. In both MOFs, three different types of adjacent neighbors (n1, n2 and n3) can be identified in relation to charge transfer. Out of these, n1 and n2 are in the a-b plane (shown by blue and green arrows), while n3 is along the c-axis (shown by red arrows). Charge transfer integrals have been calculated for the three neighbors, taking the relative orientation from the known crystal structure of NU-1000.58 Note that t falls by an order of magnitude if the carboxylate groups are removed from the structure, and it becomes negligible if the phenyl groups are also removed. This shows that the main contribution to the charge transfer integrals comes from phenyl and carboxylate groups even though the frontier orbitals are largely localized on the core. The extended pi-electron delocalization in linker 2 imparts pale yellow color to the MOFs.38 While larger HOMO/LUMO delocalization on substituents is desirable for hole/electron transport in MOFs, it is usually detrimental to charge transport in organic



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semiconductors having a closed packed molecular arrangement.23 It is important to note that carboxylate groups are an integral part of the ZrIV-node structure; therefore, we expect some delocalization of orbital density on the node as well (Figure S3). We have neglected this throughbond contribution to charge transfer integral in our analysis. With this approximation, we expect to get results with order of magnitude accuracy. The computed charge transfer integrals, transfer rates and time constants are provided in Table 5. As a first approximation, we take ∆G0=0 in polar solvents. The rates are comparable for n1 and n3, while it is negligible for n2. This indicates the presence of largely 1-D hole transport along the triangular columns (c-axis) in NU-1000, while largely 2-D transport (plane of a+b and c-axis) occurs in NU-901. Electroactive films of NU-1000 can be deposited on a conductive substrate with nanorods growing vertically or lying horizontally.18,38 If the transport were 1-D in NU-1000, we would expect faster charge transport in the former case. At room temperature, significant rotational dynamics of phenyl substituents would lead to 3-D transport in all cases. A temperature dependent study may be appropriate to decipher the role of structural dynamics in charge transfer. In a recent study, the electrochromic switching time of NU-901 thin-films was reported in the range of several seconds.18 This is slower compared to the predicted transfer time in microseconds. However this can be understood, because charge transport across multiple linkers is limited by the diffusion properties of the counterions.


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Figure 4: Crystal structures of NU-901 and NU-1000 MOFs containing linker 2 and the hexaZrIV node. NU-1000 contains hexagonal and triangular channels (cell length in Å: 39.4/39.4/16.5; cell angles: 90°/90°/120°), while NU-901 contains a diamond-shaped channel (cell length in Å: 19.1/19.1/16.0; cell angles: 90°/90°/120°). The former can be considered as a reconstructed structure of the latter (highlighted black lines).

Since MOFs are nanoporous materials exhibiting high surface areas, the binding properties of counterions to linkers in MOFs can be significantly different than to free-linkers in solution. Thus, counterion association may play a role in the charge transfer process, even in polar solvents. In the present context, the size of hexagonal pores in NU-1000 is 2.8 nm, including 0.4 nm van der Waals distance from the walls. If all six pyrene linkers are oxidized, 19 ACS Paragon Plus Environment


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planar arrangement of the six PF6- ions (0.3 nm in size) is required to compensate all charge effectively. Although the pore may accommodate all six counterions, the solvent is unlikely to screen the charge as effectively. Moreover, counterion accessibility would reduce with increase in concentration of the oxidized pyrene. To study the effect of counterion association, we performed geometry optimization using the PF6- counterion that has been used in experimental studies.18 A free energy ∆G0=0.19 eV was then determined by subtracting the optimized energy of the donor+-PF6- complex (-0.43 eV) from that for the corresponding acceptor0-PF6- complex (0.24 eV). We also note that this free energy change would have its maximum value if the 0 acceptor molecule doesn’t have a counterion in the vicinity, i.e. ∆Gmax =0.43 eV. The charge

transfer anisotropy, rates and time constants (Table 6) are qualitatively similar to the high 0 =0.43 eV), charge dielectric case (Table 5). In the absence of a counterion on the acceptor ( ∆Gmax

transfer

would

be

sluggish

(τh,max).

Moreover,

acceptor-to-donor

back-transfer,

kback/kfwd=exp(∆G0/kbT)>>1000 is substantially faster. Thus when a counterion encounters the acceptor, it accelerates forward transfer and stabilizes the hole.

Table 5: Charge transfer integrals th, hole transfer rates kh and lifetimes τh for neighbors: n1, n2 and n3 in NU-901/NU-1000 (λh=0.77eV, ∆G0=0 eV). The data refers to the case of a high dielectric solvent, where linker-counterion interaction is negligible. Neighbor type

t (eV)

6 -1 kh (10 s )

τh (µs)

n1

0.00272

1.3

1

n2

0.00003

1.6x10-4

6220

n3

0.00260

1.2

1


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Table 6: Charge transfer integrals th, hole transfer rates kh and lifetimes τh for neighbors: n1, n2 0 and n3 in NU-901/NU-1000 (∆G0=0.19 eV). The τh,max refers to ∆Gmax =0.43 eV.

Neighbor type

t (eV)

4 -1 kh (10 s )

τh (ms)

τh,max (ms)

n1

0.00272

2.15

0.046

21

n2

0.00003

2.62x10-4

4x102

1.7x105

n3

0.00260

1.97

0.051

23

Since the frontier orbitals are largely localized on the core of the linker, λ is not sensitive to the rotational conformation of phenyl substituents (see Table S1). The same is true for ∆G0 (see calculation above). Due to the weak dependence of λ and ∆G0 on linker conformation and MOF topology, it is expected that the activation energy (Ea=(λ+∆G0)2/4λ ) in MOFs will primarily depend on the properties of linkers and counterions. Therefore, Ea is an appropriate parameter to compare computed properties with the experiments. In the present case, Ea=0.39 eV to 0.54 eV depending on the value of ∆G0 we use, i.e. ∆G0=0.19 eV or ∆G0max=0.43 eV. (Here,

λ=1.14 eV is taken from Table 2). In general, we expect porous MOFs to exhibit similar values of Ea. In a recent study, activation energies in the range 0.27-0.81 eV were reported in analogs of MOF-74, where charge transport occurs via semi-infinite (Fe-S-), (Fe-O-), (Mn-S-), (Mn-O-) chains (instead of linker hopping).35 The rather large value of the activation energies in these MOFs would yield transfer rates that are inferior to organic semiconductors used in photovoltaics and transistor applications. However, this would not limit their use in certain applications, such as electrochemical catalysis and chemical sensors, where requirements for getting charges across are less strict. 4.5 Hole Transport in the Case of Redox Inactive Linkers 21 ACS Paragon Plus Environment


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It is possible to get charge transport without activating organic linkers. In a recent study, redox active ferrocene carboxylate molecules were covalently installed on hexa-ZrIV nodes in NU-1000 (Figure 5).39 In this new material, the ferrocene/ferrocenium redox potential (0.8 V against Ag/AgCl) is lower than that for pyrene linkers (1.4 V against Ag/AgCl). Surprisingly, charge transport and catalytic response were reported to be close to the redox potential of ferrocene/ferrocenium. To rationalize the results, we calculated charge transfer rates in different crystallographic directions (Table 7). While charge transfer integrals between adjacent ferrocenes were calculated explicitly, the reorganization energy λsolv+ λint = 1 eV was taken from literature.59 The charge transfer integral is non-zero only along a-/b-directions (0.0001 eV, Fe-Fe distance=1 nm) and an order of magnitude smaller than between the adjacent linkers reported earlier. It is zero between ferrocenes along the c-direction (Fe-Fe distance=1.7 nm) and across the node (Fe-Fe distance=1.3 nm), i.e. two ferrocenes attached to same node on opposite sides. Thus, charge transfer is efficient only across six ferrocenes attached to six nodes in a circular arrangement in the a/b plane, with charge transfer rates (~104 s-1) comparable to linker hopping in Table 6. Even though through-space transfer between ferrocenes is unlikely in the c-direction, charge carriers may get across by ligand-mediated superexchange. The effective charge transfer integral for this process, tsx=1.07-3.27x10-6 eV, was calculated using Equation 5 (tDB, t’DB~[0.0008-0.0014 eV] and ΕD-ΕB=0.6 eV39). The approximate transfer rate is ~7 s-1 with a

corresponding time constant of ~0.14 seconds. This is a rather small rate compared to the through-space hopping in the a-/b- directions.


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Figure 5: Redox active ferrocene carboxylate groups installed on hexa-ZrIV nodes in NU-1000. Charge transfer between ferrocenes along a-/b-axis occurs via direct electronic coupling, and along c-axis occurs by a linker mediated superexchange mechanism. Predominant covalent attachment of ferrocene to the walls of the hexagonal pores is assumed.39

Table 7: Charge transfer integrals th, hole transfer rates kh and lifetimes τh between adjacent ferrocenes along a-/b-axis and c-axis in NU-1000 (∆G0=0, λ=1 eV). Neighbor type

t (eV)

-1 kh (s )

τh (ms)

a/b

0.0001

7.73x103

0.129

c

0.00003

6.96

144

The above analysis suggests two possible mechanisms for charge transfer across redox active nodes, i.e. through-space hopping and superexchange mechanisms. Moreover, charge transfer can be as efficient as linker activated hopping. Considering the fact that catalysts are



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deposited on hexa-ZrIV nodes between the linkers and that NU-1000 has a larger pore size, it should be possible to install a larger catalyst that may enhance transport via suitable orbital overlap. This conclusion has a profound impact on the design of future MOF systems for electrochemical catalysis, as it suggests that suitable molecular catalysts can be designed and installed on nodes of MOFs with redox silent linkers and suitable band alignment. This eases several requirements on linker properties, such as the overpotential associated with their activation and stability. For electrochemical catalysis, an alternate strategy to the above is to use catalytically active linkers. In such systems, organic linkers participate in both chemical conversion and charge transport. Thus, post-synthesis modifications to install catalysts are not required, and linker activation farther away from the substrate is possible when charge transfer rates are substantially faster than turnover frequencies. MOFs constructed from linker 3, containing a suitable transition metal ion (iron, cobalt, manganese etc), are highly appropriate in this regard.60 Metal porphyrin catalysts are multivalent redox species. Thus, an applied potential will simultaneously activate different redox states of the catalyst. Since valency determines the number of pathways available for the charge carriers to move, higher valency is expected to enhance charge transfer events (pathways), and therefore charge transport, significantly. Moreover, the availability of multiple electrons from neighboring catalyst sites, such as by charge disproportionation, is expected to boost the performance of individual catalyst particles.31 4.6 Schemes for using MOFs in electrochemical catalysis Based on the above analysis, we foresee three plausible schemes for employing MOFs for electrochemical catalysis in future (Figure 6). In Scheme 1, the processes of charge transport and catalysis are compartmentalized. A redox active linker transports charge carriers that will be


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consumed by catalytically active nodes. The redox potential of the linker will have to be matched to the catalyst to minimize overpotential associated with linker activation. Although charge transport may be efficient, problems with the stability of charged linkers during operation need to be addressed. In Scheme 2,39 the linker will be redox inactive and charges will get transported between catalytically active nodes by direct hopping or the linker mediated superexchange mechanism. Here, charge transport may be slower, limiting the thickness of the MOF layer that is catalytically active during operation. In Scheme 3,31 catalytically active linkers, such as metalporphyrins, will be employed, while the nodes may or may not be redox active. This is a more promising scheme since charge transport can be as efficient as in Scheme 1, while as in Scheme 2 the overpotential is only associated with one species, i.e. the catalytically active linker.

Figure 6: Three plausible schemes for constructing devices for electrochemical catalysis.

5. Conclusions We have studied the electronic structure of three tetratopic linkers 1, 2 and 3 to determine charge transfer propensities in MOFs constructed from them. We first showed that the optimized gas phase chemical structure of linkers provides qualitative information about orbital 25 ACS Paragon Plus Environment


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delocalization and redox potential, information that can used to understand charge transfer propensity in the resulting MOFs. We also showed that the equilibrium conformation and dynamic fluctuations of linkers are essential to correctly describing the charge transfer process in MOFs. Notably, the figures of merit (χ4, λ, orbital energy, valency) are appropriate for performing large-scale screening of organic linkers and the resulting MOFs for electrochemical device applications in future. We studied hole transfer in two polymorphs, NU-901 and NU-1000, containing linker 2 and hexa-ZrIV nodes, in detail. Distinct MOF structures give quasi 1-D hole diffusion in NU1000 and quasi-2D hole diffusion in NU-901. Next, we described charge transfer in NU-1000, where hexa-ZrIV nodes are decorated with redox active ferrocene units. In this system, charges get transported across ferrocene units at lower applied potentials either via direct hopping or linker-mediated superexchange mechanisms. Based on redox and catalytic activity of linkers and nodes, we propose three possible schemes for constructing electrochemical devices with MOFs, where 1. redox active linkers transport charges while catalyst particles are installed on nodes; 2. redox active particles on nodes are responsible for charge transport and catalysis, while linkers are redox inactive; 3. redox active linkers are responsible for charge transport and catalysis, while nodes may not be redox active. Thus, we have shown that MOFs may possess the required properties (porosity, crystallinity, conductivity, redox energies, catalytic activity) to construct more efficient electrochemical devices in future.

Acknowledgments


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This work was supported as part of the ANSER center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001059. We would like to thank Professor Joseph T. Hupp of Northwestern University for critically reviewing the manuscript and valuable discussions on the subject. Supporting Information The frontiers orbitals of node, linkers and linker-constituents; reorgainization energies of structural conformations of linker-2; and coordinates of linker-2 that were used in the calculation of charge transfer integrals and free energy change have been provided in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

Notes: The authors declare no competing financial interests. References (1)

Ferey, G. Hybrid porous solids: past, present, future. Chem. Soc. Rev. 2008, 37, 191214.

(2)

Furukawa, H.; Cordova, K. E.; O'Keeffe, M.; Yaghi, O. M. The chemistry and applications of metal-organic frameworks. Science 2013, 341, 1230444.

(3)

Meek, S. T.; Greathouse, J. A.; Allendorf, M. D. Metal-organic frameworks: a rapidly growing class of versatile nanoporous materials. Adv. Mater. 2011, 23, 249-267.

(4)

Cavka, J. H.; Jakobsen, S.; Olsbye, U.; Guillou, N.; Lamberti, C.; Bordiga, S.; Lillerud, K. P. A new zirconium inorganic building brick forming metal organic frameworks with exceptional stability. J. Am. Chem. Soc. 2008, 130, 13850-13851.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(5)

Page 28 of 36

Park, K. S.; Ni, Z.; Cote, A. P.; Choi, J. Y.; Huang, R.; Uribe-Romo, F. J.; Chae, H. K.; O'Keeffe, M.; Yaghi, O. M. Exceptional chemical and thermal stability of zeolitic imidazolate frameworks. P. Natl. Acad. Sci. USA 2006, 103, 10186-10191.

(6)

Ferey, G.; Mellot-Draznieks, C.; Serre, C.; Millange, F.; Dutour, J.; Surble, S.; Margiolaki, I. A chromium terephthalate-based solid with unusually large pore volumes and surface area. Science 2005, 309, 2040-2042.

(7)

Colombo, V.; Galli, S.; Choi, H. J.; Han, G. D.; Maspero, A.; Palmisano, G.; Masciocchi, N.; Long, J. R. High thermal and chemical stability in pyrazolate-bridged metal-organic frameworks with exposed metal sites. Chem. Sci. 2011, 2, 1311-1319.

(8)

Mondloch, J. E.; Katz, M. J.; Planas, N.; Semrouni, D.; Gagliardi, L.; Hupp, J. T.; Farha, O. K. Are Zr-6-based MOFs water stable? Linker hydrolysis vs. capillary-force-driven channel collapse. Chem. Commun. 2014, 50, 8944-8946.

(9)

Li, J.-R.; Sculley, J.; Zhou, H.-C. Metal-organic frameworks for separations. Chem. Rev. 2012, 112, 869-932.

(10)

Farha, O. K.; Yazaydin, A. O.; Eryazici, I.; Malliakas, C. D.; Hauser, B. G.; Kanatzidis, M. G.; Nguyen, S. T.; Snurr, R. Q.; Hupp, J. T. De novo synthesis of a metal-organic framework material featuring ultrahigh surface area and gas storage capacities. Nat. Chem. 2010, 2, 944-948.

(11)

Furukawa, H.; Ko, N.; Go, Y. B.; Aratani, N.; Choi, S. B.; Choi, E.; Yazaydin, A. O.; Snurr, R. Q.; O'Keeffe, M.; Kim, J.; Yaghi, O. M. Ultrahigh porosity in metal-organic frameworks. Science 2010, 329, 424-428.

(12)

Ma, L.; Abney, C.; Lin, W. Enantioselective catalysis with homochiral metal-organic frameworks. Chem. Soc. Rev. 2009, 38, 1248-1256. 28 ACS Paragon Plus Environment

Page 29 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13)

Lee, J.; Farha, O. K.; Roberts, J.; Scheidt, K. A.; Nguyen, S. T.; Hupp, J. T. Metal-organic framework materials as catalysts. Chem. Soc. Rev. 2009, 38, 1450-1459.

(14)

Allendorf, M. D.; Schwartzberg, A.; Stavila, V.; Talin, A. A. A roadmap to implementing metal–organic frameworks in electronic devices: challenges and critical directions. Chem.–Eur. J. 2011, 17, 11372-11388.

(15)

Wang, C.; Xie, Z.; deKrafft, K. E.; Lin, W. Doping metal-organic frameworks for water oxidation, carbon dioxide reduction, and organic photocatalysis. J. Am. Chem. Soc. 2011, 133, 13445-13454.

(16)

Ferey, G.; Millange, F.; Morcrette, M.; Serre, C.; Doublet, M.-L.; Greneche, J.-M.; Tarascon, J.-M. Mixed-valence Li/Fe-based metal-organic frameworks with both reversible redox and sorption properties. Angew. Chem.-Int. Edit. 2007, 46, 32593263.

(17)

Diaz, R.; Gisela Orcajo, M.; Botas, J. A.; Calleja, G.; Palma, J. Co8-MOF-5 as electrode for supercapacitors. Mater. Lett. 2012, 68, 126-128.

(18)

Kung, C.-W.; Wang, T. C.; Mondloch, J. E.; Fairen-Jimenez, D.; Gardner, D. M.; Bury, W.; Klingsporn, J. M.; Barnes, J. C.; Van Duyne, R.; Stoddart, J. F. et al. Metal-organic framework thin films composed of free-standing acicular nanorods exhibiting reversible electrochromism. Chem. Mater. 2013, 25, 5012-5017.

(19)

Kobayashi, Y.; Jacobs, B.; Allendorf, M. D.; Long, J. R. Conductivity, doping, and redox chemistry of a microporous dithiolene-based metal-organic framework. Chem. Mater. 2010, 22, 4120-4122.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(20)

Page 30 of 36

Kocherzhenko, A. A.; Patwardhan, S.; Grozema, F. C.; Anderson, H. L.; Siebbeles, L. D. A. Mechanism of charge transport along zinc porphyrin-based molecular wires. J. Am. Chem. Soc. 2009, 131, 5522-5529.

(21)

Noriega, R.; Rivnay, J.; Vandewal, K.; Koch, F. P. V.; Stingelin, N.; Smith, P.; Toney, M. F.; Salleo, A. A general relationship between disorder, aggregation and charge transport in conjugated polymers. Nat. Mater. 2013, 12, 1038-1044.

(22)

Schmidt, R.; Oh, J. H.; Sun, Y.-S.; Deppisch, M.; Krause, A.-M.; Radacki, K.; Braunschweig, H.; Könemann, M.; Erk, P.; Bao, Z.; Würthner, F. High-performance air-stable n-channel organic thin film transistors based on halogenated perylene bisimide semiconductors. J. Am. Chem. Soc. 2009, 131, 6215-6228.

(23)

Demenev, A.; Eichhorn, S. H.; Taerum, T.; Perepichka, D. F.; Patwardhan, S.; Grozema, F. C.; Siebbeles, L. D. A.; Klenkler, R. Quasi temperature independent electron mobility in hexagonal columnar mesophases of an H-bonded benzotristhiophene derivative. Chem. Mater. 2010, 22, 1420-1428.

(24)

Gunbas, D. D.; Xue, C.; Patwardhan, S.; Fravventura, M. C.; Zhang, H.; Jager, W. F.; Sudholter, E. J. R.; Siebbeles, L. D. A.; Savenije, T. J.; Jin, S.; Grozema, F. C. High charge carrier

mobility

and

efficient

charge

separation

in

highly

soluble

perylenetetracarboxyl-diimides. Chem. Comm. 2014, 50, 4955-4958. (25)

Marcon, V.; Breiby, D. W.; Pisula, W.; Dahl, J.; Kirkpatrick, J.; Patwardhan, S.; Grozema, F.; Andrienko, D. Understanding structure−mobility relations for perylene tetracarboxydiimide derivatives. J. Am. Chem. Soc. 2009, 131, 11426-11432.


Page 31 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(26)

Patwardhan, S.; Sengupta, S.; Siebbeles, L. D. A.; Würthner, F.; Grozema, F. C. Efficient charge transport in semisynthetic zinc chlorin dye assemblies. J. Am. Chem. Soc. 2012, 134, 16147-16150.

(27)

Sengupta, S.; Ebeling, D.; Patwardhan, S.; Zhang, X.; von Berlepsch, H.; Böttcher, C.; Stepanenko, V.; Uemura, S.; Hentschel, C.; Fuchs, H. et al. Biosupramolecular nanowires from chlorophyll dyes with exceptional charge-transport properties. Angew. Chem. Int. Edit. 2012, 51, 6378-6382.

(28)

Patwardhan, S.; Kocherzhenko, A. A.; Grozema, F. C.; Siebbeles, L. D. A. Delocalization and mobility of charge carriers in covalent organic frameworks. J. Phys. Chem. C 2011, 115, 11768-11772.

(29)

Givaja, G.; Amo-Ochoa, P.; Gomez-Garcia, C. J.; Zamora, F. Electrical conductive coordination polymers. Chem. Soc. Rev. 2012, 41, 115-147.

(30)

Park, S. S.; Hontz, E. R.; Sun, L.; Hendon, C. H.; Walsh, A.; Van Voorhis, T.; Dincă, M. Cation-dependent

intrinsic

electrical

conductivity

in

isostructural

tetrathiafulvalene-based microporous metal–organic frameworks. J. Am. Chem. Soc. 2015, 137, 1774-1777. (31)

Ahrenholtz, S. R.; Epley, C. C.; Morris, A. J. Solvothermal preparation of an electrocatalytic metalloporphyrin MOF thin film and its redox hopping chargetransfer mechanism. J. Am. Chem. Soc. 2014, 136, 2464-2472.

(32)

Narayan, T. C.; Miyakai, T.; Seki, S.; Dinca, M. High charge mobility in a tetrathiafulvalene-based microporous metal-organic framework. J. Am. Chem. Soc. 2012, 134, 12932-12935.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(33)

Page 32 of 36

Sheberla, D.; Sun, L.; Blood-Forsythe, M. A.; Er, S.; Wade, C. R.; Brozek, C. K.; AspuruGuzik,

A.;

Dinca,

M.

High

electrical

conductivity

in

Ni-3(2,3,6,7,10,11-

hexaiminotriphenylene)(2), a semiconducting metal-organic graphene analogue. J. Am. Chem. Soc. 2014, 136, 8859-8862. (34)

Sun, L.; Miyakai, T.; Seki, S.; Dinca, M. Mn-2(2,5-disulfhydrylbenzene-1,4dicarboxylate): A microporous metal-organic framework with infinite (-Mn-S)(infinity) chains and high intrinsic charge mobility. J. Am. Chem. Soc. 2013, 135, 8185-8188.

(35)

Sun, L.; Hendon, C. H.; Minier, M. A.; Walsh, A.; Dincă, M. Million-fold electrical conductivity enhancement in Fe2(DEBDC) versus Mn2(DEBDC) (E = S, O). J. Am. Chem. Soc. 2015, 137, 6164-6167.

(36)

Talin, A. A.; Centrone, A.; Ford, A. C.; Foster, M. E.; Stavila, V.; Haney, P.; Kinney, R. A.; Szalai, V.; El Gabaly, F.; Yoon, H. P.; Leonard, F.; Allendorf, M. D. Tunable electrical conductivity in metal-organic framework thin-film devices. Science 2014, 343, 6669.

(37)

Han, S.; Warren, S. C.; Yoon, S. M.; Malliakas, C. D.; Hou, X.; Wei, Y.; Kanatzidis, M. G.; Grzybowski, B. A. Tunneling electrical connection to the interior of metal-organic frameworks. J. Am. Chem. Soc. 2015, 137, 8169-8175.

(38)

Hod, I.; Bury, W.; Karlin, D. M.; Deria, P.; Kung, C.-W.; Katz, M. J.; So, M.; Klahr, B.; Jin, D.; Chung, Y.-W.; Odom, T. W.; Farha, O. K.; Hupp, J. T. Directed growth of electroactive metal-organic framework thin films using electrophoretic deposition. Adv. Mater. 2014, 26, 6295-6300.


Page 33 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(39)

Hod, I.; Bury, W.; Gardner, D. M.; Deria, P.; Roznyatovskiy, V.; Wasielewski, M. R.; Farha, O. K.; Hupp, J. T. Bias-switchable permselectivity and redox catalytic activity of a ferrocene-functionalized, thin-film metal–organic framework compound. J. Phys. Chem. Lett. 2015, 6, 586-591.

(40)

Kung, C.-W.; Chang, T.-H.; Chou, L.-Y.; Hupp, J. T.; Farha, O. K.; Ho, K.-C. Porphyrinbased metal-organic framework thin films for electrochemical nitrite detection. Electrochem. Commun. 2015, 58, 51-56.

(41)

Zhang, X.; Ballem, M. A.; Hu, Z.-J.; Bergman, P.; Uvdal, K. Nanoscale light-harvesting metal-organic frameworks. Angew. Chem. Int. Edit. 2011, 50, 5728-5732.

(42)

Son, H.-J.; Jin, S.; Patwardhan, S.; Wezenberg, S. J.; Jeong, N. C.; So, M.; Wilmer, C. E.; Sarjeant, A. A.; Schatz, G. C.; Snurr, R. Q. et al. Light-harvesting and ultrafast energy migration in porphyrin-based metal–organic frameworks. J. Am. Chem. Soc. 2012, 135, 862-869.

(43)

Kent, C. A.; Mehl, B. P.; Ma, L.; Papanikolas, J. M.; Meyer, T. J.; Lin, W. Energy transfer dynamics in metal-organic frameworks. J. Am. Chem. Soc. 2010, 132, 12767-12769.

(44)

Wei, Z.; Gu, Z.-Y.; Arvapally, R. K.; Chen, Y.-P.; McDougald, R. N., Jr.; Ivy, J. F.; Yakovenko, A. A.; Feng, D.; Omary, M. A.; Zhou, H.-C. Rigidifying fluorescent linkers by metal-organic framework formation for fluorescence blue shift and quantum yield enhancement. J. Am. Chem. Soc. 2014, 136, 8269-8276.

(45)

Shustova,

N.

B.;

McCarthy,

tetraphenylethylene-based

B.

D.;

Dinca,

metal-organic

M.

Turn-on

frameworks:

an

fluorescence

in

alternative

to

aggregation-induced emission. J. Am. Chem. Soc. 2011, 133, 20126-20129.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(46)

Page 34 of 36

Gong, Q.; Hu, Z.; Deibert, B. J.; Emge, T. J.; Teat, S. J.; Banerjee, D.; Mussman, B.; Rudd, N. D.; Li, J. Solution processable MOF yellow phosphor with exceptionally high quantum efficiency. J. Am. Chem. Soc. 2014, 136, 16724-16727.

(47)

Coropceanu, V.; Cornil, J.; da Silva Filho, D. A.; Olivier, Y.; Silbey, R.; Brédas, J.-L. Charge transport in organic semiconductors. Chem. Rev. 2007, 107, 926-952.

(48)

May, V.; Kuhn, O.: Charge and energy transfer dynamics in molecular systems; John Wiley & Sons, Inc., 2011.

(49)

Senthilkumar, K.; Grozema, F. C.; Guerra, C. F.; Bickelhaupt, F. M.; Lewis, F. D.; Berlin, Y. A.; Ratner, M. A.; Siebbeles, L. D. A. Absolute rates of hole transfer in DNA. J. Am. Chem. Soc. 2005, 127, 14894-14903.

(50)

Amsterdam Density Funcational (ADF). In ADF2014, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com, January 2015.

(51)

te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Guerra, C. F.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931-967.

(52)

Zhao, Y. T., D.G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06class functionals and 12 other functionals. Theor. Chem. Accounts 2008, 120, 215241.

(53)

Senthilkumar, K.; Grozema, F. C.; Bickelhaupt, F. M.; Siebbeles, L. D. A. Charge transport in columnar stacked triphenylenes: effects of conformational fluctuations on charge transfer integrals and site energies. J. Chem. Phys. 2003, 119, 9809-9817.


Page 35 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(54)

Jalilov, A. S.; Patwardhan, S.; Singh, A.; Simeon, T.; Sarjeant, A. A.; Schatz, G. C.; Lewis, F. D. Structure and electronic spectra of purine-methyl viologen charge transfer complexes. J. Phys. Chem. B 2014, 118, 125-133.

(55)

Morris, W.; Volosskiy, B.; Demir, S.; Gandara, F.; McGrier, P. L.; Furukawa, H.; Cascio, D.; Stoddart, J. F.; Yaghi, O. M. Synthesis, structure, and metalation of two new highly porous zirconium metal-organic frameworks. Inorg. Chem. 2012, 51, 6443-6445.

(56)

Feng, D.; Gu, Z.-Y.; Li, J.-R.; Jiang, H.-L.; Wei, Z.; Zhou, H.-C. Zirconiummetalloporphyrin PCN-222: mesoporous metal-organic frameworks with ultrahigh stability as biomimetic catalysts. Angew. Chem-Int. Edit. 2012, 51, 10307-10310.

(57)

Ørnsø, K. B.; Jónsson, E. Ö.; Jacobsen, K. W.; Thygesen, K. S. Importance of the reorganization energy barrier in computational design of porphyrin-based solar cells with cobalt-based redox mediators. J. Phys. Chem. C 2015, 119, 12792-12800.

(58)

Deria, P.; Mondloch, J. E.; Tylianakis, E.; Ghosh, P.; Bury, W.; Snurr, R. Q.; Hupp, J. T.; Farha, O. K. Perfluoroalkane functionalization of NU-1000 via solvent-assisted ligand incorporation: synthesis and CO2 adsorption studies. J. Am. Chem. Soc. 2013, 135, 16801-16804.

(59)

Nielson, R. M.; McManis, G. E.; Safford, L. K.; Weaver, M. J. Solvent and electrolyte effects on the kinetics of ferrocenium-ferrocene self-exchange. A reevaluation. J. Phys. Chem. 1989, 93, 2152-2157.

(60)

Nakagaki, S.; Ferreira, G.; Ucoski, G.; Dias de Freitas Castro, K. Chemical reactions catalyzed by metalloporphyrin-based metal-organic frameworks. Molecules 2013, 18, 7279-7308.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table of Contents Graphic


Theoretical Investigation of Charge Transfer in Metal Organic

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