Identifying the Interactions That Allow Separation of O2 from N2 on the

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Identifying the Interactions that Allow Separation of O from N on the Open Iron Sites of Fe(dobdc) 2

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Pragya Verma, Rémi Maurice, and Donald G. Truhlar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10382 • Publication Date (Web): 30 Nov 2015 Downloaded from http://pubs.acs.org on December 1, 2015

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The Journal of Physical Chemistry

1 revised for JPC C, Nov. 25, 2015

Identifying the Interactions that Allow Separation of O2 from N2 on the Open Iron Sites of Fe2(dobdc)

Pragya Verma,1,2 Rémi Maurice,1,2,3 and Donald G. Truhlar1,2,* 1

Department of Chemistry, Minnesota Supercomputing Institute, and Chemical Theory Center, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA 2

Nanoporous Materials Genome Center, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA 3

SUBATECH, UMR CNRS 6457, IN2P3/EMN Nantes/Université de Nantes, 4 rue Alfred Kastler, BP20722, 44307 Nantes Cedex 3, France Supporting Information Available ABSTRACT. The presence of open metal sites along with a high porosity makes the Fe2(dobdc) metal–organic framework, also called Fe-MOF-74, particularly well suited for separating gaseous mixtures. For instance, since Fe2(dobdc) adsorbs O2 more strongly than N2, it can, in principle, be used to separate O2 from air [Bloch et al., J. Am. Chem. Soc. 2011, 133, 14814]. In the present work, we investigate the reversible differential adsorption of N2 and O2 on Fe2(dobdc) with Kohn-Sham density functional theory applied to an 88-atom cluster model of the MOF. The cluster is chosen such that it is large enough to allow an accurate description of the most important contributions to the binding enthalpies and small enough to perform highlevel quantum mechanical calculations. For the quantum mechanical calculations, we use wellvalidated exchange–correlation functionals to study the ground-state structures of the Fe–N2 and Fe–O2 interacting systems. The calculations agree with experiment in that O2 binds more strongly than N2, and they reveal that the ground-state structure of the Fe–O2 subsystem has the dioxygen unit in a triplet spin state ferromagnetically coupled to the high-spin state (quintet state) of the iron center. Charge Model 5 (CM5) calculations have been performed to determine the partial atomic charges on the adsorbate molecules and the iron atom, and they show that charge transfer from the open iron(II) site is more important in the case of O2 than in the case of N2. Furthermore, bond orders, vibrational frequencies, and orbital energies were calculated to rationalize the stronger binding of O2 compared to N2 on Fe2(dobdc). Keywords: adsorption enthalpy, coordination polymer, density functional theory, electronic structure, functional material, gas separation, metal–organic framework (MOF), partial atomic charges

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2 1. INTRODUCTION Metal–organic frameworks (MOFs) have attracted attention in recent years due to their interesting properties for applications to gas separations,1,2,3,4,5,6,7,8,9,10,11 catalysis,12,13,14,15,16,17,18,19,20 and gas storage,21,22,23 and solar cells.24,25,26 These systems are polymers that consist of metalcontaining nodes that are connected by bridging organic ligands, forming coordination networks. There are numerous possibilities for the choices of nodes and organic ligands; the nodes may be, for example, single metal atoms, clusters of metal atoms, or metal oxides, possibly hydrated. Many MOFs have been synthesized and experimentally characterized, and many more are hypothetical structures yet to be synthesized. Their properties are controlled not only by the chemical and electrostatic properties of the nodes and linkers but also by their geometrical arrangements and pore sizes. The property of interest in the present article is the ability to selectively bind N2 and O2 gas molecules, thereby potentially leading to the efficient separation of these gases at temperatures higher (and therefore more economical) than those required for cryogenic distillation.2 One family of MOFs with potential for gas separations has the chemical formula M2(dobdc) (where M is MgII, CdII, or a transition metal in the series from MnII to ZnII, and dobdc4– is 2,5–dioxido-1,4–benzenedicarboxylate); this family (illustrated in Figure 1) is usually called M-MOF-74 or CPO-27-M.2,27,28,29,30,31 The M-MOF-74 compounds have been widely studied experimentally and theoretically for their applications in gas storage,32,33,34 isolation of CO2 from various gaseous mixtures,35,36,37 fractionation of hydrocarbon mixtures,2,3,5,38,39,40,41,42 and catalysis.19,20 A member of this family, Fe2(dobdc), also known as Fe-MOF-74, is the subject of the present investigation. Fe2(dobdc), which is air sensitive, has been shown to be capable of separating hydrocarbon mixtures or separating O2 from N2 in air.2,43 The latter is due to its ability to bind O2 more strongly than N2 under ambient conditions. Another MOF that has been experimentally demonstrated to selectively bind O2 over N2 is Cr3(btc)2, where btc is 1,3,5benzenetricarboxylate.44 The present study reports Kohn-Sham density functional theory (KSDFT) calculations that elucidate the reasons behind the preference of Fe2(dobdc) for O2 over N2 and that identify the factors that make the separation possible.


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Figure 1. The extended structure of Fe2(dobdc) shown with its building blocks—an iron center surrounded by five oxygen atoms and the organic linker, 2,5–dioxido-1,4–benzenedicarboxylate (dobdc4‒). The view here is down the c axis; each vertex of the hexagonal pore has a helical chain of iron atoms extending along the c axis and is surrounded by three pores. The first, fourth, seventh, ... Fe in a chain face the first pore; the second, fifth, eighth, ... face the second pore; the third, sixth, ninth, ... face the third pore. [Color code: violet = iron, red = oxygen, gray = carbon, and white = hydrogen].

Previous quantum chemical calculations have already played important roles in elucidating the properties of MOFs.45 A few theoretical studies have been performed concerning the adsorption of hydrocarbons,9,46,47 and two theoretical studies48,49 have already been reported for O2 adsorption on Fe2(dobdc). The previous studies of O2 adsorption on Fe-MOF-74 used periodic boundary conditions; one, by Maximoff and Smit49 on O2 adsorption was based on Kohn-Sham density functional theory (KS-DFT) modified by empirical intra-atomic Coulomb and exchange interactions (a method called PBE+U), and the other, by Parkes et al.48 on O2 and N2 adsorption utilized KS-DFT augmented with empirical damped-dispersion interactions (a method called PBE-D2). The calculations by Maximoff and Smit were primarily addressed to the irreversible process that occurs when the MOF is dosed at high temperature; the present calculations are addressed to the low-temperature reversible adsorption. The calculations by



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4 Parkes et al. screened two families of MOFs, namely M2(dobdc) and M3(btc)2 (M = Be, Mg, Sc– Zn, Mo, and Ru), for their ability to separate O2 and N2. They found that the identity of the metal is more important than the structure of the MOF, with the early transition metals better suited for separation than the late ones. The main objective of this work is to rationalize the experimentally observed43 preferential binding of O2 over N2 on Fe2(dobdc). Unlike the previous studies that used only calculations with periodic boundary conditions, the present calculations use cluster models, by which we mean that a large but finite fragment is extracted from the bulk structure and used as a starting point for nonperiodic calculations of binding to a central site of the fragment. We note that when the same electronic structure method has been used for both periodic and cluster-model calculations on Fe2(dobdc)–adsorbate interactions in the past, quite similar results were obtained,7 as they should be if the cluster and the periodically replicated cell are both large enough and the periodic MOF structure is well represented by constraints on the cluster. One cannot use cluster models to predict phase changes, changes in the periodic Fe–Fe distance upon adsorption, or long-range cooperative effects as have been postulated to be important in the adsorption of O2 on Fe-MOF-74 under certain conditions.43,49 However, in the present case we have experimental data for the MOF structure under conditions of reversible adsorption so we can study the adsorption process with realistic Fe–Fe distances under adsorption conditions. We chose a cluster approach rather than a periodic approach for convenience. The cluster model is chosen here to be large enough to represent the main interactions at a central site without appreciable edge effects while being small enough to lead to conveniently affordable calculations with exchange–correlation functionals depending on local kinetic energy density and having a globally fixed percentage of Hartree–Fock exchange. In particular, we employ KS-DFT with the M06 exchange–correlation functional,50 which is a global-hybrid meta-GGA exchange– correlation functional that is capable of a good description of dynamic medium-range correlation energy.51,52 The use of an exchange–correlation functional that can provide a good treatment of medium-range dynamic correlation effects is motivated by the significant or even dominant role of dispersion-like interactions in the binding of guest molecules to many transition metal centers.


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5 The geometries of the interacting Fe–N2 and Fe–O2 systems in various spin states are obtained from geometry optimization of the central portion of the cluster with KS-DFT. Charge Model 5 (CM5)53 based on M06 calculations is used to determine the extent of charge transfer between the guest molecules and the MOF framework.

2. MODELING AND THEORY 2.1. Cluster Model. Electronic structure calculations require a "starting structure," either to be used as it is or to be used as the zeroth iteration for optimization. We base our calculations on the two experimental structures,43 one for bare Fe2(dobdc) and one for an experimental Fe2(dobdc)–O2 complex formed under low-temperature reversible dosing conditions; the latter will be called the low-temperature MOF(O2) structure or the low-temperature-dosing structure). Key differences between the two structures and the abbreviation used to refer to them in the manuscript are reported in Table 1. As explained below, the experimental bare Fe2(dobdc) structure was used in modeling MOF(N2) and MOF(O2) complexes by adding adsorbates to it, and the low-temperature Fe2(dobdc)–O2 complex was used in modeling the MOF(O2) complex.

Table 1. Internuclear distances (in Å) in bare MOF and low-temperature MOF(O2). Abbreviation

System

B L

Bare MOF Low-temperature MOF(O2)

Fe–Fe 3.00 3.17

Experiment O–O b NA 1.25

a

Fe–O NAb 2.08, 2.10

a

The experimental structures are taken from ref. 43. The O–O and Fe–O distances refer to the adsorbed O2.

b

NA = not applicable. Following our previous studies, we first consider here a bare cluster model9,54 that has 88

atoms (shown in Figure 2), including three Fe atoms, carved out of the experimental structure43 of bare Fe2(dobdc). In addition, we carved 88-atom clusters from the MOF portions of the lowFe2(dobdc)–O2 structure. When we add one, two, or three O2 molecules to the Fe centers of the 88-atom clusters, they have 90, 92, and 94 atoms, respectively. In most cases we add only a



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6 single O2 and it is added at Feb; the second O2 is added at Fea; the third at Fec. We say that the 90-atom cluster has one active site; the 92-atom and 94-atom clusters have two or three active sites. Note that the cluster model contains some hydrogen atoms used to cap bonds broken in extracting the fragment.9 The positions of all hydrogen atoms (either originally present in the experimental structure or added to neutralize the cluster) were not optimized in the previous work.9 For the present work, all hydrogenic coordinates are optimized with the M06-L59 exchange−correlation functional for the high-spin state (quintet on every iron center with ferromagnetic coupling between them in the bare cluster and, when O2 is present, with ferromagnetic coupling to triplet O2), and the structures with the hydrogens optimized are used as "starting structures" (with the hydrogens now frozen) for subsequent work. We use a shorthand notation to indicate the degree of geometry optimization used for the clusters. When no atom of the bare 88-atom cluster or the 88-atom MOF portion of the MOFadsorbate complex is optimized, the notation “//opt0” is used; this denotes that only the adsorbate coordinates (if one or more adsorbate is present) are optimized. We also performed calculations denoted by //opt1 and //opt6. For an 88- or 90-atom cluster, //opt1 denotes that, in addition to the coordinates of the adsorbate (if present), the coordinates of the central iron are optimized. An //opt6 calculation is like an //opt1 calculation except that the five oxygen atoms in the first coordination sphere of the active central Fe are also optimized. When calculating an adsorption energy or enthalpy, the same central iron atom as optimized in the presence of adsorbate is also optimized in the bare MOF. When // is not specified in this work, it implies an //opt0 calculation. Furthermore, abbreviations B and L are used to indicate the experimental bare MOF and the low-temperature MOF(O2) structures, respectively (see Table 1). For example, the notation //L-opt1 implies that an //opt1 calculation was performed on the low-temperature-dosing structure. Each cluster has three FeII centers, each of which is surrounded by six organic ligands that provide a total of six units of negative charge to make the structure overall neutral (Figure 2). For most of our calculations, we investigate the binding of O2 and N2 to the central iron, since the central iron has an immediate environment in the cluster that is in close agreement9 with the


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7 environment of an iron in the full structure. For the case where we tested cooperative effects (the effect that the binding of an adsorbate at one metal site has on binding at another metal site), we studied the binding of adsorbate(s) to peripheral iron centers as well. Hence, we may include an adsorbate at only the central FeII center [MOF(X2), X = N or O] or we may include n adsorbates [MOF(X2)n, where n = 2 or 3].

Figure 2. The 88-atom cluster model of Fe2(dobdc) with three FeII centers (each in a pentacoordinate environment) and six organic ligands, obtained from a combination of the experimental crystal structure and optimized hydrogen positions as described in the Section 2.1. [Color code: violet = iron, red = oxygen, gray = carbon, and white = hydrogen]. 2.2. Spin Components. As described in the preceding section, the cluster models possess three open-shell iron centers. KS-DFT calculations involve iterating to a self-consistentfield (SCF) solution, and we need to specify the charge and spin configurations for the initial step of the SCF iterations; following the usual convention this is called the initial guess. In particular, we specify the partial atomic charges q on the Fe centers and adsorbate atoms and their electron spin components MS. The SCF iterations may redistribute the partial atomic charges and spins, but the total charge q and total electron spin component MS are conserved by



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8 the iterations. Experiments2 and our previous calculations9,54 showed that the ground state has ferromagnetic coupling between the quintet iron centers along a chain. Therefore all the present KS-DFT calculations on the adsorption of guest molecules are for ferromagnetic coupling of the spins of the iron centers. However, to calculate the magnetic coupling constants (J) between the quintet FeII centers, we also consider configurations with antiferromagnetically coupled FeII centers. For the purpose of calculating magnetic coupling constants, every iron center was modeled as a quintet, while for investigating the adsorption energies, lower spin states on the central iron were also considered. The next subsection explains the various spin configurations used to calculate magnetic coupling constants. For the MOF and MOF(N2) systems, three spin states were considered. In particular, the central iron is modeled as a quintet, a triplet, or a singlet, with the two peripheral iron centers always considered to be quintets. As mentioned above, the spins on Fe centers are coupled to each other ferromagnetically, which results in MS values of 6, 5, or 4, respectively, as shown in Table 2. For the MOF(O2) system, again only results for ferromagnetic coupling between the iron centers are presented, but a greater variety of spin states is possible because both the isolated guest and the isolated host are open-shell systems and because charge transfer or partial charge transfer from the MOF to oxygen is considered. The various cases considered as initial electronic structures for the SCF iterations are listed in Table 2 along with computed charges, spin densities, S values, and energies of binding. The results in this table will be discussed in later sections.


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9

Table 2. Initial Charges, Initial MS Values, Computed CM5 Charges, Hirshfeld Spin Densities, and S Values of the Iron Atoms and the Adsorbed Guest Molecules of the Complexes (All Quantities in Atomic Units Except Energies of Binding in kcal/mol with Respect to the Separated Reactants in their Ground Spin State). a

Initial guess MOF(N2) (3 Fe) MS Charge

Adsorbed N2 MS Charge

MOF(N2) MS

2, 2, 2 2, 2, 2 2, 2, 2 2, 1, 2 2, 2, 2 2, 0, 2 MOF(O2) (3 Fe) MS Charge

0 0 0 0 0 0 Adsorbed O2 MS Charge

6 5 4 MOF(O2) MS

2, 3, 2 2, 2, 2 2, 4, 2 2, 3, 2 2, 2, 2 2, 2, 2 2, 2, 2 2, 2, 2 2, 2, 2 2, 2, 2 2, 2, 2

a

2, 2.5, 2 2, 2, 2 2, 2, 2 2, 2.5, 2 2, 2, 2 2, 1, 2 2, 2, 2 2, 1, 2 2, 0, 2 2, 1, 2 2, 0, 2

‒1 0 ‒2 ‒1 0 0 0 0 0 0 0

0.5 1 0 ‒0.5 0 1 ‒1 0 1 ‒1 0

7 7 6 6 6 6 5 5 5 4 4

Final values Adsorbed N2

MOF(N2)

MOF(N2)

charge Spin density 0.64, 0.66, 0.64 3.66, 3.69, 3.69 0.64, 0.59, 0.64 3.67, 1.94, 3.69 0.64, 0.64, 0.65 3.67, 0.02, 3.68 MOF(O2) (3 Fe)

charge Spin density 0.08 0.02 0.09 0.03 –0.03 0.00 Adsorbed O2

S 6.01 5.01 4.03 MOF(O2)

Energy –8.5 25.8 34.1 MOF(O2)

charge 0.64, 0.76, 0.64 0.64, 0.76, 0.64 0.64, 0.81, 0.65 0.64, 0.81, 0.65 0.64, 0.81, 0.65 0.65, 0.83, 0.66 0.64, 0.63, 0.64 0.64, 0.63, 0.64 0.64, 0.61, 0.65 0.64, 0.58, 0.64 0.64, 0.56, 0.65

charge –0.13 –0.13 –0.24 –0.24 –0.24 –0.27 0.08 0.08 –0.07 0.06 0.06

S 7.01 7.01 6.07 6.07 6.07 6.07 5.18 5.18 5.10 4.27 4.22

Energy –8.7 –8.7 b –1.9 b –1.9 –2.0 b –1.3 –8.3 c –8.2 d high d high d high

MOF(N2) (3 Fe)

Spin density 3.67, 3.93, 3.69 3.67, 3.93, 3.69 3.68, 3.92, 3.70 3.68, 3.92, 3.70 3.68, 3.92, 3.70 3.69, 3.96, 3.71 3.67, 3.62, 3.69 3.67, 3.61, 3.69 3.67, 0.34, 3.69 3.67, 1.79, 3.69 3.66, –1.80, 3.69

Spin density 1.65 1.65 –0.33 –0.33 –0.34 –0.44 –1.88 –1.87 1.62 –1.84 1.83

The values in this table correspond to //B-opt0 and //B–X2-opt0 calculations (X = N or O). Within convergence tolerance and rounding, this is assumed to be the same state as in the line ending as –2.0. c Within convergence tolerance and rounding, this is assumed to be the same state as in the line ending as –8.3. d Values marked as high are at least 34 kcal/mol above the quintet ground state (see Section 4.1.1). b



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10 2.3. Isotropic Coupling Constants. Since our cluster model includes three iron atoms in a single chain, we can calculate the nearest-neighbor (NN) and next-nearest-neighbor (NNN) intrachain Fe–Fe couplings but not the interchain Fe–Fe coupling. However, we expect the intrachain couplings are more important since the nearest-neighbor and next-nearest-neighbor Fe–Fe distances are respectively 3.00 and 4.96 Å, whereas the shortest interchain Fe–Fe distance is 7.37 Å in the experimental structure. The three isotropic coupling constants (two NN and one NNN) between the iron centers in the bare cluster and the MOF(N2)3 cluster were determined using the Heisenberg-Dirac-van Vleck (HDV) Hamiltonian.55,56,57 This requires the use of four Slater determinants, a high-spin one (MS = 6) and three spin-broken symmetry ones (MS = 2), arising due to the paramagnetic nature of the FeII centers. The HDV Hamiltonian used is as follows: H HDV = −2J ab Sˆa ⋅ Sˆb − 2J bc Sˆb ⋅ Sˆc − 2J ac Sˆa ⋅ Sˆc

(1)

Equation 1 has subscripts a, b, and c that correspond to three magnetic FeII centers, a, b, and c, of the clusters, effectively coupled by exchange interactions (Jij) between them. The three Jij coupling constants can be determined by solving the following equations:

222 | H HDV | 222 = E222 = −8J ab − 8J bc − 8J ac

22 2 | H HDV | 22 2 = E222 = −8 J ab + 8 J bc + 8 J ac 222 | H HDV | 222 = E222 = +8 J ab + 8 J bc − 8 J ac 222 | H HDV | 222 = E222 = +8 J ab − 8 J bc + 8 J ac

(2)

where the E values are the density functional energies of the KS determinants obtained in the SCF calculations. The determination of the three Jijvalues in the bare MOF and in the MOF(N2)3 system will allow assessment of the effect of adsorption on these constants. More details of the mapping of the KS-DFT energies onto the diagonal elements of the HDV Hamiltonian in this case are given in ref. 54, and a general discussion is given in ref. 58.


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11 3. ELECTRONIC STRUCTURE CALCULATIONS KS-DFT was used for partial geometry optimizations according to the //opt0, //opt1, and //opt6 protocols explained in Section 2.1. We employ three meta-GGA exchange−correlation functionals belonging to the Minnesota family of functionals. Of the three density functionals used, two of them, namely M06-L59 and M11-L60, are local density functionals, and one is a hybrid density functional, in particular M0650 with 27% of Hartree−Fock (HF) exchange. (Notation: for a local functional, the energy density at coordinate r depends only on local variables at r, which in the present case are spin densities, their gradients, and kinetic energy densities for each spin; for a nonlocal functional, the energy density at r depends on properties at other r as well, which in the present case is due to the inclusion of some HF exchange, which is nonlocal. A hybrid functional is one that contains some HF exchange, and therefore it is nonlocal.) We confine our discussion of results in the main text to those obtained using the M06 exchange–correlation functional, but the results obtained using the local M06-L and M11-L functionals (where “L” denotes local) are reported in the Supporting Information (SI). We use the def2-TZVP basis set (TZVP denotes triple-zeta valence plus polarization) from Ahlrichs and co-workers for all the KS-DFT calculations.61 [The Supporting Information reports single-point calculations on the M06/def2-TZVP//B-opt0 optimized geometries using M06/cc-pwCVTZ-DK62 (Fe); def2-TZVP (O, N, C, H).] An ultrafine grid that has 99 radial nodes and 590 angular nodes on each radial shell was used to perform numerical integrations on the density functional. We neglect spin–orbit coupling. The calculations were performed with the Gaussian 09 suite of programs63 and a locally modified version called MN-GFM 6.4.64 For the local density functionals, M06-L and M11-L, automatic density-fitting sets generated by the Gaussian 0963 program were utilized to reduce the computational cost. The high-spin and spinbroken-symmetry solutions were obtained by allowing all symmetries to break using the stable = opt keyword of Gaussian 09.63 Frequency calculations were performed for the 3Nopt vibrational modes associated with the atoms of the bound guest molecule and/or atoms of the cluster that were optimized, where Nopt is the number of atoms optimized, and for the single vibrational mode of the free guest molecules.



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12 We calculated enthalpies of adsorption at two temperatures: 201 K because it is one of the four temperatures (201, 211, 215, and 226 K) that were used to measure O2 and N2 isotherms and hence determine the experimental isosteric heats of adsorption43 and 298.15 K because it is the standard temperature for tabulating enthalpies. For each temperature T the enthalpy of binding is given by ΔH(T) = EBO(host–guest) – EBO(host) – EBO(guest) + Evib(host–guest) – Evib(host) – Evib(guest) – Etrans(guest) – Erot(guest) – RT

(4)

In eq 4, the first three terms yield the change in Born-Oppenheimer energy due to the binding of the guest to the cluster, and the next three terms give the change in vibrational energy. Evib(host) is the vibrational energy of the bare cluster, which is zero for //opt0 and results from 3 and 18 modes, respectively, for //opt1 and //op6 calculations, whereas Evib(host–guest) results from 6, 9, or 24 vibrational modes at these three levels of optimization; Evib(guest) is the vibrational energy of the one vibrational mode of the free guest molecule. The next two terms are respectively the translational and rotational energies of the free guest molecule, and R is the universal gas constant. Etrans and Erot for host and host–guest have been set to zero keeping in mind that these are solid surfaces before and after adsorption and hence do not translate or rotate. The Gibbs free energies of adsorption for the complexes were computed with respect to that of the separated reactants at 298.15 K. The vibrational energies Evib were calculated by the quasiharmonic approximation, which consists of using the harmonic oscillator formulas with scaled quantum mechanical frequencies, where the scaling factors we used are designed both to give more accurate zero point energies and to give more accurate fundamental frequencies.65 For M06/def2-TZVP, these factors are 0.982 and 0.956, respectively. The vibrational frequencies presented in tables always include these scaling factors. In order to characterize the electronic structure and rationalize the differential binding of O2 and N2, we also computed partial atomic charges, spin densities, bond orders, and orbital energies from the converged SCF calculations. The partial atomic charge calculations allow us to


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13 determine the direction (metal center to the guest or vice-versa) and magnitude of charge transfer between the Fe center and the guest molecule bound to it. CM5 charges53 have been computed with the CM5PAC program66 using input from Gaussian 09. The justification for using CM5 charges comes from our comparative study of popular charge models in ref. 67. The CM5 charges were validated on a set of transition metal containing molecules and were found to give more accurate dipole moments compared to other charge models tested in that study. Hirshfeld spin densities68 were used to determine the number of unpaired electrons on the open-shell atoms. Mayer bond orders69 in the natural atomic orbital basis are computed for N–N, O–O, Fe– N, and Fe–O bonds. Finally, orbital energies are computed using natural bond order (NBO) analysis70 to see how the energies of the orbitals on the Fe center are affected by adsorption of the guest molecule.

4. RESULTS AND DISCUSSION 4.1. Finding the Lowest-Energy Structures and Energies, Enthalpies, and Free Energies of Binding. As explained in Sections 1 and 2.1, we cannot fully relax the MOF in cluster calculations, but we carried out calculations for two available experimental structures by partially relaxing them. First we consider binding a single adsorbate to the bare MOF structure B, then we consider binding more than one adsorbate to B, and finally we consider binding to a distorted MOF structure that was observed experimentally (structure L in Table 1). 4.1.1. Binding a single adsorbate to the bare MOF structure. For the various initial spin configurations shown in Table 2, partial geometry optimizations were performed using the M06 exchange–correlation functional by freezing the entire 88-atom cluster and optimizing only the N2 or O2 guest molecules (//B-opt0 calculations). Figure S1 of the Supporting Information gives the resulting geometry of the first coordination sphere around the central iron of MOF(N2) and MOF(O2) complexes as a function of the spin of the central iron atom. In this section, we compare the energies of the various spin states (shown in Table 2 and Figure 3), where the complexes were obtained by adding adsorbate to structure B in Table 1. These energies are



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14 computed with respect to the ground spin states of the isolated fragments. The calculated ground spin states of the isolated fragments were found to have N2 in the singlet state, O2 in the triplet state, and the bare 88-atom cluster in the high-spin state corresponding to ferromagnetically coupled local quintets. Figure 3 shows separated species on the left and the complexes on the right; the numbers in parentheses indicate the final spins on the metal centers or the adsorbate, which were determined based on Hirshfeld spin densities given in Table 2. For MOF(N2), three possibilities were considered by changing the spin state only of the central iron atom (Table 2). On the left of Figure 3(a) we can see that when no N2 is bound to the iron center, the two cases that have triplet and singlet iron centers are 35.4 and 49.0 kcal/mol higher in energy than the quintet ground state. The adsorption of N2 on the central metal atom (shown on the right of Figure 3(a)) causes the energy level of each state to drop and makes the N2 bound cluster more stable compared to the free cluster in each case. For MOF(O2), a number of interesting features can be observed from Figure 3(b). The eleven initial guesses described in Table 2 for MOF(O2) systems were tried, and they converged to the various structures shown in Table 2. In Table 2, for any state with energy > –2.0 kcal/mol, we just mark these states as high in energy rather than giving a number because of the difficulty of converging the high-energy states quantitatively. We did not find any state with the central iron having a spin of one with an energy less than 34 kcal/mol above the quintet ground state, and we did not find any state with the central iron having a spin of zero with an energy less than 48 kcal/mol above the quintet ground state. Figure 3(b) reports the three lowest energy structures from Table 2. Similar to the N2 case, we also observe here that the adsorption of O2 causes the energy levels of the various spin states of the cluster to drop. The triplet-singlet splitting of the free O2 molecule is high (~37 kcal/mol) when it is not bound to the iron center, but when adsorbed on Fe2(dobdc), this splitting reduces to ~7 kcal/mol. The complexes that have triplet O2 either ferromagnetically or antiferromagnetically coupled to the quintet iron center have similar energies, i.e., O2 is weakly coupled to the FeII center (in terms of isotropic magnetic coupling). For both the MOF(N2) and MOF(O2) complexes, it can be seen that when the central Fe does not converge to a quintet state (which can be seen from Hirshfeld spin populations given in Table 2


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15 under “final values”), it results in high-energy structures with energies larger than the groundstate one by ~34 kcal/mol or more.

Figure 3. The energy levels of various spin states of free O2 separated from bare MOF, of the bare MOF, and of the MOF(N2) and MOF(O2) systems. The left side of the figure has separated fragments, and the right side of the figure has the associated complexes. The final spins of the atoms in each system are indicated in parentheses with the three numbers for the cluster representing its three iron centers. All calculations in this figure are //B-opt0 calculations. (a) On the right are the energy levels of MOF(N2), computed with respect to the energy levels of



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16 separated diamagnetic N2 and ferromagnetically coupled quintet iron spins of bare MOF, referred to as MOF(2,2,2) + N2(0) in the figure. (b) On the right are the energy levels of MOF(O2), computed with respect to the energy levels of separated triplet O2 and ferromagnetically coupled quintet iron spins of bare MOF, referred to as MOF(2,2,2) + O2(1) in the figure. Selected spin configurations (which corresponds to most stable MOF(N2) and three lowest energy MOF(O2) complexes) from Figure 3 were then chosen to compute enthalpies of binding at 201 and 298.15 K by considering three levels of optimization, //B-opt0, //B-opt1, and //B-opt6, as shown in Table 3. Gibbs free energies were computed for //B-opt1 and //B-opt6 complexes. The selected spin states are—the ground spin state of MOF(N2) (quintet spins on every iron center with ferromagnetic coupling between them) and the ground spin state of MOF(O2) (quintet spins on every iron center with ferromagnetic coupling between them and also with the triplet O2 molecule) plus two other spin states which have singlet O2 bound to the quintet spin central iron and triplet O2 antiferromagnetically coupled to this quintet spin center. The original experimental values for the isosteric heat of adsorption of N2 and O2 are respectively –8.4 kcal/mol and –9.8 kcal/mol;43 however, a possibly more accurate experimental value of –5.5 kcal/mol for N2 (under different experimental conditions) was reported in a recent work.7 Note that a negative sign means that adsorption of the guest molecule is exoergic or exothermic. Table 3 shows that the increase in level of optimization does not significantly change the energies and enthalpies of binding for N2 adsorption and for O2 adsorption that has triplet O2 antiferromagnetically coupled to quintet iron, but for O2 adsorption in the other two cases, slight overbinding is observed with //B-opt1 and //B-opt6 structures when compared to the //B-opt0 structure. This overbinding in the Fe–O2 system with increasing level of optimization could be due to the fact that the Fe–O distances in the //B-opt1 and the //B-opt6 structures are shorter compared to the //B-opt0 structure and also could be due to the fact that the O2 unit is more prone to charge transfer compared to N2, as discussed in the CM5 charge analyses in the next section. Nevertheless the final (i.e., //opt6) energies of adsorption at 201 K agree with experiment within 0.7 or 2.2 kcal/mol for N2 (depending on which experiment we compare to)


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17 and within 1.9 kcal/mol for O2. The difference between binding enthalpies of N2 and O2 with increasing level of optimization is similar to the C2H6 and C2H4 case discussed in our earlier work.9 In comparison, the energies of binding reported in ref. 48 for N2 and O2 with Fe2(dobdc) are respectively –1.7 kcal/mol and –21.0 kcal/mol, in much greater disagreement with experiment than the present values. It can also be seen from Table 3 that for any level of optimization, the difference between ΔE and ΔH is not more than 1 kcal/mol. The SI also reports energies of binding computed using the cc-pwCVTZ-DK basis set for Fe and def2-TZVP for the rest of the elements. The results indicate that the use of a relativistic basis set changes the energies of binding by no more than 2 kcal/mol for the four structures of Table 3. As expected, adsorption of the guest is accompanied by a decrease in entropy. Table 3 also shows the Gibbs free energy of adsorption, ΔG, which takes into account the entropy change upon adsorption. By comparing the enthalpy and free energy values at 298 K, we see from Table 3 that entropy decreases more for O2 adsorption than for N2 adsorption. Thus, in the most complete calculations (i.e., the //B-opt6 ones), the O2 enthalpy of adsorption is 4.0 kcal/mol more favorable than that of N2, but the free energy of adsorption is only 1.6 kcal/mol more favorable than that of N2. This is a classic case of enthalpy–entropy compensation. The stronger binding of O2 compared to N2 leads to higher frequencies for most of the vibrations in the adduct and therefore a more negative entropy change, which (in the free energy) cancels part of favorable binding energy. It is interesting that the differences of ΔH and ΔG from ΔE do not change greatly upon improving the calculation from //B-opt1 to //B-opt6; that gives us some confidence than the vibrational contributions are reasonably well converged. The free energy of adsorption is found to be negative for the O2 and positive for N2; a positive standard-state free energy change implies that formation of the complex is not a spontaneous process under standard-state conditions at room temperature. As one goes from //B-opt0 to //B-opt1 to //B-opt6, the binding energies do not change significantly, and hence we use the computationally less expensive //opt0 structures for rest of the analysis in this paper.



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18 Table 3. Standard-State Energies,a Enthalpies,b and Gibbs Free Energiesc of Binding (in kcal/mol) of O2 and N2 with the 88-Atom Cluster Model of Fe2(dobdc) Computed Using Three Levels of Optimization by M06/def2-TZVP. System

MS (3 Fe,X2)

Fe–N2

222, 0 222, 1 222, 0 222, –1

Fe–O2

ΔE –8.5 –8.7 –2.0 –8.3

//B-opt0 ΔH201 ΔH298 –7.8 –7.5 –8.4 –8.2 –1.7 –1.5 –7.6 –7.4

ΔE –7.8 –9.3 –2.5 –7.5

//B-opt1 ΔH201 ΔH298 –7.0 –6.8 –8.9 –8.7 –2.1 –1.9 –6.8 –6.6

ΔG298 ΔE 1.2 –8.5 1.7 –12.0 8.3 –4.2 2.8 –8.1

//B-opt6 ΔH201 ΔH298 –7.7 –7.5 –11.7 –11.5 –3.8 –3.7 –7.4 –7.2

ΔG298 0.5 –1.1 6.6 2.3

a

The energies of binding were computed with respect to the energies of the separated reactants: ΔE = E(host–guest) – E(host) – E(guest), where host is the bare 88-atom cluster and the guest is either N2 or O2. A negative sign means that adsorption of the guest molecule is exoergic. b

The enthalpies of binding were computed using eq 4. A negative sign means that adsorption of the guest molecule is exothermic. c The Gibbs free energies of binding were computed with respect to the Gibbs free energies of separated reactants: ΔG = G(host–guest) – G(host) – G(guest) 4.1.2. Binding more than one adsorbate to the bare MOF structure. Both Figure 3 and Table 3 present results for the guest molecule bound only to the central iron atom of the 88-atom cluster of structure B. The three iron centers of the cluster open into different hexagonal channels of the MOF. It is interesting to see whether or not the binding of a guest molecule in one of the channels affects binding in other channels. Hence we optimized additional guest molecules at peripheral iron sites of the cluster and calculated their energies and enthalpies of binding. The calculations were performed for the ground spin states (that were determined from Figure 3) by having one, two, or three guest molecules bound to either the peripheral iron atom or the central iron atom (Fea or Feb in Figure 2), a peripheral iron atom and a central iron atom (Fea and Feb in Figure 2), and all three iron centers (Fea, Feb, and Fec in Figure 2), respectively. We refer to these structures as MOF(X2), MOF(X2)2, and MOF(X2)3. While optimizing one or two guest molecules, we consider the centers a or/and b instead of c as these have more accurate environment(s) than c when compared to the experimental structure. For MOF(N2), we find that the energies and enthalpies of binding of an N2 molecule at iron site a or b are almost identical; the difference between the two binding sites is merely 0.1 kcal/mol (Table 4). For the MOF(N2)2 complex, the binding strength of two N2 molecules at


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19 both iron sites a and b almost equals the sum of the binding at the two sites separately. The MOF(N2)3 complex that involves the binding of an N2 molecule at every iron site of the cluster has binding energies and enthalpies that are three times that of either the MOF(N2) (Fea) or the MOF(N2) (Feb) complex. In MOF(O2), the binding of a single O2 molecule at iron sites a or b are almost identical to each other, which is similar to what was observed for the N2 case (Table 4). Also the binding enthalpies of two O2 molecules simultaneously in MOF(O2)2 (Fea, Feb) complex almost equals the sum of the binding enthalpies in MOF(O2) (Fea) and MOF(O2) (Feb) complexes, while the binding enthalpy of three O2 molecules in MOF(O2)2 complex deviates from three times the binding enthalpy of a single O2 molecule of either MOF(O2) (Fea) or MOF(O2) (Feb). This is due to the fact that the third metal site (Fec) deviates more from the experimental structure than the sites a or b, and the adsorbed O2 unit on this site has one of the Fe–O distance significantly different from the other two sites. Hence, we can conclude that, as expected, the binding of guest molecules N2 or O2 on a given metal site has no significant effect on the binding of another guest molecule at a different metal site. Since we found no significant cooperative effect at the //B-opt0 level, it is unnecessary to carry our more extensive optimization since if there is no effect at the //B-opt0 level, there is unlikely to be an important effect at higher levels of optimization. Table 4. Energiesa and Enthalpiesb of Binding (in kcal/mol) of O2 and N2 with the 88-Atom Cluster Model of Fe2(dobdc) Computed by M06/def2-TZVP. System MOF(N2) MOF(N2)

MOF(N2)2 MOF(N2)3 MOF(O2) MOF(O2)

MOF(O2)2 MOF(O2)3

site a b a and b a, b, and c a b a and b a, b, and c

ΔE –8.4 –8.5 –16.8 –25.3 –8.9 –8.7 –17.5 –24.2

a

ΔH201 –7.7 –7.8 –15.4 –23.2 –8.6 –8.4 –16.8 –23.1

ΔH298.15 –7.4 –7.5 –14.9 –22.4 –8.4 –8.2 –16.3 –22.3

This whole table is based on //B-opt0 geometries. The energies of binding were computed with respect to the energies of the separated reactants: ΔE = E(MOF(X2)n – E(MOF) – nE(X2).



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20 b

The enthalpies of binding were computed using eq 4. 4.1.3. Binding of O2 to the distorted MOF structures. Next the energies and enthalpies of

binding for the low-temperature MOF(O2) complexes (structure L in Table 1) were analyzed. When O2 is adsorbed on the MOF, various possible scenarios may be imagined, including the four listed in Table 5; we will use the classification of Table 5 in the following discussion of the results and in sections 4.2.3 and 4.2.4.

Table 5. Possible Scenarios for Oxygen Adsorbed on the MOF Case

Description

(a)

O2 binds to every iron site with little or no charge transfer – resulting in an Fe(II)–O2 complex.

(b)

O2 binds to every iron site with an electron transfer to O2 from the Fe(II) center – resulting in an Fe(III)–O2– complex.

(c)

O2 binds to every other iron site with transfer of two electrons from two Fe(II) centers (one from each) – resulting in Fe(III)–O2– complex at half the sites and Fe(III) at the other half (the high-temperature dosing scenario in ref.43).

(d)

O2 binds to every iron site with the transfer of two electrons from each Fe(II) – resulting in an Fe(IV)–O22– complex. With the low-temperature MOF(O2) structure as the starting structure, we performed //L-

opt0–O2 calculations for scenarios (a), (b), and (d) in the high-spin state. The initial spins for the three Fe and O2 are (2,2,2; 1) for (a), (2,2.5,2; 0.5) for (b), and (2,2,2; 0) for (d), which correspond respectively to triplet O2, doublet O2–, and singlet O22– bound to the central Fe of the cluster. The results are in Table 6. The (2,2,2; 1) and (2,2.5,2; 0.5) cases converged to the same solution. This also happens for the //B-opt0–O2 cluster as shown in Table 2 (the first two rows under the MOF(O2) section). Table 6 shows that the binding enthalpy for this case turns out to be 24 kcal/mol, and the binding enthalpy for the (2,2,2; 0) case is 17 kcal/mol. Therefore the predicted ground state is the (2,2,2; 1) structure. The (2,2,2; 1) case shows stronger binding than the (2,2,2; 0) case, even though greater amount of charge transfer occurs for the (2,2,2; 0) case


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21 (Table 7). This could potentially be due to the O2 unit being farther from the iron center in the former case. The Fe–OA, Fe–OB, and OA–OB distances are respectively 2.10, 2.10, 1.28 Å for the (a/b) case and 2.07, 2.10, and 1.29 Å for case (d), both in excellent agreement with the lowtemperature experimental values (Table 1), although the binding enthalpies for the two calculations show significant deviation. Unlike the //L-opt0–O2 calculations here, the binding enthalpies of //B-opt0–O2 calculation (Table 3) give excellent agreement with experiments, for the (2,2,2; 1) spin. Further analysis is provided in later subsections. Finally, we compared the M06 energies of the bare clusters that come from the the experimental MOF structures shown in Table 1. The //L-opt0 structure (Fe–Fe distance = 3.17 Å) was found to be the most stable structure and the relative energies of //B-opt0 (Fe–Fe distance = 3.00 Å) with respect to //L-opt0 was found to be 141 kcal/mol, respectively. The relative energies seem to correlate with the Fe–Fe distance, indicating a correlation, for at least these two cases, of lower stability with a smaller Fe–Fe distance.

Table 6. Energiesa and Enthalpiesb of Binding (in kcal/mol) of MOF(O2) Complexes Computed by M06/def2-TZVP. Initial guess (Fea,Feb,Fec; O2) //opt0 Structure Formal Charge Spin ΔE ΔH201 ΔH298 L: Low-temperature 2, 2, 2; 0 2, 2, 2; 1 –24.5 –24.1 –24.0 MOF(O2) 2, 4, 2; –2 2, 2, 2; 0 –17.5 –17.2 –17.0 a The energies of binding were computed with respect to the energies of the separated reactants: ΔE = E(host–guest) – E(host) – E(guest), where host is the 88-atom cluster obtained after removal of O2 and the guest is free O2. A negative sign means that adsorption of the guest molecule is exoergic. b The enthalpies of binding were computed using eq 4. A negative sign means that adsorption of the guest molecule is exothermic. 4.2. Comparing the Ground-State Structures to Experiment. The geometries of all the various spin states of the clusters described in Figure 3 (//B-opt0–X2 clusters, X= N or O) are shown in Figure S1 of the SI. Here we discuss only the ground-state structures for MOF(N2)



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22 and a few low-energy structures for MOF(O2), and we relegate discussion of other structures to the SI. 4.2.1. MOF(N2). The experimental Fe–N and N–N bond distances at 100 K were reported to be 2.30 and 1.13 Å, respectively.43 Our calculated values in //B-opt0 calculations are 2.41 and 1.09 Å, in only fair agreement with experiment. The Fe–N distances for the //B-opt1 and //Bopt6 structures were found to be 2.41 Å and 2.36 Å, respectively, with the latter showing significantly improved agreement with experiment and demonstrating that relaxing atoms of the MOF framework is necessary to get accurate metal–adsorbate distances. The N–N distances for these //B-opt1 and //B-opt6 calculations remain unchanged compared to the //B-opt0 calculation. The calculated Fe–N–N angle is 171 deg (//B-opt0), 172 deg (//B-opt1), or 170 deg (//Bopt6). The converged S value (obtained by equating S (S+1) to the expectation value of S2 for the Slater determinant) is 6.01 (same for //opt0, opt1, and //opt6), which corresponds to an almost pure spin state, which is often the case for KS-DFT calculations on high-spin states. The periodic calculations performed using PBE-D271,72 in Table 6 by Parkes et al.,48 yielded an Fe–N–N angle of 169°, an N–N bond distance of 1.13 Å, and the smallest Fe–N distance to be 1.99 Å. The Fe–N–N angle and the N–N bond distance of ref. 48 agree well with the cluster calculations performed in this study for the ground spin state, but their Fe–N distance is much smaller than either our calculated value or the experimental value. 4.2.2. MOF(O2) with the experimental bare MOF structure. Next consider //B-opt0 calculations for MOF(O2). The eleven initial guesses described in Table 2 for MOF(O2) systems were tried, and they converged to the various structures shown in Table 2 and in Figure 3. The lowest-energy structure (the one with energy –8.7 kcal/mol) has high-spin Fe ferromagnetically coupled to triplet O2 in a side-on but nonsymmetrical fashion, and the two Fe–O distances are 2.21 and 2.42 Å. In comparison, the experimental structure is more symmetrical, and the Fe–O distances are smaller, 2.10 and 2.09 Å. Optimization of atoms of the MOF framework decreases the two Fe–O distances, and for both //B-opt1 and //B-opt6 structures, one gets 2.09 and 2.17 Å, in fairly good agreement with the experimental values (the //B-opt6 value differs from


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23 experiment by only 0.00–0.08 Å). The calculated O–O distance of 1.24 Å agrees with the experimental O–O distance of 1.25 Å within the experimental error bar. The O–O distances for the //B-opt1 and //B-opt6 structures were both found to be 1.27 Å, which also agree with the experimental value quite well. The two equal Fe–O distances and the O–O distance reported in Table 3 of Parkes et al.48 are 1.89 and 1.39 Å, respectively, which deviate quite significantly from the cluster calculations of the current study and from experiments. The final calculated values for the ground state of the MOF(O2) complex are 7.01 (//B-opt0 and //B-opt1) or 7.00 (//B-opt6), again an almost pure spin state. 4.2.3. MOF(O2) with the experimental low-temperature MOF(O2) structure. The experimental low-temperature MOF(O2) structure that has an Fe–Fe distance of 3.17 Å, an O–O distance of 1.25 Å, and Fe distances to the oxygen atoms of O2 equal to 2.08 and 2.10 Å is proposed to fall in case (a) or case (b) described in Table 5. The Fe–OA, Fe–OB, and OA–OB distances are respectively 2.10, 2.10, and 1.28 Å for the lowest-energy structure obtained from (a) and (b) initial guesses. We note that the distances (in the same order) are 2.07, 2.10, and 1.29 Å for the second-lowest-energy structure, which was obtained with a case (d) initial guess, and these are also in good agreement with experiment. 4.3. Nature of the Fe–Guest Interactions, Spin Populations, Charges, Vibrational Frequencies, and Bond Order Analyses. Next we looked at the Hirshfeld spin densities, CM5 charges, vibrational frequencies of the guest molecules, and the Mayer bond orders to gain insight into the nature of bonding between the guest molecules N2 and O2 and central metal of atom of the MOF. The geometries used are: ground state //B-opt0, //B-opt0–N2 in the three spin states shown in Figure 3(a), //B-opt0–O2 for the ground spin state and two other higher-energy spin states shown in Figure 3(b), and //L-opt0, //L-opt0–O2 for the two spin states shown in Table 6. The Hirshfeld spin densities in Table 7 tell us the number of unpaired electrons on the iron center and the adsorbed guest molecule. It can be seen that the iron center has approximately four unpaired electrons in the ground spin states of the bare cluster and of MOF(N2) and



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24 MOF(O2). The natural atomic orbital occupancies obtained from a natural bond order analysis of the //B-opt0, //B-opt0–N2, and //B-opt0–O2 systems gave the difference in occupancies of α and β spin orbitals as 3.65, 3.56, and 3.70 for the central iron atom, which is consistent with the Hirshfeld spin density calculations. The guest molecules N2 and O2 in these complexes were found to be singlet and triplet, respectively, from both the analyses. Partial atomic charge calculations using CM5 show that the adsorption of N2 on the central metal atom decreases the positive charge on iron and simultaneously increases the positive charge on N2 indicating transfer of electron density from N2 to the MOF fragment. For the ground spin state and the next higher energy spin state of the two types of MOF(O2) structures considered, an opposite trend is observed. The O2 unit gains negative charge from the MOF fragment and at the same time causes the positive charge on the iron center to increase. The magnitude of the charge transfer involved in the O2 case is larger than the N2 case and this is a factor that could contribute to the higher binding strength of O2 as compared to N2; however, for the two MOF(O2)//L complexes in Table 7, a higher binding energy is not associated with higher charge transfer. An interesting result in Table 2 (which list all the spin states of //B-opt0O2) is that the converged electronic structures all have essentially neutral O2. The partial atomic charge on the molecule is between +0.06 and –0.24 a.u. for a very high-energy structure, with the lowest-energy structure having a partial charge on O2 of only –0.13 a.u. NPA and Hirshfeld partial atomic charges are reported in Table S2 of the SI where they are compared to CM5 charges. Although NPA overestimates charges compared to CM5 and Hirshfeld underestimates them, the three charge models predict similar trends. All three charge models predict negative charge on adsorbed O2 and positive charge on adsorbed N2 in their ground spin states. The charge transfer we calculate in O2 may be compared with the calculation of Maximoff and Smit.49 We observe a transfer of 0.13 electrons to O2, for the ground-state //L-opt0–O2 and //H-opt0–O2 complexes, with 0.08 coming from Fe and 0.05 from the rest of the MOF. Using a different density functional (with no Hartree–Fock exchange but with empirical changes in the


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25 Coulomb and exchange integrals), a different scheme for charge analysis, and optimizing the Fe– Fe distance (whereas we fix it), they obtain a charge transfer of 0.44 electrons to O2, with 0.27 from Fe and 0.17 from the rest of the MOF. Local density functionals tend to overestimate charge transfer,73 and the higher charge transfer in the previous calculation could be due to that factor. The larger partial charge transfer in the case of O2 relative to that in N2 is consistent with the change in vibrational frequencies, which are also shown in Table 7. The calculated vibrational frequency of free N2 is 2360 cm–1, while that of the adsorbed N2 in MOF(N2) (ground spin state) is 2356 cm–1, which is a reduction of only 4 cm–1. On the other hand, the calculated vibrational frequency of free O2 is 1636 cm–1, while that of the adsorbed O2 in //Bopt0–O2 (ground spin state) is 1343 cm–1, which is a reduction of 293 cm–1. This indicates that upon adsorption the double bond of O2 weakens more than the triple bond of N2 due to gain of antibonding electrons by O2. The ground state //L-opt0–O2 structure also shows a considerable drop in vibrational frequency of the O2 unit. This is further illustrated by comparing the calculated bond orders for these complexes in Table 8. The infrared spectrum reported in the experimental work43 on oxygenated Fe2(dobdc) shows bands at 1129, 541, and 511 cm–1 which were assigned to O–O, Fe–O2, and Fe–Olinker stretches, respectively. The MOF(O2) //opt6 calculations predict that the O–O band is at 1286 cm–1, and the Fe–Olinker band is around 500 cm–1, but the Fe–O2 band is at less than 350 cm–1. Unlike the interpretation of the experiments, our calculations predict that the Fe–Olinker and the Fe–O2 bands are quite different. This could be expected based on the fact that the natures of the Fe–Olinker and Fe–O2 bonds are quite different. If we compare the spin populations, charges, and vibrational frequencies of MOF(O2)//B MOF(O2)//L complexes, we find that quite different values for these quantities are obtained. This difference is also reflected in the binding enthalpies.



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26 Table 7. Hirshfeld Spin Densities (in atomic units), CM5 Atomic Charges (in atomic units), and Vibrational Frequencies (cm–1) for the MOF(N2) and MOF(O2) Complexes Computed by M06/def2-TZVP.

Energy (kcal/mol)

Feb

X1 + X2a

Feb

X1 + X2a

Vibrational frequency X2

0

0.0

NA

0.00

NA

0.00

2360

1

0.0

NA

0.00

NA

0.00

1636

experimental bare MOF structure 3.69 NA 0.68 0.0 b 3.69 0.02 0.66 –8.5

NA

NA

0.08

2356 2358 2301

Spin density System

MS

separated N2 separated O2 bare MOF

6 6

MOF(N2)

5 4 7

Charge

b

1.94 0.02 3.93

25.8 34.1 b

0.03 –0.001 1.65

0.59 0.64 0.76

–8.7 MOF(O2) 6 –8.3 3.92 –0.34 0.81 5 –2.0 3.62 –1.88 0.63 experimental low-temperature-dosing MOF(O2) structure b

bare MOF

6

0.0

MOF(O2)

7 6

–24.5 –17.5

b

0.09 –0.03 –0.13 –0.24 0.08

1343 1231 1585

3.67

NA

0.70

NA

NA

4.08 4.11

1.43 –0.59

0.88 0.91

–0.27 –0.32

1264 1256

a

X = O or N, and X1 and X2 are the two atoms of the X2 molecule. NA denotes not applicable. b

GS denotes the ground state.

In Table 8, Mayer bond orders for the MOF(N2) and MOF(O2) complexes were calculated for the same spin states that were discussed in the CM5 charge analyses. In these complexes, N1 and O1 are those atoms of the guest molecules N2 and O2 that are closer to the iron center than the atoms labeled N2 and O2. We can see that the Fe–N1 bond order of MOF(N2) is weaker than the Fe–O1 bond orders of the MOF(O2) structures in their ground spin states. The Fe–N2 bond order being close to zero for MS = 6 and 5 indicates that the interaction with the distant N atom has no covalent component. Furthermore, the bond order of the N2 molecule decreases only slightly, in particular from 3.03 in free N2 to 3.00 or 2.91 when bound to the cluster. This


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27 indicates that N2 is hardly perturbed upon adsorption. On the other hand, the bond order of the O2 molecule decreases from 2.03 in free O2 to 1.69 and 1.53 for the ground spin state of //Bopt0–O2 and //L-opt0–O2 clusters, indicating that the O2 unit is destabilized upon adsorption.

Table 8. Mayer Bond Order Computed Using M06/def2-TZVP (X = O or N, where X1 is closer to the metal center than X2). X

MS

Free X2a

MOF(X2) Feb–X1

Feb–X2

X1–X2

X1–X2

experimental bare MOF structure N

O

6 5 4 7 6 5

GSb

GSb

0.26 0.28 0.63 0.40 0.72 0.23

0.03 0.03 0.13 0.34 0.25 0.06

3.00 3.00 2.91 1.69 1.55 1.96

3.03

2.03

experimental low-temperature-dosing MOF(O2) structure 7 6 a b

GSb

0.49 0.47

0.48 0.49

1.53 1.53

The bond orders are calculated by NBO analysis for singlet N2 and triplet O2. GS denotes the ground state. For comparison with MOF(O2), we carried out calculations on dioxygen anion and –

potassium superoxide. The calculated bond order and bond distance of free O2 were found to be 1.54 and 1.33 Å, respectively, and for the O2 unit in KO2 they were found to be 1.47 and 1.30 Å, –

respectively. This shows that the O2 unit in KO2 is very similar to free O2 . The CM5 charge of +

O2 unit of KO2 is –0.90 a.u. Since KO2 is reasonably interpreted as an ionic linking of K and –

O2 , a calculated CM5 charge of approximately –0.90 a.u. on O2 in MOF(O2) would suggest that an essentially complete transfer of an electron from the Fe(II) center to O2 has occurred, leading –

to an Fe(III)–O2 complex.

Table 9. Comparison of Bond Distances, Bond Orders, and CM5 Charges on the Dioxygen Units.



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28 Structure

Source

O–O distance (Å)

Bond order (unitless)

CM5 charge (a.u.)

free O2

presenta

1.19

2.03

0.00

–

presenta

1.33

1.54

–1.00

KO2

presenta

1.30

1.47

–0.90

MOF(O2)//B

presenta

1.27

1.69

–0.13

MOF(O2)//L

presenta Experimentb

1.28 1.25

1.53

–0.27

O2

a b

M06/def2-TZVP. The experimental value is taken from ref. 43. Table 9 summarizes various findings discussed above regarding the state of the oxygen

molecule. We find that the O2 unit bound to the MOF has a bond order and bond distance that lie –

–

between free O2 and free O2 (or, equivalently, between free O2 and the O2 unit of KO2), and this indicates that less than an electron is transferred from the iron center to adsorbed O2. This is corroborated by a CM5 charge of –0.13 a.u. on O2 in the ground state MOF(O2) structures, which is much less than –0.90 a.u. Curiously, although both quantities in the MOF are –

–

intermediate between free O2 and O2 , the bond order is closer to that of O2 , whereas the CM5 charge is closer to that of free O2. As mentioned in Sections 4.2.3 and 4.2.4, the experiments were interpreted as involving some oxidation of Fe to Fe(III) by transfer of an electron to O2. We therefore emphasize here that, even though we started the SCF iterations with charge transferred states (see Table 2), we found no evidence for a state with full O2– character (see Table 7). Next we analyzed the orbital energies of the //B-opt0, //B-opt0–N2, and //B-opt0–O2 structures. First we compared the canonical orbital energies (in eV) of highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs). All the three systems were found to have an α-HOMO and a β-LUMO. The (α-HOMO, β-LUMO) energies of bare MOF, MOF(N2), and MOF(O2) are (–4.91, –2.32), (–4.90, –2.29), and (–4.95, –3.31),


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29 respectively. This shows that the adsorption of O2 on the MOF changes the α-HOMO energy by only small amount but causes a more significant change in the β-LUMO energy, while the adsorption of N2 causes negligible change in both the α-HOMO and β-LUMO energies. Second we considered the natural atomic orbital energies of the d orbitals of the central iron atom (to which the guest molecule binds), and we found that they show larger fluctuations with the adsorption of O2 than with N2. Both these analyses show that O2 perturbs the orbital energies more than N2 does, and this indicates that it interacts more strongly with iron. 4.4. Isotropic Couplings. Both the bare cluster and its nitrogen complex, MOF(N2)3, contain three open-shell iron atoms. This gives rise to three possible isotropic coupling constants between the three iron centers—two nearest-neighbor (Jab and Jbc) and one next-nearest neighbor (Jac) isotropic coupling constant, where the labels a, b, and c on the iron centers a, b, and c are the same as already defined in Figure 2. In the actual structure of the MOF the three iron centers are equivalent, and hence the two coupling constants Jab and Jbc are equal. Since in the approximation of the cluster model the iron centers are not precisely equivalent, we use the average of the directly calculated Jab and Jbc to obtain the value for the nearest-neighbor magnetic coupling constant. The M06/def2-TZVP energies yield (by using eq 2 followed by averaging) 3.1 cm–1 for the nearest-neighbor coupling in the bare MOF. In comparison, the nextnearest-neighbor magnetic coupling constant (Jac) is 0.5 cm–1 for the bare MOF. Comparing the results for the bare cluster with our previous work,54 we find that using the same method, the nearest-neighbor and the next-nearest neighbor coupling constants were 3.6 and 0.5 cm–1, respectively, and are in good agreement with the values in the current work. The small difference of 0.5 cm–1 for the nearest-neighbor coupling constant between the two studies can be attributed to the fact that the coordinates of all the H atoms have been optimized here. The M06/def2-TZVP calculations for MOF(N2)3 yield 1.8 cm–1 for the nearest-neighbor Fe–Fe coupling and 0.6 cm–1 for next nearest neighbors. The results show that the noncovalent adsorption of diamagnetic N2 molecules on the MOF has a small but nonnegligible effect (1.3 cm–1 for nearest neighbors and 0.1 cm–1 for the next nearest neighbors) on the magnetic couplings of the cluster.



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30

5. CONCLUSIONS In the present article, we use cluster models carved from the experimental structures of Fe2(dobdc) and Fe2(dobdc)–O2 for the purpose of investigating the interaction of the diatomic molecules O2 and N2 with the open coordination iron sites of Fe2(dobdc). The calculated ground spin states of the Fe–N2 and Fe–O2 interacting systems were found to have ferromagnetically coupled quintet Fe(II) sites bound to singlet N2 or ferromagnetically bound to triplet O2. The Fe– N and Fe–O distances that we optimized by density functional theory are in reasonably good agreement with experiment, being long by 0.06 Å for the former and by 0.00–0.08 Å for the latter. The density functional enthalpies of binding agree with experiment within about 2 kcal/mol for the ground spin states, and they are consistent with experiment in that they predict that O2 binds more strongly than N2 to Fe2(dobdc). For the MOF(O2) complex, binding enthalpies were computed using two experimental structures, and it was found that calculations with the bare MOF structure gave good agreement with experiments. In the most complete calculations (i.e., the //opt6 ones in which we optimized the coordinates of the adsorbate, the Fe to which it is bound, and the first coordination shell oxygen atoms of the iron ion), the O2 free energy of adsorption was found to be 1.6 kcal/mol more favorable than that of N2. The free energy difference between N2 and O2 is much less than the enthalpy difference due to enthalpy– entropy compensation. Binding of more than one guest molecule was studied for the Fe–N2 and Fe–O2 interacting systems, and it was found (for their ground spin states) that binding at one metal site does not significantly affect the binding at the other metal site. Our calculated vibrational spectrum shows the Fe–Olinker band is around 500 cm–1, but the Fe–O2 band is at less than 350 cm–1, whereas the experiments were interpreted as having an Fe– O2 band at 541 cm–1, which is not compatible with our theoretical prediction. Comparing the magnetic coupling constants in the bare MOF to those in which N2 is adsorbed shows only a small effect for N2, in particular 1.3 cm–1 for the nearest neighbor Fe–Fe coupling.


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31 The difference in the enthalpies of binding of the two guest molecules was rationalized in terms of charge transfer, bond order, vibrational frequencies, and orbital energies. It is especially noteworthy that whereas binding of N2 involves charge transfer of 0.08 electrons from N2 to the MOF (0.02 to Fe and 0.06 to the rest of the MOF) and lowers the vibrational frequency of the adsorbate by only 4 cm–1, adsorption of O2 involves transfer of 0.13 electrons from the MOF to O2 (0.08 from Fe and 0.05 from the rest of the MOF) and lowers the vibrational frequency of the adsorbate by 293 cm–1. Experimentally43,74 the O2 frequency is observed to drop even more, 426 cm-1 from 1555 down to 1129 cm–1. The partial charge transfer in the O2 case is also demonstrated by calculating Mayer bond orders for the two complexes; we find that the decrease in N–N bond order of N2 upon adsorption is negligible compared to the decrease in O–O bond order of O2 upon adsorption. The canonical orbital energies of α-HOMO and β-LUMO of the bare MOF were found to be affected more upon adsorption of O2 than N2. However, none of our calculations shows evidence for the superoxide structure inferred experimentally.

ASSOCIATED CONTENT Supporting Information Energies of binding, CM5 charges, Hirshfeld spin densities, Mayer bond orders, and M06/def2TZVP computed structures. This material is available free of charge via the Internet at http://pubs.acs.org.

n AUTHOR INFORMATION Corresponding Authors *Email: [email protected]. Notes The authors declare no competing financial interest.



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32

n ACKNOWLEDGMENTS The authors are thankful to Chris Cramer, Laura Gagliardi, Jeff Long, Berend Smit, and David Teze for helpful discussions. This research was supported by the Nanoporous Materials Genome Center of the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under award DE-FG02-12ER16362. P.V. acknowledges partial support from Phillips 66 Fellowship for Excellence in Graduate Studies and a Doctoral Dissertation Fellowship.


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33

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Identifying the Interactions That Allow Separation of O2 from N2 on the

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