Article pubs.acs.org/JPCA
Sorption of H2 to Open Metal Sites in a Metal−Organic Framework: A Symmetry-Adapted Perturbation Theory Analysis Joshua J. Goings,‡ Suzanna M. Ohlsen, Kara M. Blaisdell, and Daniel P. Schofield* Department of Chemistry and Biochemistry, Seattle Pacific University, Seattle, Washington 98119, United States S Supporting Information *
ABSTRACT: Metal−organic frameworks (MOFs) show considerable promise as materials for gas storage and separation. Many MOF structures have open metal sites, which allow for coordination of gas molecules to the metal centers. In this work, we use coupled-cluster and symmetry-adapted perturbation theory to probe the interaction between hydrogen gas and unsaturated metal sites in mimic structures based on the MOF HKUST-1. The interactions are of a mixed electrostatic/dispersive nature, with the relative magnitudes of these components dependent on the metal center. The strongest binding was found for magnesium- and zinc-containing MOFs, with an overall interaction energy of −4.5 kcal mol−1.
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INTRODUCTION Metal−organic frameworks (MOFs) are a class of crystalline materials composed of metal centers coordinated by rigid organic ligands. Many MOFs, in addition to being highly porous, have “open” uncoordinated metal sites that preferentially bind small gas molecules, making them excellent targets for gas adsorption.1 The search for materials to store hydrogen for use in fuel cells or to sequester carbon dioxide has led to the development of a proliferation of MOF structures.1 One example is HKUST-1 (Cu3(1,3,5-benzenetricarboxylate)2),2 a highly porous MOF with uncoordinated metal sites, as shown in Figure 1. HKUST-1 is among the most studied MOFs for gas
the activation energies required to remove the gas and regenerate the capture material are low. However, currently obtainable binding energies, on the order of 4−7 kJ mol−1 for H2 in a MOF,7 are too low to store appreciable amounts of hydrogen gas under operating conditions of ambient temperature and pressure. From a theoretical standpoint, the weak interactions between the MOF and adsorbed gas require expensive electronic structure methods capable of describing long-range correlation in order to account for the dispersion energy. It is well-known that standard variants of density functional theory (DFT) are unable to describe dispersion forces and fail to provide accurate predictions for intermolecular interaction energies.9,10 In this work, we use coupledcluster and symmetry-adapted perturbation theory (SAPT) to systematically explore the nature of the adsorption interaction between hydrogen gas and the open metal sites in two MOF structural mimics containing a variety of metal ions. While both of these methods are capable of describing dispersion interactions, SAPT has the additional advantage of being essentially free of basis set superposition error (BSSE), and each individual component of the interaction energy is calculated separately, providing insight into the physical nature of the interaction.11 We limit our study to MOFs containing metal ions that can be well-described by a single-reference wave function. The metals considered are either alkaline earths (Mg, Ca, Sr) or from period 4 (Ca, Mn, Zn).
Figure 1. The MOF HKUST-1 (left) and the paddlewheel (center) and diformate (right) mimic structures used in this work. The orientation of the hydrogen molecule with respect to the mimic structures is also shown.
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storage.3−6 Through use of neutron diffraction measurements, Peterson et al. found that hydrogen binds to the open metal sites before binding to the organic linker ligands.3 Through variation in the metal and/or the organic linker, the ability of a MOF to store or separate gases can be altered.7,8 However, the rational design of MOF structures fine-tuned for gas adsorption requires a detailed chemical understanding of the interaction between guest gas molecules and the different host sites within the MOF lattice.7 MOFs in which the guest gas molecules are physisorbed are desirable for gas capture as © 2014 American Chemical Society
COMPUTATIONAL METHODS
MOF mimic structures were generated from the experimental geometry of HKUST-1, 2 isolating either one or two Special Issue: Kenneth D. Jordan Festschrift Received: December 30, 2013 Revised: March 31, 2014 Published: April 29, 2014 7411
dx.doi.org/10.1021/jp412779q | J. Phys. Chem. A 2014, 118, 7411−7417
The Journal of Physical Chemistry A
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imation was used (DF-SAPT). Interaction energies were calculated using the DF-SAPT2+ approach15 and components grouped as described in ref 15. Due to the use of a pseudopotential for Sr and the open-shell nature of Mn, we have only performed SAPT and DF-SAPT calculations for mimics containing the metals Mg, Ca, and Zn. The high computational cost of SAPT can be reduced through use of a DFT description of the monomers. In this approach, the computationally expensive intramonomer correlation is accounted for with a DFT calculation for the monomers and the expansion of the components of the interaction energy in a single perturbative series in V. The density fitting approximation was used in all SAPT calculations where the monomers are described by DFT (DF-DFTSAPT).16 In DF-DFT-SAPT, the dispersion energy is determined from frequency-dependent density susceptibilities obtained from time-dependent DFT using a generalization of the asymptotic Casimir−Polder formula.17 We have used this approach with the B-LYP functional and corrected for the wrong asymptotic behavior of the exchange−correlation (xc) potential using the scheme of Grüning et al.18 To use this correction, the first vertical ionization potentials are required for each monomer. For H2, the experimental ionization potential of 15.426 eV was used.19 For the MOF mimics, experimental ionization potentials are unavailable, and calculated values were determined using the ionization potential equation-of-motion CCSD (IP-EOM-CCSD) theory.20 The calculated ionization potentials for each of the MOF mimics are provided in the Supporting Information. When reporting DF-DFT-SAPT calculated interaction energies, we collate net induction and dispersion contributions. The δEHF term is again included with the other induction terms.
unsaturated metal sites (Figure 1). The M 2 (HCOO) 4 (paddlewheel) and M(HCOO)2 (diformate) structures were optimized at the MP2 and CCSD(T) levels of theory, respectively. The manganese-containing mimics were studied as high-spin complexes. Mn(HCOO)2 was optimized as a sextuplet with UCCSD(T). Although single-reference, the undecaplet Mn2(HCOO)4 was optimized with the multireference-capable internally contracted second-order Rayleigh− Schrödinger perturbation theory (RS2c).12 The optimal H2− metal distance for all complexes was determined through a constrained geometry optimization, where only the intermolecular distance was optimized. The geometries of the hydrogen and MOF mimic were kept frozen at their experimental13 and optimized monomer geometries, respectively. Potential energy curves calculated at the CCSD(T) level of theory were constructed for both the paddlewheel and diformate mimics by varying the distance between the metal and the center of mass of the hydrogen molecule. The interaction energy was calculated using the so-called supramolecular approach. To avoid overestimation of the binding energy due to BSSE, all CCSD(T) potential energy curves were calculated using the counterpoise correction.14 The following orbitals were frozen as the core in all MP2 and CCSD(T) calculations: Mg(1s), Ca(1s,2s,2p), Mn and Zn(1s,2s,2p,3s,3p), and O and C (1s). Potential energy curves for H2 interacting with the mimic structures were also calculated using SAPT.11 In SAPT, the total Hamiltonian is partitioned as H = FA + FB + WA + WB + V
(1)
where FA and FB are the Fock operators for monomers A and B, V is the intermolecular interaction operator, and WA and WB are the intramonomer correlation operators. We partition our model systems as H2 (monomer A) and either the paddlewheel or diformate structure (monomer B). The four components of the interaction energy (electrostatics, exchange, induction, and dispersion) are expanded in a double perturbative series, with each component calculated to a particular order in W and V. The highest level of SAPT used in this work involves intramonomer perturbation up to third order and intermonomer perturbation to second order and is approximately equivalent to supermolecular many-body perturbation theory through fourth order. Unlike the supramolecular approach, the perturbative approach using SAPT is inherently free of BSSE.11 To facilitate interpretation of the SAPT results, we group the components of the interaction energy according to eq 2.
(10) Eexch = Eexch + ϵ(1) exch (CCSD)
Induction
(20) (20) E ind = E ind,resp + tE(22) ind + Eexch−ind (22) HF + Eexch −ind + δE
Dispersion
(20) (20) Edisp = Edisp + ϵ(2) disp(2) + Eexch−disp
(3)
(2) (2) Edisp = Edisp + Eexch −disp
(4)
As was the case with SAPT, DF-DFT-SAPT calculations were performed for Mg-, Ca-, and Zn-containing mimics only. Unless otherwise specified, the basis set for the metals and adsorbed hydrogen molecule was the def2-QZVP basis set21 augmented with diffuse functions produced by an eventempered extension of the last two exponents of each angular momentum type. For strontium, the 28 core electrons were replaced by an effective core potential.22 The formate ligands were described by the def2-TZVPP basis set.23 In the SAPT calculations, a monomer-centered plus basis set (MC+BS)24 approach was used. A dimer-centered basis set (DCBS) was used for the DF-DFT-SAPT calculations along with the corresponding density fitting auxiliary basis sets.25−28 We employed a monomer-centered basis set (MCBS) in the DFSAPT calculations. Because of the slower convergence to the basis set limit when using a MCBS, the basis set described above was supplemented with diffuse functions on the oxygen atoms. The RS2c, MP2, CCSD(T), and DF-DFT-SAPT calculations were performed with the MOLPRO package.29 The IP-EOMCCSD calculations were performed with the CFOUR package.30 The SAPT calculations were performed with the SAPT200831 program using DALTON32 as the front end. The PSI4 program33 was used for the DF-SAPT calculations.
(10) (12) (13) Electrostatics Eelst = Eelst + Eelst,resp + Eelest,resp
Exchange
(2) (2) HF E ind = E ind + Eexch −ind + δE
(2)
(nl)
The superscripts n and l in E denote the orders of perturbation in V and W, respectively. δEHF can be considered a higher-order induction and exchange−induction term and is grouped with the lower-order induction terms in eq 2. Further information on each term and their calculations can be found in ref 11. To reduce the computational cost of SAPT calculations of the M2(HCOO)4−H2 system, the density fitting approx7412
dx.doi.org/10.1021/jp412779q | J. Phys. Chem. A 2014, 118, 7411−7417
The Journal of Physical Chemistry A
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follows closely the trends expected based on the ionic radius.34 The calculated metal−oxygen distances are very similar for both the diformate and paddlewheel mimic structures, with a maximum variation of 0.06 Å between the two strontiumcontaining structures. This indicates that the diformate structure is a good geometric model for the paddlewheel motif observed in HKUST-1. For all MOF mimics, the M−H2 distance follows the same trend as that for the metal−ligand bond length, matching what would be expected on the basis of ionic radius. Within the group 2 elements, the metal−hydrogen distance increases with increasing atomic number and ionic radius. Similarly, comparing the selected period 4 elements shows that the metal−hydrogen distance decreases with increasing atomic number and the commensurate decrease in ionic radius. In addition to the optimizations with constrained monomers, the H2 bond length was allowed to vary in geometry optimizations performed for the diformate−H2 systems. For the strongest bound diformate mimic (M = Mg), the increase in H−H bond length was 0.006 Å. This in combination with weak (
