Ab initio study of hydrogen adsorption on benzenoid linkers in metalâ•fiorganic framework materials

We have computed the energies of adsorption of molecular hydrogen on a number of molecular linkers in metal–organic framework solid materials using density functional theory (DFT) and ab initio molecular orbital methods. We fi nd that the hybrid B3LYP (Becke three-parameter Lee–Yang–Parr) DFT method gives a qualitatively incorrect prediction of the hydrogen binding with benzenoid molecular linkers. Both local-density approximation (LDA) and generalized gradient approximation (GGA) DFT methods are inaccurate in predicting the values of hydrogen binding energies, but can give a qualitatively correct prediction of the hydrogen binding. When compared to the more accurate binding-energy results based on the ab initio Møller–Plesset second-order perturbation (MP2) method, the LDA results may be viewed as an upper limit while the GGA results may be viewed as a lower limit. Since the MP2 calculation is impractical for realistic metal–organic framework systems, the combined LDA and GGA calculations provide a cost-effective way to assess the hydrogen binding capability of these systems. Exploration of new hydrogen storage materials with high hydrogen uptake at ambient temperature is crucial for developing the hydrogen economy. The US Department of Energy (DOE) has set a hydrogen storage gravimetric capacity of 6.0 wt% and volumetric density of 45 kg m−3 for on-board vehicles as the targets for the year 2010, and 9.0 wt% and 81 kg m−3 as the targets for 2015 (US DOE 2004). Although a number of metal hydrides such as NaAlH4 and LiBH4 can meet the 6.0 wt% gravimetric capacity target, their relatively high stabilities require elevated temperature and pressure for re-forming the materials and releasing the hydrogen (Lee et al. 2005, Schlapbach and Züttel 2005). Recently, a new class of metal–organic framework solid materials has attracted considerable attention due to their relatively high hydrogen uptake at 77 K (Eddaoudi et al. 2002). For example, 2 GAO & ZENG IN JOURNAL OF PHYSICS: CONDENSED MATTER 19 (2007) isoreticular metal–organic framework-1 (IRMOF-1) can store 1.3 wt% hydrogen and isoreticular metal–organic framework-11 (IRMOF-11) can store 1.6 wt% hydrogen at 77 K (Rowsell et al. 2004). At room temperature and pressure of 10 bar, hydrogen uptake of 2 wt% has been observed for isoreticular metal–organic framework-8 (IRMOF-8) (Rosi et al. 2003). It has also been reported that metal–organic framework-5 (MOF-5) can adsorb up to 4.5 wt% hydrogen at 78 K but only 1 wt% at room temperature and 20 bar. A recent experiment demonstrates that the adsorption of hydrogen in MOF-177 and IRMOF20 saturates between 70 and 80 bar; within these, H2 uptakes can be as high as 7.5 and 6.7 wt% at 77 K, respectively (Wong-Foy et al. 2006). Meanwhile, Dincă et al. (2006) reported a new metal–organic framework material with previously unknown cubic topology and with exposed Mn2+ coordination sites. This new metal–organic framework material gives rise to an H2 uptake of 6.9 wt% at 77 K and 90 bar. Despite these advances, the DOE’s 2010 targets are still not met with the existing metal–organic framework materials at room temperature. It has been recognized that one possible way to enhance H2 uptake at room temperature is to design new metal–organic framework materials that can adsorb hydrogen molecules with adsorption energies in the range of 0.15–0.25 eV or 15–25 kJ mol−1 (Bhatia and Myers 2006, Kim et al. 2006). Several ab initio calculations have been reported for studying the adsorption interactions between molecular hydrogen and subunits in metal–organic framework materials. Hübner et al. (2004) applied the RIMP2/TZVPP method to calculate the energies of binding between a hydrogen molecule and the various substituted benzenes, C6H6, C6H5F, C6H5OH, C6H5NH2, C6H5CH3 and C6H5CN. These substituted benzenes were treated as simplifi ed subunits for linkers in metal– organic framework systems. The authors found that the H2 ··· C6H5NH2 interaction was the strongest, with a binding energy of 4.5 kJ mol−1 (Hübner et al. 2004). Sagara et al. (2004) carried out MP2 calculations to evaluate the energies of binding between a hydrogen molecule and metal–oxide cluster or Li-terminated 1,4-benzenedicarboxylate (BDC). The hydrogen binding energies were estimated to be 6.9 and 5.4 kJ mol−1, respectively. Moreover, the energies of hydrogen binding with isoreticular metal–organic framework (IRMOF) materials were estimated to be in the range of 4.2–5.5 kJ mol−1, based on the RIMP2/QZVPP level of theory and basis sets (Sagara et al. 2004). Later, Sagara et al. (2005) found that MOF1-4NH2 gave the highest hydrogen binding energy among the isoreticular metal–organic frameworks studied (including IRMOF-1, IRMOF-3, IRMOF-1-4NH2, IRMOF-6, IRMOF-8, IRMOF-12, IRMOF-14, IRMOF-18 and IRMOF-993) and its binding energy was appreciably larger (>10%) than that of the polybenzoid structures, such as IRMOF-993 and IFMOF-14. Lochan and Head-Gordon (2006) calculated the energies of binding between the substituted benzenedicarboxylate groups and a hydrogen molecule to be 3–5 kJ mol−1, by using the basis set superposition error (BSSE) corrected RIMP2/CBS//MP2/6-31G* method. Yang and Zhong (2006a) performed a combined grand canonical Monte Carlo simulation and density functional theory calculation of hydrogen adsorption in metal–organic framework systems with open metal sites. In another paper, Yang and Zhong (2006b) performed a molecular simulation of adsorption of carbon dioxide/methane/hydrogen mixture in metal–organic framework material. Despite these advances, much more theoretical effort is needed to accurately compute the hydrogen binding energies for the increasingly large number of metal–organic framework materials. A major obstacle for theoretical study of hydrogen adsorption in realistic metal–organic framework materials is that high level ab initio methods are computationally very expensive and even impractical. A cost-effective computational strategy is needed to assess the hydrogen binding capability of metal–organic framework materials. Density functional theory (DFT) has been widely used to study interactions of molecules with surfaces (Alfè and Gillan 2006). However, DFT with conventional approximaAB INITIO STUDY OF HYDROGEN ADSORPTION ON BENZENOID LINKERS 3 tions is known to be problematic for describing weak physisorption interactions largely because the dispersion forces and the van der Waals interactions are not properly accounted for. Development of DFT to properly treat weak interactions has been an active research area in the past ten years (Andersson et al. 1996, Kohn et al. 1998, Elstner et al. 2001, Rydberg et al. 2003, Lin et al. 2005). Jhi et al. (2000) performed DFT calculations within the local-density approximation (LDA) to study oxygen molecules binding with carbon nanotubes. Dag et al. (2003) applied the DFT method within the generalized gradient approximation (GGA) to investigate molecular and atomic oxygen adsorption on single-wall carbon nanotubes. Giannozzi et al. (2003) also studied oxygen adsorptions on carbon graphite and nanotubes using DFT methods. These DFT studies show that the LDA method generally gives notably higher binding energies than the GGA method (Dag et al. 2003). Similar conclusions have been drawn for hydrogen adsorption on graphene layers (Okamoto and Miyamoto 2001, Cabria et al. 2005). Agrawal et al. (2006) performed both LDA and GGA calculations to study CH4 molecules binding with carbon nanotubes and nanoropes. They found that the LDA method overestimates the CH4 binding with the carbon nanotubes while the GGA method underestimates the binding. The purpose of this paper is to examine the accuracy of three popular DFT methods for calculating the hydrogen binding with molecular linkers in metal–organic framework materials. Figure 1 shows the unit cell of a prototype metal–organic framework system (MOF5) which contains four molecular linkers. We employed the LDA with the Vosko– Wilk–Nusair functional (Vosko et al. 1980), the GGA with the Perdew–Burke–Ernzerhof (PBE) functional (Perdew et al. 1996, 1997), as well as the Becke three-parameter Lee–Yang–Parr (B3LYP) hybrid functional (Becke 1988, Lee et al. 1988). These DFT methods were used to optimize geometric structures of metal-terminated (Li, Cu, Zn) benzenedicarboxylate (BDC) molecular linkers, with and without an adsorbed hydrogen molecule. To calculate the hydrogen binding energies, we considered that the hydrogen moleFigure 1. The unit cell of a prototype metal–organic framework (MOF-5) solid, which contains four molecular linkers. Grey: carbon atom; red (or dark): oxygen atom; white: hydrogen atom; blue (or gray spheres): zinc atom. 4 GAO & ZENG IN JOURNAL OF PHYSICS: CONDENSED MATTER 19 (2007) cule was in a perpendicular orientation to the BDC plane, as shown in fi gure 2. Note that we did not consider hydrogen adsorption on the metal atom because our model for the metal site is highly simplifi ed; the surrounding environment is very different to that in real metal–organic framework systems. Here, the different metal atoms were selected for the purpose of testing the metal effects on the interaction of hydrogen molecules with the benzenoid linkers. In addition to the DFT calculations, we also performed geometry optimization and calculation of hydrogen binding energies using the Møller–Plesset secondorder perturbation (MP2) method, and we set the convergence threshold to be 10−6 Hartree. In general, the hydrogen binding energies were evaluated with the formula ΔEbinding = E(H2 + MOF) − E(H2) − E(MOF) where all the electronic energies were corrected using the full counterpoise procedure to account for the basis-set superposition error (BSSE) (Boys and Bernardi 1970). The BSSE corrections were undertaken for DFT and MP2 optimized structures, respectively. In both DFT and MP2 calculations, Dunning’s correlation consistent triple-zeta basis sets (cc-pVTZ and aug-cc-pVTZ) (Woon and Dunning 1993, Kendall et al. 1992) were applied for the elements C, O, H and Li, while the effectivecore pseudopotentials of the Stuttgart/Dresden basis sets (Stoll et al. 1984) were applied for Cu and Zn. All calculations were performed with the Gaussian 03 software package (Frisch et al. 2004). To confi rm that the perpendicular orientation of the hydrogen molecule was the most stable confi guration when binding with the Li-terminated BDC molecular linker, we used the highest level of theory considered in this work, namely, MP2/aug-cc-pVTZ//MP2/ccpVTZ. We examined eight possible adsorption confi gurations for the hydrogen molecule, as shown in fi gure 3. It is found that the perpendicular orientation is 1.71 kJ mol−1 lower in binding energy than the parallel orientation. The parallel orientation gives the second lowest binding energy. The calculated energies of binding between a hydrogen molecule and the metal-terminated benzenedicarboxylate, based on three DFT and the MP2 methods, are all collected in table 1. It can be seen that the hydrogen binding energies calculated using the diffusive aug-ccpVTZ basis sets are lower than those obtained using the cc-pVTZ basis sets. First, the MP2/cc-pVTZ results are between −3.80 and −4.01 kJ mol−1, while the MP2/aug-cc-pVTZ results are between −4.85 and −5.10 kJ mol−1. The former values are very close to those obtained in previous theoretical studies of hydrogen binding with the benzenoid systems (Hübner et al., H2 ··· C6H6, MP2/TVZPP: 3.91 kJ mol −1; Lochan and Figure 2. Hydrogen molecule binding with the M–BDC–M (M =Li, Cu, Zn) molecular linkers in a perpendicular orientation. Grey: carbon atom; red (or dark): oxygen atom; white: hydrogen atom; pink (or smaller gray spheres): metal atom. AB INITIO STUDY OF HYDROGEN ADSORPTION ON BENZENOID LINKERS 5 Head-Gordon, H2 ··· BDC, RIMP2/CBS//MP2/6-31G*: 4.029 kJ mol −1). Our MP2 calculations indicate that large diffusive basis sets are necessary to accurately determine the physisorption energies of hydrogen with metal-terminated benzenedicarboxylate. Second, while the LDA–VWN, GGA–PBE and MP2 calculations all show that the hydrogen molecule can bind to the metal-terminated benzenedicarboxylate, the hybrid B3LYP method predicts otherwise, that is that it is energetically unfavorable for the hydrogen molecule to bind with substituted benzenedicarboxylate. As shown in fi gure 4, the binding energies calculated on the basis of B3LYP are positive, and decrease monotonically; no energy minimum is seen. This suggests that hybrid DFT methods may be problematic for assessing weak physisorption interaction. Third, the GGA–PBE predicts notably larger binding distance between the hydrogen molecule and the benzenoid surface than LDA–VWN or MP2. Meanwhile, the LDA–VWN method consistently gives notably higher hydrogen binding energies compared to the more accurate MP2 method, while the GGA–PBE method consistently gives lower hydrogen binding energies. This situation refl ects the diffi culty of using current DFT functionals to deal with the dispersion forces. The dispersion forces do not simply come from the charge overlap, which can be well accounted for by the local or semi-local DFT approximations, but from charge fl uctuations, which go beyond the conventional DFT method. Figure 3. Relative electronic energies (kJ mol−1) among eight H2 adsorption confi gurations with the BDC–Li2 molecular linker. The electronic energies were calculated at the MP2/aug-cc-pVTZ level and based on the MP2/cc-pVTZ optimized geometries. Grey: carbon atom; red (or dark): oxygen atom; white: hydrogen atom; pink (or smaller gray spheres): lithium atom. Table 1. The calculated energies of binding (kJ mol−1) between a hydrogen molecule and M– BDC–M (M = Li, Cu, Zn) linkers in metal–organic framework systems, using three DFT (LDA– VWN, GGA–PBE) and the MP2 methods together with the cc-pVTZ or aug-cc-pVTZ basis sets, respectively, for geometry optimization (with the exception of the MP2/aug-cc-pVTZ calculation for which the geometries are based on the MP2/ccpVTZ optimization). The H2 binding distances (Å) to the benzenoid surface are shown in parentheses.