Hydrogen adsorbed in a metal organic framework-5: Coupled translation-rotation eigenstates from quantum five-dimensional calculations

Abstract

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (T-R) eigenstates of a H(2) molecule adsorbed in metal organic framework-5 (MOF-5), a prototypical nanoporous material, which was treated as rigid. The anisotropic interactions between H(2) and MOF-5 were represented by the analytical 5D intermolecular potential energy surface (PES) used previously in the simulations of the thermodynamics of hydrogen sorption in this system [Belof et al., J. Phys. Chem. C 113, 9316 (2009)]. The global and local minima on this 5D PES correspond to all of the known binding sites of H(2) in MOF-5, three of which, α-, β-, and γ-sites are located on the inorganic cluster node of the framework, while two of them, the δ- and ε-sites, are on the phenylene link. In addition, 2D rotational PESs were calculated ab initio for each of these binding sites, keeping the center of mass of H(2) fixed at the respective equilibrium geometries; purely rotational energy levels of H(2) on these 2D PESs were computed by means of quantum 2D calculations. On the 5D PES, the three adjacent γ-sites lie just 1.1 meV above the minimum-energy α-site, and are separated from it by a very low barrier. These features allow extensive wave function delocalization of even the lowest translationally excited T-R eigenstates over the α- and γ-sites, presenting significant challenges for both the quantum bound-state calculations and the analysis of the results. Detailed comparison is made with the available experimental data.

High H2 Sorption Energetics in Zeolitic Imidazolate Frameworks

“…This type of calculation was previously used to predict the rotational transitions for H 2 sorbed in various MOFs. 52,53,69,[71][72][73][74][75][76][77][78] Here, the results are discussed for calculations using the polarizable H 2 potential. For H 2 sorbed at site 1 in ZIF-68, a rotational energy level of 6.95 meV was calculated for the transition between j = 0 and the lowest j = 1 sublevel (Table S8).…”

“…The higher than expected calculated value of the j = 0 to j = 1 transition for H 2 sorbed at site 1 in ZIF-69 could result from the theoretical potential energy surface for the adsorbent or the lack of coupling to translational motion, which has shown to be important in certain cases. 71 We emphasize again that the region between the two adjacent 2-nitroimidazolate linkers in ZIF-69 imposes a high barrier to rotation on the H 2 molecule as in ZIF-68. A rotational barrier of 39.38 meV was calculated for H 2 sorbed at site 1 in ZIF-69 ( Figure S17), which is also greater than those for many MOFs according to previous INS studies.…”

HD in C 60 : theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

“…Besides H 2 @C 60 , the theoretical study of which will be reported shortly, this includes molecular hydrogen in clathrate hydrates [19,29,30], metal-organic frameworks [31][32][33][34][35] and zeolites [36,37], among others. Finally, methodological extensions are in progress in our group to the INS spectra of nanoconfined polyatomic molecules such as methane [38] and water [39].…”

Quantum dynamics of H2 in a carbon nanotube: Separation of time scales and resonance enhanced tunneling

“…3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] More recently, studies have appeared focusing on different adsorbates, such as CO, CH 4 , CO 2 , SO 2 , or H 2 O, and different substrates such as zeolites and metal-organic frameworks. 7,[23][24][25][26][27][28] One particular feature present in single-walled carbon nanotubes (SWCNTs) that makes them especially interesting materials is their cylindrical shape, which gives rise to the coexistence of a 2D confinement in the space perpendicular to the nanotube's axis and unbound motion along this latter coordinate. Even though 2D confinement has been relatively studied and reviewed in the literature, 12,16,29,30 only few studies have treated both the confined and the quasi-free coordinates in a fully quantum formalism.…”