Quantum dynamics of adsorbed ${\text{H}}_2$ in the microporous framework MOF-5 analyzed using diffuse reflectance infrared spectroscopy

Diffuse reflectance infrared spectroscopy is used to measure the quantum dynamics of molecular hydrogen adsorbed in the microporous material MOF-5. Low-temperature spectra reveal at least three distinct binding sites. The induced redshifts in the vibrational mode frequencies allow the estimation of site-specific binding energies ranging from 2.5 to 4 kJ/mol. Splittings in the rovibrational sidebands are consistent with the existing theories and indicate that ${\text{H}}_2$ is relatively freely rotating even at temperatures as low as 10 K. Ortho to para conversion of the adsorbed ${\text{H}}_2$ is observed to occur over the course of several hours. A translational sideband of $84{\text{cm}}^{-1}$ arises from the center-of-mass motion of ${\text{H}}_2$ at the primary adsorption site and indicates that the zero-point energy is a substantial fraction of the binding energy of this site.

Figure 1

(Color online) Energy level diagram (not to scale) showing the rotational-vibrational transitions for ${\text{H}}_2$ in a perturbing host, where $\upsilon$ is the vibrational quantum number and $J$ is the rotational quantum number. The scheme is modeled after the primary binding site in MOF-5, for which the absolute value of $m$ is still a good quantum number. The numbers show the gas phase transition frequencies in ${\text{cm}}^{-1}$. $E_{b0}$ and $E_{b1}$ are the binding energies in the ground and excited vibrational states, respectively. The solid arrows show transitions activated by the quadrupolar mechanism, while the dashed arrow indicates a transition activated by the isotropic mechanism $\left[Q\left(0\right)\right]$. The $Q\left(1\right)$ transition with $\Delta m=0$ (thick arrow) is activated by both mechanisms.

Figure 2

(Color online) Adsorption isotherms for ${\text{H}}_2$ $(▲)$ and ${\text{D}}_2$ $(▼)$ in MOF-5 measured at 77 K. The closed symbols are adsorption data, the open symbols are desorption data, and the solid traces are Langmuir fits to the adsorption data.

Figure 3

(Color online) Diffuse reflectance spectra of adsorbed ${\text{H}}_2$ in MOF-5 at loadings of one, two, three, four, five, six, and eight molecules per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster. The data were collected at 30 K. The band assignments are labeled according to their transition, $Q\left(0\right)$ or $Q\left(1\right)$, and corresponding adsorption site, primary $\left(1°\right)$ or secondary $\left(2°\right)$.

Figure 4

(Color online) Left: Diffuse reflectance spectra of adsorbed ${\text{H}}_2$ in MOF-5 at loadings of 8–12 molecules per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster. The data were collected at 30 K. Right: Spectra of the material loaded with 12 ${\text{H}}_2$ per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster at temperatures between 15 and 30 K. The band assignments are labeled according to their transition, $Q\left(0\right)$ or $Q\left(1\right)$, and corresponding adsorption site, primary $\left(1°\right)$ or secondary $\left(2°\right)$. Spectra are vertically offset for clarity.

Figure 5

(Color online) Diffuse reflectance spectra of adsorbed ${\text{H}}_2$ in MOF-5 at loadings of two, three, four, and six molecules per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster. The data were collected at 30 K. $Q{\left(1\right)}_{\text{ori}}$ refers to a transition in which the ${\text{H}}_2$ also undergoes an orientational change with the $m$ quantum number changing by $\pm 1$. $Q_{\text{trans}}$ refers to a transition in which the ${\text{H}}_2$ also undergoes a change in its center-of-mass translational state. $1°$ indicates that the ${\text{H}}_2$ is located in the primary site.

Figure 6

(Color online) $S\left(0\right)$ transitions in the diffuse reflectance spectra of adsorbed ${\text{H}}_2$ in MOF-5 at loadings of one, two, four, and six molecules per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster. The data were collected at 30 K. The band assignments are labeled according to their adsorption sites, primary $\left(1°\right)$ or secondary $\left(2°\right)$.

Figure 7

(Color online) $S\left(1\right)$ transitions in the diffuse reflectance spectra of adsorbed ${\text{H}}_2$ in MOF-5 at loadings of one, two, four, and six molecules per ${\text{Zn}}_4\text{O}{\left({\text{O}}_2\text{C}-\right)}_6$ cluster. The data were collected at 30 K. The band assignments are labeled according to their adsorption sites, primary $\left(1°\right)$ or secondary $\left(2°\right)$.