Parallel-Mode EPR of Atomic Hydrogen Encapsulated in POSS Cages

Abstract

In a typical EPR experiment, the transitions require that the static magnetic field $B_0$ is oriented perpendicular to the microwave field $B_1$ (perpendicular mode). This is determined by the transition rules either in the classical or in the quantum mechanical description. However, there are cases where EPR transitions are observed when $B_0$ is oriented parallel to $B_1$ (parallel mode). Quite numerous studies can be found in the literature where EPR transitions in both modes (dual-mode EPR) are feasible. In the majority of cases, dual-mode EPR studies are typically applied in $S>1/2$ systems where non-zero transition probabilities for the parallel mode are the result of the state mixing provided by the zero-field splitting interaction. On the other hand, the observation of parallel-mode EPR signals in $S=1/2$ systems becomes feasible when strong hyperfine interaction between the electronic and nuclear spin is present, as has been theoretically predicted for the hydrogen atom having a hyperfine coupling constant of $A_0=1420$ MHz (Weil in Concepts Magn Reson Part A 28:331, 2006). Herein, we report the first dual-mode X-band EPR experiments of hydrogen atom (both isotopes $^1$H and $^2$H) encapsulated in polyhedral oligomeric silsesquioxane cages. We extend the theory to the case of deuterium and we extract analytical formulas for transition probabilities. For the forbidden transitions, this study revealed a first-order dependence of resonance fields on the nuclear g-factor, $g_{\mathrm{n}}$, and the existence of a clock transition with $f=307$ MHz.