Environment-imposed selection rules for nuclear-spin conversion of H$_2$ in molecular crystals

Nuclear-spin conversion in molecular hydrogen is governed by strict symmetry rules that typically require magnetic fields or catalytic surfaces to break. Here we demonstrate that the intrinsic tensor composition of a non-magnetic molecular crystal field can impose and relax these rules without external fields. High-resolution infrared spectra of H$_2$ in crystalline CO$_2$ reveal large rank-2 (quadrupolar) crystal-field splittings of the $m$ sublevels, while nuclear-spin conversion occurs only through $\Delta m = 0$ channels. Replacing CO$_2$ with polar N$_2$O introduces rank-1 (dipole) components that partially open $\Delta m \neq 0$ pathways, while incorporation of paramagnetic NO$_2$ fully lifts the restriction. These results establish a direct correspondence between crystal-field tensor rank and nuclear-spin dynamics, introducing a general symmetry-based framework for designing and controlling spin-isomer populations and quantum-state connectivity in molecular solids.