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

TL;DR

The paper addresses how to control nuclear-spin conversion of H2 in solids without external fields by exploiting the host crystal-field tensor content. Using matrix-isolation infrared spectroscopy on H2 in CO2, N2O, and NO2-doped CO2, combined with DFT-calculated potentials $V(r)$ and $V(\theta,\phi)$, the authors map spin-conversion channels to crystal-field ranks. CO2 host yields large rank-2 splittings and enforces $\Delta m = 0$; N2O adds rank-1, partially opening channels; NO2 introduces paramagnetism, fully lifting restrictions; Four rovibrational transitions are predicted and observed, and time evolution shows ortho-para conversion in CO2; Control experiments confirm the tensor-rank dependence. This establishes a general symmetry-based framework for tensor-engineered control of spin populations in molecular solids, with implications for quantum-state connectivity and molecular qubits.

Abstract

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 $Δm = 0$ channels. Replacing CO$_2$ with polar N$_2$O introduces rank-1 (dipole) components that partially open $Δm \neq 0$ 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.

Figures (6)

• Figure 1: The CO2 crystalline lattice and H2 axis definitions with wavefunctions and energies of the perturbed eigenstates.a,H2 trapped in crystalline CO2 experiences coupling between translational (as a function of $r$) and rotational (as a function of $\theta,\phi$) energies. b, The four lowest-energy translational eigenfunctions have identical probability densities stemming from the harmonic potential. c, Reduced probability density plots of the angular wavefunctions of the four lowest-energy states (shown with state designations $nl\lambda m)$ resemble the spherical harmonics. d, The crystal field of the lattice perturbs the eigenenergies with respect to the gas phase in both para-H2 and ortho-H2 and lowers the degeneracy for $\lambda = 1$ states. Solid arrows indicate rovibrational spectroscopic transitions that are allowed in the perturbed state. Dashed arrows are allowed but suppressed. Four spectroscopic lines are therefore expected in the rotational-vibrational spectrum.
• Figure 2: Potential energy plots of H2 confined in solid CO2.a, Radial potential $V(r)$ for H2 confined in CO2 as a function of the translational distance $r$ from equilibrium. The black dots are the calculated points and the red line is a fit assuming a harmonic potential. b, Angular potential $V(\theta,\phi)$ for H2 in CO2 with respect to the two rotational degrees of freedom, $\theta$ and $\phi$. The angular potential clearly demonstrates the azimuthal anisotropy that results in splitting of all three $m$ sublevels, and the large field gradients contribute significant rank-2 contributions that enable $\Delta m= 0$ortho-to-para nuclear-spin conversion.
• Figure 3: The Q$_1$ spectral region of 1% H2 confined in CO2 at 10 K.top,$t = 0$, and bottom,$t = 40$ min. Experimental data are shown in black. The dashed lines correspond to the individual fitted Gaussian peaks, and the red line is the linear combination of all fitted peaks. Peak I (orange dashed line) is the absorption peak of ortho-H2 molecules from any $m$ sublevel with $\Delta m = 0$, and is seen to decrease with time as molecules originally in $\ket{10}$ convert to $\ket{00}$. Peak II (blue dashed line) corresponds to absorption by para-H2 molecules, with a corresponding increase in intensity with time as ortho-to-para conversion occurs. Peaks III and IV (green and purple dashed lines) are assigned to absorption by ortho-H2 initially in an $|m|=1$ state ($m=\pm1$ split, labeled $1$ and $\bar{1}$ by energy) that are weakly excited by a $|\Delta m|=1$ transition to the $\ket{10}$ state in the vibrational excited state. They do not evolve with time due to the host-conditioned selection rule for nuclear-spin conversion.
• Figure 4: The Q$_1$ spectral region of 1% H2 in N2O at 10 K.top,$t = 0$, and bottom,$t = 40$ min. Experimental data are shown in black. The dashed lines correspond to the individual fitted Gaussian peaks, and the red line is the linear combination of all fitted peaks. Peak I/III (orange dashed line) has contributions from nearly-degenerate transitions following the $\Delta m = 0$ spectroscopic selection rule and the weak $\ket{1\bar{1}} \rightarrow \ket{10}$ excitation. This peak decreases with time as molecules originally in $\ket{10}$ convert to $\ket{00}$ by the host-conditioned nuclear-spin conversion selection rule. Peak II (blue dashed line) again corresponds to absorption by para-H2 molecules, with a corresponding increase in intensity with time as ortho-to-para conversion occurs. Peak IV (green dashed line) originates from ortho-H2 weak $\ket{11}\rightarrow\ket{10}$ spectroscopic transitions. It does not evolve with time due to the host-conditioned selection rule for nuclear-spin conversion.
• Figure 5: The Q$_1$ branch of 1% H$_2$ co-trapped with 3% NO2 in CO2 ice at 10 K. Experimental data ($t=0$ min) are shown in black. The dashed lines correspond to the individual fitted Gaussian peaks, and the red line is the linear combination of all fitted peaks. Peak I (orange dashed line) is residual ortho-H2 molecules. Peak II (blue dashed line) corresponds to absorption by para-H2 molecules, showing that nearly all of the ortho-H2 molecules have converted to para-H2 in the presence of a paramagnetic impurity.