Spontaneous symmetry breaking and inversion-line spectroscopy in gas mixtures

TL;DR

The paper resolves Hund's paradox by invoking spontaneous symmetry breaking in many-molecule systems, formulating a mean-field model where dipole-dipole interactions drive a localization transition at a critical pressure $P_{\mathrm{cr}}$ that yields chiral ground states and a vanishing inversion frequency at the transition. It extends the framework to gas mixtures, deriving composition-dependent critical pressures and two-mode inversion spectra governed by universal scaling with $P/P_{\mathrm{cr}}$, and develops explicit expressions for mixtures with nonpolar partners and with two chiral species. The work provides parameter-free, testable predictions for inversion frequencies and absorption spectra in mixtures (e.g., NH$_3$–He, NH$_3$–ND$_3$), with potential implications for astrophysical observations and laboratory spectroscopy. Overall, the results offer a concrete, thermodynamically grounded route to chirality emergence via collective interactions, linking microscopic molecular properties to macroscopic spectroscopic signatures.

Abstract

According to quantum mechanics chiral molecules, that is molecules that rotate the polarization of light, should not exist. The simplest molecules which can be chiral have four or more atoms with two arrangements of minimal potential energy that are equivalent up to a parity operation. Chiral molecules correspond to states localized in one potential energy minimum and can not be stationary states of the Schrödinger equation. A possible solution of the paradox can be founded on the idea of spontaneous symmetry breaking. This idea was behind work we did previously involving a localization phase transition: at low pressure the molecules are delocalized between the two minima of the potential energy while at higher pressure they become localized in one minimum due to the intermolecular dipole-dipole interactions. Evidence for such a transition is provided by measurements of the inversion spectrum of ammonia and deuterated ammonia at different pressures. A previously proposed model gives a satisfactory account of the empirical results without free parameters. In this paper, we extend this model to gas mixtures. We find that also in these systems a phase transition takes place at a critical pressure which depends on the composition of the mixture. Moreover, we derive formulas giving the dependence of the inversion frequencies on the pressure. These predictions are susceptible to experimental test.

Figures (11)

• Figure 1: (Color online) Molecular structures of ammonia ($\mathrm{NH_3}$, left) and deuterated disulfane ($\mathrm{D_2S_2}$, right) in one of their two localized states.
• Figure 2: (Color online) Critical pressure $P_\mathrm{cr}$ as a function of the chiral species fraction $x$ for NH$_3$--He (bottom) and D$_2$S$_2$--He (top) mixtures at $T=300$ K. Note that pressure units are atm in the case of NH$_3$--He and natm in the case of D$_2$S$_2$--He.
• Figure 3: (Color online) Coefficients $a_1/\sqrt{N_1}$ and $a_2/\sqrt{N_2}$ defining the molecular states $\psi_1,\psi_2$ of a two-species mixture as a function of $P/P_\mathrm{cr}$. The coefficients have been obtained by solving numerically Eq. (\ref{['aibi']}) in the case of a $\mathrm{NH}_3$--$\mathrm{ND}_3$ mixture ($\mathrm{ND}_3$ is species $i=2$) with $x_2=0.1$ at temperature $T=300~\mathrm{K}$. The coefficients bifurcating at $P=P_\mathrm{cr}$ and tending for $P \gg P_\mathrm{cr}$ to $1/\sqrt{2}$ (dashed line) describe two degenerate molecular states, named $c_{LL}$ and $c_{RR}$, with molecules of both species in a chiral configuration of type $L$ or $R$. Notice further bifurcations appearing at $P \simeq 4 P_\mathrm{cr}$, they correspond to stationary states of higher energy.
• Figure 4: (Color online) Parameters $q_1,q_2$ encoding the difference between the delocalized symmetric state $d_{++}$ and the chiral states $c_{LL}$ and $c_{RR}$ of Table \ref{['table_chimix']} evaluated numerically for the same mixture of Fig. \ref{['states_chimix']}.
• Figure 5: (Color online) Energies $\hbar\overline{\omega}_\pm$ of the excitation normal modes as a function of pressure $P$ in the case of a $\mathrm{NH}_3$--$\mathrm{ND}_3$ mixture ($\mathrm{ND}_3$ is species $i=2$) with $x_2=0.1$ at $T=300~\mathrm{K}$. The horizontal dotted line is the asymptotic value $\hbar\overline{\omega}_+^\mathrm{as}$. The dashed lines which vanish at $P_\mathrm{cr}^{(1)}=1.69~\mathrm{atm}$ and $P_\mathrm{cr}^{(2)}=0.11~\mathrm{atm}$ correspond to the inversion frequencies of pure species. The critical pressure of the mixture, point where $\hbar\overline{\omega}_-$ vanishes, is $P_\mathrm{cr}=0.70~\mathrm{atm}$. Energy is measured in $\textrm{cm}^{-1}$.