Lost in Translation: Simulation-Informed Bayesian Inference Improves Understanding of Molecular Motion From Neutron Scattering

Abstract

Quasi-elastic neutron scattering (QENS) probes atomic and molecular motion on length and time scales central to catalysis, energy materials, and gas adsorption. However, conventional analytical fitting of QENS spectra often fails to uniquely determine the underlying dynamics. The flexibility of simplified line-shape models can make spectra generated by distinct physical processes statistically indistinguishable, leading to ambiguous or inaccurate mechanistic interpretation. By integrating molecular dynamics simulations, physically derived $Q$-dependent scattering models, Bayesian model discrimination, and polarisation analysis, we demonstrate that QENS can, for the first time, resolve anisotropic rotational motion in liquid benzene, a prototypical aromatic molecule relevant to microporous catalysis. The extracted spinning and tumbling diffusion coefficients suggest substantially stronger anisotropy than previously recognised. This integrated, Bayesian evidence-based analytical framework defines a new paradigm for QENS, enabling direct resolution of the rotational and translational dynamics that govern molecular interactions and transport; the fundamental processes and rate-limiting steps in confined hydrocarbon catalysis.

Figures (14)

• Figure 1: Comparison of the structure and dynamics of experimental (blue, error bars indicate a single standard deviation) and simulated (total dynamic structure factors, orange and incoherent-only, green) benzene: (a) a ±0.05 peak integral of the QENS spectra and (b) the reduced second spectral moment.
• Figure 2: Real-space analysis of dynamics from simulation; (a) the observed mean-squared displacement (black line) with posterior distribution of linear models (blue shading indicating $1\sigma$, $2\sigma$, and $3\sigma$ credible intervals), (a, inset) the marginal posterior distribution of self-diffusion coefficients from the linear models in (a), (b) the rotational autocorrelation function of vectors parallel ($\theta=\qty{0}{\degree}$, orange error bars, indicating a single standard deviation) and perpendicular ($\theta=\qty{90}{\degree}$, pink) to the benzene principal axis of rotation, and maximum a posteriori fitted models (solid green lines), and (b, inset) the marginal posterior distributions of the rotational diffusion coefficients found by sampling Eqs. \ref{['eqn:exp']} & \ref{['eqn:exp2']} given the in-plane rotational autocorrelation function (pink data in c).
• Figure 3: Marginal posterior distributions of the (a) tumbling and (b) spinning diffusion coefficients for \ref{['eqn:fit']} for the incoherent dynamic structure factor computed from the rotation-only simulation, vertical black lines show the mean of the marginal posterior distributions from the rotational autocorrelation function.
• Figure 4: analysis of $\omega$-dynamic range dependence of Bayesian evidence using QENS from the full simulation: (a) the Bayesian evidence for the anisotropic model compared with the isotropic model as a function of $\omega$-dynamic range, where the threshold for strong evidence is indicated with the dashed black line, and (b) the Fickian self-diffusion coefficient, (c) tumbling, and (d) spinning rotational diffusion coefficients marginal posterior distributions, obtained for the anisotropic model, given the simulated incoherent QENS signal at an $\omega$-dynamic range of $\qty{\pm1.25}{\milli\electronvolt}$, compared with the mean of the distributions obtained directly from simulation trajectory (dashed vertical black lines).
• Figure 5: Anisotropic model maximum a posteriori given experimental LET data at incident energies of $\qtylist{1.97;3.60}{\milli\electronvolt}$: comparison of the incoherent dynamic structure factor from the experimental data, co-refined anisotropic model, and their ratio. Individual $Q$-dependent line fits available in Figs. \ref{['fig:si_model360_fit']} & \ref{['fig:si_model197_fit']}.