Correlations of intra- and intermolecular dynamics and structure in liquid $\mathit{para}$-hydrogen

Although hydrogen is the simplest of all molecular species, its nuclear quantum effects dominate the structure and thermodynamical properties of the condensed phases. With a recently developed nonempirical quantum molecular dynamics simulation method, we present intuitive understandings of real-time dynamics of each $\mathit{para}$-hydrogen$\left(p\text{−}{\mathrm{H}}_2\right)$ molecule in the liquid phase including its H-H bond vibrations, molecular orientations, and librational motions. The short- and long-living memories of angular dynamics we found suggest that $p\text{−}{\mathrm{H}}_2$ should be described as a librating nonspherical diatomic molecule and can be characterized by two typical dynamics: kinetic motions inside a solvation shell and diffusive dynamics out of the shell. The real-time trajectory reveals that structural rearrangements of a $p\text{−}{\mathrm{H}}_2$ molecule such as breakout from a solvation shell significantly correlate with its intramolecular structure and fluctuations. The H-H bond power spectra completely fitted by two functions also indicate that liquid $p\text{−}{\mathrm{H}}_2$ has two typical structures. The condensed-phase effects on shifts and broadening of H-H bond stretching frequencies, intrinsic librational dynamics, and molecular orientational distributions are computationally demonstrated and physically rationalized.

Figure 1

(upper) Top views of the 3D cubic simulation cells containing $576 p\text{−}{\mathrm{H}}_2$ molecules at 14 and 25 K. The corresponding real-time movies are given as Supplementary Movies. The real-time dynamics include the H-H bond vibrations, molecular orientations, and librational dynamics of each $p\text{−}{\mathrm{H}}_2$ molecule. (lower) 2D RDFs as a function of distance between centers of two hydrogen NWPs, $r$, and an intermolecular bond angle, $\theta$. The relative angle $\theta$ symmetrically distributes near 90 degrees. The shoulder appearing in the first RDF peak of 14 K reflects the diatomic structure of a ${\mathrm{H}}_2$ molecule in the T-shape solvation shell, while the shoulder almost disappears at 25 K due to the thermal modulations.

Figure 2

(a) Distributions of the H-H bond length $r_{\mathrm{HH}}$ in the $p\text{−}{\mathrm{H}}_2$ liquid. (b) Power spectra of the H-H vibrations. The power spectra involve the two H-H stretchings of the well-structured and less-structured ${\mathrm{H}}_2$ molecule. The shrinked H-H bond at 25 K leads to the blueshift. The motional narrowing due to the fast vibrational dephasings is observed at 25 K. (c) Power spectra of the intermolecular angle $\theta$. The rigid solvation structure at 14 K leads to the higher librational frequency, $200 {\mathrm{cm}}^{-1}$, while the partially broken configuration at 25 K results in the red-shifted librational frequency, $150 {\mathrm{cm}}^{-1}$.

Figure 3

Real-time dynamics of a representative ${\mathrm{H}}_2$ molecule in the $p\text{−}{\mathrm{H}}_2$ liquid at 25 K. The vertical line in each panel divides the time window at $t=t_0$. The square displacement (upper left), the intramolecular angles $\varphi$ and $\omega$ (upper right), the H-H bond length (lower left), and the NWP width (lower right) are all significantly correlated.