Quantum Microsolvation of Protonated Methane with ${}^4\mathrm{He}$: Large-Amplitude Motion Heavily Influences Bosonic Exchange

Quantum simulations of small ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_n$ complexes disclose significant and antagonistic impact of small-amplitude local vibrational motion vs large-amplitude global fluxional motion within the ${\mathrm{CH}}_5^{+}$ impurity on helium in real and permutation space. While the former significantly enhances bosonic exchange in the surrounding ${}^4\mathrm{He}$ microsolvation shell compared to the rigid-body reference, the latter greatly suppresses long permutation cycles, which is traced back to the different nature of these quantum fluctuations. Therefore, it is expected that the resulting impact on local superfluidity is generic for fluctuating impurities in bosonic environments.

Figure 1

Distance distribution functions of the helium atoms with respect to the ${\mathrm{H}}_2$ moiety of ${\mathrm{CH}}_5^{+}$ for ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_2$ (a) and ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_4$ (b); the position of the moiety is defined by its center of mass. The ${\mathrm{CH}}_5^{+}$ molecule is either fully frozen in its $e\text{−}{\mathrm{C}}_s$ stationary-point structure corresponding to the global minimum (blue), restrained close to its $e\text{−}{\mathrm{C}}_s$ structure allowing only for nuclear quantum delocalization due to small-amplitude vibrational motion (green; see text), or fully flexible which additionally allows for large-amplitude fluxional motion and hydrogen scrambling to occur (red). The superimposed open circles denote Maxwell-Boltzmann quantum statistics as obtained by switching off the helium PIMC exchange moves. Only for the purpose of analyzing the restraint and fully flexible path integral trajectories, the molecule has been transformed beadwise to best fit the $e\text{−}{\mathrm{C}}_s$ reference structure of the respective frozen simulation by minimizing the site-site root-mean-square deviation (RMSD) of ${\mathrm{CH}}_5^{+}$. The left and right insets in (b) depict the nuclear densities in three-dimensional space at $r=3.5\pm 0.01\AA$ for $e\text{−}{\mathrm{C}}_s$ frozen and at $r=4.0\pm 0.01\AA$ for fully flexible ${\mathrm{CH}}_5^{+}$, respectively, based on 7500 statistically independent configurations each, where only those helium atoms behind the image plane are shown.

Figure 2

Visualization of the helium atom densities of ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_n$ for $n=2$ and 4 around ${\mathrm{CH}}_5^{+}$ frozen in its $e\text{−}{\mathrm{C}}_s$ stationary-point structure (top row), restrained close to this $e\text{−}{\mathrm{C}}_s$ structure (center row), and fully flexible ${\mathrm{CH}}_5^{+}$ (bottom row) based on 300 statistically independent configuration snapshots each (where only helium atoms behind the image plane are shown). Left column panels correspond to ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_2$ configurations where the two ${}^4\mathrm{He}$ atoms do not exchange, while all other panels correspond to full exchange (see text) for $n=2$ (center column) and $n=4$ (right column). Note that ${\mathrm{CH}}_5^{+}·{{}^4\mathrm{He}}_n$ has been transformed beadwise to best fit the optimized $e\text{−}{\mathrm{C}}_s$ structure to allow for visualization. The helium atoms involved in full exchange cycles are shown in green, whereas in the left column, blue and red highlight the two distinct helium atoms that are located left and right in (a) and (d) and upper and lower in (g).