Introduction

Materials with low thermal conductivities (TCs) are of fundamental importance in a variety of applications such as thermoelectrics and thermal barrier coatings. For instance, high heat-to-electricity conversion efficiency requires both high electrical conductivity and intrinsic ultralow TC. The latter is less common in crystalline compounds since their long-range order usually facilitates an effective phonon propagation and thus heat conduction. Strategies involving strong anharmonicity1, complex structures2, and lattice disorder3 can break routines and enable intrinsic low TCs of crystalline materials. In particular, static and/or dynamic disorders, such as the random stacking of two-dimensional layers in WSe24, the superionic copper cations with liquid-like mobility in Cu2Se5, and perhaps more representatively, the off-center rattling guest atoms in the clathrate Sr8Ga16Ge306, have been identified to scatter phonons efficiently. The resulting low, even glasslike TC makes these atomic crystals good candidates for high-performance thermoelectric materials and indicates the essential role of structural disorder in minimizing heat transport.

However, the disorder-induced low lattice TCs rely on unique crystalline structures and chemical bonds. There remains great interest in seeking a general method to trigger nanoscale chaos. Intriguingly, replacing atoms at lattice points with molecules to introduce extra orientational and dynamic disorders may provide a promising approach. Molecular disorders have been recognized to play essential roles in the phonon spectra and extremely low TCs of various molecular crystals7,8. They could even trigger a high-temperature glasslike heat transport. Specifically, the temperature-independent TC of the fullerene-C60 was found to be driven by its free rotations9,10. Besides, the orientational disorders in fullerene-based superatomic crystals could lead to an ultralow TC as ~ 0.2 W m−1 K−1 — a value rarely achieved in atomic systems11,12. The attractive effects of molecular components have also been observed in the so-called hybrid materials where organic molecules are inserted into the well-defined pristine crystalline framework. An example is the TC of metal halide perovskite trapping organic molecular cations can be 40% lower than that with inorganic monoatomic cations13. Molecular inclusions are expected to induce unique phonon features differing from the atomic cases and provide additional channels to suppress heat conduction, yet the underlying mechanisms have not been comprehensively understood. Besides disordered orientations (such as in plastic phases) that induce symmetry breaking akin to structural glasses12,14,15, dynamic reorientational motions disrupting lattice dynamics also deserve in-depth study. A more complicated but previously overlooked issue lies in the varying behavior of molecular guests, e.g., from almost free disordered rotations to hindered librations with specific orientations inside the hosting space16,17,18, which may induce different TC behavior. Nevertheless, manipulating rotational dynamics and molecular orientations to understand how to efficiently exploit these disorders for minimizing and even regulating heat conduction remains a challenging task.

In this paper, we aim to clarify the effects of molecular disorders on heat transport and their intrinsic nature by studying the TC of a host-guest methane hydrate MH-III; it serves as a good prototype where the methane molecular orientations and rotations can be modified by lattice compression. This enables an understanding of the interaction between the guest molecule orientations, rotational dynamics, and thermal conductivity. Note that pressure as an avenue to tune lattice dynamics has been utilized to study the structure-property relationship of various materials19,20. Here, using pressure to manipulate molecular states, we reveal the dominant roles and atomic-level mechanisms of the guest rotational/librational dynamics on the suppression of heat transport. Such reduction in TC can be ascribed to the enhanced phonon scatterings and phonon localizations controlled by the strength of host-guest coupling. Based on extended calculations of other representative compounds, we further exemplify the common TC reduction by guest rotational dynamics. The findings suggest a viable path to minimize or regulate thermal properties by controlling the rotational dynamics of molecular guests and their couplings with the host in hybrid lattices.

Results

Pressure-dependent structural characteristics of MH-III

Compression ranging from 3 to 60 GPa (at 300 K) was employed to manipulate the rotational dynamics of CH4 molecules in the one-dimensional (1D) H2O channels of MH-III (see Supplementary Note 1 and Supplementary Fig. 1 for details of the crystal structure). No structural transition occurs within this pressure range. Due to the tight packing and strong repulsive host-guest interactions, no rattling translational motions with large displacements of the CH4 molecules are observed (see the atomic trajectories in Fig. 1a). This is different from the behavior of clathrate hydrate phases at ambient pressure21. Nevertheless, depending on the pressure, CH4 molecules still execute rotation/libration in the channels. From the calculated root-mean-square displacement (RMSD) of H atoms of CH4 (using time-averaged positions as the ref. 12) and the rotational diffusion coefficient (RDC)9, a two-stage rotational dynamics over the pressure increase can be identified, evident by a transition at 20 GPa (see Fig. 1b). The inflection point of the transition agrees nicely with previous interpretations based on Raman spectra and ab initio simulations22,23. Specifically, the RMSD in the pressure range of 3–20 GPa remains nearly constant and close to the length of C–H bonds—1.09 Å (see Fig. 1b). This implies the capability of individual CH4 molecule to freely rotate, as also reinforced by the spherical-like temporal trajectories of H atoms shown in Fig. 1c. Yet, the decrease of the RDC with increasing pressure suggests more restrictive CH4 rotations upon compression. The RMSD dramatically decreases to smaller values above 20 GPa (e.g., 0.3 Å at 60 GPa). In this pressure range, the guest rotations are greatly hindered and transform into librational motions around equilibrium positions. This transition is supported by the atomic trajectories of H atoms (Fig. 1c) and the low RDC value of CH4 approaching zero (see Supplementary Fig. 2 for the entire evolution process of CH4 dynamics).

Fig. 1: The evolutions of rotational dynamics and molecular orientations of guest CH4 molecules under pressure.
figure 1

a The snapshots of partial simulation boxes superposed with the temporal trajectories of the centroid of H2O and CH4 molecules at 3 GPa (upper) and 60 GPa (lower). The orientational ordering of CH4 molecules can be seen at 60 GPa. b The root-mean-square displacement (RMSD) of H atoms in CH4 molecules with the time-averaged positions as the reference and the rotational diffusion coefficient (RDC) of the entire CH4 molecule as a function of pressure. A transition of dynamics from continuous rotations to hindered librations at 20 GPa can be identified. c Atomic trajectories of H atoms (black track) in a single CH4 molecule at 3 GPa (upper) and 60 GPa (lower) together with their projections onto the x-y (pink), x-z (blue), and y-z (green) planes. d Probability distribution maps of the C–H vector orientation (ϕ, θ) at 3 GPa (upper) and 60 GPa (lower). ϕ is the relative angle between the a-axis and the projection of the C–H vector onto the a-b plane, and θ is the relative angle between the C–H vector and the c-axis. Source data are provided as a Source Data file.

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Another consequence of lattice compression is the enhanced orientational ordering of CH4 molecules. At a low pressure of 3 GPa, the featureless probability distribution of C-H vector orientation (ϕ, θ) suggests disordered CH4 orientations (see Fig. 1d), which are consistent with the sphere-like trajectories of H atoms shown in Fig.1c. However, as pressure increases, the probability distributions of (ϕ, θ) are more localized (see Fig. 1d). At 60 GPa, four specific configurations of CH4 orientations can be recognized (see Supplementary Fig. 3). In each configuration, CH4 exhibits small-amplitude librational motions. Notably, the orientational ordering of CH4 molecules is accompanied by a sudden change in crystal axial ratios at 20 GPa (see Supplementary Fig. 4a). The theoretical observation is in good accordance with the previous findings based on diffraction experiment22. Hence, the lattice compression modifies the guest rotational dynamics and orientational ordering significantly. This offers the possibility to probe their roles in regulating heat transport.

Drastic reduction of thermal conductivity by evolving rotational dynamics

Following the aforementioned evolving CH4 rotations and orientations, the equilibrium molecular dynamics (EMD) method based on the Green-Kubo relation24,25,26 was used to compute the TC behavior of MH-III (see “Methods” section). Two different models for CH4, viz., an all-atom molecular model with the full degrees of freedom (DOFs) including orientations and rotations, and a point-mass atomic model with only translational DOF, were employed to clarify the unique influences of molecular guests on heat conduction. The interactions between the point-mass CH4 and H2O molecules were ensured to be consistent with those of the original all-atom model (see “Methods” section for the details of force fields). Surprisingly, even with the same host H2O framework, the TCs of two MH-III models exhibit significantly different pressure responses. At the same volume compression of about 36% (see Supplementary Fig. 4b), the TC of the all-atom model increases from 1.42 W m−1 K−1 at 3 GPa to 5.37 W m−1 K−1 at 60 GPa (see Fig. 2a). In comparison, the TC values and increasing rate of the point-mass model are remarkably higher, evolving from 1.68 W m−1 K−1 at 3 GPa to 13.75 W m−1 K−1 at 60 GPa. Such discrepancy is unlikely due to the differences in the interaction potentials of the two models since a higher TC is also predicted from other point-mass CH4 potentials, e.g. OPLS-UA27 (see Supplementary Fig. 5). As such, the observed almost three-fold TC reduction of the all-atom model at high pressure undoubtedly signifies the suppression effects of the molecular disorders, involving CH4 rotational dynamics, and/or “static” disordered CH4 orientations. To elucidate the intricate mechanisms, we further considered a fictitious MH-III model where CH4 rotations were removed (the torque of CH4 molecules was set to zero) with their disordered orientations retained. Interestingly, such a treatment yields significantly higher TC over the entire pressure range. For instance, the TC of the zero-torque model at 60 GPa was enhanced to 10.26 W m−1 K−1 by over 91% (see Fig. 2a), only slightly lower than that of the point-mass model. This unambiguously verifies that the dynamic disorders, i.e., CH4 rotations/librations govern the substantial TC reduction. More intriguingly, by carefully comparing the all-atom and zero-torque models, we identify that low-pressure disordered CH4 rotations only result in a limited decrease in TC ( ~ 17%). In contrast, the high-pressure CH4 librations trigger a more drastic decrease, suggesting that these restricted rotational dynamics of the guest molecules minimize TC more efficiently.

Fig. 2: Pressure-dependent total and partial thermal conductivities (TCs) of MH-III at 300 K.
figure 2

a The variation of total TC with pressure. The red dots represent the results of the point-mass model, and the black dots are those of the all-atom model. The gray dots show the TC of the fictitious model where the CH4 rotation is artificially removed by setting the torque to zero but disordered orientations remain. The inset is an enlarged view of the results of the all-atom model showing its nonlinear trend below 20 GPa. b The water-water (WW) partial TCs of the three MH-III models. c The water-methane (WM) partial TCs of the three MH-III models. The red, black, and gray open symbols in (b and c) represent the results of the point-mass, all-atom, and zero-torque models, respectively. The error bars in all these figures are determined from the standard deviation of five independent simulations. Source data are provided as a Source Data file.

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To understand how molecular disorders, especially the rotational DOFs of CH4 affect heat transport and lead to different TCs of the three MH-III models, we decomposed the total TC into the water-water (WW), methane-methane (MM), and water-methane (WM) terms28,29. This was realized by decomposing the total heat current into the partitions of water and methane subsystems and then evaluating their auto (WW and MM) or cross-correlations (WM) using the Green-Kubo relation (see “Methods” section). It is worthwhile to emphasize that the resultant partial heat conduction fundamentally differs from that in a monocomponent phase; for instance, in contrast to a pure ice phase, the WW term in MH-III is influenced by additional scattering effects from methane dynamics. Beyond these scatterings, heat can also be transferred between vibrating water and methane subsystems, which is characterized by the WM cross-term and definitely will be affected by methane dynamics as well. The detailed physical interpretation and validation of our TC decomposition are given in Supplementary Note 2. From these decompositions, we find that the MM terms of the all-atom, zero-torque, and point-mass models are almost identical (see Supplementary Fig. 6). However, the WW and WM terms differ significantly (see Fig. 2b and c). Compared to the zero-torque and point-mass models, the WW heat conduction in the all-atom model is significantly suppressed due to the presence of the additional CH4 rotational dynamics, and such suppression is amplified with increasing pressure (see Fig. 2b). Likewise, the WM cross term of the all-atom model is also dramatically lower than the other two models over the entire pressure range (see Fig. 2c). This manifests that the rotational DOFs of the guest suppress the TC through inhibiting the heat transfer within the host water lattice, as well as between host and guest.

Besides, we also notice the contrasting pressure dependence of the TC between the three MH-III models. Specifically, both the point-mass and zero-torque models show an almost linear correlation throughout the entire pressure range (see Fig. 2a), similar to the behavior of most solid materials30. In contrast, the TC of the all-atom model follows a nonlinear concave function in the low-pressure region between 3-20 GPa (see the inset of Fig. 2a), and evolves into a linear trend at higher pressures. Recalling the abovementioned two-stage CH4 rotational dynamics with a transition at 20 GPa, we reason that the unique rotational behavior of guest molecules plays a vital role. Actually, such two-stage behavior stems from the similar nonlinear trends of the partial WW and WM terms (see Supplementary Fig. 7), which vanish in both the point-mass model and artificial zero-torque model (see Fig. 2b and c). Hence, the evolving guest rotational dynamics rather than molecular orientations dominate the pressure dependency of TC. The low-pressure TC below the linear trend in the all-atom model suggests additional suppression effects of disordered CH4 rotations (see below).

Evidence of rotor-lattice coupling

The reduced thermal transport and peculiar nonlinear behavior of WM and WW terms indicate the intensive coupling between CH4 rotational dynamics and H2O lattice vibrations, which is known as the rotor-lattice coupling7. The nature of the coupling can be determined from the analysis of vibrational density of states (VDOS). We compare the partial VDOS of H2O and CH4 molecules to those of their center-of-mass (COM) counterparts to identify individual rotational/librational contribution (Fig. 3a, b), whose frequency ranges are consistent with those of the rotational density of states (RDOS) computed from the angular velocity correlation functions (see Fig. 3c). From the calculated VDOS and RDOS, we find that the CH4 rotational/librational modes are always mixed with its translational modes, resulting in a broad unimodal distribution (Fig. 3b). In particular, the translation-rotation modes of CH4 at 3 GPa overlap with the H2O translational modes in the frequency range of 0–10 THz (Fig. 3a), hinting potential couplings between guest rotations and host translations. The translation-rotation CH4 bands are noticeably broadened and hardened (shift to higher frequencies) with increasing pressure (see Fig. 3b). At 60 GPa, the broad CH4 rotational components (i.e., librations) extend over both the H2O translation and libration regions. Consequently, the system has entered a stronger coupling regime where host and guest dynamics are now fully correlated.

Fig. 3: The rotor-lattice coupling in MH-III.
figure 3

a, b The vibrational density of states (VDOS) of (a) host H2O lattices and (b) guest CH4 molecules at different pressures. The dashed lines denote the VDOS profiles of the center-of-mass (COM) of the molecules showing only the translational contribution; the resulting differences between the solid and dashed lines expose the rotational/librational contribution. There are additional CH4 bending, rocking, and stretching modes with extremely high frequencies (> 40 THz). Their contributions to the total TC are minor (see Supplementary Note 3 and Supplementary Fig. 9). c The rotational density of states (RDOS) of CH4 molecules. d The first-order Legendre reorientational correlation functions (RCFs) C1(t) of CH4 molecules under the NVT (constant volume and temperature) ensemble at 3 GPa (blue) and 60 GPa (red). The black lines denote the average of all CH4 molecules in the simulation box. The gray line shows the oscillations of the individual RCF curve at 3 GPa. e The average first-order (solid lines) and second-order (dashed lines) RCFs Cn (t) of CH4 molecules at different pressures. f The average first-order CH4-RCFs at 3 GPa (blue) and 60 GPa (red) with the vibrating H2O lattice (solid lines) and the fixed one (dash-dotted lines). The curves are plotted in the logarithmic scale to clarify the non-exponential behavior. Source data are provided as a Source Data file.

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The existence of rotor-lattice coupling can be further verified by analyzing the Legendre reorientational correlation function (RCF) of CH4 \({C}_{n}(t)=\left\langle {P}_{n}\left({{{\bf{u}}}}\left(0\right)\cdot {{{\bf{u}}}}\left(t\right)\right)\right\rangle,n={{\mathrm{1,2}}}\), in which u is the unit vector of the C–H bond, and Pn is the Legendre polynomial [P1(x) = x, P2(x) = 0.5(3x2  − 1)]31,32. Despite the rapid decay to zero of the RCFs indicating fast reorientations, the CH4 molecules at 3 GPa are not free rotors, as indicated by the significant oscillations in the individual RCF curves (see Fig. 3d). Besides, the average RCFs at 3 GPa are far from exponential and cannot be well described by the Debye reorientation diffusive model33 (see Fig. 3e and f). This is supported by the fact that the relaxation times τ1 = 0.2357 ps and τ2 = 0.1190 ps obtained from the integrations of the first and second-order RCFs at 3 GPa do not obey the ideal ratio of 3:1 (the Hubbard relation34). Hence, the CH4 rotations exhibit non-diffusive dynamics even at low pressures. Such a characteristic may originate from the rotor-lattice coupling or the coupling between CH4 molecules. To distinguish the two effects, we calculated the CH4-RCFs with the H2O lattice fixed in its equilibrium position. The comparison of resultant RCF curves against those from the original system featuring a vibrating H2O lattice confirms the impact of rotor-lattice coupling on the reorientation dynamics of CH4 (see Fig. 3f). Note that the CH4 reorientations are strongly hindered upon lattice compression, as revealed by the rather sluggish decay of RCFs (see Fig. 3e). This is accompanied by the strengthening of the rotor-lattice coupling with decreasing water-methane intermolecular distance7 (see Supplementary Fig. 8). This kind of enhanced coupling has been reported in other molecular compounds such as solid methane35 and ammonia36.

Discussion

The rotational dynamics of encapsulated disordered molecular guests greatly suppress heat transport through rotor-lattice coupling. The TC reduction can be explained by the phonon theory. Since there is less difference in the phonon group velocities between the different MH-III models (see Supplementary Fig. 10), substantially shorter phonon lifetimes of the all-atom model are expected (see the fast convergence of the integration of the heat current autocorrelation function within several picoseconds in Supplementary Fig. 11). As the CH4 rotation/librations fall in the same frequency range as the host H2O vibrations (Fig. 3a and b), these localized molecular modes (see the flat phonon bands in Supplementary Fig. 12) can contribute to TC reduction by scattering phonons. Early studies on doped alkali halides have identified the mixing of lattice vibrations with the localized librational levels of doped CN- impurities37,38. The mixing is responsible for the resonant scattering of heat-carrying phonons39,40. A similar mechanism has been applied to explain the TC plateau in the orientational glass KBr-KCN41 and anomalous low TC of clathrate hydrates42. Under this circumstance, the more efficient TC reduction by CH4 librations at increasing pressures (e.g., at 60 GPa, see Fig. 2a) can be attributed to stronger resonant scatterings upon the intensified rotor-lattice coupling.

Another important finding reported here is that the weak host-guest coupling at low pressures enables CH4-disordered rotations that increase lattice anharmonicity. The calculated potential energy surface at 3 GPa shows that CH4 must overcome several energy barriers to complete a full rotation, even for the symmetric mode about the C–H axis (Fig. 4a). For other asymmetric modes, for example, the rotation about the axis parallel to the a-axis, the significant deviation of the potential energy from the quadratic fittings around the energy minimum (see Fig. 4b) signifies anharmonic host-guest interactions. Therefore, disordered rotational motions of CH4 molecules are expected to couple anharmonically with H2O lattice dynamics, thus opening a new channel for phonon scattering. Consequently, the heat transport between the host lattice and guest molecules (the WM term), as well as through water lattices (the WW term), is damped. This results in an extra effect to reduce the TC of the all-atom model at low pressures, as demonstrated by the nonlinear behavior in Fig. 2a. Upon pressurization, the rotor scattering is diluted with progressively hindered CH4 rotations. The quasi-harmonic librational motions (see the inset of Fig. 4a) under stronger host-guest coupling then result in the expected linear pressure dependence of TC like the atomic system (see the high-pressure region of Fig. 2a). Accordingly, at high pressures (> 20 GPa), the resonant scattering mechanism dominates the TC reduction from molecular guests.

Fig. 4: The anharmonicity and phonon localization in MH-III.
figure 4

a, b The potential energy surface of the CH4 molecule at 3 GPa with respect to its rotation about different axes: (a) C–H vector; (b) parallel to the a-axis. The dashed lines are quadratic harmonic fittings at energy minimum. The inset in (a) shows the potential energy surface at 60 GPa when the CH4 molecule does quasi-harmonic librational motions about the C–H vector. c, d Phonon participation ratio (PPR) spectra for the all-atom model (black lines), the point-mass model (red lines), and the fictitious zero-torque model (gray lines) at (c) 3 GPa and (d) 60 GPa. The dashed lines mark PPR values = 0.2 and 0.4 for comparisons. Source data are provided as a Source Data file.

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Beyond the phonon scatterings caused by dynamic rotations and librations, it is also acknowledged that the static disordered orientations of guest molecules may impede the transport of heat-carrying phonons. To reveal the mechanism, we computed the phonon participation ratio (PPR), an indicator for quantitative characterization of phonon localization in disordered materials43, through the molecular dynamics method considering temperature and all orders of anharmonic effects44. A higher PPR indicates less localization and more atoms participating in heat conduction, and consequently, higher TC. As expected, the PPR of the zero-torque model is lower than that of the point-mass model (see Fig. 4c, d) due to the disordered CH4 orientations that break the long-range periodicity. This scenario is not unlike the cases in amorphous materials45. Unexpectedly, the dynamic disorders from guest rotations/librations lead to even worse phonon localization, as demonstrated by the extremely low PPR of around 0.2–0.4 in the all-atom model (black lines in Fig. 4c and d). This indicates that the motions of guest molecules significantly disrupt the overall dynamics of the lattice, thereby restricting heat conduction. The disturbance of lattice dynamics can be induced by the low-pressure disordered CH4 rotations. At high pressures, the spatial inhomogeneity of the CH4 reorientation dynamics should be taken into consideration. As shown in Fig. 3d, in addition to the slow decay of the RCFs of most CH4 molecules with relaxation times longer than 10 ps (a sign of hindered librations with small displacements), about 17% of the CH4 molecules execute faster decay with shorter relaxation times (1.2-6.4 ps), indicating less restricted environments. The observed glass-like reorientation behavior has also been identified in hybrid perovskites24 and mixed cyanide crystals38. It, combined with strong rotor-lattice couplings, can highly disrupt lattice vibrations and lead to more prominent phonon localization of MH-III under high pressure (see the comparison of PPR of the all-atom model at 3 GPa and 60 GPa shown in Fig. 4c and d).

Here, we demonstrate that the rotational dynamics of guest molecules can inhibit the heat conduction of MH-III via various mechanisms. This raises an intriguing question: can a similar TC reduction be applied to other compounds with distinct structural characteristics? To answer this question, we performed additional calculations on two representative compounds, i.e., a graphene-fullerene derivative (C60CH2) heterostructure with the C60CH2 molecules between two-dimensional (2D) graphene layers exhibiting hindered rotations, and the structure-I CH4 hydrate (MH-I) where CH4 molecules can freely rotate within the three-dimensional (3D) cage-like host lattice (See Supplementary Note 4 and Supplementary Fig. 13 for the details of relevant atomic models and force fields). In the former system, only the in-plane TC was evaluated. Interestingly, by artificially freezing guest rotations (C60CH2 or CH4), we observed significantly increased TCs compared to the original systems with molecular rotors in both compounds (see Fig. 5), i.e., from 56.63 W m−1 K−1 to 79.99 W m−1 K−1 for the layered graphene-C60CH2 heterostructure at 300 K and 0 GPa, and from 0.92 W m−1 K−1 to 1.10 W m−1 K−1 for the MH-I at 300 K and 1.0 GPa (maximum pressure for structural stability). Results from these calculations and the MH-III system indeed highlight the universal nature of TC reduction by guest rotational dynamics, regardless of the crystalline structures (1D channels in MH-III, 2D layers in graphene-C60CH2 heterostructure, and 3D cages in MH-I, see the insets of Fig. 5). More essentially, it is noteworthy that the free CH4 rotations in MH-I only contribute to a limited TC suppression (about 17%), which is most possibly due to the weak rotor-lattice coupling in much open 3D water cages. This echoes the inefficient reduction effects of rotating CH4 in MH-III and contrasts with the more than two-fold TC reduction by librating CH4 upon the intensified rotor-lattice coupling (see Fig. 2a). As such, we anticipate a strong correlation between TC changes and rotor-lattice coupling strength, which can vary in different crystalline topologies and components.

Fig. 5: Thermal conductivity (TC) reductions from guest rotational dynamics in representative compounds.
figure 5

MH-III possesses the 1D nano-channels filled by rotational CH4 molecules; the graphene-C60CH2 heterostructure has the 2D layer structure where C60CH2 molecules exhibit hindered rotations between graphene layers; MH-I consists of the 3D water cages enclosing freely rotating CH4 molecules. In all cases, besides the original models with rotating guests, the TCs of the artificial zero-torque models with frozen guest (CH4 or C60CH2) rotations are also evaluated. The calculations are carried out at 300 K and 0 GPa for the graphene-C60CH2 heterostructure and at 300 K and 1.0 GPa for the MH-I. The TC data of the MH-III at 300 K and 60 GPa are taken and compared with the other two compounds. All error bars in the figure are determined from the standard deviation of five independent simulations. Source data are provided as a Source Data file.

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In summary, we applied pressure to manipulate guest molecular disorders in MH-III and studied their effects on heat conduction. The EMD simulations combined with fictitious models reveal that the disordered rotational dynamics of guest molecules coupled with host lattices can predominately suppress the TC of MH-III when compared to their atomic counterparts. The reduction effects vary upon evolving rotating states, from almost free rotations inducing lattice anharmonicity and the non-linear pressure-dependent TC, to highly hindered librations triggering more resonant scattering and localizations of phonons. Importantly, we also verify the generality of TC reduction from guest rotational dynamics in other materials with different structural configurations. Yet like MH-III, the overall TC changes should be controlled by the rotor-lattice coupling strength. These findings highlight the strong correlations between guest rotational dynamics, the strength of rotor-lattice coupling, and heat conduction, offering an avenue for TC modulation. As such, one may minimize or regulate heat conduction by constructing hybrid systems with tailored molecular rotors and host-guest coupling. In practical scenarios, this may be realized by imposing the so-called “chemical pressure” on crystalline lattices (e.g., via chemical substitution and/or interface constraint) or engineering molecular constituents and structures.

Methods

Force fields

In all simulations, the four-point transferable intermolecular potential (TIP4P)46 was employed for the interactions between water molecules. In the all-atom model, the all-atom optimized potentials for liquid simulations (OPLS-AA)47 were used for methane molecules. It is well known that the accurate description of host-guest interactions is essential to simulate the physical properties of host-guest compounds48. So an ab initio atomic site-site potential from Sun and Duan49 was adopted for water-methane interactions. Previous work has proven that the combination of the above potentials accurately reproduces the phase equilibria conditions, vibrational dynamics, and experimental TC of the methane clathrate hydrate over a wide temperature-pressure range28,29,49,50. In this work, we found that these potentials could also accurately describe the evolution of guest vibrations with pressure, suggesting their applicability to simulating the heat transport properties of MH-III. In the point-mass model, the interactions between H2O molecules and point-mass CH4 should agree with those in the all-atom model, so the ab initio potential data from Sun and Duan49 were further fitted using a 12-6 Lennard-Jones (LJ) potential to describe the interactions between the single-point CH4 and the oxygen atom of H2O molecules. Such an LJ potential predicts lattice parameters close to those of the all-atom model (see Supplementary Fig. 4c). Besides, the deviation for the number-average water-methane potential energy per methane molecule between the two models is less than 2% (52.90 ± 0.18 kcal/mol for the point-mass model and 51.86 ± 0.15 kcal/mol for the all-atom model).

Thermal conductivity calculations

All simulations were carried out using the Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package51, with a time step of 0.5 fs. The pressure-dependent TC of MH-III was computed using EMD simulations with the Green-Kubo relation. Before TC calculation, the initial structure was relaxed under the NPT (constant pressure and temperature), NVT (constant volume and temperature), and NVE (constant volume and energy) ensembles, respectively. Then the heat current vector J of the simulation system was calculated. Its expression is defined as

$${{{\bf{J}}}}={\sum}_{i=1}^{N}{E}_{i}{{{{\bf{v}}}}}_{i}-{\sum}_{i=1}^{N}{{{{\bf{S}}}}}_{i}{{{{\bf{v}}}}}_{i}-{\sum}_{v=1}^{2}{h}_{v}{\sum}_{k}^{{N}_{v}}{{{{\bf{v}}}}}_{k},$$
(1)

where \({E}_{i}\), \({{{{\bf{v}}}}}_{i}\), and \({{{{\bf{S}}}}}_{i}\) are the total energy, velocity vector, and stress tensor of atom i, \({h}_{v}\) is the average enthalpy per molecule of species \(v\), \({{{{\bf{v}}}}}_{k}\) is the velocity of molecule \(k\), \(N\) is the number of atoms, and \({N}_{v}\) is the number of molecules of species \(v\), respectively. Particularly, when evaluating \({{{{\bf{S}}}}}_{i}\), we considered the contributions of pairwise, bond, angle, long-range electrostatic interactions, and the internal constraint forces to atom assembles to account for the rigid body dynamics. We notice that an alternative expression for heat current, considering both the translational and rotational momenta and energies of whole rigid molecules, has been proposed previously52,53 (see Supplementary Note 5). This heat current expression can be regarded as the rewritten version of Eq. (1); the latter has implicitly involved the rotational contributions of individual molecules to heat current using atomic forces and velocities. Upon the defined heat current using Eq. (1), the TC of MH-III was evaluated from the integration of heat current autocorrelation function (HCACF) through the expression below,

$${{\rm{TC}}}=\frac{1}{3V{{{{\rm{k}}}}}_{{{{\rm{B}}}}}{T}^{2}}{\int }_{0}^{\infty }\left\langle {{{\bf{J}}}}\left(t\right)\cdot {{{\bf{J}}}}\left(0\right)\right\rangle {{{\rm{d}}}}t,$$
(2)

where \({{{{\rm{k}}}}}_{{{{\rm{B}}}}}\) is the Boltzmann constant, T and V are the temperature and volume of the ensemble, J(t) and J(0) are the heat current vectors at time t and time origin, and the angular bracket denotes the time averaging during simulations, respectively. Note that one could evaluate the anisotropic heat conduction by considering direction-dependent heat currents in Eq. (2). Nevertheless, as we found only minor anisotropy of TC of MH-III (see Supplementary Fig. 14), the final TC results were the average of the values along three directions. The autocorrelation period of HCACF was selected as 100 ps, which is sufficient to get converged TC values. The HCACF was averaged from 20 short parts in 2 ns. The final TC was the average from five individual runs with different initial velocities. We also checked the size effect of the simulation box and found the 5 × 3 × 3 supercells are sufficiently large for TC calculations of MH-III (see Supplementary Fig. 15). Using the nonequilibrium molecular dynamics (NEMD) method as the benchmark, we have also validated the accuracy of our employed heat current and Green-Kubo calculations (See Supplementary Note 5 and Supplementary Fig. 16).

The total heat current J includes two parts, that is, the part contributed by water molecules JW and the part by methane molecules JM. So the total TC can be divided into three terms, i.e., the water-water (WW) term, methane-methane (MM) term, and water-methane (WM) term28,29. The first two terms were calculated from the integration of the autocorrelation function of partial heat current, and the last term was computed by integrating the cross-correlation function using the expression below

$${{\rm{TC}} }_{{{{\rm{WM}}}}}=\frac{2}{3V{{{{\rm{k}}}}}_{{{{\rm{B}}}}}{T}^{2}}{\int }_{0}^{\infty }\left\langle {{{{\bf{J}}}}}_{{{{\rm{W}}}}}\left(t\right)\cdot {{{{\bf{J}}}}}_{{{{\rm{M}}}}}\left(0\right)\right\rangle {{{\rm{d}}}}t.$$
(3)

A detailed physical interpretation of this TC decomposition can be found in Supplementary Note 2. We found that this decomposition is essentially true since the deviation between the sum of three partial terms and total TC is less than 1% (see Supplementary Table 1).

Particularly, a fictitious system with methane molecular rotations/librations removed was simulated. In this system, the structure was firstly relaxed at 300 K and target pressure, and then the torque of methane molecules was artificially set to zero with orientations remaining; therein we calculated TC without the effects of guest rotations. We noticed the good conservations of energy and momentum of this zero-torque model (see Supplementary Fig. 17), which is thereby effective in helping us understand the effects of rotational dynamics on heat conduction.