Orientational ordering of icosahedra in solid C60

H2O inside the fullerene C60: Inelastic neutron scattering spectrum from rigorous quantum calculations

We present a methodology that, for the first time, allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a triatomic molecule in a nanoscale cavity, in this case, H₂O inside the fullerene C₆₀. Both moieties are taken to be rigid. Our treatment incorporates the quantum six-dimensional translation-rotation (TR) wave functions of the encapsulated H₂O, which serve as the spatial parts of the initial and final states of the INS transitions. As a result, the simulated INS spectra reflect the coupled TR dynamics of the nanoconfined guest molecule. They also exhibit the features arising from symmetry breaking observed for solid H₂O@C₆₀ at low temperatures. Utilizing this methodology, we compute the INS spectra of H₂O@C₆₀ for two incident neutron wavelengths and compare them with the corresponding experimental spectra. Good overall agreement is found, and the calculated spectra provide valuable additional insights.

Effects of symmetry breaking on the translation-rotation eigenstates of H2, HF, and H2O inside the fullerene C60

Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

Perspective: Accurate treatment of the quantum dynamics of light molecules inside fullerene cages: Translation-rotation states, spectroscopy, and symmetry breaking

In this perspective, I review the current status of the theoretical investigations of the quantum translation-rotation (TR) dynamics and spectroscopy of light molecules encapsulated inside fullerenes, mostly C₆₀ and C₇₀. The methodologies developed in the past decade allow accurate quantum calculations of the TR eigenstates of one and two nanoconfined molecules and have led to deep insights into the nature of the underlying dynamics. Combining these bound-state methodologies with the formalism of inelastic neutron scattering (INS) has resulted in the novel and powerful approach for the quantum calculation of the INS spectra of a diatomic molecule in a nanocavity with an arbitrary geometry. These simulations have not only become indispensable for the interpretation and assignment of the experimental spectra but are also behind the surprising discovery of the INS selection rule for diatomics in near-spherical nanocavities. Promising directions for future research are discussed.

Explaining the symmetry breaking observed in the endofullerenes H2@C60, HF@C60, and H2O@C60

Symmetry breaking has been recently observed in the endofullerenes M@C₆₀ (M = H₂, HF, H₂O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H₂, ortho-H₂O and the j = 1 level of HF.

Does rotational melting make molecular crystal surfaces more slippery?

The surface of a crystal made of roughly spherical molecules exposes, above its bulk rotational phase transition at T = Tr, a carpet of freely rotating molecules, possibly functioning as "nanobearings" in sliding friction. We explored by extensive molecular dynamics simulations the frictional and adhesion changes experienced by a sliding C60 flake on the surface of the prototype system C60 fullerite. At fixed flake orientation both quantities exhibit only a modest frictional drop of order 20% across the transition. However, adhesion and friction drop by a factor of ∼2 as the flake breaks its perfect angular alignment with the C60 surface lattice suggesting an entropy-driven aligned-misaligned switch during pull-off at Tr. The results can be of relevance for sliding Kr islands, where very little frictional differences were observed at Tr, but also to the sliding of C60-coated tip, where a remarkable factor ∼2 drop has been reported.

Orientational ordering in solid C60 fullerene-cubane

We study the structure and phase behavior of fullerene-cubane C(60) x C(8)H(8) by Monte Carlo simulation. Using a simple potential model capturing the icosahedral and cubic symmetries of its molecular constituents, we reproduce the experimentally observed phase transition from a cubic to an orthorhombic crystal lattice and the accompanying rotational freezing of the C(60) molecules. We elaborate a scheme to identify the low-temperature orientations of individual molecules and to detect a pattern of orientational ordering similar to the arrangement of C(60) molecules in solid C(60). Our configuration of orientations supports a doubled periodicity along one of the crystal axes.

Study on the intermolecular interaction of C60 and simulations on the orientational properties of C60 in crystals

We developed the new intermolecular interaction model of C(60) with the quantitative accuracy for the molecular orientational properties in crystals. The energy difference (DeltaE) and the activation barrier (E(barrier)) between the two stable orientations (P and H orientations) in crystals are in the values of +14.7 and +260 meV in our model, respectively; these values are in fairly good agreement with the experimental values (DeltaE approximately +11 meV, E(barrier)=+235-+290 meV in experiments). The relaxation calculation for C(60) crystals using our model revealed that there is the reversal of the stable orientations between the P and H orientations under the high H-orientation occupancy (p(H)) in crystals, when p(H)>0.83, DeltaE<0. From the molecular dynamics calculations for C(60) crystals using our model, it is found that the phase transition is induced at T(C)=200-260 K, which is consistent with the experimental value of 260 K. Immediately below T(C), we found a great variety of molecular rotational jumps involving that between the P and H orientations every about 10(-9) s due to the thermal activation. In the high temperature phase (>T(C)), all molecules rotate irregularly like in Brownian motion involving the rotational "slumber" for approximately 10(-12)-10(-11) s.

Friction and Adhesion between C60 Single Crystal Surfaces and AFM Tips: Effects of the Orientational Phase Transition

We have investigated the nanotribological properties of C60 single crystal (111) and (100) surfaces around its orientational order-disorder phase transition temperature, approximately 260 K, by atomic force microscopy and frictional force microscopy (AFM/FFM) in high vacuum. Results show that for both surfaces across the phase transition temperature, the friction force and the adhesive force between a C60 coated AFM tip and the C60 crystal surfaces exhibit discontinuous behavior. The friction force within the applied external load range in the low temperature phase is significantly larger than that in the high temperature phase, with no obvious change in the slope of the friction force curves (the friction coefficient) in the low and high temperature phases. The abrupt change in friction was found to be caused mainly by the abrupt change in adhesion, which, in turn, can be qualitatively understood through changes in the van der Waals interaction and the short-range Coulomb interaction associated with the structural changes across the phase transition. Compared to most other degrees of freedom, the rotation of C60 molecules was found to have little effect on friction and is an ineffective energy dissipation channel.

Mutual orientation of two C60 molecules: An ab initio study

The orientational dependence of the interaction between two C(60) molecules is investigated using ab initio calculations. The binding energy, computed within density functional theory in the local density approximation, is substantially smaller than the one derived from the experimental heat of sublimation of fullerite, which calls into question the nature of inter-C(60) bonding. According to our calculations, the experimentally observed orientation with a C(60) presenting a hexagon-hexagon bond to a pentagonal face of the other C(60) is not really favored. Some other configurations are very close in energy and in fact a pentagon facing a pentagon and a hexagon facing a hexagon-hexagon bond are found to be slightly more favorable situations. Our results are compared to previous ones obtained either with previous empirical intermolecular potentials or to existing ab initio studies of crystalline C(60). In addition, the stacking of C(60) in a crystal and in a decahedral (C(60))(7) cluster is discussed.

Superexchange and electron correlations in alkali fullerides AC60, A=K, Rb, Cs

Superexchange interactions in alkali fullerides AC(60) are derived for C(60) molecular ions separated by interstitial alkali-metal ions. We use a multiconfiguration approach which comprises the lowest molecular orbital states of the C(60) molecule and the excited s and d states of the alkali-metal atom A. Interactions are described by the valence bond (Heitler-London) method for a complex (C(60)-A-C(60))(-) with two valence electrons. The electronic charge transfer between the alkali-metal atom and a neighboring C(60) molecule is not complete. The occupation probability of excited d and s states of the alkali atom is not negligible. In correspondence with the relative positions of the C(60) molecules and A atoms in the polymer crystal, we consider 180 degrees and 90 degrees (angle) superexchange pathways. For the former case the ground state is found to be a spin singlet separated from a triplet at approximately 20 K. For T<20 K there appear strong spin correlations for the 180 degrees superexchange pathway. The results are related to spin lattice relaxation experiments on CsC(60) in the polymerized and in the quenched cubic phase.

Mechanisms and rates of interstitial H2 diffusion in crystalline C60

Parallel replica dynamics and minimum energy path calculations have been used to study the diffusion mechanisms of H2 in fcc C60. Isolated interstitial H2 molecules bind preferentially in the lattice octahedral (O) sites and diffuse by hopping between O and tetrahedral sites. The simulations reveal an unexpected mechanism involving an H2 molecule diffusing through an already occupied O site, creating an H2 dimer, with a lower activation barrier than diffusion into an empty O site. Kinetic Monte Carlo simulations of a lattice model based on these mechanisms indicate that events involving dimers greatly enhance the self-diffusion rates of interstitial H2 in fcc C60.

Two-stage rotational disordering of a molecular crystal surface: C60

We propose a two-stage mechanism for the rotational surface disordering phase transition of a molecular crystal, as realized in C60 fullerite. Our study, based on Monte Carlo simulations, uncovers the existence of a new intermediate regime, between a low-temperature ordered (2x2) state, and a high-temperature (1x1) disordered phase. In the intermediate regime there is partial disorder, strongest for a subset of particularly frustrated surface molecules. These concepts and calculations provide a coherent understanding of experimental observations, with possible extension to other molecular crystal surfaces.