Experimental determination of the interaction potential between a helium atom and the interior surface of a C60 fullerene molecule

Targeting spectroscopic accuracy for dispersion bound systems from ab initio techniques: Translational eigenstates of Ne@C70

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Synthesis and Properties of the Helium Clathrate and Defect Perovskite [He2-x □ x ][CaNb]F6

The defect double perovskite [He2-x □ x ][CaNb]F6, with helium on its A-site, can be prepared by the insertion of helium into ReO3-type CaNbF6 at high pressure. Upon cooling from 300 to 100 K under 0.4 GPa helium, ∼60% of the A-sites become occupied. Helium uptake was quantified by both neutron powder diffraction and gas insertion and release measurements. After the conversion of gauge pressure to fugacity, the uptake of helium by CaNbF6 can be described by a Langmuir isotherm. The enthalpy of absorption for helium in [He2-x □ x ][CaNb]F6 is estimated to be ∼+3(1) kJ mol-1, implying that its formation is entropically favored. Helium is able to diffuse through the material on a time scale of minutes at temperatures down to ∼150 K but is trapped at 100 K and below. The insertion of helium into CaNbF6 reduces the magnitude of its negative thermal expansion, increases the bulk modulus, and modifies its phase behavior. On compressing pristine CaNbF6, at 50 and 100 K, a cubic (Fm3̅m) to rhombohedral (R3̅) phase transition was observed at <0.20 GPa. However, a helium-containing sample remained cubic at 0.4 GPa and 50 K. CaNbF6, compressed in helium at room temperature, remained cubic to >3.7 GPa, the limit of our X-ray diffraction measurements, in contrast to prior reports that upon compression in a nonpenetrating medium, a phase transition is detected at ∼0.4 GPa.

Terahertz Spectroscopy Unambiguously Determines the Orientation of Guest Water Molecules in a Structurally Elusive Metal-Organic Framework

Porous materials, particularly metal-organic frameworks (MOFs), hold great promise for advanced applications. MIL-53(Al) is an exceptionally well-studied MOF that exhibits a phase transition upon guest capture─in this case, water─resulting in a dramatic change in the pore volume. Despite extensive studies, the structure of the water-loaded narrow-pore phase, MIL-53(Al)-np, remains controversial, particularly with respect to the positions of the adsorbed water molecules. We use terahertz spectroscopy, coupled with powder X-ray diffraction and density functional theory simulations, to unambiguously resolve this controversy. We show that the low-frequency (<100 cm-1) vibrational spectrum depends on weak long-range forces that are extremely sensitive to the orientation of the adsorbed water molecules. This enables definitively determining the correct structure of MIL-53(Al)-np while highlighting the extreme sensitivity of terahertz spectroscopy to bulk structure, suggesting its potential as a robust complement to X-ray diffraction for precise characterization of host-guest complexes.

Squeezing formaldehyde into C60 fullerene

The cavity inside fullerene C60 provides a highly symmetric and inert environment for housing atoms and small molecules. Here we report the encapsulation of formaldehyde inside C60 by molecular surgery, yielding the supermolecular complex CH2O@C60, despite the 4.4 Å van der Waals length of CH2O exceeding the 3.7 Å internal diameter of C60. The presence of CH2O significantly reduces the cage HOMO-LUMO gap. Nuclear spin-spin couplings are observed between the fullerene host and the formaldehyde guest. The rapid spin-lattice relaxation of the formaldehyde 13C nuclei is attributed to a dominant spin-rotation mechanism. Despite being squeezed so tightly, the encapsulated formaldehyde molecules rotate freely about their long axes even at cryogenic temperatures, allowing observation of the ortho-to-para spin isomer conversion by infrared spectroscopy. The particle in a box nature of the system is demonstrated by the observation of two quantised translational modes in the cryogenic THz spectra.

Translational eigenstates of He@C60 from four-dimensional ab initio potential energy surfaces interpolated using Gaussian process regression

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Dual modification to stabilize Non-IPR C72 fullerene: A new theoretical strategy

The stabilization of non-IPR fullerenes for their isolation and characterization is an area of recent interest. In the present study, we have explored the stabilization techniques of C₇₂ isomers via endo and exo-modifications and finally approached dual modification. A total of four isomers of C₇₂ have been considered in this study; among them, one is IPR derivative (1), and the rest are non-IPR derivatives with one (2) and two (3 and 4) fused pentagon rings. First, we have studied the endohedral modification by encapsulating one and two La atoms in the C₇₂ cavity. Secondly, we have exohedrally modified the C₇₂ isomers via chlorination by adding four and eight chlorides, respectively. Our final approach is to study the dual modification, where we have implemented both endo exo-modifications together. This dual modification can be achieved in two ways: exo followed by endo and endo followed by exo. For each modification, the relative stability of every modified C₇₂ derivative has been checked by calculating the relative energy with respect to the most stable modified analogue. To find out whether these modifications are energetically feasible or not, we have calculated the binding energy of each modified C₇₂ isomer. The binding energy calculation reveals that the encapsulation and exo-modification techniques are good enough to stabilize the non-IPR C₇₂ derivatives. Moreover, the effectiveness of dual modification has also been established from the enhanced binding energy compared to either endo- or exo-modification. We have also studied the NPA charges on the encapsulated La atoms for each endo- and dual-modified C₇₂ derivative. Furthermore, the AIM study has also been perceived to find out the interaction between the La atom and the fullerene cages for both mono- and di-encapsulated fullerene derivatives and also between La-La centres for di-encapsulated derivatives. Overall, the present theoretical study will provide an idea about the stability of the modified C₇₂ derivatives, which will help the experimentalists to design new strategies for synthesizing modified non-IPR fullerene derivatives that have vast applications in the medicinal and industrial fields.

Synthesis of endohedral fullerenes by molecular surgery

Encapsulation of atoms or small molecules inside fullerenes provides a unique opportunity for study of the confined species in the isolated cavity, and the synthesis of closed C₆₀ or C₇₀ fullerenes with enclosed atoms or molecules has recently developed using the method of 'molecular surgery'; in which an open-cage intermediate fullerene is the host for encapsulation of a guest species, before repair of the cage opening. In this work we review the main methods for cage-opening and closure, and the achievements of molecular surgery to date.

Synthesis and 83Kr NMR spectroscopy of Kr@C60

Synthesis of Kr@C₆₀ is achieved by quantitative high-pressure encapsulation of the noble gas into an open-fullerene, and subsequent cage closure. Krypton is the largest noble gas entrapped in C₆₀ using 'molecular surgery' and Kr@C₆₀ is prepared with >99.4% incorporation of the endohedral atom, in ca. 4% yield from C₆₀. Encapsulation in C₆₀ causes a shift of the ⁸³Kr resonance by -39.5 ppm with respect to free ⁸³Kr in solution. The ⁸³Kr spin-lattice relaxation time T₁ is approximately 36 times longer for Kr encapsulated in C₆₀ than for free Kr in solution. This is the first characterisation of a stable Kr compound by ⁸³Kr NMR.

Terahertz spectroscopy of the helium endofullerene He@C60

We studied the quantized translational motion of single He atoms encapsulated in molecular cages by terahertz absorption. The temperature dependence of the THz absorption spectra of ³He@C₆₀ and ⁴He@C₆₀ crystal powder samples was measured between 5 and 220 K. At 5 K there is an absorption line at 96.8 cm^-1 (2.90 THz) in ³He@C₆₀ and at 81.4 cm (2.44 THz) in ⁴He@C₆₀, while additional absorption lines appear at higher temperature. An anharmonic spherical oscillator model with a displacement-induced dipole moment was used to model the absorption spectra. Potential energy terms with powers of two, four and six and induced dipole moment terms with powers one and three in the helium atom displacement from the fullerene cage center were sufficient to describe the experimental results. Excellent agreement is found between potential energy functions derived from measurements on the ³He and ⁴He isotopes. One absorption line corresponds to a three-quantum transition in ⁴He@C₆₀, allowed by the anharmonicity of the potential function and by the non-linearity of the dipole moment in He atom displacement. The potential energy function of icosahedral symmetry does not explain the fine structure observed in the low temperature spectra.

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.