Interactions between a water molecule and C60 in the endohedral fullerene H2O@C60.

A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bacic et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.

Visualizing the orientational dependence of an intermolecular potential.

Scanning probe microscopy can now be used to map the properties of single molecules with intramolecular precision by functionalization of the apex of the scanning probe tip with a single atom or molecule. Here we report on the mapping of the three-dimensional potential between fullerene (C60) molecules in different relative orientations, with sub-Angstrom resolution, using dynamic force microscopy (DFM). We introduce a visualization method which is capable of directly imaging the variation in equilibrium binding energy of different molecular orientations. We model the interaction using both a simple approach based around analytical Lennard-Jones potentials, and with dispersion-force-corrected density functional theory (DFT), and show that the positional variation in the binding energy between the molecules is dominated by the onset of repulsive interactions. Our modelling suggests that variations in the dispersion interaction are masked by repulsive interactions even at displacements significantly larger than the equilibrium intermolecular separation.

The effect of cooperative Jahn-Teller interactions on C60(-) anions.

Singly charged buckminsterfullerene anions, C60(-), are subject to a strong intramolecular [Formula: see text] Jahn-Teller (JT) effect. When such ions interact with other C60(-) ions in a solid through a cooperative JT effect, they will be subject to an additional interaction. There are a number of different mechanisms that can cause this interaction. However, in the molecular field approximation, all can be modelled phenomenologically in terms of a symmetry-lowering interaction written in terms of a linear combination of electronic operators for the h modes involved in the intramolecular JT effect. We will consider the combined effect of this distortion and the intramolecular JT effect. We will analyse the lowest adiabatic potential energy surface, and calculate the energies of the resultant vibronic states. The results are shown to have a complicated dependence on the particular combination of h modes chosen, and the energies of the resultant vibronic states cannot easily be deduced from the form of the potential alone.

Regulatory region single nucleotide polymorphisms of the apolipoprotein E gene and the rate of cognitive decline in Alzheimer's disease.

The aim of this study was to investigate whether single nucleotide polymorphisms (SNPs) in the regulatory regions of the apolipoprotein E (APOE) gene modify the well-established epsilon4-associated risk for Alzheimer's disease (AD). Sequencing of the APOE gene regulatory regions revealed four previously reported promoter SNPs and one novel SNP in the previously described macrophage enhancer (ME.1). In addition, we also studied the two classic allelic missense SNPs that define epsilon2/epsilon3/epsilon4 status in a case-control association study. Analysis of pair-wise linkage disequilibrium (LD) of the five regulatory region SNPs with classic APOE SNPs revealed a previously unreported 7 kb LD block covering the entire APOE gene, part of the promoter and 3' enhancer region. We report here that in a case-control association study (N=719) of the seven SNPs, the genotype at codon 112 captures all the information required to assess disease risk. To explore correlations with quantitative traits, 169 patients were studied in whom rates of cognitive decline were available. In addition to the epsilon4 allele, two regulatory region SNPs were associated with the rate of cognitive decline in AD patients. This study highlights the effect of APOE gene variation on risk of AD and rate of cognitive decline and demonstrates that a single SNP, which confers epsilon4 status, captures all of the risk of developing AD but two SNPs in the regulatory region may affect the rate of cognitive decline in AD patients.

A complete nearest-neighbor force field model for C60.

A force field model is developed for C(60) that features 13 force constants representing all interactions between nearest-neighboring atoms. The model is compared with, and tested against, other force field models in the literature. Force constants for C(60) are then deduced by fitting the model to the 14 known optically accessible vibrational frequencies of the molecule. Finally, the model is fitted to two existing theoretical calculations of the complete vibrational spectrum of C(60). Fair agreement is obtained with the theoretical calculations, implying that interactions with atoms other than nearest neighbors are small.