We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H(2) in C(60) through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H(2) in the vibrationally excited nu=1 state. The PES is based on the three-site H(2)-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H(2) has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H(2)@C(60) to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H(2)-fullerene interaction afforded by the three-site H(2)-C pair potential. The same H(2)-C pair potential spectroscopically optimized for H(2)@C(60) was also used to construct the pairwise additive 5D PES of H(2) (nu=1) in C(70). This PES, because of the lower symmetry of C(70) (D(5h)) relative to that of C(60) (I(h)), exhibits pronounced anisotropy with respect to the direction of the translational motion of H(2) away from the cage center, unlike that of H(2) in C(60). As a result, the T-R energy level structure of H(2) in C(70) from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H(2) are all qualitatively different from those determined previously for H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008).

We examined temporal changes in macrofaunal α- and β-diversity over several spatial scales (within patches, among patches, across landscapes and across regions) in Long Island Sound on the northeast USA coast. Regional ε-diversity was estimated at 144 taxa, however γ-diversity fluctuated over time as did α- and β-diversity components. Based on additive partitioning, patch- and region-scale β-diversity components generally had the highest contributions to γ-diversity; lower percentages were found at within-patch and landscape scales. Multiplicative diversity partitioning indicated highest species turnover at within- and among patch scales. For all partition results, within-patch and patch-scale β-diversity increased sharply when hypoxia impacted benthic communities. Spatial variation in diversity components can be attributed to the collection of different patch types at varying spatial scales and their associated habitats across the benthic landscapes, as well as gradients in depth and other estuarine-scale characteristics. Temporal variation in diversity components across spatial scales may be related to seasonal changes in habitat heterogeneity, species population dynamics, and seasonal disturbances. Rare species were significant and temporally consistent components of macrofaunal diversity patterns over different spatial scales. Our findings agree with other marine and terrestrial studies that show diversity components vary significantly over different spatial scales and the importance of habitat/landscape heterogeneity in supporting diversity. However, our results indicate that the relative contributions of scale-specific β-diversity components can also change significantly over time. Thus, studies of diversity patterns across patches and landscapes based on data collected at one time, or assembled into a single data set from different times, may not capture the full suite of diversity patterns that occur over varying spatial scales and any time-specific determinants of those patterns. Many factors that shape and maintain sedimentary communities vary temporally, and appear to play an important role in determining and maintaining macrofaunal diversity over different spatial scales.

We report rigorous quantum three-dimensional calculations of highly excited intermolecular vibrational states of the van der Waals (vdW) complex phthalocyanine.He (Pc.He). The Pc molecule was treated as rigid and the intermolecular potential energy surface (IPES) was represented as a sum of atom-atom Lennard-Jones pair potentials. The IPES has four equivalent global minima on the diagonals of the square-shaped Pc, inside its five-membered rings, and four slightly shallower local minima between them, creating a distinctive corrugation pattern of the molecular nanosurface. The vdW vibrational states analyzed in this work extend to about two-thirds of the well depth of the IPES. For the assignment of the in-plane (xy) vdW vibrational excitations it was necessary to resort to two sets of quantum numbers, the Cartesian quantum numbers [nu(x), nu(y)] and the quantum numbers (v, l) of the 2D isotropic oscillator, depending on the nodal structure and the symmetry of the wave functions. The delocalization of the He atom parallel to the molecular surface is large already in the ground vdW state. It increases rapidly with the number of quanta in the in-plane vdW vibrations, with the maximum root-mean-square amplitudes Deltax and Deltay of about 7 au at the excitation energies around 40 cm(-1). The wave functions of the highly excited states tend to be delocalized over the entire nanosurface and often have a square shape, reflecting that of the substrate.