Shannon Entropy and Fisher Information from a Non-Born-Oppenheimer Perspective.

We study the Shannon entropy and the Fisher information in a non-Born-Oppenheimer (nBO) regime, where these quantities are constructed from one-particle densities obtained from an exact nBO analytic wave function for a Coulomb-Hooke model of a four-particle system. This model consists of two electrons and two protons with Coulombic interactions between like particles and Hookean interactions otherwise [ Becerra , M. et al. Int. J. Quantum Chem 2013 , 113 ( 10 ), 1584 - 1590 ]. In the nBO case, there arise densities for both the nuclei and electrons. Furthermore, these densities vary with respect to a particular point of reference from which they are calculated. We consider, in the present work, electron and nuclear densities calculated from the following reference points: a global center of mass, the geometric center between the electrons, and the geometric center between the protons. A comparison of the nBO Shannon entropy and Fisher information, with respect to their counterparts computed from Born-Oppenheimer densities, suggests that the former quantities provide more insights into the chemical reactivity because of the nonuniqueness nature of the nBO electron density as well as the availability and access to the nBO nuclear density. Finally, some comments are made concerning the nBO vs the BO regimes in relation to this particular chemical reactivity indicator.

Stability of "No-Pair Ferromagnetic" Lithium Clusters.

High-spin lithium clusters, n+1Lin (n = 2-21), have been systematically studied by using density functional theory. Although these high-spin clusters have no bonding electron pairs, they are stable with respect to isolated atoms. A set of 42 density functional theory functionals were benchmarked against CCSD(T)/cc-pVQZ results for clusters from the dimer to the hexamer. For these clusters, the strong non-additivity on the binding energy is analyzed employing a many-body energy decomposition scheme, concluding that most of the binding energy is due to a balance between the three- and four-body contributions. After a quality parameter had been defined, the LC-BP86 functional was identified as the most promising one for the description of high-spin lithium clusters. We employ the dependence of the second energy difference on cluster size to predict the formation of a higher-stability cluster.

Heterodonty and double occlusion in Manidens condorensis: a unique adaptation in an Early Jurassic ornithischian improving masticatory efficiency.

New materials of the ornithischian dinosaur Manidens condorensis highlight a strong heterodonty between the upper and lower dentitions and reveal a novel occlusion type previously unreported in herbivorous dinosaurs. The diamond-shaped maxillary teeth have prominent cingular entolophs in a V- to Z-shaped configuration that are absent in dentary teeth. These cingular entolophs bear denticles and serrations with vertical wear that is coplanar with the apical wear facets, supporting their involvement in chewing. The separated apical and basal wear in dentary teeth is consistent with the apical and cingular wear in maxillary teeth, indicating an alternate occlusion, an orthal jaw motion, and shearing interactions between marginal and cingular edges in a double occlusion. Measurements of the length and wear area along the marginal and cingular edges indicate that the latter are functionally equivalent to adding eight teeth to a maxillary toothrow of ten, almost doubling the lengths of cutting edges and the degree of intraoral processing, while maintaining a plesiomorphic skull anatomy, an adaptation to herbivory unique in Ornithischia.

A DFT study of hydrogen and methane activation by B(C6F5)3/P(t-Bu)3 and Al(C6F5)3/P(t-Bu)3 frustrated Lewis pairs.

This contribution presents a computational study aimed at understanding factors affecting barriers associated with the activation of the H-H bond in molecular hydrogen and the H-CH3 bond in methane mediated by intermolecular Frustrated Lewis Pairs (FLPs). The classical phosphine P(t-Bu)3 Lewis base in conjunction with two Lewis acids, B(C6F5)3 and Al(C6F5)3, were used as representative models of intermolecular FLPs. DFT calculations were performed using the dispersion corrected ωB97x-D functional, including toluene as a solvent through the PCM-SMD implicit solvent scheme. The results show that, in all cases, the activation barrier is larger for methane than for hydrogen. We conclude that the observed increase in the barrier for methane activation is due primarily to a larger distortion in methane compared to hydrogen to reach the transition state. Second, a large distortion of the Lewis acid to attain a better interaction with the σ-bond in methane was observed. Finally, we found that, for both hydrogen and methane activation, a considerable reduction in the free energy activation barrier is observed when the Lewis acid Al(C6F5)3 is used. From the results extracted in this study, we propose the use of alanes acids as good candidates for methane activation.

A Middle Jurassic heterodontosaurid dinosaur from Patagonia and the evolution of heterodontosaurids.

Heterodontosauridae is a morphologically divergent group of dinosaurs that has recently been interpreted as one of the most basal clades of Ornithischia. Heterodontosaurid remains were previously known from the Early Jurassic of southern Africa, but recent discoveries and studies have significantly increased the geographical and temporal range for this clade. Here, we report a new ornithischian dinosaur from the Middle Jurassic Cañadón Asfalto Formation in central Patagonia, Argentina. This new taxon, Manidens condorensis gen. et sp. nov., includes well-preserved craniomandibular and postcranial remains and represents the only diagnostic ornithischian specimen yet discovered in the Jurassic of South America so far. Derived features of its anatomy indicate that Manidens belongs to Heterodontosauridae, as the sister taxon of Heterodontosaurus and other South African heterodontosaurids. The presence of posterior dentary teeth with high crowns but lacking extensive wear facets in Manidens suggests that this form represents an intermediate stage in the development of the remarkable adaptations to herbivory described for Heterodontosaurus. The dentition of Manidens condorensis also has autapomorphies, such as asymmetrically arranged denticles in posterior teeth and a mesially projected denticle in the posteriormost teeth. At an estimated total length of 60-75 cm, Manidens furthermore confirms the small size of basal heterodontosaurids.