Comparative study of Li, Na, and K adsorptions on graphite by using ab initio method

A comprehensive study has been conducted to compare the adsorptions of alkali metals (including Li, Na, and K) on the basal plane of graphite by using molecular orbital theory calculations. All three metal atoms prefer to be adsorbed on the middle hollow site above a hexagonal aromatic ring. A novel phenomenon was observed, that is, Na, instead of Li or K, is the weakest among the three types of metal atoms in adsorption. The reason is that the SOMO (single occupied molecular orbital) of the Na atom is exactly at the middle point between the HOMO and the LUMO of the graphite layer in energy level. As a result, the SOMO of Na cannot form a stable interaction with either the HOMO or the LUMO of the graphite. On the other hand, the SOMO of Li and K can form a relatively stable interaction with either the HOMO or the LUMO of graphite. Why Li has a relatively stronger adsorption than K on graphite has also been interpreted on the basis of their molecular-orbital energy levels.

Nonplanar distortions and strain energies of polycyclic aromatic hydrocarbons

On the basis of HF/6-31G(d) optimized structures, the nonplanar distortions of 135 polycyclic aromatic hydrocarbons (PAHs) have been classified as splitting (S-) and arching (A-) distortions. Three bay structures are proposed as the structural origin of S-distortion. Due to the limitation of sample molecules, a set of universal motifs for molecules containing A-distortions is not available; however, a set of motifs and parameters are developed for the semiquantitative estimation of the nonplanar strain energies of PAHs containing the corannulene structure, and the differences between the E, values from quantum calculations and those from these estimations vary from -5.60 to 5.51 kcal/mol. The above results are fundamentally important for the understanding of nonplanar distortion of PAHs and fullerenes, and this method can also be employed to semiquantitatively estimate strain energies of such molecules containing hundreds of carbon atoms.

Do chimpanzees (Pan troglodytes) and 2-year-old children (Homo sapiens) understand double invisible displacement?

Chimpanzees (Pan troglodytes) and young children (Homo sapiens) have difficulty with double invisible displacements in which an object is hidden in two nonadjacent boxes in a linear array. Experiment 1 eliminated the possibility that chimpanzees' previous poor performance was due to the hiding direction of the displacement device. As in Call (2001), subjects failed double nonadjacent displacements, showing a tendency to select adjacent boxes. In Experiments 2 and 3, chimpanzees and 24-month-old children were tested on a new adaptation of the task in which four hiding boxes were presented in a diamond-shaped array on a vertical plane. Both species performed above chance on double invisible displacements using this format, suggesting that previous poor performance was due to a response bias or inhibition problem rather than a fundamental limitation in representational capacity.

Explicit derivation of the relativistic mass-energy relation for internal kinetic and potential energies of a composite system

A straightforward derivation of relativistic expressions for the mechanical momentum, kinetic and total energies, and mass-energy equivalence (including potential energy) which does not require any knowledge of the energy-momentum relation for electromagnetic waves or consideration of elastic collisions, but is directly based on Newton's second law and Lorentz's transformations, is presented in this paper. The existence of an invariant force is shown to be important for the validity of the relativistic mechanics.

Strain energies due to nonplanar distortion of fullerenes and their dependence on structural motifs

Accurate strain energies due to nonplanar distortion of 114 isolated pentagon rule (IPR) fullerenes with 60-102 carbon atoms have been calculated based on B3LYP/6-31G(d) optimized structures. The calculated values of strain energy due to nonplanar distortion (E-np) are reproduced by three simple schemes based upon counts of 8, 16, and 30 distinct structural motifs composed of hexagons and pentagons. Using C-180 (I-h) and CN (I-h) (N is very large) as test molecules, the intrinsic limitations of the motif model based on six-membered rings (6-MRs) as the central unit have been discussed. On the basis of the relationship between the contributions of motifs to E-np and the number of five-membered rings (5-MRs) in motifs, we found that IPR fullerenes with dispersed 5-MRs present smaller nonplanar distortions.