Variational grand-canonical electronic structure of Li+Li at ~10<Superscript>4</Superscript> K with second-order perturbation theory corrections

An ab initio variational grand-canonical electronic structure mean-field method, based on the Gibbs–Peierls–Bogoliubov minimum principle for the Gibbs free energy, is applied to the di-lithium (Li+Li) system at temperatures around T ≈ 10⁴ K and electronic chemical potential of μ ≈ ?0.1E _h . The method is an extension of the Hartree–Fock approach to finite temperatures. We first study the Li₂ molecule at a frozen inter-nuclear distance of R = 3 Å as a function of temperature. The mean-field electronic structure changes smoothly as temperature increases, up to 10⁴ K, where a sharp spontaneous spin-polarization emerges as the variational mean-field solution. Further increase in the temperature extinguishes this polarization. We analyze the mean-field behavior using a correlated single-site Hubbard model and show it arises from an attempt of the mean-field to mimic the polarization of the spin–spin correlation function of the exact solution. Next, we keep constant the temperature at 10⁴ K and examine the electronic structure as a function of inter-nuclear distance R. At R = 3.7 Å, a crossing between two free energy states occurs: One state is “spin-unpolarized” (becomes lower in energy when R > 3.7 Å), while the other is “spin polarized”. This crossing causes near-discontinuous jumps in calculated properties of the system and is associated with using the noninteracting electron character of our mean-field approach. Such problems will likely plague FT-DFT calculations as well. We use second-order perturbation theory (PT2) to study effects of electron correlation on the potential of mean force between the two colliding Li atoms. We find that PT2 correlation free energy at ~10⁴ K is larger than at 0 K and tends to restore the spin-polarized state as the lowest free energy solution.     

Furanosteroid studies. Improved synthesis of the A,B,C,E-ring core of viridin

The tetracyclic core skeleton of the furanosteroid viridin is prepared in nine steps from readily available materials. The key step in the synthesis is a facile acid-promoted cyclodehydration of an aryloxyketone to prepare the benzofuran moiety. From this intermediate, the known target skeleton is prepared in four steps. This new synthesis is a six-step improvement over the previously reported one.     

Investigation of surface states on the polar (111) and (111) faces of GaAs by photoelectron spectroscopy

Photoelectron spectra from the clean polar (111) and ($\text{111}$) faces of GaAs show emission from surface states. After exposure to oxygen which produces a covarage of about one monolayer, this emission disappears.     

Departure-site spacing for liquid droplets and jets falling between horizontal circular tubes

When a liquid film falls from one tube to another below it, the flow can take the form of discrete droplets, individual jets or a continuous sheet. Experiments exploring the effects of thermophysical properties and geometrical parameters on the droplet and jet flow patterns are described. Measurements of droplet and jet departure-site spacing are reported for several fluids over a wide range of liquid flow rates, tube sizes and tube spacing. For the conditions of this study, departure-site spacing increased with decreasing Re for high-Ga fluids and was nearly independent of Re for low-Ga fluids. Departure-site spacing increased slightly with tube diameter for small tubes and was nearly independent of tube size for large tubes. Departure-site spacing was nearly independent of tube spacing for the entire range of experiments; however, a relation between jet shape, jet spacing and tube spacing was observed under some conditions. A qualitative study of liquid-jet shapes shows that this flow feature depends strongly on tube spacing, and comparisons to existing models suggest that further work in this area is needed.     

UV photoelectron spectroscopy of matrix-isolated and condensed CO and N2

UV photoelectron spectra of matrix-isolated and condensed CO and N₂ have been measured. The emission from the 4σ, 1π and 5σ orbitals show similar relaxation shifts of about 1 eV. This shift is 0.3 eV larger for the species isolated in xenon matrices. The width of the peaks is smaller by 0.3 eV in the Xe matrix in comparison with the pure solids but remains larger than those measured for the gas phase.     

Lewis acid-promoted oxidative addition of thioimidates to Pd0

The isomeric S-methyldihydropyrrins 9-Z and 9-E exhibit markedly different behavior in Pd(0)-catalyzed cross-coupling reactions. Thioimidates 9-Z are readily converted to imines 10-Z employing Pd(0)/AlkZnI. Under identical conditions 9-E are inert. Oxidative addition to Pd(0) requires activation by Zn or other Lewis acids, which is sterically unfavorable with 9-E. Analogous results were obtained with the related thioimidates 11-E,Z as well as with methylthiopyridines 19alpha-gamma. In the case of both 11 and 19 oxidative addition to Pd(0) was greatly facilitated in the presence of BF(3) x Et(2)O. The importance of Lewis acid activation to Pd(0) oxidative addition in such substrates appears to be a general phenomenon not previously recognized.