Quantum chemical modeling for 157 nm photolithography

In its continuing quest for smaller length scales, the electronics industry plans to introduce 157 nm as the next lithographic wavelength. Accordingly, there is a pressing need to develop photoresists that are more transparent, and pellicles that are both more transparent and more durable. With the advent and popularization of time-dependent density functional theory (TD-DFT), we now have a practical quantum chemical method for calculating excitation energies and transition moments in the vacuum ultraviolet (VUV) which can greatly assist in the scouting of highly transparent materials. We have performed TD-DFT calculations for a broad variety of fluorinated molecules and we will report calculated VUV photoabsorption spectra for a large family of model fluorohexanes. These calculations, which span a range from 1-fluorohexane to CH₃CF₂CF₂CF₂CF₂CH₃, illustrate some of the principles one may use to design low absorption polymeric materials.     

Erratum

A technique is reported for measuring triplet spin-lattice relaxation times in fluid solution. It is based on the observation of chemically induced electron spin polarization, in the presence of a triplet quencher. Spin-lattice relaxation times of the order of 10 ns are reported for the duroquinone triplet in various solvents.     

Applications of a distance formula in hyperbolic plane geometry

This note may be used in model-based courses on the classical geometries. Given two points P₁(x₁, y₁) and P₂(x₂, y₂) in the Poincaré upper half-plane model of hyperbolic plane geometry with x₁≠x₂, a Cartesian equation of thebowed geodesic passing through P₁ and P₂ and an integral expression for the hyperbolic distance between P₁ and P₂ are developed. These formulas depend only on the coordinates of P₁ and P₂, and it is easy to implement them with the numerical integrators of modern technology. The distance formula is used to find the coordinates of points of division along a bowed geodesic and, thus, leads to activities discovering that results such as Ceva's Theorem are valid in hyperbolic geometry. The distance formula is also used in verifying that the model satisfies the axioms of absolute geometry.     

Lifting chains of prime ideals to paravaluation rings

Résumé  SoitR ⊂T une extension des anneaux commutatifs et soit {P _α :α ∈I} une cha?ne croissante des idéaux premiers deR (I étant un ensemble totalement ordonné, peut-être infini). Alors il existe un anneau de paravaluationV deT et une cha?ne {Q _α} des idéaux premiers deV de sorte queR ⊂V etQ _α ∩R =P _α pour toutα ∈I. Tout d’abord, on établit le cas spécial dans lequelT est un corps; dans ce cas, on trouve en effet un tel anneau de valuationV deT. Ensuite, l’assertion ci-dessus pour le cas général découle comme conséquence. Dans le cas général, on peut aussi remplacer le mot “paravaluation” avec le mot “valuation” siR est un anneau de Marot etT est son anneau total de fractions.      

Novel light-fluorous TEMPO reagents and their application in oxidation reactions

The synthesis of two light-fluorous TEMPO derivatives is reported, along with their application in oxidation reactions.