Gas-liquid phase transition and singularities

A new model for the space of undercritical states of a gas-liquid system is proposed. Simple, physically motivated mathematical hypotheses among which stsbility plays an essential role, determine differential types of germs of pressure and temperature at the critical point. They are connected with the class D⁺₄ of Arnold's classification. The general configuration of vaporization and condensation curves is examined. As a result, Guggenheim's one-third law is obtained.     

Photochemical ring opening of barbital

Photolysis of barbital yields derivatives of urea and biuret. The mechanism of ring opening involves an isocyanate intermediate.     

The electronic effects of substituents at the acyl carbon in the gas-phase elimination kinetics of tert-butyl α-substituted acetates

The gas-phase eliminations of several tert-butyl esters, in a static system and in vessels seasoned with allyl bromide, have been studied in the temperature range of 171.5–280.1°C and the pressure range of 23–98 torr. The rate coefficients for the homogeneous unimolecular elimination of these esters are given by the following Arrhenius equations: for tert-butyl pivalate, log k₁(s^?1) = (13.44 ± 0.30) ? (169.1 ± 3.1) kJ · mol^?1 (2.303RT)^?1; for tert-butyl trichloroacetate, log k₁(s^?1) = (12.41 ± 0.08) ? (141.1 ± 0.7) kJ · mol^?1 (2.303RT)^?1; and for tert-butyl cyanoacetate log k₁(s^?1) = (11.31 ± 0.44) ? (137.8 ± 4.1) kJ · mol^?1 (2.303RT)^?1. The data of this work together with those reported in the literature yield a good linear relationship when plotting log k/k₀ vs. σ* values (ρ* = 0.635, correlation coefficient r = 0.972, and intercept = 0.048 at 250°C). The positive ρ* value suggests that the movement of negative charge to the acyl carbon in the transition state is rate determining. The present results along with previous investigations ratify the generalization that electron-withdrawing substituents at the acyl side of ethyl, isopropyl, and tert-butyl esters enhance the elimination rates, while electron-releasing groups tend to reduce them. The negative nature of the acyl carbon and the polarity in the transition state increases slightly from primary to tertiary esters.     

Matrix elements of one- and two-electron operators

A graphical representation of matrix elements of spin-free one- and two-electron operators is used for deriving a simple algorithm for the evaluation of their values. The method covers all the cases which may occur when wave functions are taken as mutually orthogonal antisymmetrized products of spinorbitals (which are assumed to form an orthonormal set) and are eigenfunctions of L ² and L _z operators. The resulting formulas are suitable as well for computer programming as for hand calculations.

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Zusammenfassung Mit Hilfe einer graphischen Darstellung wird ein einfacher Algorithmus zur Bestimmung der Werte der Matrix-Elemente von spinfreien Ein- und Zweielektronenoperatoren abgeleitet. Durch diese Methode werden alle Fälle erfaßt, die auftreten, wenn die Wellenfunktionen wechselweise orthogonale, antisymmetrisierte Produkte von Spinorbitalen (von denen angenommen wird, daß sie einen orthogonalen Satz bilden) darstellen und Eigenfunktion der L ² und L _z Operatoren sind. Die erhaltenen Formeln eignen sich für Rechnungen mit und ohne Verwendung eines Computers.

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Sponsored by the Mathematical Institute, Polish Academy of Sciences.     

Coupling constants in the direct configuration interaction method

A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.     

Imaging of tautomerism in a single molecule

Fluorescence imaging is used to visualize directly the transfer of two inner hydrogen atoms in single porphycene molecules. This reaction leads to a chemically equivalent but differently oriented structure and hence results in a rotation of the transition dipole moments. By probing single immobilized molecules with an azimuthally polarized laser beam in the focal spot of a confocal microscope we observe ring-like emission patterns, possible only for a chromophore with two nearly orthogonal transition dipole moments. Numerical simulations of the observed emission patterns yield a value of 72 degrees for the angle between the S0-S1 transition moments in the two tautomeric forms.