A photodissociation reaction: Experimental and computational study of 2-hydroxy-2,2-dimethylacetophenone

The photophysical parameters controlling the cleavage process of 2-hydroxy-2,2-dimethylacetophenone (HDMA) were investigated in detail. Time-resolved picosecond absorption experiments show that the formation of the triplet state occurs within 20 ps after excitation and decays within hundreds of picoseconds depending on the solvent polarity. Molecular modeling reveals that three stable conformations exist in the ground state, the most stable one exhibiting an intramolecular hydrogen bond that modifies the electronic properties of the molecule. This explains quite well the steady-state absorption properties. The conformation of the most stable triplet state is twisted by 180 degrees with respect to the ground state. Computation of the potential energy surface along the molecular coordinate for the dissociation reaction evidences an electronic state crossing yielding a final sigmasigma* state, in perfect agreement with the state correlation diagram. Optimization of the transition state allows the calculation of the activation energy and the use of the transition-state theory leads to an estimate of 100 ps for the cleavage process in the gas phase. Single-point energy calculations using a solvent model predict an increase of the dissociation rate constant with the increase of the solvent polarity, in good agreement with the value deduced from kinetic measurements.     

Linear programming solutions and distance functions under a constant returns to scale technology

In this paper, we investigate the various relationships among the linear programming solutions of data envelopment analysis (DEA) models under a constant returns to scale technology. We derive the analytical relationships among the efficiency measures and the activity variables for four separate models: the input-based, the output-based, the hyperbolic, and the proportional distance functions. We apply our results in order to derive a test of consistency that can be used in assessing the returns to scale among differing DEA models.