Transition state Spectroscopy Neumark p1446 Absorption of light hv excites a bound species to the transition state of a potential energy surface for a chemical reaction. The transition state lies at the saddle point between reactants and products. /*---------------------------------------------------------------------*/ Long-Range Casimir Interactions Normally, nonrelativistic electromagnetic theory with two-particle Coulombic interactions adequately determines the interaction potential of systems A and B if the systems are composed of particles with characteristic velocities much less than the speed of light. If , however, the time it takes to light to travel between A and B exceeds a characteristic oscillation period of A or B , the way in which the potential function depends on the separation of the systems can be altered. Called the Casimir effect, it has only recently been confirmed, and it arises in physics, chemistry, and biology. It is the clearest physical manifestation of the fact that even in a vacuum electromagnetic fields cannot all vanish. The Casimir effect Used in connection with retarded interactions between pairs of systems and changes in the energy of the vacuum produced by the imposition of boundary conditions. The force/ area F/A of two parallel metallic walls separated by a vacuum referred to as the Casimir effect. Because the separation z is assumed to be small compared with the wall's dimensions, edge effects can be ignored. The charge e and mass m of an electron play no role in an ideal conductor; the only relevant entities are h and c and z On dimensional grounds, F/A is uniquely determined to within a dimensionless constant K and is given by F= F/A = Khc/z^4. To determine K,, consider not two walls but three, with separations z and L-z. There is energy between the walls because the electromagnetic fields cannot be identically zero. The allowable modes are those that satisfy the appropriate boundary conditions, including the vanishing of the tangential components of the electric field E at the surface of the wall.