Meyer-Miller method

Benjamin and Wilson used classical molecular dynamics to study the photodissociation of model ICN in the gas phase and Xe solution. One of the novel features of this study involved the treatment of molecular dynamics on coupled surfaces in solution using the Meyer-Miller method.i For sufficiently high excitation (Benjamin and Wilson use 266 nm), ICN may be excited to a linear state that correlates with an I product. However, this excited state may couple to another state that has a bent configuration and correlates to ground state I. Benjamin and Wilson developed an extension of the Meyer-Miller method, which takes into account the interaction between the ICN and the Xe solvent. The result is a Hamiltonian that describes motion on a self-consistent average of the two excited state potentials. 

The reactive flux method is also useful in calculating rate constants in quantum systems. The path integral formulation of the reactive flux together with the use of the centroid distribution function has proved very useful for the calculation of quantum transition-state rate constants [7]. In addition new methods, such as the Meyer-Miller method [8] for semiclassical dynamics, have been used to calculate the flux-flux correlation function and the reactive flux. 

Quantum variables mapped to classical ones Meyer-Miller method... 

To meet the needs of the advanced students, preparations have now been included to illustrate, for example, reduction by lithium aluminium hydride and by the Meerwein-Ponndorf-Verley method, oxidation by selenium dioxide and by periodate, the Michael, Hoesch, Leuckart and Doebner-Miller Reactions, the Knorr pyrrole and the Hantzsch collidine syntheses, various Free Radical reactions, the Pinacol-Pinacolone, Beckmann and Arbusov Rearrangements, and the Bart and the Meyer Reactions, together with many others. 

In order to extend the linearization scheme to non-adiabatic dynamics it is convenient to represent the role of the discrete electronic states in terms of operators that simplify the evolution of the quantum subsystem with out changing its effect on the classical bath. A way to do this was first suggested by Miller, McCurdy and Meyer [28,29[ and has more recently been revisited by Thoss and Stock [30, 31[. Their method, known as the mapping formalism, represents the electronic degrees of freedom and the transitions between different states in terms of positions and momenta of a set of fictitious harmonic oscillators. Formally the approach is exact, but approximations (e.g. semi-classical, linearized SC-IVR, etc.) must be made for its numerical implementation. 

The mapping procedure introduced in Sec. 6 results in a quantum-mechanical Hamiltonian with a well-defined classical limit, and therefore extends the applicability of the established semiclassical approaches to nonadiabatic dynamics. The thus obtained semiclassical version of the mapping approach, as well as the equivalent formulation that is obtained by requantizing the classical electron analog model of Meyer and Miller, have been applied to a variety of systems with nonadiabatic dynamics in the recent years. It appears that this approach is so far the only fully semiclassical method that allows a numerical treatment of truly multidimensional nonadiabatic dynamics at conical intersections. 

The determination of reducing substances is the oldest in vitro method for demonstrating hyaluronidase activity. Meyer and co-workers (119, 125,128) measured reducing sugar by the Hagedom-Jensen method (60) or by the ceric sulfate method of Miller and Van Slyke (136) and expressed the results as percentage of total reducing substances. The latter value... 

Another topic in the classical treatment of reactive collisions which has advanced considerably in recent years concerns the treatment of electronically nonadiabatic processes. Early work on this topic followed either the semiclassical complex trajectory method of George and Miller,or the more approximate surface hopping model of Tully and Preston.Recent work in this field by McCurdy, Meyer, and Miller " has attempted to develop a purely classical description of the electronic degrees of freedom, thereby replacing the many-surface aspect of the dynamics with extra classical degrees of freedom (one for each surface beyond the first) which represent the collective electronic motions to which the nuclear motions can couple to cause transitions. This means that a multiple-surface problem can now be treated by standard" trajectory methods, which is a considerable computational simplification. Applications to the f ( Pi/2) 2... 

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