Dynamics of Ground- and Excited-State Intramolecular Proton Transfer Reactions

Dynamics of Ground- and Excited-State Intramolecular Proton Transfer Reactions 

Tautomerism Methods and Theories, First Edition. Edited by liudmil Antonov. 

The classical Liouville equation does have an equivalent in quantum mechanics, which is needed for a consistent description of quantum statistical mechanics the quantum Liouville equation. Equilibrium quantum statistical mechanics requires the introduction of the density operator on an appropriate Hilbert space, and the quantum liouvUle equation for the density operator is a logical and necessary extension of the Schrodinger equation. The quantum Liouville equation can even be written, formally at least, in a form that resembles its classical counterpart. It allows for some weak and almost internally consistent form of dissipative dynamics, known as the Redfield theory, which finds its main use in relating NMR relaxation times to spectral densities arising from solvent fluctuations, although in recent 

In addition, the polarization also plays a major dynamical role. In the classical description, this can be incorporated consistently. No consistent model along these Hnes is possible in quantum mechanics. 

Although the density operator and the quantum liouviUe equation do not nearly solve aU our problems, they nevertheless have interesting potential applications in the field we are interested in. The strong coupling of the reactive mode to skeletal vibrations can be dealt with using a cumulant expansion, and the Brownian 

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