We give a detailed account of the statistical mechanical properties of the mean field Ehrenfest quantum/classical method as applied to liquid phase vibrational energy transfer using a simple harmonic oscillator model Hamiltonian. Depending on the shape of the initial quantum wave packet, a (partial) breakdown of detailed balance is observed, where the frictional response of the classical bath is only correlated to quasiclassical features of the evolving quantum state, i.e., a classical-like fluctuation-dissipation theorem holds. Only in the case of a coherent initial state (minimum uncertainty wave packet) does the mean field method produce physically meaningful results, namely, exponential relaxation (tau=tau(cl)) towards a quasiclassical equilibrium.

In this contribution quantum/classical surface hopping methodology is applied to vibrational energy relaxation of a quantum oscillator in a classical heat bath. The model of a linearly damped (harmonic) oscillator is chosen which can be mapped onto the Brownian motion (Caldeira-Leggett) Hamiltonian. In the simulations Tully's fewest switches surface hopping scheme is adopted with inclusion of dephasing in the adiabatic basis using a simple decoherence algorithm. The results are compared to the predictions of a Redfield-type quantum master equation modeling using the classical heat bath force correlation function as input. Thereby a link is established between both types of quantum/classical approaches. Viewed from the latter perspective, surface hopping with dephasing may be interpreted as "on-the-fly" stochastic realization of a quantum/classical Pauli master equation.

In this contribution, we discuss the statistical mechanical implications of the mean field Ehrenfest method of quantum/classical dynamics for a quantum harmonic oscillator in a classical heat bath using the Brownian motion Hamiltonian as a model. A mean field quantum/classical master equation is derived and compared to the corresponding Redfield master equation, and the deficiencies of the quantum/classical approach pointed out by analyzing the nature of energy/population relaxation and decoherence.

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Fluorescence quenching through intramolecular electron transfer (ET) was studied in N‐(ω‐sulfonatoalkyl)‐ and N‐(ω‐carboxyalkyl)‐quinolinium betaines by stationary and time‐resolved fluorescence spectroscopy in the solvents water and acetonitrile. These substances are zwitterionic in the ground and local excited state of the quinolinium chromophore. In the sulfonato compounds fluorescence quenching through ET does not occur in water, whereas quenching is efficient in acetonitrile. A surprising opposite behaviour is observed for the carboxylato compounds: quenching is efficient in water whereas it is inefficient in acetonitrile. Semiempirical calculations were used to derive the parameters needed for the description of the quenching process by non‐adiabatic Bixon‐Efrima‐Jortner‐theory. These parameters include the solvent (λs) and the intrinsic (λv) contributions to the total reorganisation energy λ and the approximate free energy of reaction ΔG°. The vibrational motion of an aromatic C‐H bond influenced by the interaction with the negatively charged donor was taken as the major intramolecular accepting mode. ET fluorescence quenching in the present compounds and solvents may be interpreted in terms of the “normal” and the “inverted region” of Marcus theory.