Dynamic Stokes shift in solution: Effect of finite pump pulse duration

Abstract

The time-evolution of the fluorescence spectrum of a dissolved chromophore excited by an ultrafast pump pulse is considered. The average value of the energy difference of the solute in its excited and ground states is used to describe the relaxation of the maximum of the transient fluorescence spectrum to its equilibrium value ͑dynamic Stokes shift, DSS͒. A simple formula for the normalized DSS is obtained which generalizes an earlier standard classical expression and includes the effect of a pump pulse of finite duration. As an example, dielectric dispersion data are used for a dipolar solute in water to estimate the quantum correction to the standard DSS expression. The correction is negligible when the frequency of the pump pulse is close to the maximum in the absorption spectrum, but a deviation from the standard formula can be expected for the pump pulse tuned to a far wing of the absorption band of the chromophore. An expression is given for this deviation.

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

“…Equation ͑16͒ formally coincides with the correlation function of the collection of molecular harmonic oscillators if one introduces for J() the spectral density of their normal modes, 49,59 which justifies the usage of this title ͑spectral density͒ for J(). The spectral density of the harmonic system is temperature-independent.…”

Possible Mechanism of OH Frequency Shift Dynamics in Water

“…In particular, the normalized evolution of the spectral shift can be approximately expressed as [24][25][26][27] where ∆(t) is C V (t) normalized to unity at its maximum:…”

“…The key quantity which enters into the theory is the correlation function C v ( t ) where in the present case v is the instantaneous frequency of the main transition of the O−H stretch. In particular, the normalized evolution of the spectral shift can be approximately expressed as − where Δ( t ) is C v ( t ) normalized to unity at its maximum: …”

Time-resolved photoelectron spectroscopy of molecular dissociation: Classical trajectory versus quantum wave-packet calculations

“…27 Several authors have therefore developed schemes to simulate pump-probe spectra, based on a classical treatment of the nuclei. [28][29][30][31][32][33] In order to be able to simulate spectra for a direct comparison with experiment, proper initial conditions for the classical orbits have to be established. It is not immediately obvious how to choose the sampling function in the case of ultrashort pulse excitation, as is the case in usual molecular dynamics simulations.…”