Mixed quantum/semiclassical wave-packet dynamical method for condensed-phase molecular spectroscopy signals.

We report the successful application of a recently developed mixed quantum/semiclassical wave-packet dynamical theory to the calculation of a spectroscopic signal, the linear absorption spectrum of a realistic small-molecule chromophore in a cryogenic environment. This variational fixed vibrational basis/Gaussian bath (FVB/GB) theory avails itself of an assumed time scale separation between a few, mostly intramolecular, high-frequency nuclear motions and a larger number of slower degrees of freedom primarily associated with an extended host medium. The more rapid, large-amplitude system dynamics is treated with conventional basis-set methods, while the slower time-evolution of the weakly coupled bath is subject to a semiclassical, thawed Gaussian trial form that honors the overall vibrational ground state, and hence the initial state prepared by its Franck-Condon transfer to an excited electronic state. We test this general approach by applying it to a small, symmetric iodine-krypton cluster suggestive of molecular iodine embedded in a low-temperature matrix. Because of the relative simplicity of this model complex, we are able to compare the absorption spectrum calculated via FVB/GB dynamics using Heller's time-dependent formula with one obtained from rigorously calculated eigenenergies and Franck-Condon factors. The FVB/GB treatment proves to be accurate at approximately 15-cm-1 resolution, despite the presence of several thousand spectral lines and a sequence of various-order system-bath resonances culminating at the highest absorption frequencies in an inversion of the relative system and bath time scales.

Broad-Band Pump-Probe Spectroscopy Quantifies Ultrafast Solvation Dynamics of Proteins and Molecules.

In this work, we demonstrate the use of broad-band pump-probe spectroscopy to measure femtosecond solvation dynamics. We report studies of a rhodamine dye in methanol and cryptophyte algae light-harvesting proteins in aqueous suspension. Broad-band impulsive excitation generates a vibrational wavepacket that oscillates on the excited-state potential energy surface, destructively interfering with itself at the minimum of the surface. This destructive interference gives rise to a node at a certain probe wavelength that varies with time. This reveals the Gibbs free-energy changes of the excited-state potential energy surface, which equates to the solvation time correlation function. This method captures the inertial solvent response of water (∼40 fs) and the bimodal inertial response of methanol (∼40 and ∼150 fs) and reveals how protein-buried chromophores are sensitive to the solvent dynamics inside and outside of the protein environment.

Ultrafast transient absorption revisited: Phase-flips, spectral fingers, and other dynamical features.

We rebuild the theory of ultrafast transient-absorption/transmission spectroscopy starting from the optical response of an individual molecule to incident femtosecond pump and probe pulses. The resulting description makes use of pulse propagators and free molecular evolution operators to arrive at compact expressions for the several contributions to a transient-absorption signal. In this alternative description, which is physically equivalent to the conventional response-function formalism, these signal contributions are conveniently expressed as quantum mechanical overlaps between nuclear wave packets that have undergone different sequences of pulse-driven optical transitions and time-evolution on different electronic potential-energy surfaces. Using this setup in application to a simple, multimode model of the light-harvesting chromophores of PC577, we develop wave-packet pictures of certain generic features of ultrafast transient-absorption signals related to the probed-frequency dependence of vibrational quantum beats. These include a Stokes-shifting node at the time-evolving peak emission frequency, antiphasing between vibrational oscillations on opposite sides (i.e., to the red or blue) of this node, and spectral fingering due to vibrational overtones and combinations. Our calculations make a vibrationally abrupt approximation for the incident pump and probe pulses, but properly account for temporal pulse overlap and signal turn-on, rather than neglecting pulse overlap or assuming delta-function excitations, as are sometimes done.

How fissors works: observing vibrationally adiabatic conformational change through femtosecond stimulated Raman spectroscopy.

With the help of a two-dimensional model system comprising a slow conformational degree of freedom and a higher-frequency vibration, we investigate the molecular-level origin and dynamical information content of femtosecond stimulated Raman spectroscopy (fissors) signals. Our treatment avails itself of the time scale separation between conformational and vibrational modes by incorporating a vibrationally adiabatic approximation to the conformational dynamics. We derive an expression for the fissors signal without resort to the macroscopic concepts of light- and phonon-wave propagation employed in prior coupled-wave analyses. Numerical calculations of fissors spectra illustrate the case of relatively small conformational mass (still large enough that conformational motion does not induce any change in the vibrational quantum number) in which conformational sidebands accompany a central peak in the Raman gain at a conformationally averaged vibrational transition frequency, and the case of a larger conformational mass in which the sidebands merge with the central peak and the frequency of the latter tracks the time-evolving conformational coordinate.