M. D. Fayer

Electronic excited state transport in solution

The transport of electronic excitations between randomly distributed sites is examined. The Green function solution to the master equation is expanded as a diagrammatic series. Topological reduction of the series results in an expression for the Green function which is equivalent in form to the Green function solution of a generalized diffusion equation. The diagrammatic technique used suggests an interesting class of self‐consistent approximations. This self‐consistent method of approximation is applied to the specific case of the Forster transfer rate. The solutions obtained are well‐behaved for all times and all site densities and indicate that transport is nondiffusive at short times and diffusive at long times. The mean squared displacement of the excitation and the time derivative of the mean squared displacement are calculated. These calculations illustrate that the time regime in which diffusive transport occurs is dependent on density. For low density systems transport becomes diffusive only at v...

Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: A new approach

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.

Excitation transfer in disordered two‐dimensional and anisotropic three‐dimensional systems: Effects of spatial geometry on time‐resolved observables

A unified treatment of dipole–dipole excitation transfer in disordered systems is presented for the cases of direct trapping (DT) in two‐component systems and donor–donor transfer (DD) in one‐component systems. Using the two‐particle model proposed by Huber we calculate the configurational average of Gs(t), the probability of finding an initially excited molecule still excited at time t. For the isotropic three‐dimensional case treated by Huber excellent correspondence is found with the previously reported infinite diagrammatic approximation. The anisotropy of the dipole–dipole interaction is included in the averaging procedure. Two regimes of orientational mobility are considered: the dynamic and static limit, rotations being much faster or slower, respectively, than the energy transfer. The following geometrical distributions are investigated: (a) Infinite systems of one, two, and three dimensions which lead to Forster‐like decays. Two orientational distributions are considered for monolayers: dipoles c...

Ultrafast infrared and raman spectroscopy

Ultrafast coherent raman and infrared spectroscopy of liquid systems probing bond activation reactions with femtosecond infrared applications of broadband transient infrared spectroscopy the molecular mechanisms behind the vibrational population relaxation of small molecules in liquids time-resolved IR studies of ligand dynamics in heme proteins infrared vibrational echo experiments structure and dynamics of proteins and peptides - femtosecond two-dimensional infrared spectroscopy two-dimensional coherent infrared spectroscopy of vibrational excitons in peptides vibrational dephasing in liquids - raman echo and raman free-induction decay studies fifth order two-dimensional raman spectroscopy of the intermolecular and vibrational dynamics in liquids nonresonant intermolecular spectroscopy of liquids lattice vibrations that move at the speed of light - how to excite them, how to monitor them and how to image them before they get away vibrational energy redistribution in polyatomic liquids - ultrafast IR-raman spectroscopy Coulomb force and intramolecular energy flow effects for vibrational energy transfer for small molecules in polar solvents vibrational relaxation of polyatomic molecules in supercritical fluids and the gas phase vibrational energy relaxation in liquids and supercritical fluids.

Hydrogen bond dynamics in aqueous NaBr solutions

Hydrogen bond dynamics of water in NaBr solutions are studied by using ultrafast 2D IR vibrational echo spectroscopy and polarization-selective IR pump–probe experiments. The hydrogen bond structural dynamics are observed by measuring spectral diffusion of the OD stretching mode of dilute HOD in H2O in a series of high concentration aqueous NaBr solutions with 2D IR vibrational echo spectroscopy. The time evolution of the 2D IR spectra yields frequency–frequency correlation functions, which permit quantitative comparisons of the influence of NaBr concentration on the hydrogen bond dynamics. The results show that the global rearrangement of the hydrogen bond structure, which is represented by the slowest component of the spectral diffusion, slows, and its time constant increases from 1.7 to 4.8 ps as the NaBr concentration increases from pure water to ≈6 M NaBr. Orientational relaxation is analyzed with a wobbling-in-a-cone model describing restricted orientational diffusion that is followed by complete orientational randomization described as jump reorientation. The slowest component of the orientational relaxation increases from 2.6 ps (pure water) to 6.7 ps (≈6 M NaBr). Vibrational population relaxation of the OD stretch also slows significantly as the NaBr concentration increases.

Theory of vibrational relaxation of polyatomic molecules in liquids

A simple tractable theory of vibrational relaxation of polyatomic molecules in polyatomic solvents, which is also applicable to solid solutions, is presented. The theory takes as its starting point Fermi’s golden rule, avoids additional assumptions such as the rotating wave or random phase approximations, and treats both the internal degrees of freedom of the relaxing molecule and the bath degrees of freedom in a fully quantum mechanical manner. The results yield intuitively understandable expressions for the relaxation rates. The treatment of the annihilation as well as the creation of all participating bosons allows the theory to go beyond earlier analyses which treated only cascade processes. New predicted features include temperature effects and asymmetry effects in the frequency dependence. The theory is constructed in a manner which facilitates the use of recent developments in the analysis of instantaneous normal modes of liquids.

Optical generation of tunable ultrasonic waves

A convenient method of optically exciting and monitoring coherent acoustic waves in transparent or light‐absorbing liquids and solids is described. The acoustic frequency is easily and continuously tunable from ≊3 MHz to at least 30 GHz with our experimental apparatus and in principle over a considerably wider range. In anisotropic materials any propagation direction can be selected. The optically generated acoustic waves can be optically amplified, cancelled, or phase shifted.

Dynamics in low temperature glasses: Theory and experiments on optical dephasing, spectral diffusion, and hydrogen tunneling

Temperature dependent photon echo (PE) and nonphotochemical hole burning (NPHB) measurements are reported on resorufin in three organic glasses: ethanol (1.5–11 K), glycerol (1.1–25 K), and d‐ethanol (1.5–11 K). In all cases, the NPHB results are broadened considerably from the PE results at low temperatures, but the two measurements coalesce at high temperatures. The temperature dependences are found to deviate from the power law dependence expected for two‐level system dephasing, and the deviation is attributed to dephasing by a pseudolocal mode. The appropriate correlation functions for PE and hole burning experiments are shown to be different from each other. They also differ from the correlation function for the optical absorption (OA) experiment, which has been the basis for most calculations of optical dephasing in glasses. The broadening of hole widths beyond the PE result is shown to be a measure of the slow spectral diffusion processes in the glass. Other types of dephasing measurement are also ...

Electronic excited‐state transport and trapping in solution

A theoretical study of transport and trapping of electronic excitations in a two‐component disordered system is carried out. The results are applicable to energy transport in solutions containing randomly distributed donor and trap solute species or lattices with randomly distributed donor and trap impurities. The diagrammatic expansion of the Green function, developed by Gochanour, Andersen, and Fayer to study excited‐state energy transport in a one‐component system is applied to the trapping problem. The following quantities are calculated from the Green function: the time‐dependent probabilities that an excitation is in the donor or in the trap ensembles, the generalized diffusion coefficient, and the mean‐squared displacement of an excitation. For Forster transfer, transport properties are shown to depend on the ratio of the Forster interaction lengths RDT0 and RDD0 as well as on the reduced concentrations of donors and traps [CD = 4/3π(RDD0)3ρD, CT = 4/3π (RDT0)3ρT]. The tranport of excitations is fo...

Shocked molecular solids: Vibrational up pumping, defect hot spot formation, and the onset of chemistry

A model and detailed calculations are presented to describe the flow of energy in a shocked solid consisting of large organic molecules. The shock excites the bulk phonons, which rapidly achieve a state of phonon equilibrium characterized by a phonon quasitemperature. The excess energy subsequently flows into the molecular vibrations, which are characterized by a vibrational quasitemperature. The multiphonon up pumping process occurs because of anharmonic coupling terms in the solid state potential surface. Of central importance are the lowest energy molecular vibrations, or ‘‘doorway’’ modes, through which mechanical energy enters and leaves the molecules. Using realistic experimental parameters, it is found that the quasitemperature increase of the internal molecular vibrations and equilibration between the phonons and vibrations is achieved on the time scale of a few tens of picoseconds. A new mechanism is presented for the generation of ‘‘hot spots’’ at defects. Defects are postulated to have somewhat...