Vibrational relaxation in simulated two-dimensional infrared spectra of two amide modes in solution

Two-dimensional infrared spectroscopy is capable of following the transfer of vibrational energy between modes in real time. We develop a method to include vibrational relaxation in simulations of two-dimensional infrared spectra at finite temperature. The method takes into account the correlated fluctuations that occur in the frequencies of the vibrational states and in the coupling between them as a result of interaction with the environment. The fluctuations influence the two-dimensional infrared line shape and cause vibrational relaxation during the waiting time, which is included using second-order perturbation theory. The method is demonstrated by applying it to the amide-I and amide-II modes in N-methylacetamide in heavy water. Stochastic information on the fluctuations is obtained from a molecular dynamics trajectory, which is converted to time dependent frequencies and couplings with a map from a density functional calculation. Solvent dynamics with the same frequency as the energy gap between the two amide modes lead to efficient relaxation between amide-I and amide-II on a 560 fs time scale. We show that the cross peak intensity in the two-dimensional infrared spectrum provides a good measure for the vibrational relaxation.     

Heterogeneous exciton dynamics revealed by two-dimensional optical spectroscopy

We show that optical two-dimensional (2D) spectroscopy can recover ultrafast heterogeneous dynamics of closely spaced delocalized exciton states from a molecular exciton manifold characterized by a single absorption band. The complete experimental third-order nonlinear optical response from room-temperature J-aggregates in liquid phase is reproduced for the first time with self-consistent Frenkel exciton theory combined with modified Redfield theory. We show that exciton relaxation between the exciton states and nuclear-motion-induced exchange-narrowed energy fluctuations of individual delocalized exciton states can be distinguished because these two processes lead to a distinctively different evolution of the absolute 2D spectrum. Our technique also allows recovery of the variation of the exciton relaxation rates as well as the degree of exciton delocalization across the absorption band.     

Ultrafast exciton transfers in DNA and its nonlinear optical spectroscopy

We have calculated the nonlinear response function of a DNA duplex helix including the contributions from the exciton population and coherence transfers by developing an appropriate exciton theory as well as by utilizing a projector operator technique. As a representative example of DNA double helices, the B-form (dA)10-(dT)10 is considered in detail. The Green functions of the exciton population and coherence transfer processes were obtained by developing the DNA exciton Hamiltonian. This enables us to study the dynamic properties of the solvent relaxation and exciton transfers. The spectral density describing the DNA base-solvent interactions was obtained by adjusting the solvent reorganization energy to reproduce the absorption and steady-state fluorescence spectra. The time-dependent fluorescence shift of the model DNA system is found to be ultrafast and it is largely determined by the exciton population transfer processes. It is further shown that the nonlinear optical spectroscopic techniques such as photon echo peak shift and two-dimensional photon echo can provide important information on the exciton dynamics of the DNA double helix. We have found that the exciton-exciton coherence transfer plays critical roles in the peculiar energy transfer and ultrafast memory loss of the initially created excitonic state in the DNA duplex helix.     

Spectroscopy and dynamics of jet-cooled 1,1′ binaphthyl

Fluorescence excitation and dispersed fluorescence spectra of jet-cooled 1,1′-binaphthyl are reported and analysed. The spectra indicate that in the ground and excited state the naphthalene rings are perpendicular to one another. The spectra can be further interpreted in terms of an exciton model with an exciton splitting of 21 cm^?1 in the origin. From the structureless emission spectrum and lifetime it is concluded that, in the isolated molecule, efficient vibrational relaxation occurs through conversion of vibrational into librationaI energy.     

Exciton dynamics of GaSe nanoparticle aggregates

Time-resolved and static spectroscopic results on GaSe nanoparticle aggregates are presented to elucidate the exciton relaxation and diffusion dynamics. These results are obtained in room-temperature TOP/TOPO solutions at various concentrations. The aggregate absorption spectra are interpreted in terms of electrostatic coupling and covalent interactions between particles. The spectra at various concentrations may then be interpreted in terms of aggregate distributions calculated from a simple equilibrium model. These distributions are used to interpret concentration-dependent emission anisotropy kinetics and time-dependent emission spectral shifts. The emission spectra are reconstructed from the static emission spectra and decay kinetics obtained at a range of wavelengths. The results indicate that the aggregate z axis persistence length is about 9 particles. The results also show that the one-dimensional exciton diffusion coefficient is excitation wavelength dependent and has a value of about 2 x 10(-5) cm(2)/s following 406 nm excitation. Although exciton diffusion results in very little energy relaxation, subsequent hopping of trapped electron/hole pairs occurs by a Forster mechanism and strongly red shifts the emission spectrum.     

Collective oscillations and the linear and two-dimensional infrared spectra of inhomogeneous beta-sheets

We numerically calculate the collective amide I oscillations and the associated linear and two-dimensional infrared (2DIR) spectra for model antiparallel beta-sheets and study the effect of inhomogeneity. To visualize the collective vibrational exciton states, a new method is introduced, which proves very useful in classifying the optically dominant states with respect to their symmetry properties and phase relations, even in the absence of exact symmetries. We find that energy (diagonal) and interaction (off-diagonal) disorder may have profoundly different effects on the main peaks in the linear spectrum. We also show that in the 2DIR spectra energy disorder leads to diagonal stretching of the diagonal peaks, while the cross-peaks are typically stretched more horizontally. This offers an explanation for the recently observed overall Z-shape in experimental spectra. Finally, we find that the anharmonic splitting between associated positive and negative features in the 2DIR spectra scales inversely proportionally with the exciton delocalization size imposed by the disorder, thus offering a spectroscopic ruler for this size.     

Optical coherence and theoretical study of the excitation dynamics of a highly symmetric cyclophane-linked oligophenylenevinylene dimer

Optoelectronic properties of a polyphenylenevinylene-based oligomer and its paracylophane-linked dimer are studied using a variety of experimental and theoretical techniques. Despite the symmetrical structure and redshifted absorption of the dimer versus the monomer, an exciton picture is not the most appropriate. Electronic structure calculations establish changes in charge density upon optical excitation and show localized excitations that cannot be accounted for by a simple Frenkel exciton model. Visible frequency pump-probe anisotropy measurements suggest that the dimer should be considered as a three-level system with a fast, approximately 130 fs, internal conversion from the higher to lower energy excited electronic state. Signatures of nuclear relaxation processes are compared for electric field-resolved transient grating and two-dimensional photon echo spectra. These measurements reveal that nuclear relaxation occurs on similar time scales for the monomer and dimer. The connection between the spectral phase of four-wave mixing signals and the time dependent width of a nuclear wave packet is discussed. Semiempirical electronic structure and metropolis Monte Carlo calculations show that the dominant line broadening mechanisms for the monomer and dimer are associated with inter-ring torsional coordinates. Together, the theoretical calculations and electric field-resolved four-wave mixing experiments suggest that while the structure of dimer is more rigid than that of monomer, the difference in their rigidities is not sufficient to slow down excited state relaxation of dimer with respect to the monomer.     

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.     

Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.     

Multidimensional infrared spectroscopy of water. I. Vibrational dynamics in two-dimensional IR line shapes

In this and the following paper, we describe the ultrafast structural fluctuations and rearrangements of the hydrogen bonding network of water using two-dimensional (2D) infrared spectroscopy. 2D IR spectra covering all the relevant time scales of molecular dynamics of the hydrogen bonding network of water were studied for the OH stretching absorption of HOD in D2O. Time-dependent evolution of the 2D IR line shape serves as a spectroscopic observable that tracks how different hydrogen bonding environments interconvert while changes in spectral intensity result from vibrational relaxation and molecular reorientation of the OH dipole. For waiting times up to the vibrational lifetime of 700 fs, changes in the 2D line shape reflect the spectral evolution of OH oscillators induced by hydrogen bond dynamics. These dynamics, characterized through a set of 2D line shape analysis metrics, show a rapid 60 fs decay, an underdamped oscillation on a 130 fs time scale induced by hydrogen bond stretching, and a long time decay constant of 1.4 ps. 2D surfaces for waiting times larger than 700 fs are dominated by the effects of vibrational relaxation and the thermalization of this excess energy by the solvent bath. Our modeling based on fluctuations with Gaussian statistics is able to reproduce the changes in dispersed pump-probe and 2D IR spectra induced by these relaxation processes, but misses the asymmetry resulting from frequency-dependent spectral diffusion. The dynamical origin of this asymmetry is discussed in the companion paper.     

Relaxation spectrometry in solid polymers based on NMR and EPR measurements

Wide distribution of relaxation times is taken into consideration in determination of the activation energy of the molecular motion associated with the motional narrowings of line widths of magnetic resonance spectra. The molecular motion of rotational vibration around the chain axis of polyethylene in urea-polyethylene inclusion complex is examined. Relaxation spectra can be obtained from the data of the motional narrowings of EPR and NMR by assuming the activation energy as a parameter. Also, the representative relaxation times corresponding to EPR and NMR observations can be estimated. These relaxation times give us an activation energy since EPR and NMR observations correspond to different time constants of observations. The activation energy estimated from the data of the representative correlation times is identical with the activation energy obtained as a parameter in determination of the identical relaxation spectrum from the data of motional narrowings of EPR and NMR observations.     

Intermolecular torsional motion of a π-aggregated dimer probed by two-dimensional electronic spectroscopy

The energetic splitting of the two exciton states of a molecular dimer depends strongly on the relative orientation of the monomers with respect to each other. The curvature of the corresponding adiabatic potential energy surfaces can lead to torsional motion of the monomers. It has been suggested recently that this torsional motion could provide a possible relaxation mechanism for the upper state which proceeds via a crossing of the two singly excited state potentials. Another, competing, relaxation mechanism is provided by coupling to the environment, leading to direct exciton relaxation. Here we examine theoretically the combined dynamics of torsional motion and excitonic relaxation for a π-aggregated dimer. Using two-dimensional (2D) spectroscopy, it is shown how torsional motion through a crossing of the adiabatic excitonic potential surfaces could be distinguished from direct relaxation. For the calculations a mixed quantum/classical approach is used, where the torsional motion is treated by an Ehrenfest type of equation, while the excitonic dynamics including dephasing and direct relaxation is described by a quantum master equation.     

Influence of Higher Excited Singlet States on Ultrafast Exciton Motion in Pigment-Protein Complexes

Abstract— Numerical simulations of the ultrafast exciton motion in photosynthetic antenna complexes are used to reproduce measured data of optical pump-probe experiments. Emphasis is put on a chlorophyll aL/chlorophyll b dimer of the light-harvesting complex of the photosystem II of higher plants (LHC-II). To account for intramolecular excited-state absorption the standard exciton theory is extended to the inclusion of a second higher excited singlet state per chlorophyll molecule. The density matrix theory is applied to describe the dissipative dynamics of excitons. Different mechanisms for energy relaxation and dephasing including pure dephasing processes are discussed. As a result, a further refinement of earlier calculations on the one-color pump-probe spectra at the LHC-II can be presented. In particular, the presence of non-Markovian effects with respect to the exciton-vibrational interaction in the LHC-II, discovered previously in the two-color pump-probe spectrum, is demonstrated here for the one-color pump-probe case.     

Exciton spin relaxation in colloidal CdSe quantum dots at room temperature

Size dependence of spin dynamics in colloidal CdSe quantum dots (QDs) are investigated with circularly polarized pump-probe transmission spectroscopy at room temperature. The excitation energy is tuned to resonance with the lowest exciton (1S(h)1S(e)) energy of the CdSe QDs. The exciton spin dynamics of CdSe QD with the diameter of 5.2 nm shows monoexponential decay with a typical time constant of about 1-3 ps depending on the excitation energy. For the cases of CdSe QDs with smaller size (with the diameter of 4.0 and 2.4 nm), the exciton spin relaxation shows biexponential decay, a fast component with time constant of several ps and a slow one with time constant of hundreds of ps to nanosecond time scale. The fast spin relaxation arises from the bright-dark transition, i.e., J = ±1 ? -/+2 transition. This process is dominated by the hole spin flips, while the electron spin conserves. The slow spin relaxation is attributed to the intralevel exciton transitions (J = ±1 ? -/+1 transition), which is relevant to the electron spin flip. Our results indicate that the exciton spin relaxation pathways in CdSe QD are controllable by monitoring the particle size, and polarized pump-probe spectroscopy is proved to be a sensitive method to probe the exciton transition among the fine structures.     

Quantum master equation approach to the second hyperpolarizability of nanostar dendritic systems

We investigate the dynamic second hyperpolarizability (gamma) of nanostar dendritic systems using the quantum master equation approach. In the nanostar dendritic systems composed of three-state monomers, the multistep exciton states are obtained by the dipole-dipole interactions, and the directional energy transport, i.e., exciton migration, from the periphery to the core is predicted to occur by the relaxation between exciton states originating in the exciton-phonon coupling. The effects of the intermolcecular interaction and the exciton migration, i.e., exciton relaxation, on the gamma in the third-harmonic generation (THG) are examined in the three-photon off- and on- resonance regions using the two-exciton model. Furthermore, the method for analysis of spatial contributions of excitons to gamma is presented by partitioning the total gamma into the one- and two-exciton contributions. It turns out that the exciton relaxation between exciton states causes significant broadening of the spectra of gamma and their mutual overlap as well as the relative increase of two-exciton contributions in the nanostar dendritic system.     

Exciton dissociation dynamics in model donor-acceptor polymer heterojunctions. I. Energetics and spectra

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band offset in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band offset at the heterojunction, the exciton will remain the lowest-energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the offset is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases.     

One-dimensional exciton diffusion in perylene bisimide aggregates

The dynamics and mobility of excitons in J-aggregates of perylene bisimides are investigated by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Increasing the pump pulse energy and in that way the initial exciton density results in an accelerated signal decay and pronounced exciton-exciton annihilation dynamics. Modeling the data by assuming a diffusive exciton motion reveals that the excitons cannot migrate freely in all three directions of space but their mobility is restricted to one dimension. The observed anisotropy supports this picture and points against direct Fo?rster-transfer-mediated annihilation between the excitons. A diffusion constant of 1.29 nm(2)/ps is deduced from the fitting procedure that corresponds to a maximal exciton diffusion length of 96 nm for the measured exciton lifetime of 3.6 ns. The findings indicate that J-aggregates of perylene bisimides are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems.     

2H nuclear magnetic resonance study on the molecular motion in cyanoadamantane. II. Orientationally ordered and glassy crystalline phase

The orientationally ordered crystalline and glassy plastically crystalline phase of cyanoadamantane were investigated using (2)H NMR. Solid-echo line shape, two-dimensional spectrum, and spin-lattice relaxation were analyzed. In both phases, the molecules display solely a rotation around the molecular C(3) symmetry axis. For the orientationally ordered phase, a single correlation time characterizes the motion, and the time constant shows an Arrhenius temperature dependence. In contrast, a broad distribution G[ln(tau)] of correlation times is observed for the glassy plastically crystalline phase that leads to characteristically different NMR features such as "two-phase" spectra and pronounced nonexponential relaxation. The distribution G[ln(tau)] can be derived from a temperature independent distribution of activation energies g(E(a)), with its mean value lying significantly below the activation energy corresponding to the ordered phase. Thus, the molecular uniaxial rotation proves to be a sensitive probe for the energy landscape of the orientationally disordered glassy crystalline phase of cyanoadamantane.