Molecular vibrations-induced quantum beats in two-dimensional electronic spectroscopy

Quantum beats in nonlinear spectroscopy of molecular aggregates are often attributed to electronic phenomena of excitonic systems, while nuclear degrees of freedom are commonly included into models as overdamped oscillations of bath constituents responsible for dephasing. However, molecular systems are coupled to various high-frequency molecular vibrations, which can cause the spectral beats hardly distinguishable from those created by purely electronic coherences. Models containing damped, undamped, and overdamped vibrational modes coupled to an electronic molecular transition are discussed in this paper in context of linear absorption and two-dimensional electronic spectroscopy. Analysis of different types of bath models demonstrates how do vibrations map onto two-dimensional spectra and how the damping strength of the coherent vibrational modes can be resolved from spectroscopic signals.     

Detection of electronic and vibrational coherences in molecular systems by 2D electronic photon echo spectroscopy

Two-dimensional optical photon echo spectra are simulated for model systems which exhibit vibrational, electronic and a combination of electronic and vibrational coherent dynamics. The coherent motion manifests itself as periodic beatings of the spectrum cross-peak intensity with the population time. The intensity modulations are compared to evolution of the excited-state population and coordinate expectation value. The advantageous capabilities of the technique as well as possible difficulties in spectra interpretations are outlined. Possibilities for distinguishing electronic and vibrational coherences are discussed.     

Vibration-induced energy relaxation in two-level system

Energy decay in a general two-level electronic system coupled to a vibrational harmonic mode interacting with a thermal bath is studied theoretically. The model assumes a general form of the off-diagonal elements (in the electronic basis) of the vibrational-electronic interaction. The cases for constant, linear, and quadratic dependence with respect to the vibrational displacement are investigated. For short-time regime, fast oscillations corresponding to a coherent energy exchange between electrons and vibrations appear. Their frequency Ω corresponds to the energy difference (ħΩ) between electronic levels. Additionally, for the case of linear or quadratic coupling, the amplitude modulation of the oscillations with the frequency ω equal to that of vibrational motion is found.     

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.     

Photoinduced processes in riboflavin: superposition of pi pi*-n pi* states by vibronic coupling, transfer of vibrational coherence, and population dynamics under solvent control

Femtosecond dynamics of riboflavin, the parent chromophore of biological blue-light receptors, was measured by broadband transient absorption and stationary optical spectroscopy in polar solution. Rich photochemistry is behind the small spectral changes observed: (i) loss of oscillator strength around time zero, (ii) sub-picosecond (ps) spectral relaxation of stimulated emission (SE), and (iii) coherent vibrational motion along a' (in-) and a' (out-of-plane) modes. Loss of oscillator strength is deduced from the differences in the time-zero spectra obtained in water and DMSO, with stationary spectroscopy and fluorescence decay measurements providing additional support. The spectral difference develops faster than the time resolution (20 fs) and is explained by formation of a superposition state between the optically active (1pi pi*) S1 and closely lying dark (1n pi*) states via vibronic coupling. Subsequent spectral relaxation involves decay of weak SE in the blue, 490 nm, together with rise and red shift of SE at 550 nm. The process is controlled by solvation (characteristic times 0.6 and 0.8 ps in water and DMSO, respectively). Coherent oscillations for a' and a' modes show up in different regions of the SE band. a' modes emerge in the blue edge of the SE and dephase faster than solvation. In turn, a' oscillations are found in the SE maximum and dephase on the solvation timescale. The spectral distribution of coherent oscillations according to mode symmetry is used to assign the blue edge of the SE band to a 1n pi*-like state (A'), whereas the optically active 1pi pi* (A') state emits around the SE maximum. The following model comes out: optical excitation occurs to the Franck-Condon pi pi* state, a pi pi*-n pi* superposition state is formed on an ultrafast timescale, vibrational coherence is transferred from a' to a' modes by pi pi*-n pi* vibronic coupling, and subsequent solvation dynamics alters the pi pi*/n pi* population ratio.     

Chemical imaging by single pulse interferometric coherent anti-stokes Raman scattering microscopy

A single pulse interferometric coherent anti-Stokes Raman (CARS) spectroscopy method is used to obtain broadband CARS spectra and microscopy images of liquid and polymer samples. The pump, Stokes, and probe pulses are all selected inside a single broadband ultrafast pulse by a phase- and polarization-controlled pulse shaping technique and used to generate two spectral interference CARS signals simultaneously. The normalized difference of these two signals provides an amplified background-free broadband resonant CARS spectrum over the 400-1500 cm(-1) range with 35 cm(-1) spectral resolution. Chemically selective microscopy images of multicomponent polymer and liquid samples are investigated with this new CARS method. Multiplex CARS spectra at 10,000 spatial points are measured within a few minutes, and used to construct chemically selective microscopy images with a spatial resolution of 400 nm. The spectral bandwidth limits, sensitivity, homodyne amplification advantages, spatial resolution, depolarization, chromatic aberration, and chemical imaging aspects of this new technique are discussed in detail.     

Mode-focusing in molecules by feedback-controlled shaping of femtosecond laser pulses

The feasibility of mode-selective excitation with broadband femtosecond laser pulses is demonstrated for toluene in liquid phase. A learning-loop optimal control scheme was applied to a stimulated Raman excitation process. Modifications of the phase shape of one of the exciting pulses resulted in dramatic changes of the mode distribution reflected in coherent anti-Stokes Raman spectra. An evolutionary algorithm guided the coherent excitation process to a selective enhancement or suppression of one or more vibrational modes over the complete coherence lifetime spanning several picoseconds. New ways of spectral filtering as well as exciting possibilities of mode-selective studying of chemical reaction dynamics are indicated.     

CARS-spectra of excited states of metalloporphyrins

It is shown that resonance coherent anti-Stokes Raman scattering (RCARS) spectra of Cu- and Ni-octaethylporphyrins contain lines corresponding to molecule vibrations both in the ground and excited electronic states. Mechanisms are given which lead to the appearance of vibrations in the excited state in RCARS spectra. The RCARS methods are shown to be promising for comparing molecule vibrations in different electronic states.     

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.     

Site-directed electronic tunneling in a dissipative molecular environment

The ability to control electronic tunneling in complex molecular networks of multiple donor/acceptor sites is studied theoretically. Our past analysis, demonstrating the phenomenon of site-directed transport, was limited to the coherent tunneling regime. In this work we consider electronic coupling to a dissipative molecular environment including the effect of decoherence. The nuclear modes are classified into two categories. The first kind corresponds to the internal molecular modes, which are coupled to the electronic propagation along the molecular bridges. The second kind corresponds to the external solvent modes, which are coupled to the electronic transport between different segments of the molecular network. The electronic dynamics is simulated within the effective single electron picture in the framework of the tight binding approximation. The nuclear degrees of freedom are represented as harmonic modes and the electronic-nuclear coupling is treated within the time-dependent Redfield approximation. Our results demonstrate that site-directed tunneling prevails in the presence of dissipation, provided that the decoherence time is longer than the time period for tunneling oscillations (e.g., at low temperatures). Moreover, it is demonstrated that the strength of electronic coupling to the external nuclear modes (the solvent reorganization energy) controls the coherent intramolecular tunneling dynamics at short times and may be utilized for the experimental control of site-directed tunneling in a complex network.     

Contact effects on electronic transport in donor-bridge-acceptor complexes interacting with a thermal bath

A model for electron transfer in donor-bridge-acceptor complexes with electronic coupling to nuclear bridge modes is studied using the Redfield formulation. We demonstrate that the transport mechanism through the molecular bridge is controlled by the location of the electronic-nuclear coupling term along the bridge. As the electronic-nuclear coupling term is shifted from the donor/acceptor-bridge contact sites into the bridge, the mechanism changes from kinetic transport (incoherent, thermally activated, and bridge-length independent) to coherent tunneling oscillations. This study joins earlier works aiming to explore the factors which control the mechanism of electronic transport through molecular bridges and molecular wires.     

Broadband pump-probe spectroscopy with sub-10-fs resolution for probing ultrafast internal conversion and coherent phonons in carotenoids

We use pump-probe spectroscopy with broadband detection to study electronic energy relaxation and coherent vibrational dynamics in carotenoids. A fast optical multichannel analyzer combined with a non-collinear optical parametric amplifier allows simultaneous acquisition of the differential transmission dynamics on the 500–700 nm wavelength range with sub-10-fs temporal resolution. The broad spectral coverage enables on the one hand a detailed study of the ultrafast bright-to-dark state internal conversion process; on the other hand, the tracking of the motion of the vibrational wavepacket launched on the ground state multidimensional potential energy surface. We present results on all-trans β-carotene and on a long-chain polyene in solution. The developed experimental setup enables the straightforward acquisition and analysis of coherent vibrational dynamics, highlighting time–frequency domain features with extreme resolution.     

Stereocontrol of attosecond time-scale electron dynamics in ABCU using ultrafast laser pulses: a computational study

The attosecond time-scale electronic dynamics induced by an ultrashort laser pulse is computed using a multi configuration time dependent approach in ABCU (C(10)H(19)N), a medium size polyatomic molecule with a rigid cage geometry. The coupling between the electronic states induced by the strong pulse is included in the many electron Hamiltonian used to compute the electron dynamics. We show that it is possible to implement control of the electron density stereodynamics in this medium size molecule by varying the characteristics of the laser pulse, for example by polarizing the electric field either along the N-C axis of the cage, or in the plane perpendicular to it. The excitation produces an oscillatory, non-stationary, electronic state that exhibits localization of the electron density in different parts of the molecule both during and after the pulse. The coherent oscillations of the non-stationary electronic state are also demonstrated through the alternation of the dipole moment of the molecule.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Optical control of excited-state vibrational coherences of a molecule in solution: The influence of the excitation pulse spectrum and phase in LD690

Spectral and phase shaping of femtosecond laser pulses is used to selectively excite vibrational wave packets on the ground (S0) and excited (S1) electronic states in the laser dye LD690. The transient absorption signals observed following excitation near the peak of the ground-state absorption spectrum are characterized by a dominant 586 cm(-1) vibrational mode. This vibration is assigned to a wave packet on the S0 potential energy surface. When the excitation pulse is tuned to the blue wing of the absorption spectrum, a lower frequency 568 cm(-1) vibration dominates the response. This lower frequency mode is assigned to a vibrational wave packet on the S1 electronic state. The spectrum and phase of the excitation pulse also influence both the dephasing of the vibrational wave packet and the amplitude profiles of the oscillations as a function of probe wavelength. Excitation by blue-tuned, positively chirped pulses slows the apparent dephasing of the vibrational coherences compared with a transform-limited pulse having the same spectrum. Blue-tuned negatively chirped excitation pulses suppress the observation of coherent oscillations in the ground state.     

Electronic coherences and vibrational wave-packets in single molecules studied with femtosecond phase-controlled spectroscopy

Employing femtosecond pulse-shaping techniques we investigate ultrafast, coherent and incoherent dynamics in single molecules at room temperature. In first experiments single molecules are excited into their purely electronic 0-0 transition by phase-locked double-pulse sequences with pulse durations of 75 fs and 20 nm spectral band width. Their femtosecond kinetics can then be understood in terms of a 2-level system and modelled with the optical Bloch equations. We find that we observe the coherence decay in single molecules, and the purely electronic dephasing times can be retrieved directly in the time domain. In addition, the Rabi-frequencies and thus the transition dipole moments of single molecules are determined from these data. Upon excitation of single molecules into a vibrational level of the electronically excited state also incoherent intra-molecular vibrational relaxation is recorded. Increasing the spectral band width of the excitation pulses to up to 120 nm (resulting in a transform-limited pulse width of 15 fs) coherent superpositions of excited state vibrational modes, i.e. vibrational wave packets, are excited. The wave-packet oscillations in the excited state potential energy surface are followed in time by a phase-controlled pump-probe scheme, which permits to record wave packet interference, and to determine the energies of vibrational modes and their coupling strengths to the electronic transition.     

Correlated atomic motions in liquid deuterium fluoride studied by coherent quasielastic neutron scattering

The collective dynamics of liquid deuterium fluoride are studied by means of high-resolution quasielastic and inelastic neutron scattering over a range of four decades in energy transfer. The spectra show a low-energy coherent quasielastic component which arises from correlated stochastic motions as well as a broad inelastic feature originating from overdamped density oscillations. While these results are at variance with previous works which report on the presence of propagating collective modes, they are fully consistent with neutron diffraction, nuclear magnetic resonance, and infrared/Raman experiments on this prototypical hydrogen-bonded fluid.     

Slow periodic oscillations in time domain dynamics of NO2

The authors investigated the time domain nonadiabatic dynamics of NO2 on the coupled X 2A1 and A 2B2 electronic states by launching wave packets on the excited electronic state and focused on the evolution at long times (t>200 fs), which has received little attention up to now. The authors showed that the initial fast spreading of the wave packets is followed at all energies by slow periodic intramolecular vibronic energy redistribution (IVER) with periods in the range of 0.3 to several tens of picoseconds. These energy transfers lead to oscillations with the same periods in the population of each electronic state. Propagation of wave packets indicates that IVER frequencies also dominate the fluctuations of the squared modulus of the autocorrelation function |A(t)|2 at energies not too high above the bottom of the conical intersection, but this is no longer the case at higher energies. For example, for initial wave packets prepared by almost vertical excitation of the vibrational ground state of the ground electronic surface, the oscillations of |A(t)|2 essentially reflect the detuning from 1:2 resonance between the frequency of the bend and that of the symmetric stretch in the excited electronic state. These theoretical results were used to discuss the possible origin of the low-frequency oscillations which were recently observed in time domain experimental spectra of NO2.