Two-dimensional optical spectroscopy: Two-color photon echoes of electronically coupled phthalocyanine dimers

Anomalously Large Spectral Shifts near the Quantum Tunnelling Limit in Plasmonic Rulers with Subatomic Resolution

The resonance wavelength of a coupled plasmonic system is extremely sensitive to the distance between its metallic surfaces, resulting in "plasmon rulers". We explore this behavior in the subnanometer regime using self-assembled monolayers of bis-phthalocyanine molecules in a nanoparticle-on-mirror (NPoM) construct. These allow unprecedented subangstrom control over spacer thickness via choice of metal center, in a gap-size regime at the quantum-mechanical limit of plasmonic enhancement. A dramatic shift in the coupled plasmon resonance is observed as the gap size is varied from 0.39 to 0.41 nm. Existing theoretical models are unable to account for the observed spectral tuning, which requires inclusion of the quantum-classical interface, emphasizing the need for new treatments of light at the subnanoscale.

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

Chiroptical nature of two-exciton states of light-harvesting complex: Doubly resonant three-wave-mixing spectroscopy

Photosynthetic light-harvesting complex is a coupled multichromophore system. Due to electronic couplings between neighboring chlorophylls in the complex, the one- and two-exciton states are delocalized and they can be written as linear combinations of singly and doubly excited configurations, respectively. Despite that the chiroptical properties of one-exciton states in such a multichromophore system have been investigated by using linear optical activity measurement techniques; those of two-exciton states have not been studied before due to a lack of appropriate measurement methods. Here, we present a theoretical description on chiroptical chi((2)) spectroscopy and show that it can be used to investigate such properties of a photosynthetic light-harvesting system, which is the Fenna-Matthews-Olson complex, consisting of seven bacteriochlorophylls in its protein subunit. To simulate the doubly resonant sum- and difference-frequency-generation spectra of the complex, one- and two-exciton transition dipoles were calculated. Carrying out quantum chemistry calculations of electronically excited states of a model bacteriochlorophyll system and taking into account the dipole-induced dipole electronic transition processes between the ground state and two-exciton states, we could calculate the two-dimensional sum-frequency-generation spectra revealing dominant second-order chiroptical transition pathways and involved one- and two-exciton states. It is believed that the present computational scheme and the theoretically proposed doubly resonant two-dimensional three-wave-mixing spectroscopy would be of use to shed light on the chiroptical natures of two-exciton states of arbitrary coupled multichromophore systems.

Correlated exciton relaxation in Poly(3-hexylthiophene)

Two-color 3 pulse photon echo peak shift (2C-3PEPS) measurements on poly(3-hexylthiophene) (3PHT) demonstrate that spectral regions in the photoluminescence remain correlated with the excitation, despite large differences in energy (>0.5 eV). The observations are explained in terms of exciton-phonon coupling that is dominated by only two motions: one high frequency bond stretch and a low frequency torsional motion. Numerical simulations of the 2C-3PEPS are shown to be consistent with the experimental observations. The results demonstrate that initial intramolecular exciton relaxation in P3HT is not primarily a stochastic process, but is driven by strong, selective exciton-phonon coupling to torsional motions.

Measuring Electronic Coupling in the Reaction Center of Purple Photosynthetic Bacteria by Two-Color, Three-Pulse Photon Echo Peak Shift Spectroscopy

One- and two-color, three-pulse photon echo peak shift spectroscopy (1C and 2C3PEPS) was used to estimate the electronic coupling between the accessory bacteriochlorophyll (B) and the bacteriopheophytin (H) in the reaction center of the purple photosynthetic bacterium Rhodobacter sphaeroides as approximately 170 +/- 30 cm-1. This is the first direct experimental determination of this parameter; it is within the range of values found in previously published calculations. The 1C3PEPS signal of the Qy band of the bacteriochlorophyll B shows that it is weakly coupled to nuclear motions of the bath, whereas the 1C3PEPS signal of the Qy band of the bacteriopheophytin, H, shows that it is more strongly coupled to the bath, but has minimal inhomogeneous broadening. Our simulations capture the major features of the data with the theoretical framework developed in our group to separately calculate the response functions and population dynamics.

One- and Two-Color Photon Echo Peak Shift Studies of Photosystem I

Wavelength-dependent one- and two-color photon echo peak shift spectroscopy was performed on the chlorophyll Qy band of trimeric photosystem I from Thermosynechococcus elongatus. Sub-100 fs energy transfer steps were observed in addition to longer time scales previously measured by others. In the main PSI absorption peak (675-700 nm), the peak shift decays more slowly with increasing wavelength, implying that energy transfer between pigments of similar excitation energy is slower for pigments with lower site energies. In the far-red region (715 nm), the decay of the peak shift is more rapid and is complete by 1 ps, a consequence of the strong electron-phonon coupling present in this spectral region. Two-color photon echo peak shift data show strong excitonic coupling between pigments absorbing at 675 nm and those absorbing at 700 nm. The one- and two-color peak shifts were simulated using the previously developed energy transfer model (J. Phys. Chem. B 2002, 106, 10251; Biophysical Journal 2003, 85, 140). The simulations agree well with the experimental data. Two-color photon echo peak shift is shown to be far more sensitive to variations in the molecular Hamiltonian than one-color photon echo peak shift spectroscopy.

Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.

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.

Two-dimensional electronic spectra of symmetric dimers: Intermolecular coupling and conformational states

We study the information content of two-dimensional (2D) electronic photon-echo (PE) spectra, with special emphasis on their potential to distinguish, for waiting times T=0, between different conformations of electronically coupled symmetric dimers. The analysis is performed on the basis of an analytical formula for the frequency-domain 2D PE signal. The symmetric dimers are modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site representation. The spectra of conformationally weighted ensembles, composed of either two or four dimers, are compared with their one-dimensional linear absorption counterparts. In order to provide a realistic coupling pattern for the ensemble consisting of four dimers, excitonic couplings are estimated on the basis of optimized geometries and site-transition dipole moments, calculated by standard semiempirical methods for the bridged bithiophene structure 1,2-bithiophene-2-yl-ethane-1,2-dion (T2[CO]2). In the framework of our model, the highly readable 2D PE spectra can unambiguously identify spectral doublets, by relating peak heights and positions with mutual orientations of site-localized transition dipoles.

Anti-Correlated Spectral Motion in Bisphthalocyanines: Evidence for Vibrational Modulation of Electronic Mixing

We exploit a coherently excited nuclear wave packet to study nuclear motion modulation of electronic structure in a metal bridged phthalocyanine dimer, lutetium bisphthalocyanine, which displays two visible absorption bands. We find that the nuclear coordinate influences the energies of the underlying exciton and charge resonance states as well as their interaction; the interplay of the various couplings creates unusual anti-correlated spectral motion in the two bands. Excited state relaxation dynamics are the same regardless of which transition is pumped, with decay time constants of 1.5 and 11 ps. The dynamics are analyzed using a three-state kinetic model after relaxation from one or two additional states faster than the experimental time resolution of 50-100 fs.

The integrated photon echo and solvation dynamics. II. Peak shifts and two-dimensional photon echo of a coupled chromophore system

A theoretical description of one- and two-color photon echo peak shifts (PEPS) and two-dimensional (2D) photon echo spectrum (PES) of a coupled chromophore system are presented. The effects of population relaxation in the one-exciton states on both the PEPS and the 2D PES are investigated. For values of time T shorter than the population relaxation time, a finite two-color peak shift magnitude and nonzero cross peaks in the 2D PES provide evidence of electronic coupling between the chromophores. These two distinct observables, i.e., PEPS and off-diagonal peaks, both originate from the electronic coupling. However, it is shown that the PEPS and 2D PES methods can provide complementary information on the structure-dependent nonlinear optical responses of coupled chromophore systems.

Peak Separation and Sorting by Coherent 2D Resonance Raman Spectroscopy

The ability to separate and sort peaks is explored using a new coherent two-dimensional form of resonance Raman spectroscopy. This experimental technique distributes normally congested rotational-vibrational peaks along a series of curved lines according to vibrational sequence, rotational quantum number, and selection rule. Each line consists of rotational-vibrational peaks that have the same vibrational sequence and the same value for DeltaJ, distributed in order by rotational quantum number. For diatomic molecules, these lines originate from points where they initially travel in opposite or orthogonal directions in two-dimensional space, which helps facilitate the separation between lines. Simulations and experimental results on C2 in a flame confirm the ability to separate and sort these normally congested rotational-vibrational peaks. This method appears to provide a solution to the long-standing problems of spectral congestion and disorder in gas-phase electronic spectra.

Probing correlated spectral motion: Two-color photon echo study of Nile blue

We performed two-color three-pulse photon echo peak shift experiments on Nile blue in ethylene glycol and acetonitrile to determine the role of solvent dynamics in correlated spectral motion. The system was pumped near the absorption maximum and the correlation between the initial state and the final state was probed at a number of wavelengths, from the absorption maximum to the fluorescence maximum. In addition to solvent dynamics, we found that strongly coupled intramolecular vibrations generated correlations between different spectral regions. The inertial solvent response was found for both solvents to have a time scale on the order of 100-145 fs. This response contributed half of the solvent interaction strength for acetonitrile, but less than a third for ethylene glycol. Several diffusive time scales were observed: 500 fs and 2.5 ps for acetonitrile, and 1, 15, and 100 ps for ethylene glycol. A single description of the solvation dynamics was insufficient to quantitatively describe the dynamics at all probe wavelengths, which could indicate different dynamics in the ground and excited states or the presence of an additional contribution to the signal from the excited-state absorption.

Exciton Analysis in 2D Electronic Spectroscopy

A theoretical description of femtosecond two-dimensional electronic spectroscopy of multichromophoric systems is presented. Applying the stationary phase approximation to the calculation of photon echo spectra and taking into account exciton relaxation processes, we obtain an analytic expression for numerical simulations of time- and frequency-resolved 2D photon echo signals. The delocalization of one-exciton states, spatial overlaps between the probability densities of different excitonic states, and their influences on both one- and two-dimensional electronic spectra are studied. The nature of the off-diagonal cross-peaks and the time evolution of both diagonal and off-diagonal peak amplitudes are discussed in detail by comparing experimentally measured and theoretically simulated 2D spectra of the natural Fenna-Matthews-Olson (FMO) photosynthetic light-harvesting complex. We find that there are two noncascading exciton energy relaxation pathways.

Effect of Adiabaticity on Electron Dynamics in Zinc Myoglobin

Electron-vibration coupling in zinc substituted myoglobin has been calculated using a quantum mechanical/molecular mechanical method. The methodology has been tested by a direct comparison of the calculated optical observables, the steady-state optical spectra and three-pulse-photon-echo-peak-shift (3PEPS) function, to those experimentally measured showing a qualitative agreement. A range of experiments and calculations were performed to explain the discrepancies, which lead to the conclusion that the discrepancy originates from adiabatic coupling of the two nearly degenerate electronic transitions.

Two-dimensional spectroscopy of electronic couplings in photosynthesis

Time-resolved optical spectroscopy is widely used to study vibrational and electronic dynamics by monitoring transient changes in excited state populations on a femtosecond timescale. Yet the fundamental cause of electronic and vibrational dynamics--the coupling between the different energy levels involved--is usually inferred only indirectly. Two-dimensional femtosecond infrared spectroscopy based on the heterodyne detection of three-pulse photon echoes has recently allowed the direct mapping of vibrational couplings, yielding transient structural information. Here we extend the approach to the visible range and directly measure electronic couplings in a molecular complex, the Fenna-Matthews-Olson photosynthetic light-harvesting protein. As in all photosynthetic systems, the conversion of light into chemical energy is driven by electronic couplings that ensure the efficient transport of energy from light-capturing antenna pigments to the reaction centre. We monitor this process as a function of time and frequency and show that excitation energy does not simply cascade stepwise down the energy ladder. We find instead distinct energy transport pathways that depend sensitively on the detailed spatial properties of the delocalized excited-state wavefunctions of the whole pigment-protein complex.

Probing electronic coupling in excitonically coupled heterodimer complexes by two-color three-pulse photon echoes

Following the earlier work of Yang et al. [J. Chem. Phys. 110 (1999) 2983] analytical expressions for the downhill and uphill resonant two-color three-pulse photon echo peak shift (2C-3PEPS) of a heterodimer system are derived in the impulsive limit. It is shown how to obtain information about coupling between the components of the dimer from the combined one- and two-color peak shift measurements. Further analytical relations are derived which enable site specific information about the environment of the components, including the relative difference of the inhomogeneity and the difference between the energy-gap correlation functions on the heterodimer sites to be obtained. The simulations show only a very small influence of the laser pulse length on the measured values of coupling coefficient and other relevant quantities suggesting that current 2C-3PEPS measurements can find practical application in directly measuring couplings in excitonically coupled heterodimer complexes.