Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

Appearance of intramolecular high-frequency vibrations in two-dimensional, time-integrated three-pulse photon echo data

An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.     

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.     

Two-dimensional circularly polarized IR photon echo spectroscopy of polypeptides: four-wave-mixing optical activity measurement

A coherent two-dimensional (2D) optical spectroscopy utilizing circularly polarized (CP) beams, which was shown to be useful in studying molecular chirality in condensed phases, was theoretically proposed recently [Cho et al. J. Chem. Phys. 2003, 119, 7003]. A photon echo (PE) version of 2D optical activity spectroscopy is discussed in this paper. Considering various dipeptide and polypeptide systems, where the amide I local modes constitute the set of basis modes used to describe exciton and biexciton states as linear combinations of those basis modes, we present numerically simulated 2D circularly polarized IR PE spectra. It is shown that this novel spectroscopic method can provide additional information on the angles between the transition magnetic dipole and the transition electric dipole of two different vibrationally excited states, which are highly sensitive to the 3D structure and chirality of a given polypeptide. Also, a hierarchical relation of IR absorption, vibrational circular dichroism, 2D IR PE, and 2D CP-IR PE is discussed to show advantages of 2D optical activity spectroscopy in general.     

Signatures of beta-peptide unfolding in two-dimensional vibrational echo spectroscopy: a simulation study.

An ensemble of exciton Hamiltonians for the amide-I band of the folded and unfolded states of a helical beta-heptapeptide is generated using a molecular dynamics (MD) simulation. The correlated fluctuations of its parameters and their signatures in two-dimensional (2D) vibrational echo spectroscopy are computed. This technique uses infrared pulse sequences to provide ultrafast snapshots of molecular structural fluctuations, in analogy with multidimensional NMR. The present study demonstrates that, by combining a method of calculating the vibrational Hamiltonian from MD snapshots and the nonlinear exciton equations (NEE), it may be possible to simulate realistic multidimensional IR spectra of chemically and biologically interesting systems.     

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.     

Energy-transfer and charge-separation pathways in the reaction center of photosystem II revealed by coherent two-dimensional optical spectroscopy

The excited state dynamics and relaxation of electrons and holes in the photosynthetic reaction center of photosystem II are simulated using a two-band tight-binding model. The dissipative exciton and charge carrier motions are calculated using a transport theory, which includes a strong coupling to a harmonic bath with experimentally determined spectral density, and reduces to the Redfield, the F?rster, and the Marcus expressions in the proper parameter regimes. The simulated third order two-dimensional signals, generated in the directions -k(1)+k(2)+k(3), k(1)-k(2)+k(3), and k(1)+k(2)-k(3), clearly reveal the exciton migration and the charge-separation processes.     

Noble-gas broadening of an optical transition of I2 measured by coherent transients. II. Three-pulse stimulated photon echo experiments

Solutions are derived for the decay of a three-pulse stimulated photon echo, including the separate treatment of the spectral diffusion in the Doppler profile within and out of the spectral bandwidth of the excited molecules. Thermal cross sections are obtained for the X Σ_g⁺ (ν″ = 2, J″= 59) → B³Π_0⁺u(ν′ = 15, J′= 60) transition of iodine molecules perturbed by noble gases. It is argued that under certain experimental conditions using the results of two-pulse delayed emission measurements, direct information can be obtained for spectral diffusion restricted within the bandwidth of excited molecules.     

Novel coherent two-dimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules

We demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The third-order optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k(2) in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (Ornstein-Uhlenbeck, two-state jump, and diffusion in double well) of the dihedral angle that controls the chirality.     

Signatures of beta-sheet secondary structures in linear and two-dimensional infrared spectroscopy

Using idealized models for parallel and antiparallel beta sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition-dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel beta sheets and between beta hairpins and extended beta sheets.     

Circular dichroism and absorption spectroscopy of merocyanine dimer aggregates: molecular properties and exciton transfer dynamics from time-dependent quantum calculations

A wave packet approach to the calculation and interpretation of circular dichroism (CD) spectra is applied to the spectroscopy of aggregates of a merocyanine dye. A combined analysis of absorption and CD spectra allows for the extraction of geometric information and excited state electronic coupling. It is shown that in the case of dimer aggregates of a chiral merocyanine dye, it is possible to infer the dynamics of an exciton transfer directly from the CD spectrum. This relation is established via the Fourier relation to a time-dependent correlation function reflecting the quantum dynamics in the dye aggregate.     

Noble-gas broadening of an optical transition of I2 measured by coherent transients. III. Two-pulse photon echo and free induction decay

We report two-pulse photon echo decay and free induction decay measurements of iodine as a function of noble-gas pressure. The non-exponential behavior of the two-pulse photon echo decay which in contrast to the free induction decay shows a t³ dependence, is extensively discussed. A comparison with the results of the three-pulse stimulated echo measurements is made. The results are interpretated in terms of a quantum mechanical transport equation, and analytical expressions are derived for the three-pulse stimulated echo, two-pulse echo and free induction decay.     

The polarized electronic spectra and electric field spectra of benzo-diazoles. II. 2,1,3-benzothiadiazole

The S₁ ← S₀ absorption spectra of 2,1,3-benzothiadiazole (BTD) have been measured at 4.2 K in four different host crystals: naphthalene, durene, p-dichlorobenzene (DCB) and p-dibromobenzene. Detailed vibrational analyses are given for BTD imbedded in napthalene and DCB. The polarization measurements show that the S₁ state has B₂ symmetry, like its selenium analogue (BSD). The transition is dominated by a single totally symmetric mode - 484 cm^?1. The Herzberg-Teller coupling contributes only a very small fraction of the total intensity. The Stark measurements of a DCB sample containing both BTD and BSD enabled us to compare the charge distribution of BTD and BSD in the state S₁. The Stark splittings of BTD are 17% greater than the splittings of BSD. Reorganization of the σ-core during the excitation is used to explain the difference. The drastic change in dipole moment upon excitation implies that the S₁←S₀ transitions of BTD and BSD are not localized in the six-membered ring as suggested by previous workers. Weak phosphorescence of BTD in napthalene and DCB and singlet-triplet absorption spectrum of neat BTD have been observed. The heavy atom effect of spin-orbit coupling is to explain the ST absorption intensity of BTD and BSD.     

Theoretical studies on the electronic structures and absorption spectra of substituted benzenes with one- and two-dimensional charge transfer character

The electronic structures and absorption spectra of one- and two-dimensional charge transfer (CT) molecules based on para-nitroaniline (pNA) and 1,3-diamino-4,6-dinitro- benzene (DADB) have been studied theoretically via semi-empirical and ab initio methods. It is found that the behaviors of optical absorption are strongly influenced by the dimension of CT. Different from the well-known one-dimensional CT molecule of pNA, which shows one intense absorption related to the π → π^* CT transition, two-dimensional CT molecule of DADB exhibits more absorption peaks associated with various low-lying CT transitions in near ultraviolet range. In addition, the relative orientations of transition dipole moment and ground state dipole moment in one- and two-dimensional charge transfer molecules were also discussed.     

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.     

Localization and coherent dynamics of excitons in the two-dimensional optical spectrum of molecular J-aggregates

Two-dimensional optical spectra of J-aggregates at low temperature provide a large amount of information about the nature and dynamics of exciton states that is hidden in conventional broad band pump-probe spectra. By using numerical simulations, we study the two-dimensional absorption spectrum and find that it is dominated by a V-shaped negative peak and a blueshifted elliptic positive peak. We demonstrate a simple method to derive the energy dependence of the exciton localization size from the distance between these two features in the zero waiting time experiment. When the waiting time is turned on, the V peak is filled with an extra positive peak resulting from population relaxation. From the time evolution of this peak, energy dependent relaxation rates can be obtained. The oscillations of coherent contributions to the two-dimensional spectrum are not damped by inhomogeneous mechanisms and can be seen clearly.     

Simultaneous time and frequency detection in femtosecond coherent Raman spectroscopy. II. Application to acetonitrile

The preceding paper showed that, in principle, a high-resolution coherent Raman spectrum can be recovered using femtosecond probe pulses by combined detection in both time and frequency. This measurement is possible even when the pulses are too broad in frequency for conventional frequency-domain spectroscopy and too broad in time for conventional time-domain spectroscopy. In this paper, the method is tested on experimental coherent anti-stokes Raman spectroscopy data from acetonitrile. Compared to theoretical models, experimental data are complicated by noise and incomplete knowledge of the pulse structure. Despite these complications, most of the information in the Raman spectrum is recovered from the data: weak transitions are detected and natural-linewidth resolution is achieved across an 800 cm(-1) spectral range. However, circumstances in which experimental limitations result in missed features or ambiguities in the recovered spectrum are also identified. These results suggest where improvements in measurement and data analysis can be made.