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The Journal of Physical Chemistry C

Anharmonic Electron−Phonon Coupling in Condensed Media: 2. Application to Electronic Dephasing, Hole-Burning, and Photon Echo

Mohamad M. Toutounji

Published Nov 3, 2010• 13 citations
Publisher

Abstract

While different expressions of homogeneous linear electronic dipole moment time correlation functions and their respective absorption lineshapes of anharmonic systems were derived and discussed at length in part I [Toutounji, M. J. Phys. Chem. B 2010, in press] of this study, the electronic dephasing (zero-phonon line width), caused by pseudolocal phonons, and vibrational relaxation time scales were treated equally, hence, unphysical. In this study electronic dephasing and vibrational structure are correctly accounted for in harmonic and anharmonic multimode systems. Model calculations are presented. Anharmonic hole-burned spectra are calculated using linear anharmonic absorption lineshapes. An analytical expression of hole-burned absorption line shape in terms of the linear dipole moment time correlation function, leading to a hole-burned absorption line shape expressed in time-domain, is reported. An elementary method is utilized to treat nonlinear spectra in anharmonic molecules. The link between a hole-burned spectrum and a 2-pulse photon echo profile is established by combining the theoretical framework of Mukamel and that of Hays-Small, thereby calculating photon echo signals of anharmonic systems. Model photon echo calculations of a solvable harmonic model and an anharmonic system are reported. Applications to Al-phthaolcyanine tetrasulphonate (APT) in hyperquenched glassy ethanol and special pair bacterial reaction center are presented and discussed in detail.

DOI
10.1021/jp1069913

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While different expressions of homogeneous linear electronic dipole moment time correlation functions and their respective absorption lineshapes of anharmonic systems were derived and discussed at length in part I [Toutounji, M. J. Phys. Chem. B 2010, in press] of this study, the electronic dephasing (zero-phonon line width), caused by pseudolocal phonons, and vibrational relaxation time scales were treated equally, hence, unphysical. In this study electronic dephasing and vibrational structure are correctly accounted for in harmonic and anharmonic multimode systems. Model calculations are presented. Anharmonic hole-burned spectra are calculated using linear anharmonic absorption lineshapes. An analytical expression of hole-burned absorption line shape in terms of the linear dipole moment time correlation function, leading to a hole-burned absorption line shape expressed in time-domain, is reported. An elementary method is utilized to treat nonlinear spectra in anharmonic molecules. The link between a hole-burned spectrum and a 2-pulse photon echo profile is established by combining the theoretical framework of Mukamel and that of Hays-Small, thereby calculating photon echo signals of anharmonic systems. Model photon echo calculations of a solvable harmonic model and an anharmonic system are reported. Applications to Al-phthaolcyanine tetrasulphonate (APT) in hyperquenched glassy ethanol and special pair bacterial reaction center are presented and discussed in detail.
An approximate excited state vibrational Hamiltonian, He, which accounts for both linear and diagonal quadratic electron-phonon coupling is derived and shown to be adequate for mode frequency changes up to ~30%. The associated linear response function which is valid for finite temperature in the absence of damping is obtained. 2-point correlation function or, equivalently, the line broadening function, g(t;T), that provides a good physical description of pure electronic dephasing and vibrational damping for linearly coupled modes is postulated. A linear response function that accounts for pure electronic dephasing and damping for systems with either linearly or quadratically coupled modes is proposed. Applications of the new linear response function include the single site absorption and hole-burned spectra of the special pair band of the bacterial reaction center and the temperature dependence of the single site absorption spectrum of Al-phthalocyanine tetrasulphonate in glassy ethanol. A 4-point correlation function which is valid for finite temperature in the absence of damping using the approximate excited state vibrational Hamiltonian, He, is derived. An impulsive stimulated photon echo signal for a single-mode system with very large inhomogeneous broadening is calculated using the 4-point correlation function. An expression for ordinary photon echo with two finite pulses is derived. 4-point correlation function for linearly coupled modes is expressed in terms of g(t;T) and can be used to calculate all non-linear spectroscopic signals. Applications of the 4-point correlation function are limited to impulsive 2-pulse photon echo (IPE) signals. IPE signals are generated for different values of the Huang-Rhys factor (S) at a fixed temperature and at different temperatures for a fixed value of S in order to see how the echo profile changes as one varies S or temperature. An initial fast non-exponential decay, which reflects the contribution of the phonon sideband, followed by vibrational oscillations (quantum beats) due to linear electron-phonon coupling and a slow exponential decay, on picosecond time scales, due to the zero-phonon line are observed in the IPE signals. Application of IPE to the special pair absorption band of the bacterial reaction center is also included.
The multimode Brownian oscillator (MBO) model has been at the forefront in interpreting the subsystem−bath interaction manifestations in optical spectroscopy for probing homogeneous structure of chromophores in crystals and amorphous solids. The spectroscopic consequences of employing the underdamped MBO model with Ohmic dissipation in linear absorption, photon-echo, and hole-burning data of chromophores in solid hosts at low temperatures are investigated. The zero-phonon line (ZPL) in homogeneous linear absorption spectrum, the slow-decay component (due to ZPL) in photon-echo signal, and the zero-phonon hole (ZPH) in hole-burned spectra in host molecular solids at low temperatures are usually resolved from the multiphonon-transitions structure. In the MBO model, the harmonic vibrations (Brownian oscillators) are linearly coupled to bath modes. This coupling, with Ohmic dissipation, results in a maximum contribution of the bath modes to the ZPL region. This contribution affects the width of the ZPL profile, which should only be determined by pure electronic dephasing as dictated by experiments. It is therefore important to study how the MBO model bath modes contribute to the ZPL, ZPH, and slow-decay component profiles. Analytical expressions for the linear absorption spectrum and width and Franck−Condon factor of the ZPL are derived. Homogeneous linear absorption spectra, two-pulse photon-echo, and hole-burning calculations are carried out with model systems of which the parameter values are typical for real systems. The MBO model ZPL, ZPH, and slow-decay component were not seen in linear absorption, hole-burning, and two-pulse photon-echo profiles, respectively. The hole-burned spectrum is produced by blending the line broadening function, g ( t; T ), of the MBO model and Small hole-burning formula. This full (inclusion of Matsubara series) form of g ( t; T ) has not been exploited before in any spectroscopic calculation. It is concluded that the MBO model ZPL and ZPH widths and the electronic exponential decay are better exhibited in the corresponding profiles when using non-Ohmic spectral density.
A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.
The first two-pulse photon echo experiments on a chromophore in an organic glass are reported. The homogeneous electronic dephasing of resorufin in ethanol glass is measured from 1.5–11.4 K. The temperature dependence of the dephasing time does not fit the power law frequently predicted by theory for the dephasing characteristic of glasses. However, the temperature dependence can be accounted for by including dephasing from librations or acoustic phonons, mechanisms known to be important in crystals. The dephasing decay is found to be a single exponential for over six factors of e. The dephasing is also shown to be uncorrelated with the extent of nonphotochemical hole burning (NPHB). However, the homogeneous linewidth deduced from the photon echo is four times narrower than the linewidth obtained from NPHB, demonstrating that the hole is broadened by additional processes.
Photon echo and non-photochemical hole burning experiments on cresyl violet in ethanol glass are reported. At 1.5 K the optical dephasing time measured by the picosecond echo is eight times longer than the time measured by hole burning because of the difference in the time scales associated with the measurements. The observed temperature dependence arises from the glass's two-level systems and from a pseudolocal phonon mode at higher temperatures. Comparing the ratios of the echo to hole burning dephasing times for cresyl violet and resornfin, suggests that their dephasing is influenced by the nature of their ethanol solvation shells in addition to the dynamics of the bulk ethanol.
The vibrational photon echo measurement employs short pulses of coherent infrared radiation to discriminate among line broadening processes of different time scales. The measurement has been analyzed with the optical Bloch equations, in which the coupling of a quantum three-level system to a bath is represented by dephasing times. A detailed treatment of vibrational dynamics in a molecular liquid requires a Hamiltonian model. As such models are more readily treated in classical than in quantum mechanics, we consider the calculation of the vibrational echo in classical mechanics. Vibrational echoes are calculated for a solvated anharmonic oscillator. The classical mechanical echo is shown to share attributes of a quantum mechanical calculation.