Kuo Kan Liang

Free-energy analysis of solubilization in micelle

A statistical-mechanical treatment of the solubilization in micelle is presented in combination with molecular simulation. The micellar solution is viewed as an inhomogeneous and partially finite, mixed solvent system, and the method of energy representation is employed to evaluate the free-energy change for insertion of a solute into the micelle inside with a realistic set of potential functions. Methane, benzene, and ethylbenzene are adopted as model hydrophobic solutes to analyze the solubilization in sodium dodecyl sulfate micelle. It is shown that these solutes are more favorably located within the micelle than in bulk water and that the affinity to the micelle inside is stronger for benzene and ethylbenzene than for methane. The micellar system is then divided into the hydrophobic core, the head-group region in contact with water, and the aqueous region outside the micelle to assess the relative importance of each region in the solubilization. In support of the pseudophase model, the aqueous region is found to be unimportant to determine the extent of solubilization. The contribution from the hydrophobic-core region is shown to be dominant for benzene and ethylbenzene, while an appreciable contribution from the head-group region is observed for methane. The methodology presented is not restricted to the binding of a molecule to micelle, and will be useful in treating the binding to such nanoscale structures as protein and membrane.

Algorithmic decoherence time for decay-of-mixing non–Born–Oppenheimer dynamics

The performance of an analytical expression for algorithmic decoherence time is investigated for non-Born-Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tullys fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with reinitiation (CSDM-D). The CSDM method is demonstrated to be the most accurate method, and it has several desirable features: (i) It behaves like the representation-independent SE method in the strong nonadiabatic coupling regions; (ii) it behaves physically like the TFS method in noninteractive region; and (iii) the trajectories are continuous with continuous momenta. The CSDM method is also demonstrated to balance coherence well with decoherence, and the results are nearly independent of whether one uses the adiabatic or diabatic representation. The present results provide new insight into the formulation of a physically correct decoherence time to be used with the CSDM method for non-Born-Oppenheimer molecular dynamic simulations.

Theoretical treatments of ultrafast electron transfer from adsorbed dye molecule to semiconductor nanocrystalline surface

In studying ultrafast electron transfer from a dye molecule to a nanosized semiconductor particle, pump-probe experiments are commonly used. In this system the electron transfer (ET) rate is faster than vibrational relaxation so that the ET rate should be described by a single-level rate constant and the probing signal (often in the form of time-resolved spectra) contains the contribution from the dynamics of both population and coherence (i.e., wave packet). In this paper, we shall present the theoretical treatments for femtosecond time-resolved pump-probe experiment and the dynamics of population and coherence by the density matrix method, and the calculation of single-level ET rate constant involved in a pump-probe experiment. As an application, we show the theoretical results using parameters extracted from experiments on a specific dye/semiconductor system.

Calculation of the vibrationally non-relaxed photo-induced electron transfer rate constant in dye-sensitized solar cells

In this paper we shall show how to calculate the single vibronic-level electron-transfer rate constant, which will be compared with the thermal averaged one. To apply the theoretical results to the dye-sensitized solar cells, we use a simple model to describe how we model the final state of the electron-transfer process. Numerical calculations will be performed to demonstrate the theoretical results.

Influence of distortion and Duschinsky effects on Marcus-type theories of electron transfer rate

In this paper, we focus on the microscopic theory of intra-molecular electron transfer (ET) rate. Specifically, we examine whether or not and/or under what conditions the widely-used Marcus-type equations are applicable to displaced–distorted (D-D) and displaced–distorted-rotated (D-D-R) harmonic oscillator (HO) cases. For this purpose, we apply the cumulant expansion (CE) method to derive the ET rate constants for these cases. Within the CE method, we find the analytical condition upon which the Marcus-type equations of the Gaussian form can be obtained for the D-D HO case as well as the displaced HO case. If there is significant distortion or Duschinsky mixing (mode mixing), the Marcus-type equations of the Gaussian form are not adequate, and we discuss the reasons for the breakdown of this form. We also find that the reorganization energy and the free energy change for the D-D HO depend on the temperature. This temperature dependent feature is different from the displaced HO case in which the reorganization energy and the free energy change are independent of the temperature. As a consequence, the pre-exponential factor of the ET rate shows a temperature dependence different from the usual 1/√T behavior. We explain this analytically, and show the effect by several numerical examples.

Thermodynamics and kinetics of protein folding: A mean field theory

The kinetic Ising model in the mean field approximation is applied to study the equilibrium and kinetic behaviors of protein folding–unfolding. In our model, we regard a protein as a topological collection of interacting peptide bonds (or other protein units). According to this model, thermodynamics and kinetics of protein folding–unfolding are related to the elementary process of folding ↔ unfolding of such interacting units. We shall show that even for the so-called two-state case of protein folding–unfolding, the kinetic behaviors are predicted to be in general non-exponential and that universal curves exist separately for the thermodynamic behaviors and kinetics behaviors of protein folding–unfolding. Our model can treat the effect of temperature and denaturant concentration on the thermodynamics and kinetics of protein folding–unfolding and provide the chevron plot. Satisfactory demonstrations are presented for treating experimental observations on the thermodynamical and kinetic responses of protein folding–unfolding to the changes in temperature and denaturant concentration and for exhibiting universal plots of proteins.

Influence of the transverse velocity on TC-RFWM spectra of jet-cooled CH

A saturation dip has been observed recently by A. Kumar et al. [Chem. Phys. Lett. 297 (1998) 300] in degenerate four-wave mixing (DFWM) and two-color resonant four-wave mixing (TC-RFWM) spectra of jet-cooled CH. This observation suggests that expressions of the signal intensity established for double-resonance molecular spectroscopy in the weak field limit are no longer valid. While the line splitting has been explained, this is not the case for the asymmetry observed on this spectrum. Here, we clearly establish the origin of this asymmetry as resulting from the transverse molecular velocity which acts even for a small velocity component. The model conveniently reproduces line splitting and asymmetry.

Theoretical studies of coherent phonon generation in dense media

The theory of pump-probe femto-second time-resolved experiment will be presented. For the case in which the pump and probe pulses do not overlap, the either can be referred to as the generalized linear response theory. The fs time-resolved spectra consist of the contributions from the dynamics of both population and coherence (or phase) of the nonstationary system. Unless the dephasing is fast, the quantum beat is often observed in fs time-resolved spectra. Recently, it has been found that some polymers could exhibit semiconducting properties. In particular, the conjugated polymers, poly (phenylene-vinylene), i.e., PPV, show strong photoluminescence and can form electroluminescent layer in light-emitting diodes (LED). To study the mechanisms of the photoluminescence of PPV, fs time-resolved experiments have been performed. In this paper, the theoretical analysis of these fs time-resolved spectra will be presented. 15