The Duschinsky effect has been shown to be significant in spectroscopy and dynamics of molecules that involve the π−π* transitions. In this paper, we present a derivation of exact expressions for optical absorption and radiationless transitions in polyatomic molecules with displaced−distorted−rotated harmonic potential surfaces. In the formulation, we take into account the temperature effect exactly. The application of this new formulation is demonstrated for ethylene and allene, where the Duschinsky effect in the first singlet excited electronic state is very strong.

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.

The binding interactions between the pyridine and small noble metal clusters in different sizes (n ) 2-4) have been investigated by using quantum chemical methods. The binding energies of Py-M 2 complexes are obtained at the levels of the Hartree-Fock method (HF), the second-order Møller-Plesset perturbation theory (MP2), the local density functional method (SVWN), the nonlocal density functional method (BLYP, BPW91, G96LYP, G96PW91), and the hybrid density functional method (B3LYP and B3PW91). All calculated results show that the bonding is stronger in pyridine/copper and pyridine/gold than that in pyridine/silver. The bonding mechanism is explored in terms of the bonding molecular orbital properties. The donation interaction of the lone-pair electrons on nitrogen of the pyridine molecule to the unoccupied orbital of each metal cluster plays an important role. The force constants of the internal coordinates of interests are presented. The vibrational frequency shift has been analyzed on the basis of the coupling between the internal vibrational modes of pyridine and the nitrogen-metal stretching modes as well as the metal-metal stretching modes. For lowfrequency Raman spectra of pyridine-small silver cluster complexes, we propose a new assignment to the N-Ag and Ag-Ag stretching vibrations. The calculated infrared intensities of vibrational modes are compared with the experimental spectra.

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.

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), Tully's 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.

Excited-state twisting and relaxation of triarylpyrylium cations with various substituents attached to different parts of the molecule were studied by means of femtosecond pump−probe absorption spectroscopy and modeled numerically. The model was based on calculations of the population evolution on the excited- and ground-state potential surfaces, which are significantly different for nonstabilized and stabilized states because of the essential angular dependence of the stabilization energy. The modeling shows that a broad population distribution along the twisting angle in the ground state is transferred to the excited state, causing strong fluorescence broadening, while competition between the excited-state twisting and solvation determines a subsequent reaction path. The internal conversion rate is determined by the energy gap law and, depending on the attached substituents, is governed either by twisting or by solvation processes.

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