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In computational 3D geometric problems involving rotations, it is often that people have to convert back and forth between a rotational matrix and a rotation described by an axis and a corresponding angle. For this purpose, Rodrigues' rotation formula is a very popular expression to use because of its simplicity and efficiency. Nevertheless, while converting a rotation matrix to an axis of rotation and the rotation angle, there exists ambiguity. Further judgement or even manual interference may be necessary in some situations. An extension of the Rodrigues' formula helps to find the sine and cosine values of the rotation angle with respect to a given rotation axis is found and this simple extension may help to accelerate many applications., Comment: 9 pages, 1 figure, minor typo corrected

In the present work, we analyze the influence of the polarization effects taking place during the course of a 2DIR spectroscopy experiment performed on a molecular system undergoing an intermolecular vibrational energy transfer process. When both donor and acceptor molecules participating in the vibrational energy transfer are embedded in a host solvent, they face rotational diffusion that strongly distorts the resulting 2DIR spectra. It could be expected that the difference between rotational diffusion constants will be of particular interest. For this purpose, the polarization effects are discussed according to the different orderings of the laser-molecule interactions. Next, we study the distortions of the spectra as a function of the rotational diffusion constants of the individual molecules. The knowledge of these polarization effects are relevant to the interpretation of the spectra. Finally, the conclusions reached in this work for a vibrational energy transfer are valid for any other type of third-order optical process performed on the same molecular system., Comment: 30 pages, 9 figures. To be submitted to Journal of Chemical Physics

In the present work, we give an analytical non-perturbative treatment of mode-mode coupling and anharmonicity occurring in molecular vibrational systems analyzed by 2D-infrared spectroscopy. This analytical description allows a detailed discussion of the intricate structure of the 2D-infrared spectra resulting from the contributions provided by the various possible chronological orderings of the interactions with fields due to overlaps of the pulses. The peculiar role of the vibrational overtones and other combination states on the resonance shapes is elucidated and conditions for a better quantitative analysis are discussed., Comment: 36 pages, 11 figures. To be submitted. Replaced wrong source file in version 2

In the present work, the analytical description of an intermolecular vibrational energy transfer, analyzed by two dimensional infrared spectroscopy, is established. The energy transfer process takes place between the dark combination states of low frequency modes pertaining to different molecules. The appearance of the cross peaks results from coherent transfer between these combination states and an optically active state of the acceptor molecule. Such a process has recently been observed experimentally between the nitrile groups of acetonitrile-d3 and benzonitrile molecules. This molecular system will be used as a model for the simulations of their two-dimensional infrared spectra. The dependence of the cross-peak growth, which is a signature of the intermolecular energy transfer, will be discussed in detail as a function of the molecular dynamical constants., Comment: 25 pages, 5 figures. Added acknowledgment in the second version. To be submitted

It has long been accepted that the multiple-ion single-file transport model is appropriate for many kinds of ion channels. However, most of the purely theoretical works in this field did not capture all of the important features of the realistic systems. Nowadays, large-scale atomic-level simulations are more feasible. Discrepancy between theories, simulations and experiments are getting obvious, enabling people to carefully examine the missing parts of the theoretical models and methods. In this work, it is attempted to find out the essential features that such kind of models should possess, in order that the physical properties of an ion channel be adequately reflected., Comment: 25 pages, 5 figures. To be submitted

In this work we focused on the kinetics of a one-dimensional Ising system (1DIS) with constant nearest-neighbor interaction (NNI). The exact solution of both thermodynamics and kinetics of this system under quasi-chemical approximation (QCA) had been shown in the literature, and the equilibrium solution was exact. In this work, it was discussed why QCA applied the best in the case of 1DIS with constant NNI. Furthermore, extension had been made to discuss that due to this special reason, perhaps the kinetics of the system under QCA is the correct steady-state kinetics. Inspired by this observation, the activity and activity coefficients of the system was studied closely to re-examine the form of the equation of motion under QCA. A novel concept---the instantaneous activities and the corresponding instantaneous activity coefficients---was introduced, and in terms of these quantities the kinetics seemed to be much simpler and physically more meaningful. The chevron plot of this system was also discussed and new way of looking at the \emph{rollover} of chevron plots was presented., Comment: 26 pages, 5 figures