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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