Non-Linear Vibrational Normal Modes of Biomolecules

The vibrational harmonic normal modes of a molecule, which are valid at relatively low energies close to a potential minimum, are extended by periodic orbits to higher energies where anharmonicity and coupling of the degrees of freedom set in. The families of periodic orbits which emanate from the equilibria (minima and transition states) of a molecular potential energy function are located with multiple shooting methods and they are continued in energy. The method is well established for triatomic molecules, and recently it has been applied to biomolecules such as alanine dipeptide. Long lived localized trajectories associated with specific conformations and non-linear vibrational modes can be traced. The influence of a solvent like water to excited non-linear normal modes is examined.