Vibration modes and phonons

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In this set of exercises we will use the method of finite-differences implemented in Siesta to compute force constants in real space. We will explore the cases of a crystal and a molecule. In the former case we will focus on the need of a supercell to represent the real-space force constants, while in the second we will understand how to visualize the vibrational modes.

• Phonon dispersion of bulk Si
• Modes of vibration of the benzene molecule