  We consider atomistic geometry relaxation in the context of linear tight
binding models for point defects. A limiting model as Fermi-temperature is sent
to zero is formulated, and an exponential rate of convergence for the nuclei
configuration is established. We also formulate the thermodynamic limit model
at zero Fermi-temperature, extending the results of [H. Chen, J. Lu, C. Ortner.
Arch. Ration. Mech. Anal., 2018]. We discuss the non-trivial relationship
between taking zero temperature and thermodynamic limits in the finite
Fermi-temperature models.
