  We consider spin dynamics for implementation in an atomistic framework and we
address the feasibility of capturing processes in the femtosecond regime by
inclusion of moment of inertia. In the spirit of an {\it s-d} -like interaction
between the magnetization and electron spin, we derive a generalized equation
of motion for the magnetization dynamics in the semi-classical limit, which is
non-local in both space and time. Using this result we retain a generalized
Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and
demonstrate how the exchange interaction, damping, and moment of inertia, all
can be calculated from first principles.
