A new approach to integrate the equations of motion of adiabatically separated systems, such as electronic and nuclear degrees of freedom in first-principle simulations, is presented. The method, called Mass-zero constrained dynamics (MaZe), starts from an extended Lagrangian formulation and enforces full adiabatic separation via a rigorous zero-mass limit for the electronic degrees of freedom. Constraints are employed to impose, at each time step, the condition that the gradient of the energy with respect to the electronic degrees of freedom is null. It can be shown that MaZe dynamics samples exactly the Born-Oppenheimer probability density for the nuclear degrees of freedom.

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