In free energy calculations, we use Langevin integrator.
However, can we use md integrator with some other thermostat? Is there a fundamental problem which prevents using other kinds of thermostats for free energy calculations?
Yes, there is a fundamental problem when one decouples a molecule or degrees of freedom. Then thermostat is required that thermalizes all degrees of freedom individually. An An integrator is one of there, but an Andersen thermostat might also work.
When no degrees of freedom are decoupled, you can use any thermostat.