  Generalized Langevin Equation (GLE) thermostats have been used very
effectively as a tool to manipulate and optimize the sampling of thermodynamic
ensembles and the associated static properties. Here we show that a similar,
exquisite level of control can be achieved for the dynamical properties
computed from thermostatted trajectories. By developing quantitative measures
of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic
oscillator, we show that these analytical results accurately predict the
behavior of strongly anharmonic systems. We also show that it is possible to
correct, to a significant extent, the effects of the GLE term onto the
corresponding microcanonical dynamics, which puts on more solid grounds the use
of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and
could help improve the prediction of dynamical quantities from techniques that
use a Langevin term to stabilize dynamics. Finally we address the use of
thermostats in the context of approximate path-integral-based models of quantum
nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some
of the artifacts associated with these techniques, improving the quality of
results for the modelling of vibrational dynamics of molecules, liquids and
solids.
