  Fundamental understanding of complex dynamics in many-particle systems on the
atomistic level is of utmost importance. Often the systems of interest are of
macroscopic size but can be partitioned into few important degrees of freedom
which are treated most accurately and others which constitute a thermal bath.
Particular attention in this respect attracts the linear generalized Langevin
equation (GLE), which can be rigorously derived by means of a linear projection
(LP) technique. Within this framework a complicated interaction with the bath
can be reduced to a single memory kernel. This memory kernel in turn is
parametrized for a particular system studied, usually by means of time-domain
methods based on explicit molecular dynamics data. Here we discuss that this
task is most naturally achieved in frequency domain and develop a Fourier-based
parametrization method that outperforms its time-domain analogues. Very
surprisingly, the widely used rigid bond method turns out to be inappropriate
in general. Importantly, we show that the rigid bond approach leads to a
systematic underestimation of relaxation times, unless the system under study
consists of a harmonic bath bi-linearly coupled to the relevant degrees of
freedom.
