  Formulating a rigorous system-bath partitioning approach remains an open
issue. In this context the famous Caldeira-Leggett model that enables quantum
and classical treatment of Brownian motion on equal footing has enjoyed
popularity. Although this model is by any means a useful theoretical tool, its
ability to describe anharmonic dynamics of real systems is often taken for
granted. In this Letter we show that the mapping between a molecular system
under study and the model cannot be established in a self-consistent way,
unless the system part of the potential is taken effectively
harmonic.Mathematically, this implies that the mapping is not invertible. This
`invertibility problem' is not dependent on the peculiarities of particular
molecular systems under study and is rooted in the anharmonicity of the system
part of the potential.
