On the Applicability of the Caldeira-Leggett Model to Condensed Phase   Vibrational Spectroscopy
  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. 
Sergei D. Ivanov, Fabian Gottwald, Oliver K\"uhn
physics.chem-ph