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.