Applicability of the Caldeira-Leggett Model to Vibrational Spectroscopy in Solution

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 and is rooted in the anharmonicity of the system part of the Caldeira-Leggett model potential.