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.PACS numbers: 78.20. Bh, 33.20.Ea, 05.40.Jc Introduction and Theory. Model systems play an important role for our understanding of complex manybody dynamics. Reducing the description to a few parameters can not only ease the interpretation, but enable the identification of key properties [1]. In condensed phase dynamics the spin-boson [2] and Caldeira-Leggett (CL) [3, 4] models have been the conceptual backbone of countless studies [5]. The latter has been extended to describe linear and non-linear spectroscopy within the second-order cumulant approximation, termed multimode Brownian oscillator model in this context [6,7]. It has become a popular tool for assigning spectroscopic signals in the last two decades.The CL model comprises an arbitrary system (coordinates x, potential V S (x)), which is bi-linearly coupled to a bath of harmonic oscillators (coordinates Q i , potential V B ({Q i })) via a system-bath coupling potential V S−B (x, {Q i }) [3]. Later Caldeira and Leggett extended the model to an arbitrary function of system coordinates in the coupling and motivated the linearity of the coupling on the bath side [4]. Here, we limit ourselves to the bi-linear version for the reasons that will become apparent later. Restricting ourselves to a one-dimensional case yields [5]

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. INTRODUCTIONStudying complex dynamics of many-particle systems has become one of the main goals in modern molecular physics. The fundamental understanding of the underlying microscopical processes requires the interplay of elaborate experimental techniques and sophisticated theoretical approaches. Experimentally, (non-)linear spectroscopy revealed itself as a powerful tool for probing the dynamics and for determining the characteristic timescales, such as dephasing/relaxation times and reaction rates to name but two. For interpreting the experimental spectra theoretical models are needed which can give insight into the atomistic dynamics. Often, a reduction of the description to few variables is convenient in many cases since this can not only ease the interpretation, but enable the identification of key properties [1]. Such a reduced description can formally be obtained from the so-called system-bath partitioning, where only a small subset of degrees of freedom (DOFs), referred to as system, is considered as important for describing a physical process under study. All the other DOFs, referred to as bath, are regarded as irrelevant in the sense that they might influence the time evolution of the system but do not explicitly enter any dynamical variable of interest. Practically, such a separation is often natural, for instance, when studying a reaction with a clearly defined reaction center or solute dynamics in a solvent environment. Further, reduced equations of motion (EOMs) for the system DOFs can be derived in which the influence of the bath is limited to dissipation and fluctuations.The most simple formulation of this idea is provided by the Markovian Langevin equation, where dissipation and fluctuations take the form of static friction and stochastic white noise, respectively [2][3][4]. Sit...

Semiclassical techniques constitute a promising route to approximate quantum dynamics based on classical trajectories starting from a quantum-mechanically correct distribution. One of their main drawbacks is the so-called zero-point energy (ZPE) leakage, that is artificial redistribution of energy from the modes with high frequency and thus high ZPE to that with low frequency and ZPE due to classical equipartition. Here, we show that an elaborate semiclassical formalism based on the Herman-Kluk propagator is free from the ZPE leakage despite utilizing purely classical propagation. This finding opens the road to correct dynamical simulations of systems with a multitude of degrees of freedom that cannot be treated fully quantum-mechanically due to the exponential increase of the numerical effort.

Abstract. The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [J. Phys. Chem. Lett., 6, 2722Lett., 6, (2015] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particular example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics [J. Chem. Phys., 142, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give handy empirical criteria and discuss the effect of the potential renormalization term. The obtained results provide evidence that the CL model can be used for describing a potentially broad class of systems.

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. It is shown that the numerical protocol for the Herman-Kluk propagator, which contains the van Vleck one as a particular case, coincides in both representations. The flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states, being not bound to minimal uncertainty, is investigated numerically on prototypical potentials. Exploiting this flexibility provides neither qualitative nor quantitative improvements. Thus, the well-established Herman-Kluk propagator in Hilbert space remains the best choice to date given the large number of semiclassical developments and applications based on it.