Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials

Abstract

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.

On computing spectral densities from classical, semiclassical, and quantum simulations

“…For this situation, the developed Fourier method provides a way to map the true environment onto the CL model resulting in an effective spectral density that tries to mimic its influence on the system by fluctuations and dissipation. Although we have shown in a previous study that such a mapping can be inconsistent due to the 'invertibility problem' [19], chances are high to find a proper example in the solid regime or on surfaces [20,57]. For these cases, it will be interesting to check if the obtained spectral density depends on whether the underlying explicit dynamics is performed classically or quantum-mechanically.…”

“…One way is to follow the same pathway as in Refs. 19,20 and to multiply the GLE by the initial momentum p(0) followed by an average ... with respect to the initially factorized system and bath states. Irrespectively of whether a classical or quantum average is performed, this amounts to an integro-differential equation in terms of the momentum autocorrelation function (MAF) C pp (t) ≡ p(0)p(t) and the momentum-force correlation function (MFC)…”

“…Semiclassical quantities were evaluated via importance sampling using 10 As it was intensively discussed in Refs. [19,20], the numerical noise stemming from the usually unconverged tails of the time domain functions needed to be properly reduced. For this purpose, a Gaussian low-pass filter was applied before the half-sided Fourier transform, i.e.…”

“…In this respect, the CL model can be viewed as a promising framework for open dynamics connecting explicit classical MD simulations with a corresponding reduced quantum-dynamical treatment based on spectral densities. However, doubts about this mindset can arise from previous studies, where the CL model has been shown to suffer from the so-called invertibility problem [19,20]. It states that a mapping of a realistic system onto a model is not invertible, thereby undermining the self-consistency and, thus, validity of the CL model.…”

Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

“…The parameters τ k and ω k , along with the coupling strengths, G k (r), can be either deduced from the first principle system-bath Lagrangian (in the classical case, [35,41]) or fitted to an approximate memory kernel, K, obtained from benchmark molecular dynamics simulations [42][43][44][45]. While the second case is most useful in practise, the exact mapping between the first principle Lagrangian and the parametrisation of the GLE kernel ensures that both the equilibrium and relaxation of the physical DoFs are correctly modelled, at least in the classical case.…”