Vibrational relaxation and decoherence in structured environments: a numerical investigation

Abstract

Vibrational relaxation is a key issue in chemical reaction dynamics in condensed phase and at the gas-surface interface, where the enviroment is typically highly structured and cannot be condensed in a simple friction coefficient. Rather, full knowledge of the coupling of the molecular oscillator to the environment is required, as typically subsumed in the so-called spectral density (of the environmental coupling). Here, we focus on harmonic Brownian motion and investigate the effectiveness of classical, canonical position autocorrelation functions to compute the spectral density of the coupling needed to describe vibrational relaxation in complex environments. Classical dynamics is performed on model systems, and several effects investigated in detail, e.g. the presence of anharmonicity, the role of a high-frequency "Debye" cutoff in the environment and the influence of the detailed structure of the latter. The spectral densities are then used in standard independent oscillator Hamiltonian models which are numerically solved at T=0 K to investigate quantum relaxation and decoherence.

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling

“…As a result, the spectral densities still contain some undesired high frequency features recently discussed in Ref. 40 and, in particular, a growing base line that is due to the slow decay ofC(ω) above ω D . To remedy this numerical problem, we applied a low frequency filter to damp out the high frequency contributions, namely, we defined the working frequency-dependent correlation functionC H (ω) as…”

“…As discussed in Ref. 40, in such a situation where the system frequency exceeds the Debye frequency of the environment, only a δ-peak should ideally appear in a bilinear coupling model. In realistic situations, some broadening always occurs, for at least three main reasons: (i) the system anharmonicities (see below), (ii) the failure of the bilinear coupling assumption, and (iii) the dissipative-like trajectory propagation conditions.…”

“…A simple extension of the IO model with an exponential coupling based on the properties of the "true" bath only (i.e., on the SD at frequencies smaller than ω D ) has been discussed in Ref. 40. It only requires an additional length scale α −1 for the interaction that can be obtained, at least in principle from the knowledge of the full potential once the transformation to effective modes [41][42][43][44]55 has been performed, namely, through…”

“…Even though this relaxation incidentally turns out to occur on the right time scale, the coupling encoded in J C (ω) at these frequencies has little physical meaning and more than likely reflects artifacts of the MD approach (for a thorough investigation on this point, we refer to Ref. 40). Quantum dynamical calculations were performed using the MCTDH method, as described in Section IV, using three different bath discretization schemes: a low frequency model suited for relaxation of low-frequency modes (model I, with ω ∈ [0, 900] cm −1 ), a high-frequency one optimized for the relaxation of the stretching mode (model II, ω ∈ [2100, 2900] cm −1 ), and a combination of both (model III) to investigate combined excitation of different modes.…”

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

“…for harmonic system potentials [29]; note that a similar in spirit but technically different method for linear GLEs was developed independently [46] and applied to quantum dynamics of hydrogen atoms on graphene [47,48]. In the following, we extend the method to the non-linear GLEs, Eq.…”