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

Abstract

The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix propagation. When using these methods, a spectral density has to be computed from dynamical properties of system and environment, which is commonly done using classical molecular dynamics simulations. However, there are situations, where quantum effects could play a role. Therefore, we reformulate our recently developed Fourier method in order to enable spectral density calculations from semiclassical simulations which approximately consider quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested for the linearized semiclassical initial-value representation (LSC-IVR), the thawed Gaussian wave packet dynamics (TGWD) and hybrid schemes combining the two with the more accurate Herman-Kluk (HK) formula. Surprisingly, spectral densities from the LSC-IVR method, based on a completely classical propagation, are extremely accurate whereas those from the single-trajectory TGWD are of poor quality in the anharmonic regime. The hybrid methods provide reasonable quality when the system is close to the classical regime, although, at finite temperature, the computation protocol from expectation values turns out to be more robust. If stronger quantum effects are observed, both hybrid methods turn out as too inaccurate.

All-DFTB Approach to the Parametrization of the System-Bath Hamiltonian Describing Exciton-Vibrational Dynamics of Molecular Assemblies

“…Whether quantum effects in the sampling of the vibrational distribution have a significant influence on the character of the displacement vectors remains to be shown. Here, the recently suggested use of the linearized semiclassical initial-value representation for sampling the initial quantum distribution in SD simulations could provide a starting point.…”

Modeling Intermolecular and Intramolecular Modes of Liquid Water Using Multiple Heat Baths: Machine Learning Approach

“…[21][22][23][58][59][60][61][62][63] The SDFs of entire molecular systems have also been evaluated directly from molecular dynamics (MD) trajectories on the basis of normal modes, [64][65][66][67][68][69][70][71][72][73][74][75] the velocity-velocity autocorrelation function, 65,69 and Fourier transformations. 76 While the method based on optical spectra does not allow estimation of optically inactive system modes, the approaches based on MD trajectories have the capability to describe all intermolecular and intramolecular vibrational motions. However, in such trajectory-based methods, it is not easy to separate the system and the heat-bath, in particular in the case of the intermolecular modes.…”

“…Because the key feature of environments is determined by the system–bath coupling and the SDF, a methodology to determine these is significant. Typically, the SDF is estimated from linear and nonlinear infrared and Raman spectra, both experimentally − and numerically. − ,− The SDFs of entire molecular systems have also been evaluated directly from molecular dynamics (MD) trajectories on the basis of normal modes, − the velocity–velocity autocorrelation function, , and Fourier transformations . While the method based on optical spectra does not allow estimation of optically inactive system modes, the approaches based on MD trajectories have the capability to describe all intermolecular and intramolecular vibrational motions.…”

Complexified phase spaces, initial value representations, and the accuracy of semiclassical propagation

“…another expression for the semiclassical propagator in the position representation, discovered in the mid 1980s [3]. Used either raw or as a starting point to other approximation methods, it is the most popular Initial Value Representation (IVR) in chemistry, although the development of benchmark semiclassical methods is truly non-stop (see [4,5,6,7,8,9,10,11] for some examples). In addition to providing high-accuracy results for the complicated processes inherent to the chemical sciences, the H-K propagator was also scrutinized by the physical community, who attested for its remarkable accuracy and implementation ease (e.g.…”