Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath

Abstract

The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed.

Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

“…First, it can be rigorously derived from the so-called Caldeira-Leggett (CL) model, where the environment is assumed to be a collection of independent harmonic oscillators bi-linearly coupled to the system [4,6,[18][19][20]. This model has been widely used in analyzing and interpreting (non-)linear spectroscopic experiments on systems in condensed phase, termed multi-mode Brownian oscillator (MBO) model in this context [21][22][23][24][25][26]. The second, more formal ansatz is to employ projection operator techniques in order to recast the system's EOMs into linear or nonlinear GLE forms [4,5,7,27].…”

“…Still, if one is interested only in linear properties, like transport coefficients or linear absorption spectra, the GLE gives the correct description [41] and provides a very simple and intuitive model. In the general case the linear GLE does not reflect all dynamical features of the real system and, thus, one partly looses the true atomistic picture when using it.The Caldeira-Leggett ModelAnother way to derive a GLE is to employ the CL model that has enjoyed popularity in condensed phase spectroscopy [21][22][23][24][25][26]. This model assumes that the bath consists of independent harmonic oscillators bi-linearly coupled to the system.…”

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

“…It becomes apparent at this point that for anharmonic systems this procedure cannot be exploited anymore and one has to use both, the MAF and the MFC, to obtain the spectral densityξ(ω) directly via Eq. (12). This equation, thus, constitutes the generalization of the Fourier method for anharmonic systems.…”

“…The CL model has enjoyed great popularity in condensed phase spectroscopy [7][8][9][10][11][12]36]. It assumes that the bath consists of independent harmonic oscillators bi-linearly coupled to the system.…”

“…Particularly, in the CaldeiraLeggett (CL) model, the environment is assumed to be a collection of independent harmonic oscillators, bi-linearly coupled to the system [2][3][4][5]. This model has been widely used in analyzing and interpreting (non-)linear spectroscopic experiments on systems in condensed phase, termed multi-mode Brownian oscillator (MBO) model in this context [6][7][8][9][10][11][12]. The resulting reduced EOM is known as the generalized Langevin equation (GLE), where the bath's influence is described by a frequency-dependent friction and a stochastic force with a finite correlation time.…”