Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water

Abstract

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects

“…The GLE in eq 1 neglects nonlinear friction effects, which is valid when correlations between velocities and random forces are independent of x 52 and has been successfully used to model the dynamics of protein folding and molecular vibrations. 31,51 We will further below validate the linear friction GLE in eq 1 by comparison with MD data. All parameters in eq 1 are extracted from simulation trajectories: The mass is obtained from the equipartition theorem…”

“…In order to reveal the mechanisms that control the pair-reaction dynamics, we use the GLE that includes a general nonlinear potential U ( x ) and a memory friction kernel Γ( t ): m ẍ false( t false) = − ∫ 0 t Γ false( t − t ′ false) ẋ false( t ′ false) d t ′ − ∇ U false[ x ( t ) false] + η false( t false) Here, m is the effective mass and η( t ) is a Gaussian random force with vanishing mean ⟨η( t )⟩ = 0 and correlations ⟨η( t )η( t ′)⟩ = k B T Γ( t – t ′). The GLE in eq neglects nonlinear friction effects, which is valid when correlations between velocities and random forces are independent of x and has been successfully used to model the dynamics of protein folding and molecular vibrations. , We will further below validate the linear friction GLE in eq by comparison with MD data. All parameters in eq are extracted from simulation trajectories: The mass is obtained from the equipartition theorem m = k normalB T / ⟨ ẋ 2 false( t false) ⟩ and is demonstrated to be independent of x in SI section II, as indeed expected for a linear distance coordinate .…”

“…Different analytical rate theories based on the GLE have been developed but necessarily rely on various approximations, the effects of which are difficult to disentangle. ,,, This is where numerical solutions of accurately parametrized GLEs become instrumental. The extraction of memory kernels from general time series data is an active field of research, ,− in particular in the context of reaction kinetics. ,,− With recent methodological advances, it is possible to extract memory kernels from trajectories in the presence of arbitrary, not necessarily harmonic, potentials and to numerically solve the resulting GLE by Markovian embedding techniques. ,,, While the one-dimensional GLE may in principle contain nonlinear friction contributions, the approximate linear friction GLE, which only includes a linear coupling of the velocity to a friction kernel with no further dependencies on position or velocity, becomes valid for a broad class of systems under well-defined conditions; this explains why it accurately describes the dynamics of very different physical systems. , In this connection, it is important to note that most existing reaction-rate theories are in fact based on the approximate linear friction GLE.…”

The Local Vibrational Mode Theory and Its Place in the Vibrational Spectroscopy Arena

“…Using linear spectroscopy, such as FTIR and Raman, can reveal essential information about hydrogen bond strengths and the local environment of water through the OH stretching mode frequency; however, these spectra often suffer from spectral congestion and band broadening. 181,182 Beyond purely vibrational spectroscopy, vibrational SFG has recently been used in visualizing the extent of interfacial water and probing water− surface interactions. 24,183,184 This technique improves upon pure IR measurements by distinct electronic excitations that suggest molecular locality and directionality in addition to characteristic vibrational modes.…”

“…A common theme in determining the vibrational spectroscopy of water is unraveling site-specific interactions in water clusters, namely in characterizing the free and bound O–H stretches. Using linear spectroscopy, such as FTIR and Raman, can reveal essential information about hydrogen bond strengths and the local environment of water through the OH stretching mode frequency; however, these spectra often suffer from spectral congestion and band broadening. , Beyond purely vibrational spectroscopy, vibrational SFG has recently been used in visualizing the extent of interfacial water and probing water–surface interactions. ,, This technique improves upon pure IR measurements by distinct electronic excitations that suggest molecular locality and directionality in addition to characteristic vibrational modes. A special case of SFG is Second Harmonic Generation (SHG) spectra where the visible and IR excitation frequencies are identical; recent studies emphasizing second order nonlinear susceptibility measured in SHG have diminished some issues researchers have experienced in modeling more distinct features in charged interfaces and water–silica interfaces, − including acceptor–donor, acceptor–donor–donor (ADD), acceptor–acceptor–donor (AAD), as the main examples .…”