Vibrational Spectral Diffusion and Hydrogen Bond Dynamics in Heavy Water from First Principles

Abstract

We present a first-principles theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in heavy water without using any empirical model potentials. The calculations are based on ab initio molecular dynamics simulations for trajectory generation and a time series analysis using the wavelet method for frequency calculations. It is found that, in deuterated water, although a one-to-one relation does not exist between the instantaneous frequency of an OD bond and the distance of its associated hydrogen bond, such a relation does hold on average. The dynamics of spectral diffusion is investigated by means of frequency-time correlation and spectral hole dynamics calculations. Both of these functions are found to have a short-time decay with a time scale of approximately 100 fs corresponding to dynamics of intact hydrogen bonds and a slower long-time decay with a time constant of approximately 2 ps corresponding to lifetimes of hydrogen bonds. The connection of the slower time scale to the dynamics of local structural relaxation is also discussed. The dynamics of hydrogen bond making is shown to have a rather fast time scale of approximately 100 fs; hence, it can also contribute to the short-time dynamics of spectral diffusion. A damped oscillation is also found at around 150-200 fs, which is shown to have come from underdamped intermolecular vibrations of a hydrogen-bonded water pair. Such assignments are confirmed by independent calculations of power spectra of intermolecular motion and hydrogen bond kinetics using the population correlation function formalism. The details of the time constants of frequency correlations and spectral shifts are found to depend on the frequencies of chosen OD bonds and are analyzed in terms of the dynamics of hydrogen bonds of varying strengths and also of free non-hydrogen-bonded OD groups.

A first principles simulation study of vibrational spectral diffusion in aqueous NaBr solutions: Dynamics of water in ion hydration shells

“…The details of the wavelet analysis are available in Refs. [26,27,32,46]. In this method, a time dependent function f ðtÞ is expressed in terms of basis functions which are constructed as translations and dilations of a mother wavelet w…”

“…[32], the inverse of the scale factor a is proportional to the frequency and thus the wavelet transform at each b gives the frequency content of f ðtÞ over a time window about b. Following our recent work on other aqueous systems [26][27][28][29]40], the time dependent function f ðtÞ for a given OD bond is constructed to be a complex function with its real and imaginary parts corresponding to the instantaneous fluctuations in OD distance and the corresponding momentum along the OD bond at time t. The stretch frequency of this bond at a given time t ¼ b is then determined from the scale a that maximizes the modulus of the corresponding wavelet transform at b and the process is then repeated for all the OD bonds that are present in the current simulation systems.…”

“…The results are for the dilute solution (System 1). The corresponding frequency distributions for pure water [26] are also shown for comparison. The hydrogen bonds in the current systems are defined by employing the commonly used geometric criteria where a hydrogen bond between two water molecules or between a water molecule and ion exists if the following distance criteria are satisfied: R ðXOÞ < R ðXOÞ C and R ðXHÞ < R ðXHÞ C , where X denotes the oxygen of the first water molecule in the case of water-water hydrogen bonds and it denotes the Br À ion in the case of anionwater hydrogen bonds.…”

“…The temporal evolution of such frequency fluctuations, known as vibrational spectral diffusion, has been studied in many time dependent vibrational spectroscopic experiments to unearth the dynamics of hydrogen bond fluctuations in water and aqueous solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. There have also been a number of theoretical studies on vibrational spectral diffusion in aqueous media [20][21][22][23][24][25][26][27][28][29] and all these studies have provided much detailed information on the dynamical fluctuations in these systems at molecular level.…”

“…On the theoretical side, the method of classical molecular dynamics simulation was employed to calculate the frequency fluctuations in aqueous NaI and NaBr solutions [23,25]. Very recently, theoretical studies were also conducted that went beyond the use of classical models and looked at the dynamics of spectral diffusion in water, supercritical water and aqueous solutions from first principles without using any empirical models [26][27][28][29]. In the latter studies, the method of ab initio molecular dynamics [30,31] was employed for the generation of dynamical trajectories and the fluctuating frequencies were calculated directly from the dynamical trajectories through a time series analysis [32].…”