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 theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in aqueous ionic solutions is presented from first principles without employing any empirical potential models. The present calculations are based on ab initio molecular dynamics for trajectory generation and wavelet analysis of the simulated trajectories for time dependent frequency calculations. Results are obtained for two different deuterated aqueous solutions: the first one is a relatively dilute solution of a single Cl(-) ion and the second one is a concentrated solution of NaCl ( approximately 3M) dissolved in liquid D(2)O. It is found that the frequencies of OD bonds in the anion hydration shell, i.e., those which are hydrogen bonded to the chloride ion, have a higher stretch frequency than those in the bulk water. Also, on average, the frequencies of hydration shell OD modes are found to increase with increase in the anion-water hydrogen bond distance. On the dynamical side, when the vibrational spectral diffusion is calculated exclusively for the hydration shell water molecules in the first solution, the dynamics reveals three time scales: a short-time relaxation ( approximately 200 fs) corresponding to the dynamics of intact ion-water hydrogen bonds, a slower relaxation ( approximately 3 ps) corresponding to the lifetimes of chloride ion-water hydrogen bonds, and another longer-time constant ( approximately 20 ps) corresponding to the escape dynamics of water from the anion hydration shell. Existence of such three time scales for hydration shell water molecules was also reported earlier for water containing a single iodide ion using classical molecular dynamics [B. Nigro et al., J. Phys. Chem. A 110, 11237 (2006)]. Hence, the present study confirms the basic results of this earlier work using a different methodology. However, when the vibrational spectral diffusion is calculated over all the OD modes, only two time scales of approximately 150 fs and approximately 2.7 ps are found without the slowest component of approximately 20 ps. This is likely because of the very small weight that the hydration shell water molecules carry to the overall spectral diffusion in the solution containing a single ion. For the concentrated solution also, the slowest component of approximately 20 ps is not found in the spectral diffusion of all water molecules because a distinct separation between the hydration shell and bulk water in terms of their stretch frequencies does not hold at this high concentration regime. The present first principles results are compared with those of the available experiments and classical simulations.

Intramolecular dynamics of highly excited DCO ( X 2 A ′ ) is studied from a classical-quantum correspondence perspective using the effective spectroscopic Hamiltonian proposed recently by Tröllsch and Temps (Z. Phys. Chem. 215, 207 (2001)). This work focuses on the polyads P = 3 and P = 4 corresponding to excitation energies Ev ≈ 5100 cm −1 and 7000 cm −1 respectively. The majority of states belonging to these polyads are dynamically assigned, despite extensive stochasticity in the classical phase space, using the recently proposed technique of level velocities. A wavelet based time-frequency analysis is used to reveal the nature of phase space transport and the relevant dynamical bottlenecks. The local frequency analysis clearly illustrates the existence of mode-specific IVR dynamics i.e., differing nature of the IVR dynamics ensuing from CO stretch and the DCO bend bright states. In addition the role of the weak Fermi resonance involving the CO stretch and DCO bend modes is investigated. A key feature of the present work is that the techniques utilized for the analysis i.e., parametric variations and local frequency analysis are not limited by the dimensionality of the system. This study, thus, explores the potential for understanding IVR in larger molecules from both time domain and frequency domain perspectives.

We study the nature of highly excited eigenstates of strongly coupled multimode systems with three degrees of freedom. Attempts to dynamically assign the eigenstates using classical-quantum correspondence techniques poses a considerable challenge, due to both the number of degrees of freedom and the extensive chaos in the underlying classical phase space. Nevertheless, we show that sequences of localized states interspersed between delocalized states can be identified readily by using the parametric variation technique proposed earlier by us. In addition, we introduce a novel method to lift the quantum eigenstates onto the classical resonance web using a wavelet-based local time-frequency approach. It is shown that the lifting procedure provides clear information on the various dominant nonlinear resonances that influence the eigenstates. Analyzing the spectroscopic Hamiltonians for CDBrClF and CF(3)CHFI as examples, we illustrate our approach and demonstrate the consistency between state space and phase space perspectives of the eigenstates. Two exemplary cases of highly mixed quantum states are discussed to highlight the difficulties associated with their assignment. In particular, we provide arguments to distinguish between the states in terms of their predominantly classical or quantum nature of the mixing.

We study the intramolecular vibrational energy redistribution (IVR) dynamics of an effective spectroscopic Hamiltonian describing the four coupled high frequency modes of CDBrClF. The IVR dynamics ensuing from nearly isoenergetic zeroth-order states, an edge (overtone) and an interior (combination) state, is studied from a state space diffusion perspective. A wavelet based timefrequency analysis reveals an inhomogeneous phase space due to the trapping of classical trajectories. Consequently the interior state has a smaller effective IVR dimension as compared to the edge state.Investigating the dynamics of an initially localized vibrational excitation of a molecule in terms of timescales, final destinations and competing pathways has been of considerable interest to chemical physicists for a number of decades [1,2,3,4,5,6,7]. Due to the sustained theoretical [1,2,3,7] and experimental efforts [4,5,6,7] it is only now that a fairly detailed picture of the intramolecular vibrational energy flow is beginning to emerge. Recent studies [8,9,10,11] suggest that IVR can be described as a diffusion in the zeroth-order quantum number space (also known as the state space) mediated by the anharmonic resonances coupling the zeroth-order states. The state space approach[6] makes several predictions on the observables associated with IVR. Foremost among them is that an initial zeroth-order bright state |b diffuses anisotropically on a manifold of dimension D much smaller than N (or N − 1 with energy constraint). N is the number of vibrational modes in the molecule. As a result the survival probability P b (t) exhibits power law behaviour on intermediate time scaleswith σ b = α | b|α | 4 being the dilution factor of the zeroth-order state |b and |α denoting the eigenstates of the system. Wong and Gruebele[12] explained the power law behaviour from the state space perspective by providing a perturbative estimate for D as:with n = |n i − n b | being the distance, in state space, from the state |b to other states |i and the sum is over all states |i such that |n i − n b | ≤ n. The zeroth-order quantum numbers n k are associated with the state |k and the symbol ∆ indicates a finite difference evaluation of the dimension due to the discrete nature of the state space. In practice one chooses two different distances n in the state space and evaluates eq. 2 and thus D ≈ D(n). The quantityis a measure of the number of states locally coupled to |b . The difference in the zeroth-order energies is denoted by ∆E 0 ib = E 0 i − E 0 b and V ib = i|V |b . Notice that in the strong coupling limit, ∆E 0 ib ≪ V ib , L ib ≈ 1 whereas in the opposite limit L ib ≈ 0. Thus D v (n) can range between the full state space dimension and zero [12]. For further discussions on the origin and approximations inherent to eq. 2 we refer the reader to the original reference [12]. In the context of the present study it is sufficient to note that D ∝ N loc which has been confirmed in the earlier work [12].Clearly Eq. 2 explicitly includes the various anharmonic re...