An Accurate Classical Simulation of a Two-Dimensional Vibrational Spectrum: OD Stretch Spectrum of a Hydrated HOD Molecule

Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators

Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.

Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water

A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopies provides access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

Ab Initio Molecular Dynamics Study of Aqueous Solutions of Magnesium and Calcium Nitrates: Hydration Shell Structure, Dynamics and Vibrational Echo Spectroscopy

Ab initio molecular dynamics simulations are performed to study the hydration shell structure, dynamics, and vibrational echo spectroscopy of aqueous Mg(NO₃)₂ and Ca(NO₃)₂ solutions. The hydration shell structure is probed through calculations of various ion-ion and ion-water radial and spatial distribution functions. On the dynamical side, calculations have been made for the hydrogen bond dynamics of hydration shells and also residence dynamics and lifetimes of water in different solvation environments. Subsequently, we looked at the dynamics of frequency fluctuations of OD modes of heavy water in different hydration environments. Specifically, the temporal decay of spectral observables of two-dimensional infrared (2DIR) spectroscopy, three pulse echo peak shift (3PEPS) measurements and also of time correlations of frequency fluctuations are calculated to investigate the dynamics of vibrational spectral diffusion of water in different hydration environments in these solutions. The OD stretch frequencies of water molecules in the vicinity of both divalent cations are found to be red-shifted and also fluctuating at a slower rate than other water molecules present in the solutions. The Mg²⁺ ions are found to be strongly hydrated which can be linked to their lower tendency to form contact ion-pairs and essentially no water exchange between the cationic hydration shells and bulk during the time scale of the current simulations. The stronger hydration of Mg²⁺ ions make their hydration shells structurally and dynamically more rigid and make the dynamics of hydrogen bonds and vibrational spectral diffusion, as revealed through spectral observables of 2DIR and 3PEPS slower than that for the Ca²⁺ ions. The structural and spectral dynamics of water molecules outside the cationic solvation shells in the Mg(NO₃)₂ solution are also found to be relatively slower than that of the Ca(NO₃)₂ solution and pure water which show the effects of stronger electric fields of Mg²⁺ ions extending beyond their first hydration shells. Also, water molecules in the hydration shells of the NO₃^- ions are found to relax at a slower rate in the Mg(NO₃)₂ solution which manifests the effect countercations have on anionic hydration shells for divalent metal nitrate solutions.

Temperature dependence of the ultrafast vibrational echo spectroscopy of OD modes in liquid water from first principles simulations

The temperature dependence of the vibrational spectral diffusion of OD modes in liquid water is investigated through calculations of vibrational echo spectral observables from first principles molecular dynamics.

Ultrafast Vibrational Echo Spectroscopy of Liquid Water from First-Principles Simulations

Vibrational echo spectroscopy has become a powerful technique to study vibrational spectral diffusion in water and aqueous solutions. The dynamics of vibrational spectral diffusion is intimately related to the hydrogen bond fluctuations in liquid water and other hydrogen bonded liquids. Earlier theoretical calculations of vibrational echo spectroscopy of aqueous systems were based on classical molecular dynamics simulations involving empirical force fields of water. In the current work, we have employed the method of ab initio molecular dynamics simulation to calculate the spectral observables of vibrational echo and two-dimensional infrared (2D-IR) spectroscopy of liquid water at room temperature under Condon and cumulant approximations. The time scales extracted from the temporal decay of the frequency-time correlation function (FTCF), short-time slope of three pulse photon echo (SP3E), dynamic line width (DLW), and the slope of nodal line of 2D-IR spectra are found to be in reasonably close agreement with each other which reinforces the assertion that signatures of FTCF can be captured using three pulse photon echo and 2D-IR spectroscopy.

Simultaneous spectral and temporal analyses of kinetic energies in nonequilibrium systems: theory and application to vibrational relaxation of O-D stretch mode of HOD in water

A time series of kinetic energies (KE) from classical molecular dynamics (MD) simulation contains fundamental information on system dynamics. It can also be analyzed in the frequency domain through Fourier transformation (FT) of velocity correlation functions, providing energy content of different spectral regions. By limiting the FT time span, we have previously shown that spectral resolution of KE evolution is possible in the nonequilibrium situations [Jeon and Cho, J. Chem. Phys. 2011, 135, 214504]. In this paper, we refine the method by employing the concept of instantaneous power spectra, extending it to reflect an instantaneous time-correlation of velocities with those in the future as well as with those in the past, and present a new method to obtain the instantaneous spectral density of KE (iKESD). This approach enables the simultaneous spectral and temporal resolution of KE with unlimited time precision. We discuss the formal and novel properties of the new iKESD approaches and how to optimize computational methods and determine parameters for practical applications. The method is specifically applied to the nonequilibrium MD simulation of vibrational relaxation of the OD stretch mode in a hydrated HOD molecule by employing a hybrid quantum mechanical/molecular mechanical (QM/MM) potential. We directly compare the computational results with the OD band population relaxation time profiles extracted from the IR pump-probe measurements for 5% HOD in water. The calculated iKESD yields the OD bond relaxation time scale ∼30% larger than the experimental value, and this decay is largely frequency-independent if the classical anharmonicity is accounted for. From the integrated iKESD over intra- and intermolecular bands, the major energy transfer pathways were found to involve the HOD bending mode in the subps range, then the internal modes of the solvent until 5 ps after excitation, and eventually the solvent intermolecular modes. Also, strong hydrogen-bonding of HOD is found to significantly hinder the initial intramolecular energy transfer process.