A generalized van't Hoff relation for the temperature dependence of complex-valued nonlinear spectra

The temperature dependence of spectra can reveal important insights into the structural and dynamical behavior of the system being probed. In the case of linear spectra, this has been exploited to investigate the thermodynamic driving forces governing the spectral response. Indeed, the temperature derivative of a spectrum can be used to obtain effective energetic and entropic profiles as a function of the measured frequency. The former can further be used to predict the temperature-dependent spectrum via a van't Hoff relation. However, these approaches are not directly applicable to nonlinear, complex-valued spectra, such as vibrational sum-frequency generation (SFG) or two-dimensional infrared (2D-IR) photon echo spectra. Here, we show how the energetic and entropic driving forces governing such nonlinear spectra can be determined and used within a generalized van't Hoff relation to predict their temperature dependence. The central idea is to allow the underlying energetic profiles to themselves be complex-valued. We illustrate this approach for 2D-IR spectra of water and SFG spectra of the air-water interface and demonstrate the accuracy of the generalized van't Hoff relationship and its implications for the origin of temperature-dependent spectral changes.

Temperature Dependence of Non-Condon Effects in Two-Dimensional Vibrational Spectroscopy of Water

Non-Condon effects in vibrational spectroscopy refers to the dependence of a molecule's vibrational transition dipole and polarizability on the coordinates of the surrounding environment. Earlier studies have shown that such effects can be pronounced for hydrogen-bonded systems like liquid water. Here, we present a theoretical study of two-dimensional vibrational spectroscopy under the non-Condon and Condon approximations at varying temperatures. We have performed calculations of both two-dimensional infrared and two-dimensional vibrational Raman spectra to gain insights into the temperature dependence of non-Condon effects in nonlinear vibrational spectroscopy. The two-dimensional spectra are calculated for the OH vibration of interest in the isotopic dilution limit where the coupling between the oscillators is ignored. Generally, both the infrared and Raman line shapes undergo red shifts with decrease in temperature due to strengthening of hydrogen bonds and decrease in the fraction of OH modes with weaker or no hydrogen bonds. The infrared line shape is further red-shifted under the non-Condon effects at a given temperature, while the Raman line shape does not show any such red shift due to non-Condon effects. The spectral dynamics becomes slower on decrease of temperature due to slower hydrogen bond relaxation and, for a given temperature, the spectral diffusion occurs at a faster rate upon inclusion of non-Condon effects. The time scales of spectral diffusion extracted from different metrics agree well with each other and also with experiments. The changes in the spectrum due to non-Condon effects are found to be more significant at lower temperatures.

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.

"On-The-Fly" Calculation of the Vibrational Sum-Frequency Generation Spectrum at the Air-Water Interface

In the present work, we provide an electronic structure based method for the "on-the-fly" determination of vibrational sum frequency generation (v-SFG) spectra. The predictive power of this scheme is demonstrated at the air-water interface. While the instantaneous fluctuations in dipole moment are obtained using the maximally localized Wannier functions, the fluctuations in polarizability are approximated to be proportional to the second moment of Wannier functions. The spectrum henceforth obtained captures the signatures of hydrogen bond stretching, bending, as well as low-frequency librational modes.

Structural Features of Triethylammonium Acetate through Molecular Dynamics

I have explored the structural features and the dynamics of triethylammonium acetate by means of semi-empirical (density functional tight binding, DFTB) molecular dynamics. I find that the results from the present simulations agree with recent experimental determinations with only few minor differences in the structural interpretation. A mixture of triethylamine and acetic acid does not form an ionic liquid, but gives rise to a very complex system where ionization is only a partial process affecting only few molecules (1 over 4 experimentally). I have also found that the few ionic couples are stable and remain mainly embedded inside the AcOH neutral moiety.

Time-dependent vibrational sum-frequency generation spectroscopy of the air-water interface

Vibrational sum-frequency generation spectroscopy is a powerful method to study the microscopic structure and dynamics of interfacial systems. Here we demonstrate a simple computational approach to calculate the time-dependent, frequency-resolved vibrational sum-frequency generation spectrum (TD-vSFG) of the air-water interface. Using this approach, we show that at the air-water interface, the transition of water molecules with bonded OH modes to free OH modes occurs at a time scale of $$\sim$$ ~ 3 ps, whereas water molecules with free OH modes rapidly make a transition to a hydrogen-bonded state within $$\sim$$ ~ 2 ps. Furthermore, we also elucidate the origin of the observed differential dynamics based on the time-dependent evolution of water molecules in the different local solvent environments.

Vibrational echo spectroscopy of aqueous sodium bromide solutions from first principles simulations

A theoretical study of the time-dependent vibrational echo spectroscopy of sodium bromide solutions in deuterated water at two different concentrations of 0.5 and 5.0 M and at temperatures of 300 and 350 K is presented using the method of ab initio molecular dynamics simulations. The instantaneous fluctuations in frequencies of local OD stretch modes are calculated using time-series analysis of the simulated trajectories. The third-order polarization and intensities of three pulse photon-echo are calculated from ab initio simulations. The timescales of vibrational spectral diffusion are determined from the frequency time correlation functions (FTCF) and short-time slope of three pulse photon echo (S3PE) calculated within the second-order cumulant and Condon approximations. It is found that under ambient conditions, the rate of vibrational spectral diffusion becomes slower with increase in ionic concentration. Decay of S3PE calculated for different systems give timescales, which are in close agreement with those of FTCF and also with the results of experimental time-dependent vibrational spectroscopic experiments. © 2019 Wiley Periodicals, Inc.