Temperature Dependence of the Water Infrared Spectrum: Driving Forces, Isosbestic Points, and Predictions

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.

Site specifically probing the unfolding process of human telomere i-motif DNA using vibrationally enhanced alkynyl stretch

The microscopic unfolding process of a cytosine-rich DNA forming i-motif by hemi-protonated base pairs is related to gene regulation. However, the detailed thermal unfolding mechanism and the protonation/deprotonation status of site-specific cytosine in DNA in a physiological environment are still obscure. To address this issue, a vibration-enhanced CC probe tagged on 5'E terminal cytosine of human telomere i-motif DNA was examined using linear and nonlinear infrared (IR) spectroscopies and quantum-chemistry calculations. The CC probe extended into the major groove of the i-motif was found using nonlinear IR results only to introduce a minor steric effect on both steady-state structure and local structure dynamics; however, its IR absorption profile effectively reports the cleavage of the hemi-protonated base pair of C1-C13 upon the unfolding with C1 remaining protonated. The temperature mid-point (Tm) of the local transition reported using the CC tag was slightly lower than the Tm of global transition, and the enthalpy of the former exceeds 60% of the global transition. It is shown that the base-pair unraveling is noncooperative, with outer base pairs breaking first and being likely the rate limiting step. Our results offered an in-depth understanding of the macroscopic unfolding characteristics of the i-motif DNA and provided a nonlinear IR approach to monitoring the local structural transition and dynamics of DNA and its complexes.

Combinational Vibration Modes in H2O/HDO/D2O Mixtures Detected Thanks to the Superior Sensitivity of Femtosecond Stimulated Raman Scattering

Overtones and combinational modes frequently play essential roles in ultrafast vibrational energy relaxation in liquid water. However, these modes are very weak and often overlap with fundamental modes, particularly in isotopologues mixtures. We measured VV and HV Raman spectra of H₂O and D₂O mixtures with femtosecond stimulated Raman scattering (FSRS) and compared the results with calculated spectra. Specifically, we observed the mode at around 1850 cm^-1 and assigned it to H-O-D bend + rocking libration. Second, we found that the H-O-D bend overtone band and the OD stretch + rocking libration combination band contribute to the band located between 2850 and 3050 cm^-1. Furthermore, we assigned the broad band located between 4000 and 4200 cm^-1 to be composed of combinational modes of high-frequency OH stretching modes with predominantly twisting and rocking librations. These results should help in a proper interpretation of Raman spectra of aqueous systems as well as in the identification of vibrational relaxation pathways in isotopically diluted water.

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.

Identification of Ion Pairs in Aqueous NaCl and KCl Solutions in Combination with Raman Spectroscopy, Molecular Dynamics, and Quantum Chemical Calculations

This work summarizes a theoretical analysis of the perturbation on Raman spectra in aqueous NaCl and KCl solutions with the aim to detect ion pairs. The experimental Raman spectra, both polarized and depolarized, are perturbed by these ions to a comparable extent or somewhat less by KCl than NaCl. This result appears to be contrary to the molecular dynamics (MD) simulation showing that the isolated and separated ions of KCl should have a larger perturbation than NaCl, as the solvation shell of K⁺ is larger than that of Na⁺. The apparent discrepancy signifies the ion pair formation which is more substantial for KCl than NaCl. The MD simulations and quantum chemical calculations revealed that KCl forms ion pairs more than NaCl and that the ion pair formation reduces the perturbation on the Raman spectra more for KCl. The present analysis shows that the perturbed Raman spectra provide a useful sign to evaluate the ion pair formation in aqueous solutions.

Direct calculation of the temperature dependence of 2D-IR spectra: Urea in water

A method for directly calculating the temperature derivative of two-dimensional infrared (2D-IR) spectra from simulations at a single temperature is presented. The approach is demonstrated by application to the OD stretching spectrum of isotopically dilute aqueous (HOD in H₂O) solutions of urea as a function of concentration. Urea is an important osmolyte because of its ability to denature proteins, which has motivated significant interest in its effect on the structure and dynamics of water. The present results show that the temperature dependence of both the linear IR and 2D-IR spectra, which report on the underlying energetic driving forces, is more sensitive to urea concentration than the spectra themselves. Additional physical insight is provided by calculation of the contributions to the temperature derivative from different interactions, e.g., water-water, water-urea, and urea-urea, present in the system. Finally, it is demonstrated how 2D-IR spectra at other temperatures can be obtained from only room temperature simulations.

Development of Efficient Computational Analysis of Difference Infrared and Raman Spectroscopies

Computational analysis of difference spectra between two analogous systems is a challenging issue, as reliable estimation of a tiny difference spectrum requires an extraordinary precision of the two original spectra. We have developed an alternative new method to calculate the difference spectra in background-free conditions, which greatly improved the efficiency of computation. In this paper we report further improvement by using efficient parallel implementation and the time correlation formula based on time derivative quantities. As a consequence, the present work achieved further remarkable acceleration in the calculations of difference infrared and Raman spectra in the order of magnitude, and thereby allowed us with analyzing these difference spectra at a practical cost of computation.

Shining (Infrared) Light on the Hofmeister Series: Driving Forces for Changes in the Water Vibrational Spectra in Alkali-Halide Salt Solutions

The Hofmeister series is frequently used to rank ions based on their behavior from chaotropes ("structure breakers"), which weaken the surrounding hydrogen-bond network, to kosmotropes ("structure makers"), which enhance it. Here, we use fluctuation theory to investigate the energetic and entropic driving forces underlying the Hofmeister series for aqueous alkali-halide solutions. Specifically, we exploit the OH stretch infrared (IR) spectrum in isotopically dilute HOD/D₂O solutions as a probe of the effect of the salt on the water properties for different concentrations and choice of halide anion. Fluctuation theory is used to calculate the temperature derivative of these IR spectra, including decomposition of the derivative into different energetic contributions. These contributions are used to determine the thermodynamic driving forces in terms of effective internal energy and entropic contributions. This analysis implicates entropic contributions as the key factor in the Hofmeister series behavior of the OH stretch IR spectra, while the effective internal energy is nearly ion-independent.

Hydration and Hydrogen Bond Order of Octadecanoic Acid and Octadecanol Films on Water at 21 and 1 °C

The temperature-dependent hydration structure of long-chain fatty acids and alcohols at air-water interfaces has great significance in the fundamental interactions underlying ice nucleation in the atmosphere. We present an integrated theoretical and experimental study of the temperature-dependent vibrational structure and electric field character of the immediate hydration shells of fatty alcohol and acid headgroups. We use a combination of surface-sensitive infrared reflection-absorption spectroscopy (IRRAS), surface potentiometry, and ab initio molecular dynamics simulations to elucidate detailed molecular structures of the octadecanoic acid and octadecanol (stearic acid and stearyl alcohol) headgroup hydration shells at room temperature and near freezing. In experiments, the alcohol at high surface concentration exhibits the largest surface potential; yet we observe a strengthening of the hydrogen-bonding for the solvating water molecules near freezing for both the alcohol and the fatty acid IRRAS experiments. Results reveal that the hydration shells for both compounds screen their polar headgroup dipole moments reducing the surface potential at low surface coverages; at higher surface coverage, the polar headgroups become dehydrated, which reduces the screening, correlating to higher observed surface potential values. Lowering the temperature promotes tighter chain packing and an increase in surface potential. IRRAS reveals that the intra- and intermolecular vibrational coupling mechanisms are highly sensitive to changes in temperature. We find that intramolecular coupling dominates the vibrational relaxation pathways for interfacial water determined by comparing the H₂O and the HOD spectra. Using ab initio molecular dynamics (AIMD) calculations on cluster systems of propanol + 6H₂O and propionic acid + 10H₂O, a spectral decomposition scheme was used to correlate the OH stretching motion with the IRRAS spectral features, revealing the effects of intra- and intermolecular coupling on the spectra. Spectra calculated with AIMD reproduce the red shift and increase in intensity observed in experimental spectra corresponding to the OH stretching region of the first solvation shell. These findings suggest that intra- and intermolecular vibrational couplings strongly impact the OH stretching region at fatty acid and fatty alcohol water interfaces. Overall, results are consistent with ice templating behavior for both the fatty acid and the alcohol, yet the surface potential signature is strongest for the fatty alcohol. These findings develop a better understanding of the complex surface potential and spectral signatures involved in ice templating.

Using Activation Energies to Elucidate Mechanisms of Water Dynamics

Recent advances in the calculation of activation energies are shedding new light on the dynamical time scales of liquid water. In this Perspective, we examine how activation energies elucidate the central, but not singular, role of the exchange of hydrogen-bond (H-bond) partners that rearrange the H-bond network of water. The contributions of other motions to dynamical time scales and their associated activation energies are discussed along with one case, vibrational spectral diffusion, where H-bond exchanges are not mechanistically significant. Nascent progress on outstanding challenges, including descriptions of non-Arrhenius effects and activation volumes, are detailed along with some directions for future investigations.

Molecular Simulations of Phase Equilibria and Transport Properties in a Model CO2-Expanded Lithium Perchlorate Electrolyte

Carbon-dioxide (CO₂)-expanded liquids, in which a significant mole fraction of CO₂ is dissolved into an organic solvent, have been of significant interest, especially as catalytic support media. Because the CO₂ mole fraction and density can be controlled over a significant range by changing the CO₂ partial pressure, the transport properties of these solvents are highly tunable. Recently, these liquids have garnered interest as potential electrolyte solutions for catalytic electrochemistry; however, little is currently known about the influence of the electrolyte on CO₂ expansion. In the present work, we use molecular-dynamics simulations to study diffusion and viscosity in a model lithium perchlorate electrolyte in CO₂-expanded acetonitrile and demonstrate that these properties are highly dependent on the concentration of the electrolyte. Our present results indicate that the electrolyte slows down diffusion of both CO₂ and MeCN, and that the slowed diffusion in the former is driven by changes in the activation entropy, whereas slowed diffusion in the latter is driven by changes in the activation energy.

Examining the Role of Different Molecular Interactions on Activation Energies and Activation Volumes in Liquid Water

There are a large number of force fields available to model water in molecular dynamics simulations, which each have their own strengths and weaknesses in describing the behavior of the liquid. One particular weakness in many of these models is their description of dynamics away from ambient conditions, where their ability to reproduce measurements is mixed. To investigate this issue, we use the recently developed fluctuation theory for dynamics to directly evaluate measures of the local temperature and pressure dependence: the activation energy and the activation volume. We examine these activation parameters for hydrogen-bond jump exchange times, OH reorientation times, and diffusion coefficients calculated from the SPC/E, SPC/Fw, TIP3P-PME, TIP3P-PME/Fw, OPC3, TIP4P/2005, TIP4P/Ew, E3B2, and E3B3 water models. Activation energy decompositions available through the fluctuation theory approach provide mechanistic insight into the origins of different temperature dependences between the various models, as well as the influence of three-body effects and flexibility.

Temperature Dependence of Peptide Conformational Equilibria from Simulations at a Single Temperature

Understanding the structure of proteins is key to unraveling their function in biological processes. Thus, significant attention has been paid to the calculation of conformational free energies. In this paper, we demonstrate a simple extension of fluctuation theory that permits the calculation of the temperature derivative of the conformational free energy, and hence the internal energy and entropy, from single-temperature simulations. The method further enables the decomposition into the contribution of different interactions present in the system to the internal energy surface. We illustrate the method for the canonical test system of alanine dipeptide in aqueous solution, for which we examine the free energy as a function of two dihedral angles. This system, like many, is most effectively treated using accelerated sampling methods and we show how the present approach is compatible with an important class of these, those that introduce a bias potential, by implementing it within metadynamics.

On the role of hydrogen-bond exchanges in the spectral diffusion of water

The dynamics of a vibrational frequency in a condensed phase environment, i.e., the spectral diffusion, has attracted considerable interest over the last two decades. A significant impetus has been the development of two-dimensional infrared (2D-IR) photon-echo spectroscopy that represents a direct experimental probe of spectral diffusion, as measured by the frequency-frequency time correlation function (FFCF). In isotopically dilute water, which is perhaps the most thoroughly studied system, the standard interpretation of the longest timescale observed in the FFCF is that it is associated with hydrogen-bond exchange dynamics. Here, we investigate this connection by detailed analysis of both the spectral diffusion timescales and their associated activation energies. The latter are obtained from the recently developed fluctuation theory for the dynamics approach. The results show that the longest timescale of spectral diffusion obtained by the typical analysis used cannot be directly associated with hydrogen-bond exchanges. The hydrogen-bond exchange time does appear in the decay of the water FFCF, but only as an additional, small-amplitude (<3%) timescale. The dominant contribution to the long-time spectral diffusion dynamics is considerably shorter than the hydrogen-bond exchange time and exhibits a significantly smaller activation energy. It thus arises from hydrogen-bond rearrangements, which occur in between successful hydrogen-bond partner exchanges, and particularly from hydrogen bonds that transiently break before returning to the same acceptor.