Pronounced non-Condon effects in the ultrafast infrared spectroscopy of water

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.

Simulation of the Pump-Probe Spectra and Excitation Energy Relaxation of the B850 Band of the LH2 Complex in Purple Bacteria

Ultrafast spectroscopic techniques have been vital in studying excitation energy transfer (EET) in photosynthetic light harvesting complexes. In this paper, we simulate the pump-probe spectra of the B850 band of the light harvesting complex 2 (LH2) of purple bacteria, by using the hierarchical equation of motion method and the optical response function approach. The ground state bleach, stimulated emission, and excited state absorption components of the pump-probe spectra are analyzed in detail. The laser pulse-induced population dynamics are also simulated to help understand the main features of the pump-probe spectra and the EET process. It is shown that the excitation energy relaxation is an ultrafast process with multiple time scales. The first 40 fs of the pump-probe spectra is dominated by the relaxation of the k = ±1 states to both the k = 0 and higher energy states. Dynamics on a longer time scale around 200 fs reflects the relaxation of higher energy states to the k = 0 state.

Impact of interfacial curvature on molecular properties of aqueous interfaces

The curvature of soft interfaces plays a crucial role in determining their mechanical and thermodynamic properties, both at macroscopic and microscopic scales. In the case of air/water interfaces, particular attention has recently focused on water microdroplets, due to their distinctive chemical reactivity. However, the specific impact of curvature on the molecular properties of interfacial water and interfacial reactivity has so far remained elusive. Here, we use molecular dynamics simulations to determine the effect of curvature on a broad range of structural, dynamical, and thermodynamical properties of the interface. For a droplet, a flat interface, and a cavity, we successively examine the structure of the hydrogen-bond network and its relation to vibrational spectroscopy, the dynamics of water translation, rotation, and hydrogen-bond exchanges, and the thermodynamics of ion solvation and ion-pair dissociation. Our simulations show that curvature predominantly impacts the hydrogen-bond structure through the fraction of dangling OH groups and the dynamics of interfacial water molecules. In contrast, curvature has a limited effect on solvation and ion-pair dissociation thermodynamics. For water microdroplets, this suggests that the curvature alone cannot fully account for the distinctive reactivity measured in these systems, which are of great importance for catalysis and atmospheric chemistry.

Fermi Resonance of the N-D Stretching Mode Probing the Local Hydrogen-Bonding Environment in Proteins

Local H-bonding interactions are crucial for proteins to undergo various structural transitions and form different secondary structures. However, identifying slight distinctions in the local H-bonding of proteins is rather challenging. Here, we demonstrate that the Fermi resonance of the N-D stretching mode can provide an effective probe for the localized H-bonding environment of proteins both at the surface/interface and in the bulk. Using sum frequency generation vibrational spectroscopy and infrared spectroscopy, we established a correlation between the Fermi resonance of the N-D mode and protein secondary structures. The H-bond of N-D···C═O splits the N-D modes into two peaks (∼2410 and ∼2470 cm-1). The relative strength ratio (R) between the ∼2410 cm-1 peak and the ∼2470 cm-1 peak is very sensitive to H-bond strength and protein secondary structure. R is less than 1 for α-helical peptides, while R is greater than 1 for β-sheet peptides. For R < 2.5, both α-helical/loop structures and β-sheet structures exhibit almost identical Fermi coupling strengths (W = 28 cm-1). For R > 2.5, W decreases from 28 to 14 cm-1 and depends on the aggregation degree of the β-sheet oligomers or fibrils. The initial local H-bonding status impacts the misfolding dynamics of proteins at the lipid bilayer interface.

Theoretical and experimental OD-stretch vibrational spectroscopy of heavy water

In view of the current situation in which the OD-stretch vibrational spectra have been scarcely computed with non-polarizable rigid D2O models, we investigate the IR and Raman spectra of D2O by using a newly-reported model TIP4P/2005-HW. From the comparison between the calculations and experimental data, we find the excellent performance of TIP4P/2005-HW for vibrational spectroscopy of D2O in the same manner as TIP4P/2005 for H2O, although one may still conveniently employ an alternative method that regards OH as putative OD to calculate the OD-stretch spectra with similar quality from TIP4P/2005 trajectories. We also demonstrate that the appropriate setting for the spectral simulation of D2O under the time-averaging approximation reflects the slower dynamics (i.e., slower motion of translation and rotation due to the heavier mass and stronger hydrogen bond) of D2O than H2O. Moreover, we show from the theoretical calculations that the established interpretation of the OH-stretch spectra of H2O is finely applicable to the OD-stretch of D2O.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Time-resolved vibrational dynamics: Novel opportunities for sensing and imaging

The evolution of time-resolved spectroscopies has resulted in significant advancements across numerous scientific disciplines, particularly those concerned with molecular electronic states. However, the intricacy of molecular vibrational spectroscopies, which provide comprehensive molecular-level information within complex structures, has presented considerable challenges due to the ultrashort dephasing time. Over recent decades, an increasing focus has been placed on exploring the temporal progression of bond vibrations, thereby facilitating an improved understanding of energy redistribution within and between molecules. This review article focuses on an array of time-resolved detection methodologies, each distinguished by unique technological attributes that offer exclusive capabilities for investigating the physical phenomena propelled by molecular vibrational dynamics. In summary, time-resolved vibrational spectroscopy emerges as a potent instrument for deciphering the dynamic behavior of molecules. Its potential for driving future progress across fields as diverse as biology and materials science is substantial, marking a promising future for this innovative tool.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Predicting the Raman Spectra of Liquid Water with a Monomer-Field Model

The Raman spectrum of liquid water is quite complex, reflecting its strong sensitivity to the local environment of the individual waters. The OH-stretch region of the spectrum, which captures the influence of hydrogen bonding, has only just begun to be unraveled. Here we develop a model for predicting the Raman spectra of the OH-stretch region by considering how local electric fields distort the energy surface of each water monomer. We find that our model is capable of reproducing the bimodal nature of the main peak, with the shoulder at 3250 cm-1 resulting almost entirely from Fermi resonance. Furthermore, we capture the temperature and polarization dependence of the shoulder, which has proven to be difficult to obtain with previous methods, and analyze the origin of this dependence. We expect our model to be generally useful for understanding and predicting how Raman spectra change under different conditions and with different probe reporters beyond water.

Vibrational Probe at the Electrochemical Interface: Dependence on Plasmon Coupling and Potential of the Lineshape in Two-Dimensional Infrared Spectroscopy

Two-dimensional infrared spectroscopy of vibrational probes at an electrode surface shows promise for studying the structural dynamics at an active electrochemical interface. This interface is a complex environment where the solution structures in response to the applied potential. A strategy for achieving the necessary monolayer sensitivity is to use a plasmonically active electrode, which enhances the electromagnetic fields that produce the spectroscopic response. Here, we show how the coupling between the plasmon and the vibrations of the molecular monolayer impacts the FTIR and 2D IR spectroscopy, with an emphasis on the electrochemical potential difference spectra. We show how mixing between the vibrational and plasmonic states gives rise to the distortions that are observed in these measurements. This provides an important step toward 2D IR measurements of vibrational probes at the electrochemical interface as a tool for probing the structural dynamics in the double layer.

Counteracting Effects of Trimethylamine N-Oxide against Urea in Aqueous Solutions: Insights from Theoretical Two-Dimensional Infrared Spectroscopy

The study of small osmolytes in their aqueous solutions has gained significant attention because of their relevance to structure and thermodynamics of proteins in aqueous media. Special attention has been given to the binary and ternary aqueous solutions of urea and trimethylamine N-oxide (TMAO). Urea is a well-known protein denaturant, while TMAO protects proteins in their native states. Interestingly, TMAO counteracts urea's ability to denature proteins when present in solutions with approximately half of the concentration of urea. Vibrational spectroscopy can improve our understanding of the molecular origin of this counteracting effect because of its sensitivity to local structure and dynamics. We present results of theoretical linear vibrational and two-dimensional infrared (2DIR) spectroscopy of water in the binary and ternary aqueous solutions of TMAO and urea. The 2DIR spectra are calculated using the electronic structure/molecular dynamics approach. The non-Condon effects in spectral transitions are incorporated in the theoretical calculations of 2DIR spectra. It is found that TMAO disrupts the local structure of water, while urea leaves it essentially unaffected. The 2DIR results show that both TMAO and urea slow down the dynamics of spectral diffusion of water. The extent of slowing down is found to be particularly significant for both hydration and bulk water in the presence of TMAO which can be attributed to strong hydrogen bonds between the water and TMAO molecules. The water molecules present in the hydration layer of the solutes in the ternary solutions are found to relax at even slower rates compared to that in their binary solutions in water. The hydrogen bonds between TMAO and urea are found to be not stable. Thus, the counteracting effect of TMAO against urea is seen to take place mainly through water-mediated interactions. Such TMAO-induced effects giving rise to more structured and slower hydrogen-bonded network are successfully captured through 2DIR spectroscopic calculations.

Asymmetry of the Electrostatic Environment as the Origin of the Symmetry Breaking Effect of the Nitrate Ion in Aqueous Solution

Elucidating the mechanism of how vibrational modes are affected by intermolecular interactions is important for a better understanding of the nature of the former as probes of the latter. Here, such an analysis is carried out for the N-O stretching modes of the nitrate ion interacting with water, with an emphasis on the symmetry breaking effect. On the basis of theoretical calculations on the structural, vibrational, and electrostatic properties of molecular clusters and spectral simulations for an aqueous solution, a transparent view is demonstrated on the mechanism that modulations of spatially local electrostatic environment give rise to structural and spectroscopic symmetry breaking effect. The electrostatic interaction model constructed here is a seven-parameter model; the use of a single electrostatic parameter, such as the electric field on a single atomic site, is found to be insufficient for quantitative evaluation. It is also shown that the frequency modulations of the N-O stretching modes in aqueous solution occur on a time scale much shorter than 0.1 ps.

Calculating Vibrational Excited State Absorptions with Excited State Constrained Minimized Energy Surfaces

The modeling and interpretation of vibrational spectra are crucial for studying reaction dynamics using vibrational spectroscopy. Most prior theoretical developments focused on describing fundamental vibrational transitions while fewer developments focused on vibrational excited state absorptions. In this study, we present a new method that uses excited state constrained minimized energy surfaces (CMESs) to describe vibrational excited state absorptions. The excited state CMESs are obtained similarly to the previous ground state CMES development in our group but with additional wave function orthogonality constraints. Using a series of model systems, including the harmonic oscillator, Morse potential, double-well potential, quartic potential, and two-dimensional anharmonic potential, we demonstrate that this new procedure provides good estimations of the transition frequencies for vibrational excited state absorptions. These results are significantly better than those obtained from harmonic approximations using conventional potential energy surfaces, demonstrating the promise of excited state CMES-based methods for calculating vibrational excited state absorptions in real systems.

Ion/Water Network Structural Dynamics in Highly Concentrated Lithium Chloride and Lithium Bromide Solutions Probed with Ultrafast Infrared Spectroscopy

The structural dynamics of highly concentrated LiCl and LiBr aqueous solutions were observed from 1-4 to 1-16 water molecules per ion pair using ultrafast polarization-selective pump-probe (PSPP) experiments on the OD stretch of dilute HOD. At these high salt concentrations, an extended ion/water network exists with complex structural dynamics. Population decays from PSPP experiments highlight two distinct water components. From the frequency-dependent amplitudes of the decays, the spectra of hydroxyls bound to halides and to water oxygens are obtained, which are not observable in the FT-IR spectra. PSPP experiments also measure frequency-dependent water orientational relaxation. At short times, wobbling dynamics within a restricted angular cone occurs. At high concentrations, the cone angles are dependent on frequency (hydrogen bond strength), but at higher water concentrations (>10 waters per ion pair), there is no frequency dependence. The average cone angle increases as the ion concentration decreases. The slow time constant for complete HOD orientational relaxation is independent of concentration but slower in LiCl than in LiBr. Comparison to structural MD simulations of LiCl from the literature indicates that the loss of the cone angle wavelength dependence and the increase in the cone angles as the concentration decreases occur as the prevalence of large ion/water clusters gives way to contact ion pairs.

Theoretical Two Dimensional Infrared Spectroscopy of Aqueous Solutions of tert-Butyl Alcohol: Variation of the Dynamics of Spectral Diffusion along the Percolation Transition

Binary mixtures of water and tert-butyl alcohol (TBA) are known to exhibit the so-called percolation transition where small clusters of TBA molecules span into large aggregates beyond a threshold concentration of the alcohol. In the present study, we have investigated the linear and two-dimensional infrared spectral features of aqueous solutions of TBA for varying concentration of the alcohol along the percolation transition. The percolation transition is characterized through calculations of intermolecular radial distribution functions and average size of the largest cluster of TBA molecules. It is found that, with variation of alcohol concentration, the radial distribution functions of the central carbon atoms of TBA molecules show a nonmonotonic change in the height of the first peak and also the size of the largest cluster of TBA molecules show a jump in the increase of its size for TBA mole fraction between 0.04 and 0.06 corresponding to a transition from smaller clusters to larger spanning aggregates. However, it is found that the linear infrared spectrum of water does not exhibit any noticeable changes on variation of TBA concentration along the percolation transition. Subsequently, two-dimensional infrared (2DIR) spectra and vibrational frequency time correlation function of water are calculated for all the TBA-water solutions considered in this study. The spectral diffusion of water calculated from 2DIR is found to slow down with increase of the TBA concentration. The time scales of spectral diffusion of water, as characterized by the relaxation of frequency time correlation function, 2DIR metric of central line slope, and also the hydrogen bond time correlation functions, are found to exhibit a noticeable jump along the percolation transition. The hydrophilic group of TBA is found to retard the water dynamics more effectively than the hydrophobic groups. Also, the jump in the dynamical slowdown along the percolation transition is found to be more significant for water molecules at the hydrophilic sites.

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid 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.

Modeling the Infrared Spectroscopy of Oligonucleotides with 13C Isotope Labels

The carbonyl stretching modes have been widely used in linear and two-dimensional infrared (IR) spectroscopy to probe the conformation, interaction, and biological functions of nucleic acids. However, due to their universal appearance in nucleobases, the IR absorption bands of nucleic acids are often highly congested in the 1600-1800 cm^-1 region. Following the fruitful applications in proteins, ¹³C isotope labels have been introduced to the IR measurements of oligonucleotides to reveal their site-specific structural fluctuations and hydrogen bonding conditions. In this work, we combine recently developed frequency and coupling maps to develop a theoretical strategy that models the IR spectra of oligonucleotides with ¹³C labels directly from molecular dynamics simulations. We apply the theoretical method to nucleoside 5'-monophosphates and DNA double helices and demonstrate how elements of the vibrational Hamiltonian determine the spectral features and their changes upon isotope labeling. Using the double helices as examples, we show that the calculated IR spectra are in good agreement with experiments and the ¹³C isotope labeling technique can potentially be applied to characterize the stacking configurations and secondary structures of nucleic acids.

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.

Unified master equation for molecules in phonon and radiation baths

We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg–Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.

Molecular Simulation-Guided Spectroscopy of Imidazolium-Based Ionic Liquids and Effects of Methylation on Ion-Cage and -Pair Dynamics

Classical molecular dynamics simulations were performed to assess an atomistic interpretation of the ion-probe structural interactions in two typical ionic liquids (ILs), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [BMIm][NTf₂] and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BDimIm][NTf₂] through computational ultrafast spectroscopy. The nitrile stretching vibrations of the thiocyanate anion, [SCN]^-, serve as the local mode of the ultrafast system dynamics within the imidazolium-based ionic liquid environment. The wavelet transform of classical trajectories determines the time-varying fluctuating frequencies and the stretch spectral signatures of SCN^- in the normalized distribution. However, computational modeling of the two-dimensional (2D) spectra from the wavelet-derived vibrational frequencies yields time evolution of the local molecular structure along with the varied time-dependent dynamics of the spectral diffusion process. We calculated the frequency-frequency correlation functions (FFCFs), time correlations associated with the ion-pair and -cage dynamics, and mean square displacements as a function of time, depicting diffusive dynamics. The calculated results based on the pair correlation functions and the distribution of atomic density suggest that the hydrogen and methylated carbon at the two-position of the imidazolium ring of [BMIm] and [BDimIm] cations, respectively, strongly interact with the probe through the N of the thiocyanate anion rather than the S atom. The center-of-mass center-of-mass (COM-COM) cation-probe radial distribution functions (RDFs) in conjunction with the site-specific structural analysis further reveal well-structured interactions of the thiocyanate ion and [BMIm]⁺ cation rather than the [BDimIm] cation. In contrast, the anion-probe COM-COM RDFs depict weak interactive associations within the vibrational probe [SCN]^- and [NTf₂]^- ions. Methylation at the two-position of the imidazolium ring predicts slower structural reorganization and breaking and reformation dynamics of the ion pairs and cages within the ionic liquid framework.

Experimental and Theoretical Heterodyne-Detected Sum Frequency Generation Spectroscopy of Isotopically Pure and Diluted Water Surfaces

The χ⁽²⁾ (second-order nonlinear optical susceptibility) spectrum of the water surface has been a matter of debate for a few decades. Here, we report that we experimentally measured the isotopic dilution dependence of the χ⁽²⁾ spectrum and theoretically reproduced it by employing the quantum/classical mixed approach with a new idea to subtract an artifact. The present theoretical framework allows for clarifying the effects of the intramolecular, intermolecular, and Fermi resonance couplings on the OH-stretch vibrational spectra of water at the surface as well as in the bulk.

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.

Multiple Ensembles of the Hydrogen-bonded Network in Ethylammonium Nitrate versus Water from Vibrational Spectral Dynamics of SCN- Probe

We performed classical molecular dynamics simulations to monitor the structural interactions and ultrafast dynamical and spectral response in the protic ionic liquid, ethylammonium nitrate (EAN) and water using the nitrile stretching mode of thiocyanate ion (SCN-) as the vibrational probe. The normalized stretch frequency distribution of nitrile stretch of SCN- attains an asymmetric shape in EAN, indicating the existence of more than one hydrogen-bonding environment in EAN. We computed the 2D IR spectrum from classical trajectories, applying the response function formalism. Spectral diffusion dynamics in EAN undergo an initial rattling of the SCN - inside the local ion-cage occurring at a timescale of 0.10 ps, followed by the breakup of the ion-cage activating molecular diffusion at 7.86 ps timescale. In contrast, the dynamics of structural reorganization occur at a timescale of 0.58 ps in H 2 O. Hence, the time dependence of the frequency-frequency correlation function decay hints at the local molecular structure and ultrafast ion dynamics of the SCN - probe. The loss of frequency correlation read from the peak shape changes in the 2D correlation spectrum as a function of waiting time is faster in H 2 O than in EAN due to the enhanced structural ordering and higher viscosity of the latter. We provide an atomic-level interpretation of the solvation environment around SCN - in EAN and water, which indicates the multiple ensembles of the hydrogen bond network in EAN.

Ionic Dynamics and Vibrational Spectral Diffusion of a Protic Alkylammonium Ionic Salt through Intrinsic Cationic N-H Vibrational Probe from FPMD Simulations

We employed density functional theory (DFT)-based molecular dynamics simulations to explore the structure, dynamics, and spectral properties of the protic ionic entity trimethylammonium chloride (TMACl). Structural investigations include calculating the site-site radial distribution functions (RDFs), the distribution of constituent cations and anions in three-dimensional space, and combined distribution functions of the hydrogen-bonded pair RDF versus angle, revealing the structural characteristics of the ionic solvation and the intermolecular interactions within ions. Further, we determined the instantaneous vibrational stretching frequencies of the intrinsic N-H stretch probe modes by applying the time-series wavelet method. The associated ionic dynamics within the protic ionic compound were investigated by calculating the time-evolution of the fluctuating frequencies and the frequency-time correlation functions (FFCFs). The time scale related to the local structural relaxation process and the average hydrogen bond lifetime, ion cage dynamics, and mean squared displacement were investigated. The faster decay component of the FFCFs, depicting the intermolecular motion of intact hydrogen bonds in TMACl, is 0.07 ps for the Perdew-Burke-Ernzerhof (PBE)-based simulation and 0.06 ps for the PBE-D2 representation. The slower time scale of the longer picosecond decay time component of PBE and PBE-D2 representations are 3.13 and 2.87 ps, respectively. These picosecond time scales represent more significant fluctuations of the hydrogen-bonding partners in the ionic entity and hydrogen-bond jump events accompanied by large angular jumps. The longest picosecond time scales represent structural relaxation, including large angular jumps and ion-pair dynamics. Also, ion cage lifetimes correlate with the slowest time scale of the associated dynamics of vibrational spectral diffusion despite the type of DFT functional. This study benchmarks DFT treatments of the exchange-correlation functional with and without the van der Waals (vdW) dispersion correction scheme. The inclusion of vdW interactions to the PBE functional represents a less structured state of the ionic entity and faster dynamics of the molecular motions relative to the one predicted by the PBE system. All the results illustrate the necessity of accurately describing the Coulomb interactions, vdW dispersive interactive forces, and localized hydrogen bonds required to sustain the energetic balance in this ionic salt.

Generative Adversarial Neural Networks for Denoising Coherent Multidimensional Spectra

Ultrafast spectroscopy often involves measuring weak signals and long data acquisition times. Spectra are typically collected as a "pump-probe" spectrum by measuring differences in intensity across laser shots. Shot-to-shot intensity fluctuations are most often the primary source of noise in ultrafast spectroscopy. Here, we present a novel approach for denoising ultrafast two-dimensional infrared (2D IR) spectra using conditional generative adversarial neural networks (cGANNs). The cGANN approach is able to eliminate shot-to-shot noise and reconstruct the line shapes present in the noisy input spectrum. We present a general approach for training the cGANN using matched pairs of noisy and clean synthetic 2D IR spectra based on the Kubo-line shape model for a three-level system. Experimental shot-to-shot laser noise is added to synthetic spectra to recreate the noise profile present in measured experimental spectra. The cGANNs can recover line shapes from synthetic 2D IR spectra with signal-to-noise ratios as low as 2:1, while largely preserving the key features such as center frequencies, line widths, and diagonal elongation. In addition, we benchmark the performance of the cGANN using experimental 2D IR spectra of an ester carbonyl vibrational probe and demonstrate that, by applying the cGANN denoising approach, we can extract the frequency-frequency time correlation function (FFCF) from reconstructed spectra using a nodal-line slope analysis. Finally, we provide a set of practical guidelines for extending the denoising method to other coherent multidimensional spectroscopies.

Infrared Spectra and Hydrogen-Bond Configurations of Water Molecules at the Interface of Water-Insoluble Polymers under Humidified Conditions

Elucidating the state of interfacial water, especially the hydrogen-bond configurations, is considered to be key for a better understanding of the functions of polymers that are exhibited in the presence of water. Here, an analysis in this direction is conducted for two water-insoluble biocompatible polymers, poly(2-methoxyethyl acrylate) and cyclic(poly(2-methoxyethyl acrylate)), and a non-biocompatible polymer, poly(n-butyl acrylate), by measuring their IR spectra under humidified conditions and by carrying out theoretical calculations on model complex systems. It is found that the OH stretching bands of water are decomposed into four components, and while the higher-frequency components (with peaks at ∼3610 and ∼3540 cm^-1) behave in parallel with the C═O and C-O-C stretching and CH deformation bands of the polymers, the lower-frequency components (with peaks at ∼3430 and ∼3260 cm^-1) become pronounced to a greater extent with increasing humidity. From the theoretical calculations, it is shown that the OH stretching frequency that is distributed from ∼3650 to ∼3200 cm^-1 is correlated to the hydrogen-bond configurations and is mainly controlled by the electric field that is sensed by the vibrating H atom. By combining these observed and calculated results, the configurations of water at the interface of the polymers are discussed.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

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.

Quantum vibration perturbation approach with polyatomic probe in simulating infrared spectra

The quantitative prediction of vibrational spectra of chromophore molecules in solution is challenging and numerous methods have been developed. In this work, we present a quantum vibration perturbation (QVP) approach, which is a procedure that combines molecular quantum vibration and molecular dynamics with perturbation theory. In this framework, an initial Newtonian molecular dynamics simulation is performed, followed by a substitution process to embed molecular quantum vibrational wave functions into the trajectory. The instantaneous vibrational frequency shift at each time step is calculated using the Rayleigh-Schrödinger perturbation theory, where the perturbation operator is the difference in the vibrational potential between the reference chromophore and the perturbed chromophore in the environment. Semi-classical statistical mechanics is employed to obtain the spectral lineshape function. We validated our method using HCOOH·nH₂O (n = 1-2) clusters and HCOOH aqueous solution as examples. The QVP method can be employed for rapid prediction of the vibrational spectrum of a specific mode in solution.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Intramolecular O-H⋯S hydrogen bonding in threefold symmetry: Line broadening dynamics from ultrafast 2DIR-spectroscopy and ab initio calculations

The dynamics of intramolecular hydrogen-bonding involving sulfur atoms as acceptors is studied using two-dimensional infrared (2DIR) spectroscopy. The molecular system is a tertiary alcohol whose donating hydroxy group is embedded in a hydrogen-bond potential with torsional C₃-symmetry about the carbon-oxygen bond. The linear and 2DIR-spectra recorded in the OH-stretching region of the alcohol can be simulated very well using Kubo's line shape theory based on the cumulant expansion for evaluating the linear and nonlinear optical response functions. The correlation function for OH-stretching frequency fluctuations reveals an ultrafast component decaying with a time constant of 700 fs, which is in line with the apparent decay of the center line slopes averaged over absorption and bleach/emission signals. In addition, a quasi-static inhomogeneity is detected, which prevents the 2DIR line shape to fully homogenize within the observation window of 4 ps. The experimental data were then analyzed in more detail using a full ab initio approach that merges time-dependent structural information from classical molecular dynamics (MD) simulations with an OH-stretching frequency map derived from density functional theory (DFT). The latter method was also used to obtain a complementary transition dipole map to account for non-Condon effects. The 2DIR-spectra obtained from the MD/DFT method are in good agreement with the experimental data at early waiting delays, thereby corroborating an assignment of the fast decay of the correlation function to the dynamics of hydrogen-bond breakage and formation.

Role of Intermolecular Charge Fluxes in the Hydrogen-Bond-Induced Frequency Shifts of the OH Stretching Mode of Water

The relation between the vibrational properties and the electrostatic situations of the vibrating functional group is useful to predict vibrational spectroscopic features based on, for example, classical molecular dynamics of liquids or biomolecular systems, but to pursue its generality or the extent of applicability, it is required to understand the mechanisms giving rise to it. Here such an analysis is carried out for the OH stretching mode of water. By examining the correlations among various (structural, vibrational, and electrostatic) properties and by analyzing the spatial characteristics of the behavior of electrons occurring upon the vibration, it is shown that the dependence of the vibrational frequency and the dipole derivative of the OH stretching mode on the electric field is not of purely electrostatic origin, and the delocalized electronic motions occurring with this mode, called intermolecular charge fluxes, related to both the dipole first and second derivatives play important roles.

Coupling of three intramolecular vibration modes of liquid H2O molecules in the framework of the fluctuation theory of hydrogen bonding

Vibrational spectra of liquid water contain a wealth of information about its structure and dynamics but there are no generally acknowledged interpretation of their band profiles, unfortunately. We have tried to calculate them taking into account only the coupling of three intramolecular vibrations in the set of H₂O molecules with different initial oscillator frequencies and intensities. The matter is that each water molecule forms hydrogen bonds of different strengths; thus the OH stretching band spans several hundreds of wave numbers (the fluctuation theory of hydrogen bonding). This distribution overlaps with the similar band of the first overtone of the HOH bending frequencies thus triggering a Fermi resonance between three vibrations. There were some problems causing some simplifications in previous theoretical modeling of vibrational transitions in condensed water. To solve them we extract the statistical distribution of OH frequencies of H₂O molecules directly from the experimental spectra of HOD molecules at the same conditions instead of defining it theoretically. Also the bending overtone is allowed to have non-zero intrinsic intensity when calculating the Fermi resonance. The test calculation of the isotropic component of the Raman spectrum which is most critical for interpretation shows that our algorithm can reproduces the characteristic peculiarities of the experiment. The spectrum consists of three non-Gaussian contours. The overtone of bending vibration, being strengthened by Fermi resonance, makes the greatest contribution to the dominating low-frequency spectrum component that was previously attributed to intermolecular coupling of adjacent OH oscillators by some authors. Further we plan to calculate similar band profiles in the IR and also Raman isotropic and anisotropic spectra of Н₂О and D₂О molecules within a wide temperature range for their quantitative comparison with experiment.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Quantitative Analysis of Infrared Spectra of Binary Alcohol + Cyclohexane Solutions with Quantum Chemical Calculations

Hydrogen bonding has profound effects on the behavior of molecules. Fourier-transform infrared spectroscopy is the technique most commonly used to qualitatively identify hydrogen-bonding moieties present in a chemical sample. However, quantitative analysis of infrared (IR) spectra is nontrivial for the hydroxyl stretching region where hydrogen bonding is most prominently expressed in organic alcohols and water. Specifically, the breadth and extreme overlap of the O-H stretching bands, and the order of magnitude variability of their IR attenuation coefficients complicates the analysis. In the present work, sequential molecular dynamics simulations and quantum mechanical calculations are used to develop a function to relate the integrated IR attenuation coefficient to the vibrational frequencies of hydroxyl bands across the O-H stretching region. This relationship is then used as a guide to develop an attenuation coefficient scaling function to quantitatively determine concentrations of alcohols in a hydrocarbon solution from experimental IR spectra by integration across the entire hydroxyl frequency range.

Dephasing and Decoherence in Vibrational and Electronic Line Shapes

Absorption and emission line shapes of vibrational and electronic transitions in liquids are broadened by interactions with the "bath" (in this case, the rotational and translational degrees of freedom of all the molecules in the liquid). If these degrees of freedom are treated classically, the broadening process is often known as dephasing. If, on the other hand, the bath degrees of freedom are instead treated quantum mechanically, there is additional broadening due to what is known in the chemical-physics literature as decoherence. The question addressed in this paper is the relative importance of decoherence (bath quantum effects) and dephasing. We present general developments of this subject for absorption and emission line shapes, discover several new relationships connecting classical and quantum treatments of the bath, and also consider the Stokes shift (difference in peak frequencies in absorption and emission). We next draw some general conclusions by considering a model system whose transition-frequency time-correlation function has only one bath time scale. We then consider a realistic system of the vibrational OH stretch transition of dilute HOD in liquid D₂O at room temperature. For this system, we conclude that bath quantum effects are not very important, except for the Stokes shift. More generally, we argue that this is the case for many vibrational and most electronic transitions in room-temperature liquids.

Distinctive behavior and two-dimensional vibrational dynamics of water molecules inside glycine solvation shell

We present a first principles molecular dynamics study of a deuterated aqueous solution of a single glycine moiety to explore the structure, dynamics, and two-dimensional infrared spectra of water molecules found in the solvation shell of glycine.

Bulk-like and Interfacial Water Dynamics in Nafion Fuel Cell Membranes Investigated with Ultrafast Nonlinear IR Spectroscopy

The water confined in the hydrophilic domains of Nafion fuel cell membranes is central to its primary function of ion transport. Water dynamics are intimately linked to proton transfer and are sensitive to the structural features and length scales of confinement. Here, ultrafast polarization-selective pump-probe and two-dimensional infrared vibrational echo (2D IR) experiments were performed on fully hydrated Nafion membranes with sodium counterions to explicate the water dynamics. Like aerosol-OT reverse micelles (AOT RMs), the water dynamics in Nafion are attributed to bulk-like core water in the central region of the hydrophilic domains and much slower interfacial water. Population and orientational dynamics of water in Nafion are slowed by polymer confinement. Comparison of the observed dynamics to those of AOT RMs helps identify local interactions between water and sulfonate anions at the interface and among water molecules in the core. This comparison also demonstrates that the well-known spherical cluster morphology of Nafion is not appropriate. Spectral diffusion of the interfacial water, which arises from structural dynamics, was obtained from the 2D IR experiments taking the core water to have dynamics similar to bulk water. Like the orientational dynamics, spectral diffusion was found to be much slower at the interface compared to bulk water. Together, the dynamics indicate slow reorganization of weakly hydrogen-bonded water molecules at the interface of Nafion. These results provide insights into proton transport mechanisms in fuel cell membranes, and more generally, water dynamics near the interface of confining systems.