Non-Gaussian statistics of amide I mode frequency fluctuation of N-methylacetamide in methanol solution: linear and nonlinear vibrational spectra

Chasing weakly-bound biological water in aqueous environment near the peptide backbone by ultrafast 2D infrared spectroscopy

There has been a long-standing debate as to how many hydrogen bonds a peptide backbone amide can form in aqueous solution. Hydrogen-bonding structural dynamics of N-ethylpropionamide (a β-peptide model) in water was examined using infrared (IR) spectroscopy. Two amide-I sub bands arise mainly from amide C=O group that forms strong H-bonds with solvent water molecules (SHB state), and minorly from that involving one weak H-bond with water (WHB state). This picture is supported by molecular dynamics simulations and ab-initio calculations. Further, thermodynamics and kinetics of the SHB and WHB species were examined mainly by chemical-exchange two-dimensional IR spectroscopy, yielding an activation energy for the SHB-to-WHB exchange of 13.25 ± 0.52 kJ mol‒1, which occurs in half picosecond at room temperature. Our results provided experimental evidence of an unstable water molecule near peptide backbone, allowing us to gain more insights into the dynamics of the protein backbone hydration.

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.

Infrared Spectroscopy of Liquid Solutions as a Benchmarking Tool of Semiempirical QM Methods: The Case of GFN2-xTB

The accurate description of large molecular systems has triggered the development of new computational methods. Due to the computational cost of modeling large systems, the methods usually require a trade-off between accuracy and speed. Therefore, benchmarking to test the accuracy and precision of the method is an important step in their development. The typical gold standard for evaluating these methods is isolated molecules, because of the low computational cost. However, the advent of high-performance computing has made it possible to benchmark computational methods using observables from more complex systems such as liquid solutions. To this end, infrared spectroscopy provides a suitable set of observables (i.e., vibrational transitions) for liquid systems. Here, IR spectroscopy observables are used to benchmark the predictions of the newly developed GFN2-xTB semiempirical method. Three different IR probes (i.e., N-methylacetamide, benzonitrile, and semiheavy water) in solution are selected for this purpose. The work presented here shows that GFN2-xTB predicts central frequencies with errors of less than 10% in all probes. In addition, the method captures detailed properties of the molecular environment such as weak interactions. Finally, the GFN2-xTB correctly assesses the vibrational solvatochromism for N-methylacetamide and semiheavy water but does not have the accuracy needed to properly describe benzonitrile. Overall, the results indicate not only that GFN2-xTB can be used to predict the central frequencies and their dependence on the molecular environment with reasonable accuracy but also that IR spectroscopy data of liquid solutions provide a suitable set of observables for the benchmarking of computational methods.

Molecular Photothermal Effects on Time-Resolved IR Spectroscopy: Solute-Solvent Intermolecular Energy Transfer

Time-resolved IR pump-probe (IR-PP) and two-dimensional IR (2D-IR) spectroscopy are valuable tools for studying ultrafast chemical and biological processes in solutions. However, the corresponding signals at long times are obscured by the molecular photothermal effects resulting from the heat dissipation of vibrationally photoexcited molecules to the surroundings. Recently, a phenomenology model was used to describe molecular photothermal effects on IR-PP signals and the diagonal and cross-peaks of 2D-IR spectra at long pump-probe delay times. Here, we consider the thermal diffusion equation with a time-dependent heat source term to describe the solute-solvent energy transfer process. An approximate solution to the nonhomogeneous differential equation shows that the molecular photothermal effect is determined by the mean intermolecular distance between IR-absorbing molecules. We show that the time profile of heat dissipation from a vibrationally excited molecule to the surroundings, which provides information about the mechanisms involved in the solute-solvent intermolecular energy transfer process in solutions, can be directly measured by analyzing the molecular photothermal IR-PP and 2D-IR signals. We anticipate that the present work can be used to interpret local heating-induced time-resolved IR spectroscopic signals and understand the rate of and the mechanisms involved in the conversion from high-frequency molecular vibrational energy to solvent kinetic energy in condensed phases.

Molecular photothermal effects on time-resolved IR spectroscopy

Time-resolved IR pump-probe (IR-PP) and two-dimensional IR (2D-IR) spectroscopy are valuable techniques for studying various ultrafast chemical and biological processes in solutions. The time-dependent changes of nonlinear IR signals reflecting fast molecular processes such as vibrational energy transfer and chemical exchange provide invaluable information on the rates and mechanisms of solvation dynamics and structural transitions of multi-species vibrationally interacting molecular systems. However, due to the intrinsic difficulties in distinguishing the contributions of molecule-specific processes to the time-resolved IR signals from those resulting from local heating, it becomes challenging to interpret time-resolved IR-PP and 2D-IR spectra exhibiting transient growing-in spectral components and cross-peaks unambiguously. Here, theoretical considerations of various effects of vibrational coupling, energy transfer, chemical exchange, the generation of hot ground states, molecular photothermal process, and their combinations on the lineshapes and time-dependent intensities of IR-PP spectra and 2D-IR diagonal and cross-peaks are presented. We anticipate that the present work will help researchers using IR pump-probe and 2D-IR techniques to distinguish local heating-induced photothermal signals from genuine nonlinear IR signals.

Origin of thiocyanate spectral shifts in water and organic solvents

Vibrational spectroscopy is a useful technique for probing chemical environments. The development of models that can reproduce the spectra of nitriles and azides is valuable because these probes are uniquely suited for investigating complex systems. Empirical vibrational spectroscopic maps are commonly employed to obtain the instantaneous vibrational frequencies during molecular dynamics simulations but often fail to adequately describe the behavior of these probes, especially in its transferability to a diverse range of environments. In this paper, we demonstrate several reasons for the difficulty in constructing a general-purpose vibrational map for methyl thiocyanate (MeSCN), a model for cyanylated biological probes. In particular, we found that electrostatics alone are not a sufficient metric to categorize the environments of different solvents, and the dominant features in intermolecular interactions in the energy landscape vary from solvent to solvent. Consequently, common vibrational mapping schemes do not cover all essential interaction terms adequately, especially in the treatment of van der Waals interactions. Quantum vibrational perturbation (QVP) theory, along with a combined quantum mechanical and molecular mechanical potential for solute-solvent interactions, is an alternative and efficient modeling technique, which is compared in this paper, to yield spectroscopic results in good agreement with experimental FTIR. QVP has been used to analyze the computational data, revealing the shortcomings of the vibrational maps for MeSCN in different solvents. The results indicate that insights from QVP analysis can be used to enhance the transferability of vibrational maps in future studies.

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.

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.

Computing the frequency fluctuation dynamics of highly coupled vibrational transitions using neural networks

The description of frequency fluctuations for highly coupled vibrational transitions has been a challenging problem in physical chemistry. In particular, the complexity of their vibrational Hamiltonian does not allow us to directly derive the time evolution of vibrational frequencies for these systems. In this paper, we present a new approach to this problem by exploiting the artificial neural network to describe the vibrational frequencies without relying on the deconstruction of the vibrational Hamiltonian. To this end, we first explored the use of the methodology to predict the frequency fluctuations of the amide I mode of N-methylacetamide in water. The results show good performance compared with the previous experimental and theoretical results. In the second part, the neural network approach is used to investigate the frequency fluctuations of the highly coupled carbonyl stretch modes for the organic carbonates in the solvation shell of the lithium ion. In this case, the frequency fluctuation predicted by the neural networks shows a good agreement with the experimental results, which suggests that this model can be used to describe the dynamics of the frequency in highly coupled transitions.

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.

Two-Dimensional Infrared Spectroscopy of Aqueous Solutions of Metal Nitrates: Slowdown of Spectral Diffusion in the Presence of Divalent Cations

The hydrogen-bonded network of water can be affected both structurally and dynamically by the presence of ions. In the present study, we have considered three aqueous solutions of metal nitrates to investigate the effects of divalent cations (Mg²⁺ and Ca²⁺), compared to that of monovalent Na⁺ ions, on hydrogen-bond fluctuations and vibrational spectral diffusion through calculations of linear and two-dimensional infrared spectra of these solutions at room temperature. We have employed the methods of molecular dynamics simulations using effective polarizable models of ions combined with quantum mechanical calculations of transition variables and statistical mechanical calculations of spectral response functions of vibrational spectroscopy. Divalent cations are found to have much stronger and longer-ranged effects on the structure and dynamics of the hydrogen-bonded network than that induced by the monovalent sodium ions. The blue shifts in the calculated linear spectra are found to follow the Hofmeister trend for the cations. The 2D-IR spectral lineshape and intensity corresponding to three-pulse echo peak shift (3PEPS) experiments are calculated. The timescales of these nonlinear spectral responses and also frequency-time correlations show significant slowing down of spectral diffusion for solutions containing divalent Mg²⁺ and Ca²⁺ ions compared to the corresponding dynamics of the solution containing Na⁺ ions. Unlike NaNO₃ solution, the relaxation of frequency and dipole orientational fluctuations of anion-bound water in Mg(NO₃)₂ and Ca(NO₃)₂ solutions are found to be somewhat slower than bulk water, which can be attributed to the presence of divalent cations whose effects go beyond their first solvation shells. This is also seen in the dynamics of bulk water in these solutions which is found to be notably slower for the solutions containing divalent cations than that in the NaNO₃ solution. Unlike Mg²⁺ and Ca²⁺ ions, no specific cationic effect is observed for the Na⁺ ions.

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.

Two-dimensional infrared spectral explorations into bilayer and monolayer self-assemblies of amphiphilic polypeptides

Poly(2-(3-((2-hydroxyethyl)amino)-3-oxopropyl)ethyleneamido) (PHAOE) is an amphiphilic polypeptide. The self-assembly is significant, but the ultrafast dynamic analyses of the peptide self-assembly are exiguous and worth further exploring. In this investigation, the temporal dynamic characteristics of the aggregates and unaggregated PHAOEs are mined by the two-dimensional infrared (2D IR) spectroscopy. The homogeneous and inhomogeneous diffusion processes of the carbonyl stretching modes of the unaggregated PHAOEs are slower than those of the self-assemblies. The inhomogeneous spectral diffusion proportion of the biopolymer PHAOE in methanol is greater than that in dimethyl sulfoxide (DMSO). The solvation shells surround the aggregates and unaggregated PHAOEs in the protic solvent methanol, but there are not any solvation shells around the aggregates or unaggregated PHAOEs in the dipolar solvent DMSO. The massive hydrogen-bonded monolayer self-assembly has merely an aggregate of PHAOEs and no solvation shell in DMSO. But the hydrogen-bonded bilayer self-assembly has a self-assembled methanol shell and an interior aggregate of PHAOEs in methanol. The self-assemblies of PHAOEs motivate the methanols to self-assemble. The large delocalized amide structure results in the fast spectral diffusion of the carbonyl stretching mode.Communicated by Ramaswamy H. Sarma.

Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics

Current simulations of ultraviolet-visible absorption lineshapes and dynamics of condensed phase systems largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems, this approximation no longer suffices. We elucidate nonstandard harmonic and anharmonic effects on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. First, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilized. Using this model, it is shown that curvature difference gives rise to an additional substructure in the vibronic progression of absorption spectra. This effect is explained and subsequently quantified via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential and parameters that correspond to the diatomic molecule H₂ for differing displacements and environment interaction. Finally, using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch are presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

Vibrational Coupling on Stepwise Hydrogen Bond Formation of Amide I

Despite the key roles of proteins and nucleic acids in biology, understanding their labile structures and hydrogen bond interactions with guest molecules has posed a critical challenge to the scientific community. In this report, I have used dimethylformamide as a model amide to account for amide hydrogen bond interactions of protein. To quantify hydrogen bond conformation and the structural change, I have monitored the amide I infrared (IR) stretching frequencies while varying the pK_a of phenol derivatives. For all phenol derivatives, amide I has formed one hydrogen bond and two hydrogen bond conformation. It has been observed that the formation constant for one hydrogen bond is higher than that of two hydrogen bonds for all phenol derivatives. During the formation of hydrogen bond with amide I, IR absorbance of C═C transition is enhanced for all phenol derivatives. Enhancement of the IR absorbance of the C═C transition indicates hydrogen bond-assisted vibrational coupling between the amide I and phenol ring transition. The relative coupling constant is estimated to be higher for single hydrogen-bonded conformer than the double hydrogen-bonded conformer. This is an intriguing result as the frequency difference between the two coupled transitions predicts otherwise. Using IR absorption spectroscopy, a delicate interplay between hydrogen bonding conformations and intermolecular vibrational coupling between amide I and H-bond donor phenol molecules has been shown. This study can be used as a point of reference for understanding the structural information of proteins, peptides, and nucleosides having hydrogen bond interaction with any drug or ligand molecules. My results as well provide an insight into the vibrational coupling of carbonyl and C═C transition of nucleobases.

Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches

Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.

Spectral line shapes in linear absorption and two-dimensional spectroscopy with skewed frequency distributions

The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional correlation spectra as a function of the waiting time between pump and probe fields. Non-Gaussian effects are not as well understood, even though these effects are common in nature. The interpretation of the spectra, thus far, relies on complex case to case analysis. We investigate spectra resulting from two physical mechanisms for non-Gaussian dynamics, one relying on the anharmonicity of the bath and the other on non-linear couplings between bath coordinates. These results are compared with outcomes from a simpler log-normal dynamics model. We find that the skewed spectral line shapes in all cases can be analyzed in terms of the log-normal model, with a minimal number of free parameters. The effect of log-normal dynamics on the spectral line shapes is analyzed in terms of frequency correlation functions, maxline slope analysis, and anti-diagonal linewidths. A triangular line shape is a telltale signature of the skewness induced by log-normal dynamics. We find that maxline slope analysis, as for Gaussian dynamics, is a good measure of the solvent dynamics for log-normal dynamics.

A Direct, Quantitative Connection between Molecular Dynamics Simulations and Vibrational Probe Line Shapes

A quantitative connection between molecular dynamics simulations and vibrational spectroscopy of probe-labeled systems would enable direct translation of experimental data into structural and dynamical information. To constitute this connection, all-atom molecular dynamics (MD) simulations were performed for two SCN probe sites (solvent-exposed and buried) in a calmodulin-target peptide complex. Two frequency calculation approaches with substantial nonelectrostatic components, a quantum mechanics/molecular mechanics (QM/MM)-based technique and a solvatochromic fragment potential (SolEFP) approach, were used to simulate the infrared probe line shapes. While QM/MM results disagreed with experiment, SolEFP results matched experimental frequencies and line shapes and revealed the physical and dynamic bases for the observed spectroscopic behavior. The main determinant of the CN probe frequency is the exchange repulsion between the probe and its local structural neighbors, and there is a clear dynamic explanation for the relatively broad probe line shape observed at the "buried" probe site. This methodology should be widely applicable to vibrational probes in many environments.

Simple Quantum Dynamics with Thermalization

In this paper, we introduce two simple quantum dynamics methods. One is based on the popular surface-hopping method, and the other is based on rescaling of the propagation on the bath ground-state potential surface. The first method is special, as it avoids specific feedback from the simulated quantum system to the bath and can be applied for precalculated classical trajectories. It is based on the equipartition theorem to determine if hops between different potential energy surfaces are allowed. By comparing with the formally exact Hierarchical Equations Of Motion approach for four model systems we find that the method generally approximates the quantum dynamics toward thermal equilibrium very well. The second method is based on rescaling of the nonadiabatic coupling and also neglect the effect of the state of the quantum system on the bath. By the nature of the approximations, they cannot reproduce the effect of bath relaxation following excitation. However, the methods are both computationally more tractable than the conventional fewest switches surface hopping, and we foresee that the methods will be powerful for simulations of quantum dynamics in systems with complex bath dynamics, where the system-bath coupling is not too strong compared to the thermal energy.

Enhanced vibrational solvatochromism and spectral diffusion by electron rich substituents on small molecule silanes

Fourier transform infrared and two-dimensional IR (2D-IR) spectroscopies were applied to two different silanes in three different solvents. The selected solutes exhibit different degrees of vibrational solvatochromism for the Si-H vibration. Density functional theory calculations confirm that this difference in sensitivity is the result of higher mode polarization with more electron withdrawing ligands. This mode sensitivity also affects the extent of spectral diffusion experienced by the silane vibration, offering a potential route to simultaneously optimize the sensitivity of vibrational probes in both steady-state and time-resolved measurements. Frequency-frequency correlation functions obtained by 2D-IR show that both solutes experience dynamics on similar time scales and are consistent with a picture in which weakly interacting solvents produce faster, more homogeneous fluctuations. Molecular dynamics simulations confirm that the frequency-frequency correlation function obtained by 2D-IR is sensitive to the presence of hydrogen bonding dynamics in the surrounding solvation shell.

Electrostatic frequency maps for amide-I mode of β-peptide: Comparison of molecular mechanics force field and DFT calculations

The spectroscopy of amide-I vibrations has been widely utilized for the understanding of dynamical structure of polypeptides. For the modeling of amide-I spectra, two frequency maps were built for β-peptide analogue (N-ethylpropionamide, NEPA) in a number of solvents within different schemes (molecular mechanics force field based, GM map; DFT calculation based, GD map), respectively. The electrostatic potentials on the amide unit that originated from solvents and peptide backbone were correlated to the amide-I frequency shift from gas phase to solution phase during map parameterization. GM map is easier to construct with negligible computational cost since the frequency calculations for the samples are purely based on force field, while GD map utilizes sophisticated DFT calculations on the representative solute-solvent clusters and brings insight into the electronic structures of solvated NEPA and its chemical environments. The results show that the maps' predicted amide-I frequencies present solvation environmental sensitivities and exhibit their specific characters with respect to the map protocols, and the obtained vibrational parameters are in satisfactory agreement with experimental amide-I spectra of NEPA in solution phase. Although different theoretical schemes based maps have their advantages and disadvantages, the present maps show their potentials in interpreting the amide-I spectra for β-peptides, respectively.

Vibrational Probes: From Small Molecule Solvatochromism Theory and Experiments to Applications in Complex Systems

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have developed a systematic approach to simulating vibrational solvatochromic data based on the effective fragment potential approach, one of the most accurate and rigorous theories on intermolecular interactions. We have further elucidated the interplay of local electric field with the general vibrational solvatochromism of small IR probes in either solvents or complicated biological systems, with emphasis on contributions from non-Coulombic intermolecular interactions to vibrational frequency shifts and fluctuations. With its rigorous foundation and close relation to quantitative interpretation of experimental data, this and related theoretical approaches and experiments will be of use in studying and quantifying the structure and dynamics of biomolecules with unprecedented time and spatial resolution when combined with time-resolved vibrational spectroscopy and chemically sensitive vibrational imaging techniques.

Probing the dynamics of N-methylacetamide in methanol via ab initio molecular dynamics

Two-dimensional infrared (2D IR) spectroscopy of amide 1 vibrational bands provides a valuable probe of proteins as well as molecules such as N-methylacetamide (NMA), which present peptide-like H-bonding possibilities to a solvent.

Vibrational solvatochromism. II. A first-principle theory of solvation-induced vibrational frequency shift based on effective fragment potential method

Vibrational solvatochromism is a solvation-induced effect on fundamental vibrational frequencies of molecules in solutions. Here we present a detailed first-principle coarse-grained theory of vibrational solvatochromism, which is an extension of our previous work [B. Błasiak, H. Lee, and M. Cho, J. Chem. Phys. 139(4), 044111 (2013)] by taking into account electrostatic, exchange-repulsion, polarization, and charge-transfer interactions. By applying our theory to the model N-methylacetamide-water clusters, solute-solvent interaction-induced effects on amide I vibrational frequency are fully elucidated at Hartree-Fock level. Although the electrostatic interaction between distributed multipole moments of solute and solvent molecules plays the dominant role, the contributions from exchange repulsion and induced dipole-electric field interactions are found to be of comparable importance in short distance range, whereas the charge-transfer effect is negligible. The overall frequency shifts calculated by taking into account the contributions of electrostatics, exchange-repulsion, and polarization terms are in quantitative agreement with ab initio results obtained at the Hartree-Fock level of theory.

Testing for memory-free spectroscopic coordinates by 3D IR exchange spectroscopy

Using 3D infrared (IR) exchange spectroscopy, the ultrafast hydrogen-bond forming and breaking (i.e., complexation) kinetics of phenol to benzene in a benzene/CCl4 mixture is investigated. By introducing a third time point at which the hydrogen-bonding state of phenol is measured (in comparison with 2D IR exchange spectroscopy), the spectroscopic method can serve as a critical test of whether the spectroscopic coordinate used to observe the exchange process is a memory-free, or Markovian, coordinate. For the system under investigation, the 3D IR results suggest that this is not the case. This conclusion is reconfirmed by accompanying molecular dynamics simulations, which furthermore reveal that the non-Markovian kinetics is caused by the heterogeneous structure of the mixed solvent.

OH-stretching in synthetic hydrogen-bonded chains

We study hydrogen bond dynamics in stereoselectively synthesized polyalcohols by combining linear and two-dimensional (2D) infrared spectroscopy experiments with simulations. We consider two variants of the polyalcohols: the all-syn and all-anti tetrol, which because of their different stereochemistry of the hydroxyl groups form a linear hydrogen-bonded chain that is stable for tens of picoseconds or a system where hydrogen bonds are formed and broken on a picosecond timescale, respectively. The differences in structure and hydrogen bond dynamics gives rise to significant differences in the linear spectra for the two compounds. Furthermore, we show that the stronger hydrogen bonding for the all-syn variant leads to faster fluctuations of the site frequencies than for the all-anti one, which is reflected in the higher degree of homogeneous broadening in the 2D spectra. Because of the different stereochemistry, the coupling in the all-syn molecule is stronger than for the all-anti one, which leads to a faster delocalization of a local excitation. This explains the previously observed pump-frequency independent vibrational lifetime for the all-syn variant, since the excitation loses the memory of the pump frequency before relaxation. For the all-anti form, the coupling is weak and the excitation remains in the initially excited state, maintaining the memory of the pump frequency.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Linear absorption and two-dimensional infrared spectra of N-methylacetamide in chloroform revisited: polarizability and multipole effects

The effect of solvent polarizability and multipole effects on the amide I vibrational spectra of a peptide unit is investigated. Four molecular dynamics force fields of increasing complexity for the solvent are used to model both the linear absorption and two-dimensional infrared spectra. It is observed that, at least in chloroform solution, the predicted solvent shift is considerably improved when accounting for the polarizabiltiy and multipole effects. The latter are typically connected with halogen bonding. Significant deviations are still observed for more sensitive line shape parameters such as the spectral width and line skewness. However, the findings demonstrate that previously observed deviations have an origin in the force field treatment rather than in the electrostatic mapping procedure frequently employed to simulate linear absorption and two-dimensional infrared spectroscopy.

Vibrational solvatochromism: towards systematic approach to modeling solvation phenomena

Vibrational solvatochromic frequency shift of IR probe is an effect of interaction between local electric field and IR probe in condensed phases. Despite prolonged efforts to develop empirical maps for vibrational frequency shifts and transition dipoles of IR probes, a systematic approach to ab initio calculation of vibrational solvatochromic charges and multipoles has not been developed. Here, we report on density functional theory (DFT) calculations of N-methylacetamide (NMA) frequency shifts using implicit and coarse-grained models. The solvatochromic infrared spectral shifts are estimated based on the distributed multipole analysis of electronic densities calculated for gas-phase equilibrium structure of NMA. Thus obtained distributed solvatochromic multipole parameters are used to calculate the amide I vibrational frequency shifts of NMA in water clusters that mimic the instantaneous configurations of the liquid water. Our results indicate that the spectral shifts are primarily electrostatic in nature and can be quantitatively reproduced using the proposed model with semi-quantitative accuracy when compared to the corresponding DFT results.

Amide I IR probing of core and shell hydrogen-bond structures in reverse micelles

The properties of N-methylacetamide (NMA) molecules encapsulated in the reverse micelles (RMs) formed by anionic surfactant aerosol OT (AOT), are studied with vibrational spectroscopy and computation. Vibrational spectra of the amide I′ mode of the fully deuterated NMA-d7 show gradual increase of peak frequencies and line broadening as the size of RMs decreases. Analyses of the spectral features reveal the presence of three states of NMA-d7 that correspond to NMA located in the core of water phase (absorption frequency of 1606 cm–1) and two types of interfacial NMA near the surfactant layer (1620 and 1644 cm–1). In larger RMs with water content w0 = [D2O]/[AOT] ≥ 10, only the first two states are observed, whereas in smaller RMs, the population of the third state grows up to 25 % at w0 = 2. These results indicate the general validity of the two-state core/shell model for the confined aqueous solution of NMA, with small modifications due to the system-dependent solute-interface interaction. However, simulations of small RM systems with w0 ≤ 15 show continuous variations of the population, frequency shifts, and the solute-solvent interaction strengths at solute-interface distance less than 4 Å. Thus, the distinction of solute core/shell states tends to be blurred in small RMs but is still effective in interpreting the average spectroscopic observables.

Molecular mechanics force field-based general map for the solvation effect on amide I probe of peptide in different micro-environments

A general electrostatic potential map based on molecular mechanics force field for modeling the amide I frequency is presented. This map is applied to N-methylacetamide (NMA) and designed to be transferable in different micro-environments. The electrostatic potentials from solvent and peptide side chain are projected on the amide unit of NMA to induce the frequency shift of amide I mode. It is shown that the predicted amide I frequency reproduces the experimental data satisfactorily, especially when NMA in polar solvents. The amide I frequency shift is largely determined by the solvents in aqueous solution while it is dominated by the local structure of peptide in other solvent environments. The map parameters are further applied on NMA-MeOH system and the obtained IR spectra show doublet peak profile with negligible deviation from the experimental data, suggesting the usefulness of this general map for providing information about vibrational parameters of amide motions of peptide in different environments.

Computational infrared and two-dimensional infrared photon echo spectroscopy of both wild-type and double mutant myoglobin-CO proteins

The CO stretching mode of both wild-type and double mutant ( T67R / S92D ) MbCO (carbonmonoxymyoglobin) proteins is an ideal infrared (IR) probe for studying the local electrostatic environment inside the myoglobin heme pocket. Recently, to elucidate the conformational switching dynamics between two distinguishable states, extensive IR absorption, IR pump-probe, and two-dimensional (2D) IR spectroscopic studies for various mutant MbCO's have been performed by the Fayer group. They showed that the 2D IR spectroscopy of the double mutant, which has a peroxidase enzyme activity, reveals a rapid chemical exchange between two distinct states, whereas that of the wild-type does not. Despite the fact that a few simulation studies on these systems were already performed and reported, such complicated experimental results have not been fully reproduced nor described in terms of conformational state-to-state transition processes. Here, we first develop a distributed vibrational solvatochromic charge model for describing the CO stretch frequency shift reflecting local electric potential changes. Then, by carrying out molecular dynamic simulations of the two MbCO's and examining their CO frequency trajectories, it becomes possible to identify a proper reaction coordinate consisting of His64 imidazole ring rotation and its distance to the CO ligand. From the 2D surfaces of the resulting potential of mean forces, the spectroscopically distinguished A1 and A3 states of the wild-type as well as two more substates of the double mutant are identified and their vibrational frequencies and distributions are separately examined. Our simulated IR absorption and 2D IR spectra of the two MbCO's are directly compared with the previous experimental results reported by the Fayer group. The chemical exchange rate constants extracted from the two-state kinetic analyses of the simulated 2D IR spectra are in excellent agreement with the experimental values. On the basis of the quantitative agreement between the simulated spectra and experimental ones, we further examine the conformational differences in the heme pockets of the two proteins and show that the double mutation, T67R / S92D , suppresses the A1 population, restricts the imidazole ring rotation, and increases hydrogen-bond strength between the imidazole Nε-H and the oxygen atom of the CO ligand. It is believed that such delicate change of distal His64 imidazole ring dynamics induced by the double mutation may be responsible for its enhanced peroxidase catalytic activity as compared to the wild-type myoglobin.

Folding of a heterogeneous β-hairpin peptide from temperature-jump 2D IR spectroscopy

We provide a time- and structure-resolved characterization of the folding of the heterogeneous β-hairpin peptide Tryptophan Zipper 2 (Trpzip2) using 2D IR spectroscopy. The amide I' vibrations of three Trpzip2 isotopologues are used as a local probe of the midstrand contacts, β-turn, and overall β-sheet content. Our experiments distinguish between a folded state with a type I' β-turn and a misfolded state with a bulged turn, providing evidence for distinct conformations of the peptide backbone. Transient 2D IR spectroscopy at 45 °C following a laser temperature jump tracks the nanosecond and microsecond kinetics of unfolding and the exchange between conformers. Hydrogen bonds to the peptide backbone are loosened rapidly compared with the 5-ns temperature jump. Subsequently, all relaxation kinetics are characterized by an observed 1.2 ± 0.2-μs exponential. Our time-dependent 2D IR spectra are explained in terms of folding of either native or nonnative contacts from a common compact disordered state. Conversion from the disordered state to the folded state is consistent with a zip-out folding mechanism.

Vibrational solvatochromism and electrochromism. II. Multipole analysis

Small infrared probe molecules have been widely used to study local electrostatic environment in solutions and proteins. Using a variety of time- and frequency-resolved vibrational spectroscopic methods, one can accurately measure the solvation-induced vibrational frequency shifts and the timescales and amplitudes of frequency fluctuations of such IR probes. Since the corresponding frequency shifts are directly related to the local electric field and its spatial derivatives of the surrounding solvent molecules or amino acids in proteins, one can extract information on local electric field around an IR probe directly from the vibrational spectroscopic results. Here, we show that, carrying out a multipole analysis of the solvatochromic frequency shift, the solvatochromic dipole contribution to the frequency shift is not always the dominant factor. In the cases of the nitrile-, thiocyanato-, and azido-derivatized molecules, the solvatochromic quadrupole contributions to the corresponding stretch mode frequency shifts are particularly large and often comparable to the solvatochromic dipole contributions. Noting that the higher multipole moment-solvent electric field interactions are short range effects in comparison to the dipole interaction, the H-bonding interaction-induced vibrational frequency shift can be caused by such short-range multipole-field interaction effects. We anticipate that the present multipole analysis method specifically developed to describe the solvatochromic vibrational frequency shifts will be useful to understand the intermolecular interaction-induced vibrational property changes and to find out a relationship between vibrational solvatochromism and electrochromism of IR probes in condensed phases.

Solvent and conformation dependence of amide I vibrations in peptides and proteins containing proline

We present a mixed quantum-classical model for studying the amide I vibrational dynamics (predominantly CO stretching) in peptides and proteins containing proline. There are existing models developed for determining frequencies of and couplings between the secondary amide units. However, these are not applicable to proline because this amino acid has a tertiary amide unit. Therefore, a new parametrization is required for infrared-spectroscopic studies of proteins that contain proline, such as collagen, the most abundant protein in humans and animals. Here, we construct the electrostatic and dihedral maps accounting for solvent and conformation effects on frequency and coupling for the proline unit. We examine the quality and the applicability of these maps by carrying out spectral simulations of a number of peptides with proline in D(2)O and compare with experimental observations.