Collective Solvent Coordinates for the Infrared Spectrum of HOD in D2O Based on an ab Initio Electrostatic Map

Correlations between the Structures and Spectra of Protonated Water Clusters

Badger's rule-like correlations between OH stretching frequencies and intensities and the OH bond length are used to develop a spectral mapping procedure for studies of pure and protonated water clusters. This approach utilizes the vibrationally averaged OH bond lengths, which were obtained from diffusion Monte Carlo simulations that were performed using the general potential developed by Yu and Bowman. Good agreement is achieved between the spectra obtained using this approach and previously reported spectra for H+(H2O)n clusters, with n = 3, 4, and 5, as well as their perdeuterated analogues. The analysis of the spectra obtained by this spectral mapping approach supports previous work that assigned the spectrum of H+(H2O)6 to a mixture of Eigen and Zundel-like structures. Analysis of the calculated spectra also suggests a reassignment of the frequency of one of the transitions that involves the OH stretching vibration of the OH bonds in the hydronium core in the Eigen-like structure of H+(H2O)6 from 1917 cm-1 to roughly 2100 cm-1. For D+(D2O)6, comparison of the measured spectrum to those obtained by using the spectral mapping approach suggests that the carrier of the measured spectrum is one or more of the isomers of D+(D2O)6 that contain a four-membered ring and two flanking water molecules. While there are several candidate structures, the two flanking water molecules most likely form a chain that is bound to the hydronium core.

Design of an Electrostatic Frequency Map for the NH Stretch of the Protein Backbone and Application to Chiral Sum Frequency Generation Spectroscopy

We develop an electrostatic map for the vibrational NH stretch (amide A) of the protein backbone with a focus on vibrational chiral sum frequency generation spectroscopy (chiral SFG). Chiral SFG has been used to characterize protein secondary structure at interfaces using the NH stretch and to investigate chiral water superstructures around proteins using the OH stretch. Interpretation of spectra has been complicated because the NH stretch and OH stretch overlap spectrally. Although an electrostatic map for water OH developed by Skinner and co-workers was used previously to calculate the chiral SFG response of water structures around proteins, a map for protein NH that is directly responsive to biological complexity has yet to be developed. Here, we develop such a map, linking the local electric field to vibrational frequencies and transition dipoles. We apply the map to two protein systems and achieve much better agreement with experiment than was possible in our previous studies. We show that couplings between NH and OH vibrations are crucial to the line shape, which informs the interpretation of chiral SFG spectra, and that the chiral NH stretch response is sensitive to small differences in structure. This work increases the utility of the NH stretch in biomolecular spectroscopy.

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.

The mutual interactions of RNA, counterions and water - quantifying the electrostatics at the phosphate-water interface

The structure and dynamics of polyanionic biomolecules, like RNA, are decisively determined by their electric interactions with the water molecules and the counterions in the environment. The solvation dynamics of the biomolecules involves a subtle balance of non-covalent and many-body interactions with structural fluctuations due to thermal motion occurring in a femto- to subnanosecond time range. This complex fluctuating many particle scenario is crucial in defining the properties of biological interfaces with far reaching significance for the folding of RNA structures and for facilitating RNA-protein interactions. Given the inherent complexity, suited model systems, carefully calibrated and benchmarked by experiments, are required to quantify the relevant interactions of RNA with the aqueous environment. In this feature article we summarize our recent progress in the understanding of the electrostatics at the biological interface of double stranded RNA (dsRNA) and transfer RNA (tRNA). Dimethyl phosphate (DMP) is introduced as a viable and rigorously accessible model system allowing the interaction strength with water molecules and counterions, their relevant fluctuation timescales and the spatial reach of interactions to be established. We find strong (up to ≈90 MV cm-1) interfacial electric fields with fluctuations extending up to ≈20 THz and demonstrate how the asymmetric stretching vibration νAS(PO2)- of the polarizable phosphate group can serve as the most sensitive probe for interfacial interactions, establishing a rigorous link between simulations and experiment. The approach allows for the direct interfacial observation of interactions of biologically relevant Mg2+ counterions with phosphate groups in contact pair geometries via the rise of a new absorption band imposed by exchange repulsion interactions at short interatomic distances. The systematic extension to RNA provides microscopic insights into the changes of the hydration structure that accompany the temperature induced melting of the dsRNA double helix and quantify the ionic interactions in the folded tRNA. The results show that pairs of negatively charged phosphate groups and Mg2+ ions represent a key structural feature of RNA embedded in water. They highlight the importance of binding motifs made of contact pairs in the electrostatic stabilization of RNA structures that have a strong impact on the surface potential and enable the fine tuning of the local electrostatic properties which are expected to be relevant for mediating the interactions between biomolecules.

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.

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.

Infrared Difference Spectroscopy of Proteins: From Bands to Bonds

Infrared difference spectroscopy probes vibrational changes of proteins upon their perturbation. Compared with other spectroscopic methods, it stands out by its sensitivity to the protonation state, H-bonding, and the conformation of different groups in proteins, including the peptide backbone, amino acid side chains, internal water molecules, or cofactors. In particular, the detection of protonation and H-bonding changes in a time-resolved manner, not easily obtained by other techniques, is one of the most successful applications of IR difference spectroscopy. The present review deals with the use of perturbations designed to specifically change the protein between two (or more) functionally relevant states, a strategy often referred to as reaction-induced IR difference spectroscopy. In the first half of this contribution, I review the technique of reaction-induced IR difference spectroscopy of proteins, with special emphasis given to the preparation of suitable samples and their characterization, strategies for the perturbation of proteins, and methodologies for time-resolved measurements (from nanoseconds to minutes). The second half of this contribution focuses on the spectral interpretation. It starts by reviewing how changes in H-bonding, medium polarity, and vibrational coupling affect vibrational frequencies, intensities, and bandwidths. It is followed by band assignments, a crucial aspect mostly performed with the help of isotopic labeling and site-directed mutagenesis, and complemented by integration and interpretation of the results in the context of the studied protein, an aspect increasingly supported by spectral calculations. Selected examples from the literature, predominately but not exclusively from retinal proteins, are used to illustrate the topics covered in this review.

Empirical S=O stretch vibrational frequency map

Dimethyl sulfoxide (DMSO) water mixtures have been widely studied due to their unique concentration-dependent bulk properties. Here, we present an empirical spectroscopic map for the sulfinyl (S=O) stretching mode. The model can be used to interpret infrared (IR) absorption and ultrafast two-dimensional infrared (2D IR) spectra and quantify hydrogen bond populations and lifetimes by directly connecting spectroscopic measurements with structures and dynamics from molecular dynamics simulations. The electrostatic map is directly parameterized against experimental absorption spectra in the S=O stretching region (980-1100 cm^-1) of dilute DMSO in water. A comparison of center peak frequencies shows that the map performs well across the entire DMSO concentration range, accurately reproducing the ∼10 cm^-1 red-shift per hydrogen bond observed in the experiments. We further benchmark the map by comparing experimental and simulated 2D IR spectra generated by direct numerical integration of the Schrödinger equation. We expect that this empirical frequency map will provide a quantitative platform for investigating intermolecular interactions, microscopic heterogeneity, and ultrafast dynamics in complex liquid mixtures containing DMSO.

Differential evolution algorithm approach for describing vibrational solvatochromism

We model the solvation-induced vibrational frequency shifts of the amide I and amide II modes of N-methylacetamide in water and the nitrile stretch mode of acetonitrile in water by expressing the frequency shift as a polynomial function expanded by the inverse power of interatomic distances. The coefficients of the polynomial are optimized to minimize the deviation between the predicted frequency shifts and those calculated with quantum chemistry methods. Here, we show that a differential evolution algorithm combined with singular value decomposition is useful to find the optimum set of coefficients of polynomial terms. The differential evolution optimization shows that only a few terms in the polynomial are dominant in the contribution to the vibrational frequency shifts. We anticipate that the present work paves the way for further developing different genetic algorithms and machine learning schemes for their applications to vibrational spectroscopic studies.

Probing the Differential Dynamics of the Monomeric and Dimeric Insulin from Amide-I IR Spectroscopy

The monomer-dimer equilibrium for insulin is one of the essential steps in forming the receptor-binding competent monomeric form of the hormone. Despite this importance, the thermodynamic stability, in particular for modified insulins, is quite poorly understood, in part, due to experimental difficulties. This work explores one- and two-dimensional infrared spectroscopy in the range of the amide-I band for the hydrated monomeric and dimeric wild-type hormone. It is found that for the monomer the frequency fluctuation correlation function (FFCF) and the one-dimensional infrared spectra are position sensitive. The spectra of the -CO probes at the dimerization interface (residues Phe24, Phe25, and Tyr26) split and indicate an asymmetry despite the overall (formal) point symmetry of the dimer structure. Also, the decay times of the FFCF for the same -CO probe in the monomer and the dimer can differ by up to 1 order of magnitude, for example, for residue PheB24, which is solvent exposed for the monomer but at the interface for the dimer. The spectroscopic shifts correlate approximately with the average number of hydration waters and the magnitude of the FFCF at time zero. However, this correlation is only qualitative due to the heterogeneous and highly dynamical environment. Based on density functional theory calculations, the dominant contribution for solvent-exposed -CO is found to arise from the surrounding water (∼75%), whereas the protein environment contributes considerably less. The results suggest that infrared spectroscopy is a positionally sensitive probe of insulin dimerization, in particular in conjunction with isotopic labeling of the probe.

Development of Vibrational Frequency Maps for Nucleobases

Vibrational spectroscopy provides a powerful tool to probe the structure and dynamics of nucleic acids because specific normal modes, particularly the base carbonyl stretch modes, are highly sensitive to the hydrogen bonding patterns and stacking configurations in these biomolecules. In this work, we develop vibrational frequency maps for the C═O and C═C stretches in nucleobases that allow the calculations of their site frequencies directly from molecular dynamics simulations. We assess the frequency maps by applying them to nucleobase derivatives in aqueous solutions and nucleosides in organic solvents and demonstrate that the predicted infrared spectra are in good agreement with experimental measurements. The frequency maps can be readily used to model the linear and nonlinear vibrational spectroscopy of nucleic acids and elucidate the molecular origin of the experimentally observed spectral features.

Deconstructing water's diffuse OH stretching vibrational spectrum with cold clusters

The diffuse vibrational envelope displayed by water precludes direct observation of how different hydrogen-bond topologies dictate the spectral response of individual hydroxy group (OH) oscillators. Using cold, isotopically labeled cluster ions, we report the spectral signatures of a single, intact water (H₂O) molecule embedded at various sites in the clathrate-like cage structure adopted by the Cs⁺·(D₂O)₂₀ ion. These patterns reveal the site-dependent correlation between the frequencies of the two OH groups on the same water molecule and establish that the bound OH companion of the free OH group exclusively accounts for bands in the lower-energy region of the spectrum. The observed multiplet structures reveal the homogeneous linewidths of the fundamentals and quantify the anharmonic contributions arising from coupling to both the intramolecular bending and intermolecular soft modes.

The spatial range of protein hydration

Proteins interact with their aqueous surroundings, thereby modifying the physical properties of the solvent. The extent of this perturbation has been investigated by numerous methods in the past half-century, but a consensus has still not emerged regarding the spatial range of the perturbation. To a large extent, the disparate views found in the current literature can be traced to the lack of a rigorous definition of the perturbation range. Stating that a particular solvent property differs from its bulk value at a certain distance from the protein is not particularly helpful since such findings depend on the sensitivity and precision of the technique used to probe the system. What is needed is a well-defined decay length, an intrinsic property of the protein in a dilute aqueous solution, that specifies the length scale on which a given physical property approaches its bulk-water value. Based on molecular dynamics simulations of four small globular proteins, we present such an analysis of the structural and dynamic properties of the hydrogen-bonded solvent network. The results demonstrate unequivocally that the solvent perturbation is short-ranged, with all investigated properties having exponential decay lengths of less than one hydration shell. The short range of the perturbation is a consequence of the high energy density of bulk water, rendering this solvent highly resistant to structural perturbations. The electric field from the protein, which under certain conditions can be long-ranged, induces a weak alignment of water dipoles, which, however, is merely the linear dielectric response of bulk water and, therefore, should not be thought of as a structural perturbation. By decomposing the first hydration shell into polarity-based subsets, we find that the hydration structure of the nonpolar parts of the protein surface is similar to that of small nonpolar solutes. For all four examined proteins, the mean number of water-water hydrogen bonds in the nonpolar subset is within 1% of the value in bulk water, suggesting that the fragmentation and topography of the nonpolar protein-water interface has evolved to minimize the propensity for protein aggregation by reducing the unfavorable free energy of hydrophobic hydration.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Experimentally probing the libration of interfacial water: the rotational potential of water is stiffer at the air/water interface than in bulk liquid

Most properties of liquid water are determined by its hydrogen-bond network. Because forming an aqueous interface requires termination of this network, one might expect the molecular level properties of interfacial water to markedly differ from water in bulk. Intriguingly, much prior experimental and theoretical work has found that, from the perspective of their time-averaged structure and picosecond structural dynamics, hydrogen-bonded OH groups at an air/water interface behave the same as hydrogen-bonded OH groups in bulk liquid water. Here we report the first experimental observation of interfacial water's libration (i.e. frustrated rotation) using the laser-based technique vibrational sum frequency spectroscopy. We find this mode has a frequency of 834 cm(-1), ≈165 cm(-1) higher than in bulk liquid water at the same temperature and similar to bulk ice. Because libration frequency is proportional to the stiffness of water's rotational potential, this increase suggests that one effect of terminating bulk water's hydrogen bonding network at the air/water interface is retarding rotation of water around intact hydrogen bonds. Because in bulk liquid water the libration plays a key role in stabilizing reaction intermediates and dissipating excess vibrational energy, we expect the ability to probe this mode in interfacial water to open new perspectives on the kinetics of heterogeneous reactions at aqueous interfaces.

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

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

Histidine Orientation Modulates the Structure and Dynamics of a de Novo Metalloenzyme Active Site

The ultrafast dynamics of a de novo metalloenzyme active site is monitored using two-dimensional infrared spectroscopy. The homotrimer of parallel, coiled coil α-helices contains a His3-Cu(I) metal site where CO is bound and serves as a vibrational probe of the hydrophobic interior of the self-assembled complex. The ultrafast spectral dynamics of Cu-CO reveals unprecedented ultrafast (2 ps) nonequilibrium structural rearrangements launched by vibrational excitation of CO. This initial rapid phase is followed by much slower ∼40 ps vibrational relaxation typical of metal-CO vibrations in natural proteins. To identify the hidden coupled coordinate, small molecule analogues and the full peptide were studied by QM and QM/MM calculations, respectively. The calculations show that variation of the histidines' dihedral angles in coordinating Cu controls the coupling between the CO stretch and the Cu-C-O bending coordinates. Analysis of different optimized structures with significantly different electrostatic field magnitudes at the CO ligand site indicates that the origin of the stretch-bend coupling is not directly due to through-space electrostatics. Instead, the large, ∼3.6 D dipole moments of the histidine side chains effectively transduce the electrostatic environment to the local metal coordination orientation. The sensitivity of the first coordination sphere to the protein electrostatics and its role in altering the potential energy surface of the bound ligands suggests that long-range electrostatics can be leveraged to fine-tune function through enzyme design.

Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation

The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions that represent radiation-matter interactions. Here, we extend the OMT to include additional vibrational coherence and energy transfer processes. This generalized approximation is applied to a pair of anharmonic chromophores coupled to a bath. The resulting 2D spectra are shown to reflect coherence transfer between normal modes.

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.

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.

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.

Amide-I characteristics of helical β-peptides by linear infrared measurement and computations

In this work, we have examined the amide-I characteristics of three β-peptide oligomers in typical helical conformations (two in 14-helix and one in 12/10-helix), solvated in water, methanol, and chloroform, respectively. Local-mode frequencies and their distributions were computed using a molecular-mechanics force field based frequency map that was constructed on the basis of molecular dynamics simulations. The local-mode frequencies were found to be determined primarily by peptide backbone and side chain, rather by solvent, suggesting their local structural sensitivities. Intermode vibrational couplings computed using a transition dipole scheme were found to be very sensitive to peptide conformation, with their signs and magnitudes varying periodically along the peptide chain. Linear infrared absorption spectra of the three peptides, simulated using a frequency-frequency time-correlation function method, were found to be in fair agreement with experimental results. Normalized potential energy distribution analysis indicated that the amide-I mode can delocalize over a few amide units. However, the IR band structure appears to be more sophisticated in helical β-peptides than in helical α-peptides.

Charge and electric field fluctuations in aqueous NaCl electrolytes

Crystalloluminescence, the long-lived emission of visible light during the crystallization of certain salts, was first observed over 200 years ago; however, the origin of this luminescence is still not well understood. The observations suggest that the process of crystallization may not be purely classical but also involves an essential electronic structure component. Strong electric field fluctuations may play an important role in this process by providing the necessary driving force for the observed electronic structure changes. The main objective of this work is to provide a basic understanding of the fluctuations in charge, electric potentials, and electric fields for concentrated aqueous NaCl electrolytes. Our charge analysis reveals that the water molecules in the first solvation shell of the ions serve as a sink for electron density originating on Cl(-). We find that the electric fields inside aqueous electrolytes are extremely large (up to several V/Å) and thus may alter the ground and excited electronic states in the condensed phase. Furthermore, our results show that the potential and field distributions are largely independent of concentration. We also find the field component distributions to be Gaussian for the ions and non-Gaussian for the O and H sites (computed in the lab frame of reference), however, these non-Gaussian distributions are readily modeled via an orientationally averaged nonzero mean Gaussian plus a zero mean Gaussian. These calculations and analyses provide the first steps toward understanding the magnitude and fluctuations of charge, electric potentials, and fields in aqueous electrolytes and what role these fields may play in driving charge redistribution/transfer during crystalloluminescence.

Broadband infrared and Raman probes of excited-state vibrational molecular dynamics: simulation protocols based on loop diagrams

Vibrational motions in electronically excited states can be observed either by time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both signals. Three representations which suggest different simulation protocols for the signals are developed. These are based on the forward and the backward propagation of the wavefunction, sum over state expansion using an effective vibrational Hamiltonian or a semiclassical treatment of a bath. We show that the effective temporal (Δt) and spectral (Δω) resolution of the techniques is not controlled solely by experimental knobs but also depends on the system dynamics being probed. The Fourier uncertainty ΔωΔt > 1 is never violated.

Fluctuations and Relaxation Dynamics of Liquid Water Revealed by Linear and Nonlinear Spectroscopy

Many efforts have been devoted to elucidating the intra- and intermolecular dynamics of liquid water because of their important roles in many fields of science and engineering. Nonlinear spectroscopy is a powerful tool to investigate the dynamics. Because nonlinear response functions are described by more than one time variable, it is possible to analyze static and dynamic mode couplings. Here we review the intra- and intermolecular dynamics of liquid water revealed by recent linear and nonlinear spectroscopic experiments and computer simulations. In particular, we discuss the population relaxation, anisotropy decay, and spectral diffusion of the intra- and intermolecular motions of water and their temperature dependence, which play important roles in ultrafast dynamics and relaxations in water.

Water interfaces, solvation, and spectroscopy

Liquid water consistently expands our appreciation of the rich statistical mechanics that can emerge from simple molecular constituents. Here I review several interrelated areas of recent work on aqueous systems that aim to explore and explain this richness by revealing molecular arrangements, their thermodynamic origins, and the timescales on which they change. Vibrational spectroscopy of OH stretching features prominently in these discussions, with an emphasis on efforts to establish connections between spectroscopic signals and statistics of intermolecular structure. For bulk solutions, the results of these efforts largely verify and enrich existing physical pictures of hydrogen-bond network connectivity, dynamics, and response. For water at interfaces, such pictures are still emerging. As an important example I discuss the solvation of small ions at the air-water interface, whose surface propensities challenge a basic understanding of how aqueous fluctuations accommodate solutes in heterogeneous environments.

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.