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

Dissecting amide-I vibrations in histidine dipeptide

The amide-I vibrational characteristics and conformational preferences of the model compound - histidine dipeptide (Ac-His-NHCH₃, HISD) in gas phase and solution have been revealed with the help of ab initio calculations and wavefunction analyses. The Gibbs free energy surfaces (FESs) of solvated HISD were smoothed by solvent effect to exhibit different structural populations concerning various external environments. It was shown that the most stable conformations of HISD in CHCl₃ and gas phase are C7eq, while those in DMSO and water are β and PPII, respectively. Compared with ALAD, the number of accessible conformational states on these FESs was predicted to be reduced due to the steric effect of imidazole group. The two amide-I normal modes of HISD were found to have intrinsically secondary structural dependencies, and be sensitive to surrounding environments. The average amide-I_a frequencies of HISD isomers in these environments were predicted to be almost the same as those of ALAD, while the amide-I_b mean frequencies were estimated to be lower than ALAD due to the intramolecular interactions between the imidazole group and amino-terminal amide unit. The good linear correlations between amide-I frequencies and the atomic electrostatic potentials (ESPs) of amide groups were also found to interpret the solvent-induced amide-I frequency shifts of HISD at the electronic structure level. These results allow us to gain a deep understanding of amide-I vibrations of HISD, and would be helpful for the site-specific conformational monitoring and spectral interpretation of solvated polypeptides.

Unraveling the initial steps of the ignition chemistry of the hypergolic ionic liquid 1-ethyl-3-methylimidazolium cyanoborohydride ([EMIM][CBH]) with nitric acid (HNO3) exploiting chirped pulse triggered droplet merging

The composition of the products and the mechanistic routes for the reaction of the hypergolic ionic liquid (HIL) 1-ethyl-3-methylimidazolium cyanoborohydride ([EMIM][CBH]) and nitric acid (HNO₃) at various concentrations from 10% to 70% were explored using a contactless single droplet merging within an ultrasonic levitation setup in an inert atmosphere of argon to reveal the initial steps that cause hypergolicity. The reactions were initiated through controlled droplet-merging manipulation triggered by a frequency chirp pulse amplitude modulation. Utilizing the high-speed optical and infrared cameras surrounding the levitation process chamber, intriguing visual images were unveiled: (i) extensive gas release and (ii) temperature rises of up to 435 K in the merged droplets. The gas development was validated qualitatively and quantitatively with Fourier Transform Infrared Spectroscopy (FTIR) indicating the major gas-phase products to be hydrogen cyanide (HCN) and nitrous oxide (N₂O). The merged droplet was also probed by pulsed Raman spectroscopy which deciphered features for key functional groups of the reaction products and intermediates (-BH, -BH₂, -BH₃, -NCO); reaction kinetics revealed that the reaction was initiated by the interaction of the [CBH]^- anion of the HIL with the oxidizer (HNO₃) through proton transfer. Computations indicate the formation of a van-der-Waals complex between the [CBH]^- anion and HNO₃ initially, followed by proton transfer from the acid to the anion and subsequent extensive isomerization; these rearrangements were found to be essential for the formation of HCN and N₂O. The exoergicity observed during the merging process provides a molar enthalpy change up to 10 kJ mol^-1 to the system, which could be sufficient for a significant fraction of the reactants of about 11% to overcome the reaction barriers in the individual steps of the computationally determined minimum energy pathways.

Frequency Changes in Terminal Alkynes Provide Strong, Sensitive, and Solvatochromic Raman Probes of Biochemical Environments

The C≡C stretching frequencies of terminal alkynes appear in the "clear" window of vibrational spectra, so they are attractive and increasingly popular as site-specific probes in complicated biological systems like proteins, cells, and tissues. In this work, we collected infrared (IR) absorption and Raman scattering spectra of model compounds, artificial amino acids, and model proteins that contain terminal alkyne groups, and we used our results to draw conclusions about the signal strength and sensitivity to the local environment of both aliphatic and aromatic terminal alkyne C≡C stretching bands. While the IR bands of alkynyl model compounds displayed surprisingly broad solvatochromism, their absorptions were weak enough that alkynes can be ruled out as effective IR probes. The same solvatochromism was observed in model compounds' Raman spectra, and comparisons to published empirical solvent scales (including a linear regression against four meta-aggregated solvent parameters) suggested that the alkyne C≡C stretching frequency mainly reports on local electronic interactions (i.e., short-range electron donor-acceptor interactions) with solvent molecules and neighboring functional groups. The strong solvatochromism observed here for alkyne stretching bands introduces an important consideration for Raman imaging studies based on these signals. Raman signals for alkynes (especially those that are π-conjugated) can be exceptionally strong and should permit alkynyl Raman signals to function as probes at very low concentrations, as compared to other widely used vibrational probe groups like azides and nitriles. We incorporated homopropargyl glycine into a transmembrane helical peptide via peptide synthesis, and we installed p-ethynylphenylalanine into the interior of the Escherichia coli fatty acid acyl carrier protein using a genetic code expansion technique. The Raman spectra from each of these test systems indicate that alkynyl C≡C bands can act as effective and unique probes of their local biomolecular environments. We provide guidance for the best possible future uses of alkynes as solvatochromic Raman probes, and while empirical explanations of the alkyne solvatochromism are offered, open questions about its physical basis are enunciated.

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.

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.

Machine Learning Approach for Describing Water OH Stretch Vibrations

A machine learning approach employing neural networks is developed to calculate the vibrational frequency shifts and transition dipole moments of the symmetric and antisymmetric OH stretch vibrations of a water molecule surrounded by water molecules. We employed the atom-centered symmetry functions (ACSFs), polynomial functions, and Gaussian-type orbital-based density vectors as descriptor functions and compared their performances in predicting vibrational frequency shifts using the trained neural networks. The ACSFs perform best in modeling the frequency shifts of the OH stretch vibration of water among the types of descriptor functions considered in this paper. However, the differences in performance among these three descriptors are not significant. We also tried a feature selection method called CUR matrix decomposition to assess the importance and leverage of the individual functions in the set of selected descriptor functions. We found that a significant number of those functions included in the set of descriptor functions give redundant information in describing the configuration of the water system. We here show that the predicted vibrational frequency shifts by trained neural networks successfully describe the solvent-solute interaction-induced fluctuations of OH stretch frequencies.

An effective potential for Frenkel excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is introduced that is valid in a wide range of intermolecular distances. The proposed approach is based on the effective elimination of electron repulsion integrals from the excitonic Hamiltonian matrix elements via the density-fitting approach and distributed multipole approximation. The excitonic Hamiltonian represented in a basis including charge transfer (CT) states is re-cast in terms of the effective one-electron potential functions (EOPs) and adapted into the effective fragment parameter (EFP) framework. Calculations for model systems indicate that the speedup of at least three orders of magnitude, as compared to the state-of-the-art methods, can be achieved while maintaining the accuracy of the EET couplings even at short intermolecular distances.

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.

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.

Mapping the amide-I vibrations of model dipeptides with secondary structure sensitivity and amino acid residue specificity, and its application to amyloid β-peptide in aqueous solution

Vibrational spectroscopy has been known as particularly well-suited for deciphering the polypeptide's structure. To decode structural information encoded in IR spectra, we developed amide-I frequency maps on the basis of model dipeptides to correlate the amide-I frequency of interest to the combination of the calculated secondary structure dependent amide-I frequency by using DFT method and the electrostatic potentials that projected onto the amide unit from the micro-environment within molecular mechanics force field. The constructed maps were applied to model dipeptides and amyloid β-peptide fragment (Aβ_25-35). The dipeptide specified map (DS map) and the hybrid map (HYB map) predicted amide-I bands of Aβ_25-35 in solution satisfactorily reproduce experimental observation, and indicate the preference of forming β-sheet and random coil structure for Aβ_25-35 in D₂O just as the results of cluster analysis suggested. These maps with secondary structural sensitivity and amino acid residue specificity open up a way for the interpretation of amide-I vibrations and show their potentials in the understanding of molecular structure of polypeptides in solution.

One-particle density matrix polarization susceptibility tensors

The electric field-induced change in the one-electron density has been expressed as a series of the one-particle density matrix susceptibilities interacting with the spatial distribution of the electric field. The analytic approximate expressions are derived at the Hartree-Fock theory, which serves as a basis for the construction of the generalized model that is designed for an arbitrary form of wavefunction and any type of one-particle density matrix. It is shown that it is possible to accurately predict the changes in the one-electron ground-state density of water molecule in a spatially uniform electric field, as well as in spatially non-uniform electric field distribution generated by point charges. When both linear and quadratic terms with respect to the electric field are accounted for, the electric field-induced polarization energies, dipole moments, and quadrupole moments are quantitatively described by the present theory in electric fields ranging from weak to very strong (0.001-0.07 a.u.). It is believed that the proposed model could open new routes in quantum chemistry for fast and efficient calculations of molecular properties in condensed phases.

Cyanylated Cysteine Reports Site-Specific Changes at Protein-Protein-Binding Interfaces Without Perturbation

To investigate the cyanylated cysteine vibrational probe group’s ability to report on binding-induced changes along a protein–protein interface, the probe group was incorporated at several sites in a peptide of the calmodulin (CaM)-binding domain of skeletal muscle myosin light chain kinase. Isothermal titration calorimetry was used to determine the binding thermodynamics between calmodulin and each peptide. For all probe positions, the binding affinity was nearly identical to that of the unlabeled peptide. The CN stretching infrared band was collected for each peptide free in solution and bound to calmodulin. Binding-induced shifts in the IR spectral frequencies were correlated with estimated solvent accessibility based on molecular dynamics simulations. This work generally suggests (1) that site-specific incorporation of this vibrational probe group does not cause major perturbations to its local structural environment and (2) that this small probe group might be used quite broadly to map dynamic protein-binding interfaces. However, site-specific perturbations due to artificial labeling groups can be somewhat unpredictable and should be evaluated on a site-by-site basis through complementary measurements. A fully quantitative, simulation-based interpretation of the rich probe IR spectra is still needed but appears to be possible given recent advances in simulation techniques.

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.

Conformational Ensembles of Calmodulin Revealed by Nonperturbing Site-Specific Vibrational Probe Groups

Seven native residues on the regulatory protein calmodulin, including three key methionine residues, were replaced (one by one) by the vibrational probe amino acid cyanylated cysteine, which has a unique CN stretching vibration that reports on its local environment. Almost no perturbation was caused by this probe at any of the seven sites, as reported by CD spectra of calcium-bound and apo calmodulin and binding thermodynamics for the formation of a complex between calmodulin and a canonical target peptide from skeletal muscle myosin light chain kinase measured by isothermal titration. The surprising lack of perturbation suggests that this probe group could be applied directly in many protein–protein binding interfaces. The infrared absorption bands for the probe groups reported many dramatic changes in the probes’ local environments as CaM went from apo- to calcium-saturated to target peptide-bound conditions, including large frequency shifts and a variety of line shapes from narrow (interpreted as a rigid and invariant local environment) to symmetric to broad and asymmetric (likely from multiple coexisting and dynamically exchanging structures). The fast intrinsic time scale of infrared spectroscopy means that the line shapes report directly on site-specific details of calmodulin’s variable structural distribution. Though quantitative interpretation of the probe line shapes depends on a direct connection between simulated ensembles and experimental data that does not yet exist, formation of such a connection to data such as that reported here would provide a new way to evaluate conformational ensembles from data that directly contains the structural distribution. The calmodulin probe sites developed here will also be useful in evaluating the binding mode of calmodulin with many uncharacterized regulatory targets.

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.

Conformational Heterogeneity and the Affinity of Substrate Molecular Recognition by Cytochrome P450cam

The broad and variable substrate specificity of cytochrome P450 enzymes makes them a model system for studying the determinants of protein molecular recognition. The archetypal cytochrome P450cam (P450cam) is a relatively specific P450, a feature once attributed to the high rigidity of its active site. However, increasingly studies have provided evidence of the importance of conformational changes to P450cam activity. Here we used infrared (IR) spectroscopy to investigate the molecular recognition of P450cam. Toward this goal, and to assess the influence of a hydrogen bond (H-bond) between active site residue Y96 and substrates, two variants in which Y96 is replaced by a cyanophenyl (Y96CNF) or phenyl (Y96F) group were characterized in complexes with the substrates camphor, isoborneol, and camphane. These combinations allow for a comparison of complexes in which the moieties on both the protein and substrate can serve as a H-bond donor, acceptor, or neither. The IR spectra of heme-bound CO and the site-specifically incorporated CN of Y96CNF were analyzed to characterize the number and nature of environments in each protein, both in the free and bound states. Although the IR spectra do not support the idea that protein-substrate H-bonding is central to P450cam recognition, the data altogether suggest that the differing conformational heterogeneity in the active site of the P450cam variants and changes in heterogeneity upon binding of different substrates likely contribute to their variable affinities via a conformational selection mechanism. This study further extends our understanding of the molecular recognition of archetypal P450cam and demonstrates the application of IR spectroscopy combined with selective protein modification to delineate protein-ligand interactions.

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.

Solvent-Independent Anharmonicity for Carbonyl Oscillators

The physical origins of vibrational frequency shifts have been extensively studied in order to understand noncovalent intermolecular interactions in the condensed phase. In the case of carbonyls, vibrational solvatochromism, MD simulations, and vibrational Stark spectroscopy suggest that the frequency shifts observed in simple solvents arise predominately from the environment's electric field due to the vibrational Stark effect. This is contrary to many previously invoked descriptions of vibrational frequency shifts, such as bond polarization, whereby the bond's force constant and/or partial nuclear charges are altered due to the environment, often illustrated in terms of favored resonance structures. Here we test these hypotheses using vibrational solvatochromism as measured using 2D IR to assess the solvent dependence of the bond anharmonicity. These results indicate that the carbonyl bond's anharmonicity is independent of solvent as tested using hexanes, DMSO, and D₂O and is supported by simulated 2D spectra. In support of the linear vibrational Stark effect, these 2D IR measurements are consistent with the assertion that the Stark tuning rate is unperturbed by the electric field generated by both hydrogen and non-hydrogen bonding environments and further extends the general applicability of carbonyl probes for studying intermolecular interactions.

Perturbation Approach for Computing Infrared Spectra of the Local Mode of Probe Molecules

Linear and two-dimensional infrared (IR) spectroscopy of site-specific probe molecules provides an opportunity to gain a molecular-level understanding of the local hydrogen-bonding network, conformational dynamics, and long-range electrostatic interactions in condensed-phase and biological systems. A challenge in computation is to determine the time-dependent vibrational frequencies that incorporate explicitly both nuclear quantum effects of vibrational motions and an electronic structural representation of the potential energy surface. In this paper, a nuclear quantum vibrational perturbation (QVP) method is described for efficiently determining the instantaneous vibrational frequency of a chromophore in molecular dynamics simulations. Computational efficiency is achieved through the use of (a) discrete variable representation of the vibrational wave functions, (b) a perturbation theory to evaluate the vibrational energy shifts due to solvent dynamic fluctuations, and (c) a combined QM/MM potential for the systems. It was found that first-order perturbation is sufficiently accurate, enabling time-dependent vibrational frequencies to be obtained on the fly in molecular dynamics. The QVP method is illustrated in the mode-specific linear and 2D-IR spectra of the H-Cl stretching frequency in the HCl-water clusters and the carbonyl stretching vibration of acetone in aqueous solution. To further reduce computational cost, a hybrid strategy was proposed, and it was found that the computed vibrational spectral peak position and line shape are in agreement with experimental results. In addition, it was found that anharmonicity is significant in the H-Cl stretching mode, and hydrogen-bonding interactions further enhance anharmonic effects. The present QVP method complements other computational approaches, including path integral-based molecular dynamics, and represents a major improvement over the electrostatics-based spectroscopic mapping procedures.

Vibrational solvatochromism. III. Rigorous treatment of the dispersion interaction contribution

A rigorous first principles theory of vibrational solvatochromism including the intermolecular dispersion interaction, which is based on the effective fragment potential method, is developed. The present theory is an extended version of our previous vibrational solvatochromism model that took into account the Coulomb, exchange-repulsion, and induction interactions. We show that the frequency shifts of the amide I mode of N-methylacetamide in H2O and CDCl3, when combined with molecular dynamics simulations, can be quantitatively reproduced by the theory, which indicates that the dispersion interaction contribution to the vibrational frequency shift is not always negligibly small. Nonetheless, the reason that the purely Coulombic interaction model for vibrational solvatochromism works well for describing amide I mode frequency shifts in polar solvents is because the electrostatic contribution is strong and highly sensitive to the relative orientation of surrounding solvent molecules, which is in stark contrast with polarization, dispersion, and exchange-repulsion contributions. It is believed that the theory presented and discussed here will be of great use in quantitatively describing vibrational solvatochromism and electrochromism of infrared probes in not just polar solvent environments but also in biopolymers such as proteins.

Vibrational Stark Effects of Carbonyl Probes Applied to Reinterpret IR and Raman Data for Enzyme Inhibitors in Terms of Electric Fields at the Active Site

IR and Raman frequency shifts have been reported for numerous probes of enzyme transition states, leading to diverse interpretations. In the case of the model enzyme ketosteroid isomerase (KSI), we have argued that IR spectral shifts for a carbonyl probe at the active site can provide a connection between the active site electric field and the activation free energy (Fried et al. Science 2014, 346, 1510-1514). Here we generalize this approach to a much broader set of carbonyl probes (e.g., oxoesters, thioesters, and amides), first establishing the sensitivity of each probe to an electric field using vibrational Stark spectroscopy, vibrational solvatochromism, and MD simulations, and then applying these results to reinterpret data already in the literature for enzymes such as 4-chlorobenzoyl-CoA dehalogenase and serine proteases. These results demonstrate that the vibrational Stark effect provides a general framework for estimating the electrostatic contribution to the catalytic rate and may provide a metric for the design or modification of enzymes. Opportunities and limitations of the approach are also described.

Site-Specific Characterization of Cytochrome P450cam Conformations by Infrared Spectroscopy

Conformational changes are central to protein function but challenging to characterize with both high spatial and temporal precision. The inherently fast time scale and small chromophores of infrared (IR) spectroscopy are well-suited for characterization of potentially rapidly fluctuating environments, and when frequency-resolved probes are incorporated to overcome spectral congestion, enable characterization of specific sites in proteins. We selectively incorporated p-cyanophenylalanine (CNF) as a vibrational probe at five distinct locations in the enzyme cytochrome P450cam and used IR spectroscopy to characterize the environments in substrate and/or ligand complexes reflecting those in the catalytic cycle. Molecular dynamics (MD) simulations were performed to provide a structural basis for spectral interpretation. Together the experimental and simulation data suggest that the CN frequencies are sensitive to both long-range influences, resulting from the particular location of a residue within the enzyme, as well as short-range influences from hydrogen bonding and packing interactions. The IR spectra demonstrate that the environments and effects of substrate and/or ligand binding are different at each position probed and also provide evidence that a single site can experience multiple environments. This study illustrates how IR spectroscopy, when combined with the spectral decongestion and spatial selectivity afforded by CNF incorporation, provides detailed information about protein structural changes that underlie function.

Application of two-dimensional infrared spectroscopy to benchmark models for the amide I band of proteins

In this paper, we present a novel benchmarking method for validating the modelling of vibrational spectra for the amide I region of proteins. We use the linear absorption spectra and two-dimensional infrared spectra of four experimentally well-studied proteins as a reference and test nine combinations of molecular dynamics force fields, vibrational frequency mappings, and coupling models. We find that two-dimensional infrared spectra provide a much stronger test of the models than linear absorption does. The best modelling approach in the present study still leaves significant room for future improvement. The presented benchmarking scheme, thus, provides a way of validating future protocols for modelling the amide I band in proteins.

General Applicable Frequency Map for the Amide-I Mode in β-Peptides

In this work, a general applicable amide-I vibrational frequency map (GA map) for β-peptides in a number of common solvents was constructed, based on a peptide derivative, N-ethylpropionamide (NEPA). The map utilizes force fields at the ab initio computational level to accurately describe molecular structure and solute-solvent interactions, and also force fields at the molecular mechanics level to take into account long-range solute-solvent interactions. The results indicate that the GA map works reasonably for mapping the vibrational frequencies of the amide-I local-modes for β-peptides, holding promises for understanding the complicated infrared spectra of the amide-I mode in β-polypeptides.

Vibrational solvatochromism of nitrile infrared probes: beyond the vibrational Stark dipole approach

Systematic probing of local environments around biopolymers is important for understanding their functions.

Quantum Beats and Phase Shifts in Two-Dimensional Electronic Spectra of Zinc Naphthalocyanine Monomer and Aggregate

The origin of quantum coherence in two-dimensional (2D) electronic spectra of molecular aggregates and light-harvesting complexes still remains an open question. In particular, it could be challenging to distinguish between electronic and vibrational coherences for a coupled system, where both degrees of freedom can be simultaneously excited. In this Letter, we examine quantum beats in the 2D spectra of zinc naphthalocyanine (ZnNc) aggregate and monomer, and compare their characteristic features in terms of the frequency and relative phase of diagonal and off-diagonal amplitude oscillations. The long-lasting oscillating components (>1 ps) at 600-700 cm(-1) observed in both the aggregate and monomer are found to be attributed to the vibrational coherence. The wide phase variations of the 2D spectral amplitude oscillations are observed not just in the aggregate but also in the monomer state. This suggests that the unusual 90° phase shift may be attributed to neither quantum population-to-coherence transfer nor vibronic exciton coupling.

Hydration Effect on Amide I Infrared Bands in Water: An Interpretation Based on an Interaction Energy Decomposition Scheme

The sensitivity of some infrared bands to the local environment can be exploited to shed light on the structure and the dynamics of biological systems. In particular, the amide I band, which is specifically related to vibrations within the peptide bonds, can give information on the ternary structure of proteins, and can be used as a probe of energy transfer. In this work, we propose a model to quantitatively interpret the frequency shift on the amide I band of a model peptide induced by the formation of hydrogen bonds in the first solvation shell. This method allows us to analyze to what extent the electrostatic interaction, electronic polarization and charge transfer affect the position of the amide I band. The impact of the anharmoniticy of the pontential energy surface on the hydration induced shift is elucidated as well.