Calculations of the electric fields in liquid solutions

Local electric field in nanocavities dictates the vibrational relaxation dynamics of interfacial molecules

Plasmonic nanocavities enable the generation of strong light-matter coupling and exhibit great potential in plasmon-mediated chemical reactions (PMCRs). Although an electric field generated by nanocavities (E n) has recently been reported, its effect on the vibrational energy relaxation (VER) of the molecules in the nanocavities has not been explored. In this study, we reveal the impact of an electric field sensed by molecules (para-substituted thiophenol derivatives) in a nanocavity (E f) on VER processes by employing advanced time-resolved femtosecond sum frequency generation vibrational spectroscopy (SFG-VS) supplemented by electrochemical measurements. The magnitude of E n is almost identical (1.0 ± 0.2 V nm-1) beyond the experimental deviation while E f varies from 0.3 V nm-1 to 1.7 V nm-1 depending on the substituent. An exponential correlation between E f and the complete recovery time of the ground vibrational C[double bond, length as m-dash]C state (T 2) of the phenyl ring is observed. Substances with a smaller T 2 are strongly correlated with the reported macroscopic chemical reactivity. This finding may aid in enriching the current understanding of PMCRs and highlights the possibility of regulating vibrational energy flow into desired reaction coordinates by using a local electric field.

Evaluating aliphatic CF, CF2, and CF3 groups as vibrational Stark effect reporters

Given the extensive use of fluorination in molecular design, it is imperative to understand the solvation properties of fluorinated compounds and the impact of the C-F bond on electrostatic interactions. Vibrational spectroscopy can provide direct insights into these interactions by using the C-F bond stretching [v(C-F)] as an electric field probe through the vibrational Stark effect (VSE). In this work, we explore the VSE of the three basic patterns of aliphatic fluorination, i.e., mono-, di-, and trifluorination in CF, CF2, and CF3 groups, respectively, and compare their response to the well-studied aromatic v(C-F). Magnitudes (i.e., Stark tuning rates) and orientations of the difference dipole vectors of the v(C-F)-containing normal modes were determined using density functional theory and a molecular dynamics (MD)-assisted solvatochromic analysis of model compounds in solvents of varying polarity. We obtain Stark tuning rates of 0.2-0.8 cm-1/(MV/cm), with smallest and largest electric field sensitivities for CFaliphatic and CF3,aliphatic, respectively. While average electric fields of solvation were oriented along the main symmetry axis of the CFn, and thus along its static dipole, the Stark tuning rate vectors were tilted by up to 87° potentially enabling to map electrostatics in multiple dimensions. We discuss the influence of conformational heterogeneity on spectral shifts and point out the importance of multipolar and/or polarizable MD force fields to describe the electrostatics of fluorinated molecules. The implications of this work are of direct relevance for studies of fluorinated molecules as found in pharmaceuticals, fluorinated peptides, and proteins.

Evaluating Polarizable Biomembrane Simulations against Experiments

Owing to the increase of available computational capabilities and the potential for providing a more accurate description, polarizable molecular dynamics force fields are gaining popularity in modeling biomolecular systems. It is, however, crucial to evaluate how much precision is truly gained with increasing cost and complexity of the simulation. Here, we leverage the NMRlipids open collaboration and Databank to assess the performance of available polarizable lipid models─the CHARMM-Drude and the AMOEBA-based parameters─against high-fidelity experimental data and compare them to the top-performing nonpolarizable models. While some improvement in the description of ion binding to membranes is observed in the most recent CHARMM-Drude parameters, and the conformational dynamics of AMOEBA-based parameters are excellent, the best nonpolarizable models tend to outperform their polarizable counterparts for each property we explored. The identified shortcomings range from inaccuracies in describing the conformational space of lipids to excessively slow conformational dynamics. Our results provide valuable insights for the further refinement of polarizable lipid force fields and for selecting the best simulation parameters for specific applications.

Perturbation of Fermi Resonance on Hydrogen-Bonded > C═O: 2D IR Studies of Small Ester Probes

We utilized linear and 2D infrared spectroscopy to analyze the carbonyl stretching modes of small esters in different solvents. Particularly noteworthy were the distinct carbonyl spectral line shapes in aqueous solutions, prompting our investigation of the underlying factors responsible for these differences. Through our experimental and theoretical calculations, we identified the presence of the hydrogen-bond-induced Fermi resonance as the primary contributor to the varied line shapes of small esters in aqueous solutions. Furthermore, our findings revealed that the skeletal deformation mode plays a crucial role in the Fermi resonance for all small esters. Specifically, the first overtone band of the skeletal deformation mode intensifies when hydrogen bonds form with the carbonyl group of esters, whereas such coupling is rare in aprotic organic solvents. These spectral insights carry significant implications for the utilization of esters as infrared probes in both biological and chemical systems.

From random to rational: improving enzyme design through electric fields, second coordination sphere interactions, and conformational dynamics

Enzymes are versatile and efficient biological catalysts that drive numerous cellular processes, motivating the development of enzyme design approaches to tailor catalysts for diverse applications. In this perspective, we investigate the unique properties of natural, evolved, and designed enzymes, recognizing their strengths and shortcomings. We highlight the challenges and limitations of current enzyme design protocols, with a particular focus on their limited consideration of long-range electrostatic and dynamic effects. We then delve deeper into the impact of the protein environment on enzyme catalysis and explore the roles of preorganized electric fields, second coordination sphere interactions, and protein dynamics for enzyme function. Furthermore, we present several case studies illustrating successful enzyme-design efforts incorporating enzyme strategies mentioned above to achieve improved catalytic properties. Finally, we envision the future of enzyme design research, spotlighting the challenges yet to be overcome and the synergy of intrinsic electric fields, second coordination sphere interactions, and conformational dynamics to push the state-of-the-art boundaries.

AMOEBA Force Field Predicts Accurate Hydrogen Bond Counts of Nitriles in SNase by Revealing Water-Protein Interaction in Vibrational Absorption Frequencies

Precisely quantifying the magnitude and direction of electric fields in proteins has long been an outstanding challenge in understanding biological functions. Nitrile vibrational Stark effect probes have been shown to be minimally disruptive to the protein structure and can be better direct reporters of local electrostatic field in the native state of a protein than other measures such as pKa shifts of titratable residues. However, interpretations of the connection between measured vibrational energy and electric field rely on the accurate molecular understanding of interactions of the nitrile group and its environment, particularly from hydrogen bonding. In this work, we compared the extent of hydrogen bonding calculated in two common force fields, the fixed charge force field Amber03 and polarizable force field AMOEBA, at 10 locations of cyanocysteine (CNC) in staphylococcal nuclease (SNase) against the experimental nitrile absorption frequency in terms of full width at half-maximum (FWHM) and frequency temperature line slope (FTLS). We observed that the number of hydrogen bonds correlated well in AMOEBA trajectories with respect to both the FWHM (r = 0.88) and the FTLS (r = -0.85), whereas the correlation of Amber03 trajectories was less reliable because the Amber03 force field predicted more hydrogen bonds in some mutants. Moreover, we demonstrated that contributions from the interactions between CNC and nearby water molecules were significant in AMOEBA trajectories but were not predicted by Amber03. We conclude that although the nitrile absorption peak shape could be qualitatively predicted by the fixed charge Amber03 force field, the detailed electrostatic environment measured by the nitrile probe in terms of the extent of hydrogen bonding could only be accurately observed in the AMOEBA trajectories, where the permanent dipole, quadrupole, and dipole-induced-dipole polarizable interactions were all taken into account. The significance of this finding to the goal of accurately predicting electric fields in complex biomolecular environments is discussed.

Theoretical Investigation of the X-ray Stark Effect in Small Molecules

We have studied the Stark effect in the soft x-ray region for various small molecules by calculating the field-dependent x-ray absorption spectra. This effect is explained in terms of the response of molecular orbitals (core and valence), the molecular dipole moment, and the molecular geometry to the applied electric field. A number of consistent trends are observed linking the computed shifts in absorption energies and intensities with specific features of the molecular electronic structure. We find that both the virtual molecular orbitals (valence and/or Rydberg) as well as the core orbitals contribute to observed trends in a complementary fashion. This initial study highlights the potential impact of x-ray Stark spectroscopy as a tool to study electronic structure and environmental perturbations at a submolecular scale.

Rethinking Vibrational Stark Spectroscopy: Peak Shifts, Line Widths, and the Role of Non-Stark Solvent Coupling

A vibration's transition frequency is partly determined by the first-order Stark effect, which accounts for the electric field experienced by the mode. Using ultrafast infrared pump-probe and FT-IR spectroscopies, we characterized both the 0 → 1 and 1 → 2 vibrational transitions' field-dependent peak positions and line widths of the CN stretching mode of benzonitrile (BZN) and phenyl selenocyanate (PhSeCN) in ten solvents. We present a theoretical model that decomposes the observed line width into a field-dependent Stark contribution and a field-independent non-Stark solvent coupling contribution (NSC). The model demonstrates that the field-dependent peak position is independent of the line width, even when the NSC dominates the latter. Experiments show that when the Stark tuning rate is large compared to the NSC (PhSeCN), the line width has a field dependence, albeit with major NSC-induced excursions from linearity. When the Stark tuning rate is small relative to the NSC (BZN), the line width is field-independent. BZN's line widths are substantially larger for the 1 → 2 transition, indicating a 1 → 2 transition enhancement of the NSC. Additionally, we examine, theoretically and experimentally, the difference in the 0 → 1 and 1 → 2 transitions' Stark tuning rates. Second-order perturbation theory combined with density functional theory explain the difference and show that the 1 → 2 transition's Stark tuning rate is ∼10% larger. The Stark tuning rate of PhSeCN is larger than BZN's for both transitions, consistent with the theoretical calculations. This study provides new insights into vibrational line shape components and a more general understanding of the vibrational response to external electric fields.

Electrostatics and Chemical Reactivity at the Air-Water Interface

It has been recently discovered that chemical reactions at aqueous interfaces can be orders of magnitude faster compared to conventional bulk phase reactions, but despite its wide-ranging implications, which extend from atmospheric to synthetic chemistry or technological applications, the phenomenon is still incompletely understood. The role of strong electric fields due to space asymmetry and the accumulation of ions at the interface has been claimed as a possible cause from some experiments, but the reorganization of the solvent around the reactive system should provide even greater additional electrostatic contributions that have not yet been analyzed. In this study, with the help of first-principles molecular dynamics simulations, we go deeper into this issue by a careful assessment of solvation electrostatics at the air-water interface. Our simulations confirm that electrostatic forces can indeed be a key factor in rate acceleration compared to bulk solution. Remarkably, the study reveals that the effect cannot simply be attributed to the magnitude of the local electric field and that the fluctuations of the full electrostatic potential resulting from unique dynamical behavior of the solvation shells at the interface must be accounted for. This finding paves the way for future applications of the phenomenon in organic synthesis, especially for charge transfer or redox reactions in thin films and microdroplets.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

AMOEBA Force Field Trajectories Improve Predictions of Accurate pKa Values of the GFP Fluorophore: The Importance of Polarizability and Water Interactions

Precisely quantifying the magnitude, direction, and biological functions of electric fields in proteins has long been an outstanding challenge in the field. The most widely implemented experimental method to measure such electric fields at a particular residue in a protein has been through changes in pKa of titratable residues. While many computational strategies exist to predict these values, it has been difficult to do this accurately or connect predicted results to key structural or mechanistic features of the molecule. Here, we used experimentally determined pKa values of the fluorophore in superfolder green fluorescent protein (GFP) with amino acid mutations made at position Thr 203 to evaluate the pKa prediction ability of molecular dynamics (MD) simulations using a polarizable force field, AMOEBA. Structure ensembles from AMOEBA were used to calculate pKa values of the GFP fluorophore. The calculated pKa values were then compared to trajectories using a conventional fixed charge force field (Amber03 ff). We found that the position of water molecules included in the pKa calculation had opposite effects on the pKa values between the trajectories from AMOEBA and Amber03 force fields. In AMOEBA trajectories, the inclusion of water molecules within 35 Å of the fluorophore decreased the difference between the predicted and experimental values, resulting in calculated pKa values that were within an average of 0.8 pKa unit from the experimental results. On the other hand, in Amber03 trajectories, including water molecules that were more than 5 Å from the fluorophore increased the differences between the calculated and experimental pKa values. The inaccuracy of pKa predictions determined from Amber03 trajectories was caused by a significant stabilization of the deprotonated chromophore's free energy compared to the result in AMOEBA. We rationalize the cutoffs for explicit water molecules when calculating pKa to better predict the electrostatic environment surrounding the fluorophore buried in GFP. We discuss how the results from this work will assist the prospective prediction of pKa values or other electrostatic effects in a wide variety of folded proteins.

Solvent Organization and Electrostatics Tuned by Solute Electronic Structure: Amide versus Non-Amide Carbonyls

The ability to exploit carbonyl groups to measure electric fields in enzymes and other complex reactive environments by using the vibrational Stark effect has inspired growing interest in how these fields can be measured, tuned, and ultimately designed. Previous studies have concentrated on the role of the solvent in tuning the fields exerted on the solute. Here, we explore instead the role of the solute electronic structure in modifying the local solvent organization and electric field exerted on the solute. By measuring the infrared absorption spectra of amide-containing molecules, as prototypical peptides, and contrasting them with non-amide carbonyls in a wide range of solvents, we show that these solutes experience notable differences in their frequency shifts in polar solvents. Using vibrational Stark spectroscopy and molecular dynamics simulations, we demonstrate that while some of these differences can be rationalized by using the distinct intrinsic Stark tuning rates of the solutes, the larger frequency shifts for amides and dimethylurea primarily result from the larger solvent electric fields experienced by their carbonyl groups. These larger fields arise due to their stronger p-π conjugation, which results in larger C═O bond dipole moments that further induce substantial solvent organization. Using electronic structure calculations, we decompose the electric fields into contributions from solvent molecules that are in the first solvation shell and those from the bulk and show that both of these contributions are significant and become larger with enhanced conjugation in solutes. These results show that structural modifications of a solute can be used to tune both the solvent organization and electrostatic environment, indicating the importance of a solute-centric paradigm in modulating and designing the electrostatic environment in condensed-phase chemical processes.

A two-directional vibrational probe reveals different electric field orientations in solution and an enzyme active site

The catalytic power of an electric field depends on its magnitude and orientation with respect to the reactive chemical species. Understanding and designing new catalysts for electrostatic catalysis thus requires methods to measure the electric field orientation and magnitude at the molecular scale. We demonstrate that electric field orientations can be extracted using a two-directional vibrational probe by exploiting the vibrational Stark effect of both the C=O and C-D stretches of a deuterated aldehyde. Combining spectroscopy with molecular dynamics and electronic structure partitioning methods, we demonstrate that, despite distinct polarities, solvents act similarly in their preference for electrostatically stabilizing large bond dipoles at the expense of destabilizing small ones. In contrast, we find that for an active-site aldehyde inhibitor of liver alcohol dehydrogenase, the electric field orientation deviates markedly from that found in solvents, which provides direct evidence for the fundamental difference between the electrostatic environment of solvents and that of a preorganized enzyme active site.

Stochastic Analysis of Molecular Dynamics Reveals the Rotation Dynamics Distribution of Water around Lysozyme

Water dynamics is essential to biochemical processes by mediating all such reactions, including biomolecular degeneration in solutions. To disentangle the molecular-scale distribution of water dynamics around a solute biomolecule, we investigated here the rotational dynamics of water around lysozyme by combining molecular dynamics (MD) simulations and broadband dielectric spectroscopy (BDS). A statistical analysis using the relaxation times and trajectories of every single water molecule was proposed, and the two-dimensional probability distribution of water at a distance from the lysozyme surface with a rotational relaxation time was given. For the observed lysozyme solutions of 34-284 mg/mL, we discovered that the dielectric relaxation time obtained from this distribution agrees well with the measured γ relaxation time, which suggests that rotational self-correlation of water molecules underlies the gigahertz domain of the dielectric spectra. Regardless of protein concentration, water rotational relaxation time versus the distance from the lysozyme surface revealed that the water rotation is severely retarded within 3 Å from the lysozyme surface and is nearly comparable to pure water when farther than 10 Å. The dimension of the first hydration layer was subsequently identified in terms of the relationship between the acceleration of water rotation and the distance from the protein surface.

Oxazaborolidinone-Mediated Asymmetric Bisvinylogous Mukaiyama Aldol Reaction

A bisvinylogous Mukaiyama aldol reaction using oxazaborolidinones as a source of chirality was developed. This methodology allows the fast assembly of conjugated dienols by expanding the vinylogy principle by two additional carbons, and can be conducted using a readily available Lewis acid at reasonable reaction times. A broad range of aromatic and aliphatic aldehydes can be used providing access to complex building blocks for polyketide synthesis.

Electric fields and potentials in condensed phases

The electric fields and potentials inside and at the interface of matter are relevant to many branches of physics, chemistry, and biology. Accurate quantification of these fields and/or potentials is essential to control and exploit chemical and physical transformations. Before we understand the response of matter to external fields, it is first important to understand the intrinsic interior and interfacial fields and potentials, both classically and quantum mechanically, as well as how they are probed experimentally. Here we compare and contrast, beginning with the hydrogen atom in vacuum and ending with concentrated aqueous NaCl electrolyte, both classical and quantum mechanical electric potentials and fields. We make contact with experimental vibrational Stark, electrochemical, X-ray, and electron spectroscopic probes of these potentials and fields, outline relevant conceptual difficulties, and underscore the advantage of electron holography as a basis to better understand electrostatics in matter.

Local Electric Fields in Aqueous Electrolytes

Vibrational Stark shifts were explored in aqueous solutions of organic molecules with carbonyl- and nitrile-containing constituents. In many cases, the vibrational resonances from these moieties shifted toward lower frequency as salt was introduced into solution. This is in contrast to the blue-shift that would be expected based upon Onsager's reaction field theory. Salts containing well-hydrated cations like Mg²⁺ or Li⁺ led to the most pronounced Stark shift for the carbonyl group, while poorly hydrated cations like Cs⁺ had the greatest impact on nitriles. Moreover, salts containing I^- gave rise to larger Stark shifts than those containing Cl^-. Molecular dynamics simulations indicated that cations and anions both accumulate around the probe in an ion- and probe-dependent manner. An electric field was generated by the ion pair, which pointed from the cation to the anion through the vibrational chromophore. This resulted from solvent-shared binding of the ions to the probes, consistent with their positions in the Hofmeister series. The "anti-Onsager" Stark shifts occur in both vibrational spectroscopy and fluorescence measurements.

Vibrational Stark shift spectroscopy of catalysts under the influence of electric fields at electrode-solution interfaces

External control of chemical processes is a subject of widespread interest in chemical research, including control of electrocatalytic processes with significant promise in energy research. The electrochemical double-layer is the nanoscale region next to the electrode/electrolyte interface where chemical reactions typically occur. Understanding the effects of electric fields within the electrochemical double layer requires a combination of synthesis, electrochemistry, spectroscopy, and theory. In particular, vibrational sum frequency generation (VSFG) spectroscopy is a powerful technique to probe the response of molecular catalysts at the electrode interface under bias. Fundamental understanding can be obtained via synthetic tuning of the adsorbed molecular catalysts on the electrode surface and by combining experimental VSFG data with theoretical modelling of the Stark shift response. The resulting insights at the molecular level are particularly valuable for the development of new methodologies to control and characterize catalysts confined to electrode surfaces. This Perspective article is focused on how systematic modifications of molecules anchored to surfaces report information concerning the geometric, energetic, and electronic parameters of catalysts under bias attached to electrode surfaces.

Heterogeneous electrocatalysis: characterization of interfacial electric field within the electrochemical double layer.

Testing the Limitations of MD-Based Local Electric Fields Using the Vibrational Stark Effect in Solution: Penicillin G as a Test Case

Noncovalent interactions underlie nearly all molecular processes in the condensed phase from solvation to catalysis. Their quantification within a physically consistent framework remains challenging. Experimental vibrational Stark effect (VSE)-based solvatochromism can be combined with molecular dynamics (MD) simulations to quantify the electrostatic forces in solute-solvent interactions for small rigid molecules and, by extension, when these solutes bind in enzyme active sites. While generalizing this approach toward more complex (bio)molecules, such as the conformationally flexible and charged penicillin G (PenG), we were surprised to observe inconsistencies in MD-based electric fields. Combining synthesis, VSE spectroscopy, and computational methods, we provide an intimate view on the origins of these discrepancies. We observe that the electric fields are correlated to conformation-dependent effects of the flexible PenG side chain, including both the local solvation structure and solute conformational sampling in MD. Additionally, we identified that MD-based electric fields are consistently overestimated in three-point water models in the vicinity of charged groups; this cannot be entirely ameliorated using polarizable force fields (AMOEBA) or advanced water models. This work demonstrates the value of the VSE as a direct method for experiment-guided refinements of MD force fields and establishes a general reductionist approach to calibrating vibrational probes for complex (bio)molecules.

How Oriented External Electric Fields Modulate Reactivity

A judiciously oriented external electric field (OEEF) can catalyze a wide range of reactions and can even induce endo/exo stereoselectivity of cycloaddition reactions. The Diels-Alder reaction between cyclopentadiene and maleic anhydride is studied by using quantitative activation strain and Kohn-Sham molecular orbital theory to pinpoint the origin of these catalytic and stereoselective effects. Our quantitative model reveals that an OEEF along the reaction axis induces an enhanced electrostatic and orbital interaction between the reactants, which in turn lowers the reaction barrier. The stronger electrostatic interaction originates from an increased electron density difference between the reactants at the reactive center, and the enhanced orbital interaction arises from the promoted normal electron demand donor-acceptor interaction driven by the OEEF. An OEEF perpendicular to the plane of the reaction axis solely stabilizes the exo pathway of this reaction, whereas the endo pathway remains unaltered and efficiently steers the endo/exo stereoselectivity. The influence of the OEEF on the inverse electron demand Diels-Alder reaction is also investigated; unexpectedly, it inhibits the reaction, as the electric field now suppresses the critical inverse electron demand donor-acceptor interaction.

Local Electric Field Controls Fluorescence Quantum Yield of Red and Far-Red Fluorescent Proteins

Genetically encoded probes with red-shifted absorption and fluorescence are highly desirable for imaging applications because they can report from deeper tissue layers with lower background and because they provide additional colors for multicolor imaging. Unfortunately, red and especially far-red fluorescent proteins have very low quantum yields, which undermines their other advantages. Elucidating the mechanism of nonradiative relaxation in red fluorescent proteins (RFPs) could help developing ones with higher quantum yields. Here we consider two possible mechanisms of fast nonradiative relaxation of electronic excitation in RFPs. The first, known as the energy gap law, predicts a steep exponential drop of fluorescence quantum yield with a systematic red shift of fluorescence frequency. In this case the relaxation of excitation occurs in the chromophore without any significant changes of its geometry. The second mechanism is related to a twisted intramolecular charge transfer in the excited state, followed by an ultrafast internal conversion. The chromophore twisting can strongly depend on the local electric field because the field can affect the activation energy. We present a spectroscopic method of evaluating local electric fields experienced by the chromophore in the protein environment. The method is based on linear and two-photon absorption spectroscopy, as well as on quantum-mechanically calculated parameters of the isolated chromophore. Using this method, which is substantiated by our molecular dynamics simulations, we obtain the components of electric field in the chromophore plane for seven different RFPs with the same chromophore structure. We find that in five of these RFPs, the nonradiative relaxation rate increases with the strength of the field along the chromophore axis directed from the center of imidazolinone ring to the center of phenolate ring. Furthermore, this rate depends on the corresponding electrostatic energy change (calculated from the known fields and charge displacements), in quantitative agreement with the Marcus theory of charge transfer. This result supports the dominant role of the twisted intramolecular charge transfer mechanism over the energy gap law for most of the studied RFPs. It provides important guidelines of how to shift the absorption wavelength of an RFP to the red, while keeping its brightness reasonably high.

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

Electrostatics Plays a Crucial Role in HIV-1 Protease Substrate Binding, Drugs Fail to Take Advantage

HIV-1 protease (HIVPR) is an important drug target for combating AIDS. This enzyme is an aspartyl protease that is functionally active in its dimeric form. Nuclear magnetic resonance reports have convincingly shown that a pseudosymmetry exists at the HIVPR active site, where only one of the two aspartates remains protonated over the pH range of 2.5-7.0. To date, all HIVPR-targeted drug design strategies focused on maximizing the size-shape complementarity and van der Waals interactions of the small molecule drugs with the deprotonated, symmetric active site envelope of crystallized HIVPR. However, these strategies were ineffective with the emergence of drug resistant protease variants, primarily due to the steric clashes at the active site. In this study, we traced a specificity in the substrate binding motif that emerges primarily from the asymmetrical electrostatic potential present in the protease active site due to the uneven protonation. Our detailed results from atomistic molecular dynamics simulations show that while such a specific mode of substrate binding involves significant electrostatic interactions, none of the existing drugs or inhibitors could utilize this electrostatic hot spot. As the electrostatic is long-range interaction, it can provide sufficient binding strength without the necessity of increasing the bulkiness of the inhibitors. We propose that introducing the electrostatic component along with optimal fitting at the binding pocket could pave the way for promising designs that might be more effective against both wild type and HIVPR resistant variants.

Effect of Oriented External Electric Fields on the Photo and Thermal Isomerization of Azobenzene

Azobenzene is a prototype molecule with potential applications in molecular switches, solar thermal batteries, sensors, photoresponsive membranes, molecular electronics, data storage, and nonlinear optics. Photo and thermal isomerization pathways exhibit different charge-transfer character and dipole moments, implying that the use of electric fields can be used to modulate the reactivity of azobenzene. This article examines the differential effect of orientated electric fields on the rotation and inversion thermal and photoisomerization pathways of azobenzene to explore the feasibility of using electric fields in the design of azobenzene-based molecular devices. Our findings demonstrate that the application of orientated electric fields modifies the accessibility of the S₀/S₁ seam of electronic degeneracy, as well as changes the energetically favored relaxation pathway in the branching space to yield different photoproducts. In addition, we observed strong-field dipole-inversion effects that cause a topographical change in the response of the potential energy surface to the applied field and can result in geometric minima that do not exist under field-free conditions. On the S₀ surface, transition barriers can be modified on the order of ±10 kcal mol^-1, enabling control of thermal isomerization rates.

A Critical Evaluation of Vibrational Stark Effect (VSE) Probes with the Local Vibrational Mode Theory

Over the past two decades, the vibrational Stark effect has become an important tool to measure and analyze the in situ electric field strength in various chemical environments with infrared spectroscopy. The underlying assumption of this effect is that the normal stretching mode of a target bond such as CO or CN of a reporter molecule (termed vibrational Stark effect probe) is localized and free from mass-coupling from other internal coordinates, so that its frequency shift directly reflects the influence of the vicinal electric field. However, the validity of this essential assumption has never been assessed. Given the fact that normal modes are generally delocalized because of mass-coupling, this analysis was overdue. Therefore, we carried out a comprehensive evaluation of 68 vibrational Stark effect probes and candidates to quantify the degree to which their target normal vibration of probe bond stretching is decoupled from local vibrations driven by other internal coordinates. The unique tool we used is the local mode analysis originally introduced by Konkoli and Cremer, in particular the decomposition of normal modes into local mode contributions. Based on our results, we recommend 31 polyatomic molecules with localized target bonds as ideal vibrational Stark effect probe candidates.

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.

Kemp Elimination Reaction Catalyzed by Electric Fields

The Kemp elimination reaction is the most widely used in the de novo design of new enzymes. The effect of two different kinds of electric fields in the reactions of acetate as a base with benzisoxazole and 5-nitrobenzisoxazole as substrates have been theoretically studied. The effect of the solvent reaction field has been calculated using the SMD continuum model for several solvents; we have shown that solvents inhibit both reactions, the decrease of the reaction rate being larger as far as the dielectric constant is increased. The diminution of the reaction rate is especially remarkable between aprotic organic solvents and protic solvents as water, the electrostatic term of the hydrogen bonds being the main factor for the large inhibitory effect of water. The presence of an external electric field oriented in the direction of the charge transfer (z axis) increases it and, so, the reaction rate. In the reaction of the nitro compound, if the electric field is oriented in an orthogonal direction (x axis) the charge transfer to the NO₂ group is favored and there is a subsequent increase of the reaction rate. However, this increase is smaller than the one produced by the field in the z axis. It is worthwhile mentioning that one of the main effects of external electric fields of intermediate intensity is the reorientation of the reactants. Finally, the implications of our results in the de novo design of enzymes are discussed.

Elucidating Solvent Effects on Strong Intramolecular Hydrogen Bond: DFT-MD Study of Dibenzoylmethane in Methanol Solution

The dynamic aspect of solvation plays a crucial role in determining properties of strong intramolecular hydrogen bonds since solvent fluctuations modify instantaneous hydrogen-bonded proton transfer barriers. Previous studies pointed out that solvent-solute interactions in the first solvation shell govern the position of the proton but the ability of the electric field due to other solvent molecules to localize the proton remains an important issue. In this work, we examine the structure of the O-H⋅⋅⋅O intramolecular hydrogen bond of dibenzoylmethane in methanol solution by employing density functional theory-based molecular dynamics and quantum chemical calculations. Our computations showed that homogeneous electric fields with intensities corresponding to those found in polar solvents are able to considerably alter the proton transfer barrier height in the gas phase. In methanol solution, the proton position is correlated with the difference in electrostatic potentials on the oxygen atoms of dibenzoylmethane even when dibenzoylmethane-methanol hydrogen bonding is lacking. On a timescale of our simulation, the hydrogen bonding and solvent electrostatics tend to localize the proton on different oxygen atoms. These findings provide an insight into the importance of the solvent electric field on the structure of a strong intramolecular hydrogen bond.

Hydrated Excess Protons in Acetonitrile/Water Mixtures: Solvation Species and Ultrafast Proton Motions

The solvation structure of protons in aqueous media is highly relevant to electric properties and to proton transport in liquids and membranes. At ambient temperature, polar liquids display structural fluctuations on femto- to picosecond time scales with a direct impact on proton solvation. We use two-dimensional infrared (2D-IR) spectroscopy to follow proton dynamics in acetonitrile/water mixtures with the Zundel cation H₅O₂⁺ prepared in neat acetonitrile as a benchmark. The 2D-IR spectra of the proton transfer mode of H₅O₂⁺ demonstrate stochastic large-amplitude motions in the double-minimum proton potential, driven by fluctuating electric fields. In all cases, the excess proton is embedded in a water dimer, forming an H₅O₂⁺ complex as the major solvation species. This observation is rationalized by quantum mechanics/molecular mechanics molecular dynamics simulations including up to four water molecules embedded in acetonitrile. The Zundel motif interacts with its closest water neighbor in an H₇O₃⁺ unit without persistent proton localization.

Combining Iteration-Free Polarization with Large Time Step Stochastic-Isokinetic Integration

In order to accelerate molecular dynamics simulations using polarizable force fields, we combine a new extended Lagrangian approach that eliminates the self-consistent field step (iEL/0-SCF) with a stochastic integration scheme that allows for a long time step using a multiple time scale algorithm (SIN(R)). We consider different algorithms for the combined scheme that places different components of the nonbonded forces into different time scales, as well as splitting individual nonbonded forces across time scales, to demonstrate that the combined method works well for bulk water as well as for a concentrated salt solution, aqueous peptide, and solvated protein. Depending on system and desired accuracy, the iEL/0-SCF and SIN(R) combination yields lower bound computational speed-ups of ∼6-8 relative to a molecular dynamics Verlet integration using a standard SCF solver implemented in the reference program TINKER 8.1. The combined approach embodies a significant advance for equilibrium simulations in the canonical ensemble of many-body potential energy surfaces for condensed phase systems with speed-ups that exceed what is possible by either method alone.

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18-Crown-6/Urea (1:5) Host-Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis

High-resolution synchrotron and neutron single-crystal diffraction data of 18-crown-6/(pentakis)urea measured at 30 K are combined, with the aim of better appreciating the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown-6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a cocrystal or host-guest system incorporating such a large number of unique molecules. The dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared to values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range of 10-19 GV m^-1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

Site-specific 2D IR spectroscopy: a general approach for the characterization of protein dynamics with high spatial and temporal resolution

The conformational heterogeneity and dynamics of protein side chains contribute to function, but investigating exactly how is hindered by experimental challenges arising from the fast timescales involved and the spatial heterogeneity of protein structures. The potential of two-dimensional infrared (2D IR) spectroscopy for measuring conformational heterogeneity and dynamics with unprecedented spatial and temporal resolution has motivated extensive effort to develop amino acids with functional groups that have frequency-resolved absorptions to serve as probes of their protein microenvironments. We demonstrate the full advantage of the approach by selective incorporation of the probe p-cyanophenylalanine at six distinct sites in a Src homology 3 domain and the application of 2D IR spectroscopy to site-specifically characterize heterogeneity and dynamics and their contribution to cognate ligand binding. The approach revealed a wide range of microenvironments and distinct responses to ligand binding, including at the three adjacent, conserved aromatic residues that form the recognition surface of the protein. Molecular dynamics simulations performed for all the labeled proteins provide insight into the underlying heterogeneity and dynamics. Similar application of 2D IR spectroscopy and site-selective probe incorporation will allow for the characterization of heterogeneity and dynamics of other proteins, how heterogeneity and dynamics are affected by solvation and local structure, and how they might contribute to biological function.

Quantifying conformations of ester vibrational probes with hydrogen-bond-induced Fermi resonances

Solvatochromic shifts of local vibrational probes report on the strength of the surrounding electric fields and the probe's hydrogen bonding status. Stretching vibrational mode of the ester carbonyl group is a popular solvatochromic reporter used in the studies of peptides and proteins. Small molecules, used to calibrate the response of the vibrational probes, sometimes involve Fermi resonances (FRs) induced by inter-molecular interactions. In the present work, we focus on the scenario where FR does not appear in the infrared spectrum of the ester carbonyl stretching mode in aprotic solvents; however, it is intensified when a hydrogen bond with the reporter is established. When two molecules form hydrogen bonds to the same carbonyl oxygen atom, FR leads to strong hybridization of the involved modes and splitting of the absorption peak. Spectral overlap between the Fermi doublets associated with singly and doubly hydrogen-bonded carbonyl groups significantly complicates quantifying different hydrogen-bonded conformations. We employed a combination of linear and third-order (2DIR) infrared spectroscopy with chemometrics analysis to reveal the individual line shapes and to estimate the occupations of the hydrogen-bonded conformations in methyl acetate, a model small molecule. We identified a hydrogen-bond-induced FR in complexes of methyl acetate with alcohols and water and found that FR is lifted in larger molecules used for control experiments-cholesteryl stearate and methyl cyanoacetate. Applying this methodology to analyze acetonitrile-water solutions revealed that when dissolved in neat water, methyl acetate occupies a single hydrogen-bonding conformation, which is in contrast to the conclusions of previous studies. Our approach can be generally used when FRs prevent direct quantification of the hydrogen bonding status of the vibrational probe.

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.

Long-Range Modulations of Electric Fields in Proteins

Electrostatic interactions are essential for controlling the protein structure and function. Whereas so far experimental and theoretical efforts focused on the effect of local electrostatics, this work aims at elucidating the long-range modulation of electric fields in proteins upon binding to charged surfaces. The study is based on cytochrome c (Cytc) variants carrying nitrile reporters for the vibrational Stark effect that are incorporated into the protein via genetic engineering and chemical modification. The Cytc variants were thoroughly characterized with respect to possible structural perturbations due to labeling. For the proteins in solution, the relative hydrogen bond occupancy and the calculated electric fields, both obtained from molecular dynamics (MD) simulations, and the experimental nitrile stretching frequencies were used to develop a relationship for separating hydrogen-bonding and non-hydrogen-bonding electric field effects. This relationship provides an excellent description for the stable Cytc variants in solution. For the proteins bound to Au electrodes coated with charged self-assembled monolayers (SAMs), the underlying MD simulations can only account for the electric field changes Δ E_ads due to the formation of the electrostatic SAM-Cytc complexes but not for the additional contribution, Δ E_int, representing the consequences of the potential drops over the electrode/SAM/protein interfaces. Both Δ E_ads and Δ E_int, determined at distances between 20 and 30 Å with respect to the SAM surface, are comparable in magnitude to the non-hydrogen-bonding electric field in the unbound protein. This long-range modulation of the internal electric field may be of functional relevance for proteins in complexes with partner proteins (Δ E_ads) and attached to membranes (Δ E_ads + Δ E_int).

Mesh-free hierarchical clustering methods for fast evaluation of electrostatic interactions of point multipoles

Electrostatic interactions involving point multipoles are being increasingly implemented to achieve higher accuracy in molecular simulations. A major drawback of multipolar electrostatics is the increased computational cost. Here we develop and compare two Cartesian tree algorithms which employ Taylor approximations and hierarchical clustering to speed up the evaluation of point multipole interactions. We present results from applying the algorithms to compute the free space Coulomb potential and forces of different sets of interacting point multipoles with different densities. The methods achieve high accuracy and speedup of more than an order of magnitude over direct sum calculations and scale well in parallel.

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.

Anomalies in the equilibrium and nonequilibrium properties of correlated ions in complex molecular environments

Emergent statistical attributes, and therefore the equations of state, of an assembly of interacting charge carriers embedded within a complex molecular environment frequently exhibit a variety of anomalies, particularly in the high-density (equivalently, the concentration) regime, which are not well understood, because they do not fall under the low-concentration phenomenologies of Debye-Hückel-Onsager and Poisson-Nernst-Planck, including their variants. To go beyond, we here use physical concepts and mathematical tools from quantum scattering theory, transport theory with the Stosszahlansatz of Boltzmann, and classical electrodynamics (Lorentz gauge) and obtain analytical expressions both for the average and the frequency-wave vector-dependent longitudinal and transverse current densities, diffusion coefficient, and the charge density, and therefore the analytical expressions for (a) the chemical potential, activity coefficient, and the equivalent conductivity for strong electrolytes and (b) the current-voltage characteristics for ion-transport processes in complex molecular environments. Using a method analogous to the notion of Debye length and thence the electrical double layer, we here identify a pair of characteristic length scales (longitudinal and the transverse), which, being wave vector and frequency dependent, manifestly exhibit nontrivial fluctuations in space-time. As a unifying theme, we advance a quantity (inverse length dimension), g_{scat}^{(a)}, which embodies all dynamical interactions, through various quantum scattering lengths, relevant to molecular species a, and the analytical behavior which helps us to rationalize the properties of strong electrolytes, including anomalies, in all concentration regimes. As an example, the behavior of g_{scat}^{(a)} in the high-concentration regime explains the anomalous increase of the Debye length with concentration, as seen in a recent experiment on electrolyte solutions. We also put forth an extension of the standard diffusion equation, which manifestly incorporates the effects arising from the underlying microscopic collisions among constituent molecular species. Furthermore, we show a nontrivial connection between the current-voltage characteristics of electrolyte solutions and the Landauer's approach to electrical conduction in mesoscopic solids and thereby establish a definite conceptual bridge between the two disjoint subjects. For numerical insight, we present results on the aqueous solution of KCl as an example of strong electrolyte, and the transport (conduction as well as diffusion) of K^{+} ions in water, as an example of ion transport across the voltage-gated channels in biological cells.

Water Dynamics in the Hydration Shells of Biomolecules

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Accurate Classical Polarization Solution with No Self-Consistent Field Iterations

We present a new solution for classical polarization that does not require any self-consistent field iterations, the aspect of classical polarization that makes it computationally expensive. The new method builds upon our iEL/SCF Lagrangian scheme that defines a set of auxiliary induced dipoles whose original purpose was to serve as a time-reversible initial guess to the SCF solution of the set of real induced dipoles. In the new iEL/0-SCF approach the auxiliary dipoles now drive the time evolution of the real induced dipoles such that they stay close to the Born-Oppenheimer surface in order to achieve a truly SCF-less method. We show that the iEL/0-SCF exhibits no loss of simulation accuracy when analyzed across bulk water, low to high concentration salt solutions, and small solutes to large proteins in water. In addition, iEL/0-SCF offers significant computational savings over more expensive SCF calculations based on traditional 1 fs time step integration using symplectic integrators and is as fast as reversible reference system propagator algorithms with an outer 2 fs time step.