Calculations of the electric fields in liquid solutions

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.

Insights into acid dissociation of HCl and HBr with internal electric fields

A critical electric field exerted by the solvent on the ionizable group leads to acid dissociation.

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise-additive force field. Although AMOEBA results give mean errors close to "chemical accuracy," GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non-potential-specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Advanced Potential Energy Surfaces for Molecular Simulation

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

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.

Evaluating Parametrization Protocols for Hydration Free Energy Calculations with the AMOEBA Polarizable Force Field

Hydration free energy (HFE) calculations are often used to assess the performance of biomolecular force fields and the quality of assigned parameters. The AMOEBA polarizable force field moves beyond traditional pairwise additive models of electrostatics and may be expected to improve upon predictions of thermodynamic quantities such as HFEs over and above fixed-point-charge models. The recent SAMPL4 challenge evaluated the AMOEBA polarizable force field in this regard but showed substantially worse results than those using the fixed-point-charge GAFF model. Starting with a set of automatically generated AMOEBA parameters for the SAMPL4 data set, we evaluate the cumulative effects of a series of incremental improvements in parametrization protocol, including both solute and solvent model changes. Ultimately, the optimized AMOEBA parameters give a set of results that are not statistically significantly different from those of GAFF in terms of signed and unsigned error metrics. This allows us to propose a number of guidelines for new molecule parameter derivation with AMOEBA, which we expect to have benefits for a range of biomolecular simulation applications such as protein-ligand binding studies.

Conformational Heterogeneity in the Michaelis Complex of Lactate Dehydrogenase: An Analysis of Vibrational Spectroscopy Using Markov and Hidden Markov Models

Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate. Recent isotope-edited IR spectroscopy suggests that conformational heterogeneity exists within the Michaelis complex of LDH, and this heterogeneity affects the propensity toward the on-enzyme chemical step for each Michaelis substate. By combining molecular dynamics simulations with Markov and hidden Markov models, we obtained a detailed kinetic network of the substates of the Michaelis complex of LDH. The ensemble-average electric fields exerted onto the vibrational probe were calculated to provide a direct comparison with the vibrational spectroscopy. Structural features of the Michaelis substates were also analyzed on atomistic scales. Our work not only clearly demonstrates the conformational heterogeneity in the Michaelis complex of LDH and its coupling to the reactivities of the substates, but it also suggests a methodology to simultaneously resolve kinetics and structures on atomistic scales, which can be directly compared with the vibrational spectroscopy.

Internal electric fields in small water clusters [(H2O)n; n = 2-6]

The electric field experienced by a water molecule within a water cluster depends on its position relative to the rest of the water molecules. The stabilization energies and the red-shifts in the donor O-H stretching vibrations in the water clusters increase with the cluster size concomitant with the increase in the electric field experienced by the donor O-H of a particular water molecule due to the hydrogen bonding network. The red-shifts in O-H stretching frequencies show a spread of about ±100 cm(-1) against the corresponding electric fields. Deviations from linearity were marked in the region of 100-160 MV cm(-1), which can be attributed to the strain in the hydrogen bonding network, especially for structures with DDAA and DDA motifs. The linear Stark effect holds up to 200 MV cm(-1) of internal electric field for the average red-shifts in the O-H stretching frequencies, with a Stark tuning rate of 2.4 cm(-1) (MV cm(-1))(-1), suggesting the validity of the classical model in small water clusters.

Dual Ionic and Organic Nature of Ionic Liquids

Inherited the advantages of inorganic salts and organic solvents, ionic liquids (ILs) exhibit many superior properties allowing them promising green solvents for the future. Although it has been widely acknowledged that the unique features of ILs originate from their dual ionic and organic nature, its microscopic physical origin still remains blurry. In this work, by comparing the ion/molecule cage structures obtained from molecular dynamics simulations for seven prototypic liquids--a molten inorganic salt, four ILs, a strongly polar organic solvent, and a weakly polar organic solvent, we have revealed that the depth of the cage energy landscape characterizes the ionic nature of ILs, whereas the slope and curvature of its mimimum determine the organic nature of ILs. This finding advances our understanding of ILs and thus will help their efficient utilization as well as the systematic design of novel functionalized ILs.

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.

Excited states in large molecular systems through polarizable embedding

Using the polarizable embedding model enables rational design of light-sensitive functional biological materials.

Molecular quantum mechanical gradients within the polarizable embedding approach--application to the internal vibrational Stark shift of acetophenone

We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn-Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C=O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange-repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters.

ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB

Molecular mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Average errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a physically motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reproduction of NMR χ1 scalar coupling measurements for proteins in solution. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.

Two-photon voltmeter for measuring a molecular electric field

We present a new approach for determining the strength of the dipolar solute-induced reaction field, along with the ground- and excited-state electrostatic dipole moments and polarizability of a solvated chromophore, using exclusively one-photon and two-photon absorption measurements. We verify the approach on two benchmark chromophores N,N-dimethyl-6-propionyl-2-naphthylamine (prodan) and coumarin 153 (C153) in a series of toluene/dimethyl sulfoxide (DMSO) mixtures and find that the experimental values show good quantitative agreement with literature and our quantum-chemical calculations. Our results indicate that the reaction field varies in a surprisingly broad range, 0-10(7)  V cm(-1) , and that at close proximity, on the order of the chromophore radius, the effective dielectric constant of the solute-solvent system displays a unique functional dependence on the bulk dielectric constant, offering new insight into the close-range molecular interaction.

Measuring electric fields and noncovalent interactions using the vibrational stark effect

Over the past decade, we have developed a spectroscopic approach to measure electric fields inside matter with high spatial (<1 Å) and field (<1 MV/cm) resolution. The approach hinges on exploiting a physical phenomenon known as the vibrational Stark effect (VSE), which ultimately provides a direct mapping between observed vibrational frequencies and electric fields. Therefore, the frequency of a vibrational probe encodes information about the local electric field in the vicinity around the probe. The VSE method has enabled us to understand in great detail the underlying physical nature of several important biomolecular phenomena, such as drug-receptor selectivity in tyrosine kinases, catalysis by the enzyme ketosteroid isomerase, and unidirectional electron transfer in the photosynthetic reaction center. Beyond these specific examples, the VSE has provided a conceptual foundation for how to model intermolecular (noncovalent) interactions in a quantitative, consistent, and general manner. The starting point for research in this area is to choose (or design) a vibrational probe to interrogate the particular system of interest. Vibrational probes are sometimes intrinsic to the system in question, but we have also devised ways to build them into the system (extrinsic probes), often with minimal perturbation. With modern instruments, vibrational frequencies can increasingly be recorded with very high spatial, temporal, and frequency resolution, affording electric field maps correspondingly resolved in space, time, and field magnitude. In this Account, we set out to explain the VSE in broad strokes to make its relevance accessible to chemists of all specialties. Our intention is not to provide an encyclopedic review of published work but rather to motivate the underlying framework of the methodology and to describe how we make and interpret the measurements. Using certain vibrational probes, benchmarked against computer models, it is possible to use the VSE to measure absolute electric fields in arbitrary environments. The VSE approach provides an organizing framework for thinking generally about intermolecular interactions in a quantitative way and may serve as a useful conceptual tool for molecular design.

Extreme electric fields power catalysis in the active site of ketosteroid isomerase

Enzymes use protein architecture to impose specific electrostatic fields onto their bound substrates, but the magnitude and catalytic effect of these electric fields have proven difficult to quantify with standard experimental approaches. Using vibrational Stark effect spectroscopy, we found that the active site of the enzyme ketosteroid isomerase (KSI) exerts an extremely large electric field onto the C=O chemical bond that undergoes a charge rearrangement in KSI's rate-determining step. Moreover, we found that the magnitude of the electric field exerted by the active site strongly correlates with the enzyme's catalytic rate enhancement, enabling us to quantify the fraction of the catalytic effect that is electrostatic in origin. The measurements described here may help explain the role of electrostatics in many other enzymes and biomolecular systems.

Site-specific infrared probes of proteins

Infrared spectroscopy has played an instrumental role in the study of a wide variety of biological questions. However, in many cases, it is impossible or difficult to rely on the intrinsic vibrational modes of biological molecules of interest, such as proteins, to reveal structural and environmental information in a site-specific manner. To overcome this limitation, investigators have dedicated many recent efforts to the development and application of various extrinsic vibrational probes that can be incorporated into biological molecules and used to site-specifically interrogate their structural or environmental properties. In this review, we highlight recent advancements in this rapidly growing research area.

Experimental Determination of the Electrostatic Nature of Carbonyl Hydrogen-Bonding Interactions Using IR-NMR Correlations

Hydrogen-bonding plays a fundamental role in the structure, function, and dynamics of various chemical and biological systems. Understanding the physical nature of interactions and the role of electrostatics in hydrogen-bonding has been the focus of several theoretical and computational research. We present an experimental approach involving IR-(13)C NMR correlations to determine the electrostatic nature of carbonyl hydrogen-bonding interactions. This report provides a direct experimental evidence of the classical nature of hydrogen-bonding interaction in carbonyls, independent of any theoretical approximation. These results have important implications in chemistry and biology and can be applied to probe the reaction mechanisms involving carbonyl activation/stabilization by hydrogen bonds using spectroscopic techniques.

Probing the electrostatics of active site microenvironments along the catalytic cycle for Escherichia coli dihydrofolate reductase

Electrostatic interactions play an important role in enzyme catalysis by guiding ligand binding and facilitating chemical reactions. These electrostatic interactions are modulated by conformational changes occurring over the catalytic cycle. Herein, the changes in active site electrostatic microenvironments are examined for all enzyme complexes along the catalytic cycle of Escherichia coli dihydrofolate reductase (ecDHFR) by incorporation of thiocyanate probes at two site-specific locations in the active site. The electrostatics and degree of hydration of the microenvironments surrounding the probes are investigated with spectroscopic techniques and mixed quantum mechanical/molecular mechanical (QM/MM) calculations. Changes in the electrostatic microenvironments along the catalytic environment lead to different nitrile (CN) vibrational stretching frequencies and ¹³C NMR chemical shifts. These environmental changes arise from protein conformational rearrangements during catalysis. The QM/MM calculations reproduce the experimentally measured vibrational frequency shifts of the thiocyanate probes across the catalyzed hydride transfer step, which spans the closed and occluded conformations of the enzyme. Analysis of the molecular dynamics trajectories provides insight into the conformational changes occurring between these two states and the resulting changes in classical electrostatics and specific hydrogen-bonding interactions. The electric fields along the CN axes of the probes are decomposed into contributions from specific residues, ligands, and solvent molecules that make up the microenvironments around the probes. Moreover, calculation of the electric field along the hydride donor–acceptor axis, along with decomposition of this field into specific contributions, indicates that the cofactor and substrate, as well as the enzyme, impose a substantial electric field that facilitates hydride transfer. Overall, experimental and theoretical data provide evidence for significant electrostatic changes in the active site microenvironments due to conformational motion occurring over the catalytic cycle of ecDHFR.

Ester carbonyl vibration as a sensitive probe of protein local electric field

The ability to quantify the local electrostatic environment of proteins and protein/peptide assemblies is key to gaining a microscopic understanding of many biological interactions and processes. Herein, we show that the ester carbonyl stretching vibration of two non-natural amino acids, L-aspartic acid 4-methyl ester and L-glutamic acid 5-methyl ester, is a convenient and sensitive probe in this regard, since its frequency correlates linearly with the local electrostatic field for both hydrogen-bonding and non-hydrogen-bonding environments. We expect that the resultant frequency-electric-field map will find use in various applications. Furthermore, we show that, when situated in a non-hydrogen-bonding environment, this probe can also be used to measure the local dielectric constant (ε). For example, its application to amyloid fibrils formed by Aβ(16-22) revealed that the interior of such β-sheet assemblies has an ε value of approximately 5.6.

Modeling organochlorine compounds and the σ-hole effect using a polarizable multipole force field

The charge distribution of halogen atoms on organochlorine compounds can be highly anisotropic and even display a so-called σ-hole, which leads to strong halogen bonds with electron donors. In this paper, we have systematically investigated a series of chloromethanes with one to four chloro substituents using a polarizable multipole-based molecular mechanics model. The atomic multipoles accurately reproduced the ab initio electrostatic potential around chloromethanes, including CCl₄, which has a prominent σ-hole on the Cl atom. The van der Waals parameters for Cl were fitted to the experimental density and heat of vaporization. The calculated hydration free energy, solvent reaction fields, and interaction energies of several homo- and heterodimer of chloromethanes are in good agreement with experimental and ab initio data. This study suggests that sophisticated electrostatic models, such as polarizable atomic multipoles, are needed for accurate description of electrostatics in organochlorine compounds and halogen bonds, although further improvement is necessary for better transferability.