Effects Of Long-range Electrostatic Interactions Research Articles

Cluster expansions of multicomponent ionic materials: Formalism and methodology

The cluster expansion (CE) method has seen continuous and increasing use in the study of configuration-dependent properties of crystalline materials. The original development of the CE method along with the underlying mathematical formalism and assumptions was focused on the study of metallic alloys. Since then the methodology has been actively and successfully used in the study of ionic materials as well. In this work, we present a cohesive reformulation of the mathematical formalism underlying the CE method based on a synthesis of its original formulation, several additions and extensions that have been proposed since, and a revised representation of its constituent mathematical objects. We then proceed to describe some of the formal implications of using the methodology for charge-neutral configurations in ionic systems. In particular, we discuss the reduction of the size of configuration spaces and the resulting linear dependencies that arise among correlation functions that span the larger unconstrained configuration space. Additionally, we explore the effects of long-range electrostatic interactions. We also demonstrate how the previously proposed use of a point electrostatic term successfully accounts for the majority of the longer-range electrostatic interactions, and leaves the cluster expansion terms to capture mostly short-range interactions. Finally, we present and discuss a variety of recently developed methodologies, including training structure selection, oxidation state assignment, structure mapping, and regression algorithms, that are necessary to address these formal mathematical notions for a practical implementation of the CE method in the study of multicomponent ionic materials.

Thermal fluctuations in crystalline membranes with long-range dipole interactions

We study the effects of long-range electrostatic interactions on the thermal fluctuations of free-standing crystalline membranes exhibiting spontaneous electric polarization directed at each point along the local normal to the surface. We show that the leading effect of dipole–dipole interactions in the long-wavelength limit consists in renormalizations of the bending rigidity and the elastic coefficients. A completely different result was obtained in the case of scalar two-point interactions decaying as R−3, where R is the distance. In the latter case, which was addressed in previous theoretical research, the energy of long-wavelength bending fluctuations is controlled by power-law interactions and it scales with the wavevector q as q3, leading to a modified large-distance behaviour of correlation functions. By contrast, in the case of dipole interactions, the q3 dependence of the bending energy vanishes. Non-local terms generated by the expansion of the electrostatic energy are suppressed in the limit of small wavevectors. This suggests that the universal scaling behaviour of elastic membranes holds even in presence of dipole interactions. At the same time, the shift of the Lamé coefficients and the bending rigidity induced by electrostatic interactions can be quantitatively important for two-dimensional materials with a permanent out-of-plane polarization.

QM/MM hybrid calculation of biological macromolecules using a new interface programconnecting QM and MM engines

An interface program connecting a quantum mechanics (QM) calculation engine,GAMESS, and a molecular mechanics (MM) calculation engine, AMBER, has beendeveloped for QM/MM hybrid calculations. A protein–DNA complex is used as a testsystem to investigate the following two types of QM/MM schemes. In a ‘subtractive’scheme, electrostatic interactions between QM/MM regions are truncated in QMcalculations; in an ‘additive’ scheme, long-range electrostatic interactions within a cut-offdistance from QM regions are introduced into one-electron integration terms of a QMHamiltonian. In these calculations, 338 atoms are assigned as QM atoms usingHartree–Fock (HF)/density functional theory (DFT) hybrid all-electron calculations. Bycomparing the results of the additive and subtractive schemes, it is found that electronicstructures are perturbed significantly by the introduction of MM partial chargessurrounding QM regions, suggesting that biological processes occurring in functional sitesare modulated by the surrounding structures. This also indicates that the effects oflong-range electrostatic interactions involved in the QM Hamiltonian are crucialfor accurate descriptions of electronic structures of biological macromolecules.

Modeling Subtype-Selective Agonists Binding with α4β2 and α7 Nicotinic Acetylcholine Receptors: Effects of Local Binding and Long-Range Electrostatic Interactions

The subtype-selective binding of 14 representative agonists with alpha4beta2 and alpha7 nicotinic acetylcholine receptors (nAChRs) has been studied by performing homology modeling, molecular docking, geometry optimizations, and microscopic and phenomenological binding free energy calculations. All of the computational results demonstrate that the subtype selectivity of the agonists binding with alpha4beta2 and alpha7 7 nAChRs is affected by both local binding and long-range electrostatic interactions between the receptors and the protonated structures of the agonists. The effects of the long-range electrostatic interactions are mainly due to the distinct difference in the net charge of the ligand-binding domain between the two nAChR subtypes. For the alpha4beta2-selective agonists examined, the microscopic binding modes with the alpha4beta2 nAChR are very similar to the corresponding modes with the alpha7 nAChR, and therefore, the subtype selectivity of these agonists binding with alpha4beta2 and alpha7 nAChRs is dominated by the long-range electrostatic interactions. For the alpha7-selective agonists, their microscopic binding modes with the alpha7 nAChR are remarkably different from those with the alpha4beta2 nAChR so that the local binding (including the hydrogen bonding and cation-pi interactions) with the alpha7 nAChR is much stronger than that with the alpha4beta2 nAChR. The calculated phenomenological binding free energies are in good agreement with available experimental data for the relative binding free energies concerning the subtype selectivity of agonists binding with the two different nAChR subtypes. The fundamental insights obtained in the present study should be valuable for future rational design of potential therapeutic agents targeted to specific nAChR subtypes.

Molecular crystals: the crystal field effect on molecular electronic structure.

The effect of crystal packing on the electronic structure of organic molecules was modeled by incorporation of the external electrostatic potential into the semiempirical Hamiltonian of the molecule. An empirical correction procedure was devised in order to compensate for systematic errors in the charge distribution typical of semiempirical methods. The model was applied to 79 crystal structures belonging to various syngonies and space groups. The effect of the crystal field is subject to wide variations depending on the crystal packing motif. The difference between the effect of the crystal field on the molecular electronic structure and the solvent effect modeled with COSMO is highlighted. The effect of intermolecular hydrogen bonds on the molecular electronic structure and electronic spectra was modeled with this approach, and it does not predominate over the effect of long-range electrostatic interactions. INDO/S calculations employing the crystal electrostatic potential give an insight into the origin of crystallochromy, in particular, they properly predict color difference for several groups of polymorphs.

CALCULATING ACCURATE REDOX POTENTIALS IN ENZYMES WITH A COMBINED QM/MM FREE ENERGY PERTURBATION APPROACH

An approach for computing accurate redox potentials in enzymes is developed based on the free energy perturbation technique in a QM/MM framework. With an appropriate choice of the QM level and QM/MM coupling scheme, the intermolecular interaction between the redox center and the protein environment can be adequately described; the speed of QM/MM methods also allows a sufficient configurational sampling for the convergence of free energy derivatives. Following the implementation into the simulation package CHARMM, the method was tested with an application to the first reduction potential of FAD in cholesterol oxidase (Chox). In addition to an accurate QM level and adequate conformational samplings, the effect of long-range electrostatic interactions due to the bulk solvent was also found to be essential. Using a semi-empirical density functional theory (SCC-DFTB) as the QM level, and a multi-stage charge-scaling scheme based on Poisson–Boltzmann calculations for the solvation effect, satisfactory agreements with experimental measurements were obtained. The study of Chox also indicates that large errors in the calculated redox potential might arise if changes in the conformational properties of the protein during the redox process are not taken into account, such as in energy minimization type of studies based on only the X-ray structure of the enzyme in one redox state.

Electrochemical promotion of catalysis: the use of transition state theory for the prediction of reaction rate modification

A simple model to describe rate changes during the reversible electrochemical promotion of supported metal catalysts has been formulated. Polarisation of the interface between the ion-conducting support and the metal modifies the electron extraction potential of the metal as a result of the spillover of ionic oxygen species. By considering a simple reaction mechanism that involves a charged transition state and accounting for the effect of long-range electrostatic interactions, it is possible to express reaction rates as a function of applied overpotential. It is shown that under certain conditions reaction rates are predicted to increase on application of both negative and positive overpotentials, in agreement with some experimental studies (e.g. Refs. [Catal. Today 11 (1992) 303; J. Catal. 159 (1996) 189]), as a result of electron donation and acceptance from both the metal catalyst and the surface O/O 2− redox couple.

Energy correction to simulation of volume polarization in reaction field theory

Reaction field theory is useful in electronic structure calculations of solute properties to evaluate the effects of long-range electrostatic interactions with solvent. The reaction field is affected by quantum mechanical penetration of solute charge density outside the surface of the solvent cavity that nominally encloses it. Exact treatment of the effect of this charge penetration is possible, within the context of a simple dielectric continuum model, by invoking a certain volume polarization in addition to the usually treated surface polarization. However, with general nonspherical molecular cavities this is difficult and computationally demanding to handle, so more tractable means to optimally simulate or otherwise approximate the effect of volume polarization in terms of modified surface polarization are useful in practice. This work proposes and tests a simple formula for a correction term to estimate the energy difference between exact treatment of volume polarization and its optimal surface simulation.

Molecular Dynamics of the tRNAAla Acceptor Stem: Comparison between Continuum Reaction Field and Particle-Mesh Ewald Electrostatic Treatments

Molecular dynamics simulations with an explicit solvent model are used to investigate the effect of long-range electrostatic interactions on the structure and dynamics of a 22-nucleotide RNA hairpin in solution, the E. coli tRNA A l a minihelix 5p-GGGGCUC(UUCG)GAGCUCC(ACCA). Two different treatments of long-range electrostatics are compared: a continuum reaction field method (CRF; two 1.2 ns simulations) and the particle-mesh Ewald method (PME; one 2.5 ns simulation). The reaction field simulations are the first for an RNA solute. The simulations converge rapidly to within 1.5 A of each other and of the X-ray structure, despite two starting conformations (taken from the ensemble of NMR structures) that differ from each other by 3.3 A and from the X-ray structure by 1.3 and 2.1 A, respectively. After 1000 ps of one CRF simulation, the helix begins to unfold, with the first two base pairs opening. Except for the last part of this simulation, the RNA helical parameters and atomic fluctuations and the solvent structure around the G3.U16 wobble pair are all in good agreement with experiment and between simulations, whereas counterions are more ordered with PME than with CRF.

Electrochemical Promotion of Catalysis: II: The Role of a Stable Spillover Species and Prediction of Reaction Rate Modification

A simple model to describe the reversible electrochemical promotion of supported metal catalysts has been formulated. This model is derived from first principles and allows for the presence of two forms of catalyst surface oxygen, one ionic and one neutral. Both forms of surface oxygen are able to undergo charge-transfer reactions with the solid–electrolyte ion-conducting support. The ionic oxygen is assumed to be the only ion present with a significant surface coverage and, as such, dictates the properties of the catalyst surface double layer. Using the adsorption isotherm for oxygen ions it is easy to show that in the presence of significant lateral interactions the change in catalyst surface potential must be less than the overpotential applied to the catalyst/support interface. By considering a simple reaction mechanism that involves a charged transition state and accounting for the effect of long-range electrostatic interactions it is possible to express reaction rates as a function of applied overpotential. It is shown that under certain conditions reaction rates are predicted to increase on application of both negative and positive overpotentials (for both positively charged and negatively charged transition states), in agreement with some experimental studies, as a result of electron donation and acceptance from both the metal catalyst and the surface O/O2− redox couple. In addition the enhancement factor (the ratio of change in reaction rate to electrochemical oxygen flux) is shown to depend upon the selectivity for oxygen ion formation from charge-transfer and adsorption processes.

Long-range electrostatic effects on peptide folding

The reversible folding/unfolding of a short peptide in solution is studied by molecular dynamics simulations. The effects of long-range electrostatic interactions are examined and found to be important both for the equilibrium between folded and unfolded states and the dynamics of the folding process. The neglect of long-range electrostatics leads to an increased population of unfolded states and increased structural fluctuations. When such interactions are taken into account, the peptide unfolds and folds to the experimentally determined structure several times during a 25 ns trajectory, with approximately equal populations of folded and unfolded states in the neighborhood of its proposed melting temperature. The effect of using spherical boundary conditions rather than periodic ones does not appear to have any major effect on the folding dynamics.

Calculation of absolute binding free energies for charged ligands and effects of long-range electrostatic interactions

Calculation of Absolute Binding Free Energies for Charged Ligands and the Effects of Long-Range Electrostatic Interactions

The effect of long-range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods

Simulations of the HIV-1 protease unit cell using a 9 Å cutoff, 9/18 Å ‘‘twin-range’’ cutoff, and full Ewald sums have been carried out to 300 ps. The results indicate that long-range electrostatic interactions are essential for proper representation of the HIV-1 protease crystal structure. The 9 Å simulation did not converge in 300 ps. Inclusion of a 9/18 Å ‘‘twin-range’’ cutoff showed significant improvement. Simulation using the Ewald summation convention gave the best overall agreement with x-ray crystallographic data, and showed the least internal differences in the time average structures of the asymmetric units. The Ewald simulation represents an efficient implementation of the Particle Mesh Ewald method [Darden et al., J. Chem. Phys. 98, 10 089 (1993)], and illustrates the importance of including long-range electrostatic forces in large macromolecular systems.