Polarizable Point Research Articles

"Blade of Polarized Water Molecule" Is the Key to Hydrolase Catalysis Regulation.

Hydrolysis catalyzed by aspartic proteases is a crucial reaction in many biological processes. However, anchoring water molecules and unifying multiple catalytic pathways remain significant challenges. Consequently, molecular design often compromises by focusing on enhancing substrate specificity. Using our self-developed polarizable point charge (PPC) force field, we determined the significant role of polarization in the hydrolase of pepsin for the first time. To be stably anchored in the active site, the water should be intensely polarized with a charge higher than -0.94e. Induced by this polarization, the pepsin was shown to support three general base/general acid pathways, with a preference for the gemdiol-intermediate-based pathway. Consequently, we proposed the "Blade of Polarized Water Molecule" model for rational enzyme design, highlighting that the polarization of both the attacking water and the attacked carbonyl is crucial for enhancing hydrolysis. Mutants D290Q and S172P showed activity enhancements of 191.23% and 324.70%, respectively. The improved polarization of water, carbonyl, and relevant nucleophilic attack distances in the mutants reaffirmed the crucial role of polarization in improving hydrolysis. This study provides a new perspective on hydrolase analysis and modification.

Lattice relaxation effects on the collective resonance spectra of a finite dipole array.

Dielectric/plasmonic lattice relaxation spectroscopy is theoretically discussed in this work. A lattice relaxation effect generally occurs in nanocrystals, which means that from the bulk phase to the crystal surface, lattice parameters show a gradual shift. Here, lattice relaxation is introduced into finite polarizable point arrays or rod arrays as an adjusting tool, and its effect on lattice resonance extinction spectrum peaks is calculated. DDA (discrete dipole approximation) and FDTD (finite difference time domain) methods are applied. Different from an ideal infinite array, a finite array exhibits a broad, rippled extinction spectral peak. The application of an expanded/contracted lattice relaxation to the finite array can compress the ripple on one shoulder of the peak, as a cost, and the other shoulder of the peak gets more rippled, showing a "ripple transfer" effect. The strategy introduced in this work can contribute to the micro/nano optical measurement, on-chip adjustable optical cavity for OPOs (optical parameter oscillators)/lasers and controlling of fluorescence or hot-electron chemistry.

Investigation of the Second Harmonic Generation at the Water-Vacuum Interface by Using Multi-Scale Modeling Methods.

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water-vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the βHRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (βzzz ) as well as of β// . Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.

The role of distributed atomic point charges and polarizabilities of solvent molecules on one‐ and two‐photon absorption spectra of aqueous p‐nitroaniline

AbstractIn this work, we demonstrated the electrostatic and polarization effects created from distributed atomic point charges and polarizabilities of solvent molecules, respectively, when calculating optical response properties of solution‐phase molecule within the context of the discrete solvent reaction field. Aqueous p‐nitroaniline molecule was selected as the model system for our research purpose. One‐ and two‐photon absorption spectra were constructed by carrying out the damped response theory calculations within time‐dependent density functional theory. As compared to the full treatment, we investigated different effects of electrostatics and polarizations on spectral parameters of interest. Our calculations showed that the larger contributions to the calculated red shift in excitation energy was from electrostatic term, but polarization contribution was comparable in magnitude. On the other hand, electrostatic term was the principal feature for absorption strength and spectral width.

Electromagnetic curves of the polarized light wave along the optical fiber in De-Sitter 2-space $${\mathbb{S}}_{1}^{2}$$

We review the geometric evolution of a linearly polarized light wave coupling into an optical fiber and the rotation of the polarization plane in De-Sitter 2-space. The optical fiber is assumed to be a one-dimensional object imbedded in the De-Sitter 2-space $${\mathbb{S}} _{1}^{2}$$ along with the paper. Mathematically, De-Sitter 2-space $${\mathbb{S}}_{1}^{2}$$ is described to be a 2-sphere in a Lorentzian space with positive curvature. Thus, in the De-Sitter 2-space, we have demonstrated that the evolution of a linearly polarized light wave is associated with the Berry phase or more commonly known as the geometric phase. The ordinary condition for parallel transportation is defined by the Fermi–Walker parallelism law. We define other Fermi–Walker parallel transportation laws and connect them with the famous Rytov parallel transportation law for an electric field $${\mathcal{E}}$$ , which is considered as the direction of the state of the linearly polarized light wave traveling through the optical fiber in De-Sitter 2-space. Later, we have defined a special class of magnetic curves called by Lorentzian spherical electromagnetic curves ( $${\mathcal{LSEM}}$$ curves), which are generated by the electric field $${\mathcal{E}}$$ along with the linearly polarized monochromatic light wave propagating in the optical fiber. In this way, not only we are able to define a special class of linearly polarized point particles corresponding to $${\mathcal{LSEM}}$$ -curves of the electromagnetic field along with the optical fiber in the De-Sitter 2-space, but we can also calculate, both numerically and analytically, the electromagnetic force, Poynting vector, energy-exchanges rate, optical angular and linear momentum, and optical magnetic torque experienced by the linearly polarizable point particles along with the optical fiber in the De-Sitter 2-space.

The Role of Computational Chemistry in the Experimental Determination of the Dipole Moment of Molecules in Solution.

The methods for the experimental determination of electric dipole moment of molecules in solution from measurements of dielectric permittivity and refractive index are traditionally based on the classical Onsager model. In this model the molecular solute is approximated as a simple polarizable point dipole inside a spherical or ellipsoidal cavity of a dielectric medium representing the solvent. However, the inadequacies of the model resulting from the assumption of a simple shape of the cavity, for the evaluation of the cavity field effect, and from the uncertainty of the polarizability of the molecular solute influences the results and hampers the comparison with the electric dipole moments computed from quantum chemical solvation models. In this article we propose a new method for the experimental determination of the electric dipole moment in solution in which information from the Polarizable Continuum Model calculations are used in place of the Onsager model. The new method overcomes the limitations of this latter model regarding both the cavity field effect and the polarizability of the molecular solutes, and thus allows a coherent comparison between experimental and computed dipole moments of solvated molecules. © 2019 Wiley Periodicals, Inc.

Pushing the Limits of Multiple-Time-Step Strategies for Polarizable Point Dipole Molecular Dynamics.

We propose an incremental construction of multi-time-step integrators to accelerate polarizable point dipole molecular dynamics while preserving sampling efficiency. We start by building integrators using frequency-driven splittings of energy terms and a Velocity-Verlet evaluation of the most rapidly varying forces and compare a standard bonded/nonbonded split to a three-group split dividing nonbonded forces (including polarization) into short- and long-range contributions. We then introduce new approaches by coupling these splittings to Langevin dynamics and to Leimkuhler's BAOAB integrator in order to reach larger time steps (6 fs) for long-range forces. We further increase sampling efficiency by (i) accelerating the polarization evaluation using a fast/noniterative truncated conjugate gradient (TCG-1) as a short-range solver and (ii) pushing the outer time step to 10 fs using hydrogen mass repartitioning. The new BAOAB-RESPA1 integrators demonstrate up to a 7-fold acceleration over standard 1 fs (Tinker-HP) integration and reduce the performance gap between polarizable and classical force fields while preserving static and dynamical properties.

Extending electrostatics of dielectric spheres to arbitrary charge distributions with applications to biosystems.

A previously developed classical model of electrostatic interactions, based on a formalism of dielectric spheres, which has been found to have surprising accuracy for S state atoms, is extended by allowing higher-order moments of the intrinsic charge distribution. Two methods to introduce the charge distribution (point moments at the center vs surface charge) are shown to be equivalent and are compared with another common model for polarizable atoms that utilizes polarizable point dipoles. Unlike the polarizable point dipole model, the polarizable spheres models do not suffer from a divergence at small separation of atoms and are easily generalized to higher multipoles.

A New Method for Treating Drude Polarization in Classical Molecular Simulation.

With polarization becoming an increasingly common feature in classical molecular simulation, it is important to develop methods that can efficiently and accurately evaluate the many-body polarization solution. In this work, we expand the theoretical framework of our inertial extended Langrangian, self-consistent field iteration-free method (iEL/0-SCF), introduced for point induced dipoles, to the polarization model of a Drude oscillator. When applied to the polarizable simple point charge model (PSPC) for water, our iEL/0-SCF method for Drude polarization is as stable as a well-converged SCF solution and more stable than traditional extended Lagrangian (EL) approaches or EL formulations based on two temperature ensembles where Drude particles are kept "colder" than the real degrees of freedom. We show that the iEL/0-SCF method eliminates the need for mass repartitioning from parent atoms onto Drude particles, obeys system conservation of linear and angular momentum, and permits the extension of the integration time step of a basic molecular dynamics simulation to 6.0 fs for PSPC water.

Evaluation of Representations and Response Models for Polarizable Force Fields.

For classical simulations of condensed-phase systems, such as organic liquids and biomolecules, to achieve high accuracy, they will probably need to incorporate an accurate, efficient model of conformation-dependent electronic polarization. Thus, it is of interest to understand what determines the accuracy of a polarizable electrostatics model. This study approaches this problem by breaking polarization models down into two main components: the representation of electronic polarization and the response model used for mapping from an inducing field to the polarization within the chosen representation. Among the most common polarization representations are redistribution of atom-centered charges, such as those used in the fluctuating charge model, and atom-centered point dipoles, such as those used in a number of different polarization models. Each of these representations has been combined with one or more response models. The response model of fluctuating charge, for example, is based on the idea of electronegativity equalization in the context of changing electrostatic potentials (ESPs), whereas point-dipole representations typically use a response model based on point polarizabilities whose induced dipoles are computed based on interaction with other charges and dipoles. Here, we decouple polarization representations from their typical response models to analyze the strengths and weaknesses of various polarization approximations. First, we compare the maximal possible accuracies achievable by the charge redistribution and point-dipole model representations, by testing their ability to replicate quantum mechanical (QM) ESPs around small molecules polarized by external inducing charges. Perhaps not surprisingly, the atom-centered dipole model can yield higher accuracy. Next, we test two of the most commonly used response functions used for the point-dipole representations, self-consistent and direct (or first-order) inducible point polarizabilities, where the polarizabilities are optimized to best fit the full set of polarized QM potentials for each molecule studied. Strikingly, the induced-dipole response model markedly degrades accuracy relative to that obtainable with optimal point dipoles. In fact, the maximal accuracy achievable with this response model is even lower than that afforded by an optimal charge-redistribution representation. This means that, if coupled with a sufficiently accurate response function, the point-charge representation could outperform the standard induced-dipole model. Furthermore, although a key advantage of the point-dipole representation, relative to charge redistribution, is its ability to capture out-of-plane polarization, the inducible dipole response model causes it to be less accurate than optimal charge redistribution for out-of-plane induction of the planar nitrobenzene molecule. Thus, the widely used inducible dipole response function falls short of the full potential accuracy achievable with the point-dipole representation it employs. Additional results reported here bear on the relative accuracy of self-consistent inducible dipoles versus that of the first-order, or direct, approximation and on methods for assigning partial atomic charges for use in conjunction with inducible dipole models. In sum, these results point to the improvement of polarization response models as an important direction for future research aimed at improving the accuracy of molecular simulations.

Collective scattering and oscillation modes of optically bound point particles trapped in a single mode waveguide field.

Collective coherent scattering of laser light induces strong light forces between polarizable point particles. These dipole forces are strongly enhanced in magnitude and distance within the field of an optical waveguide so that at low temperature the particles self-order in strongly bound regular patterns. The stationary configurations typically exhibit super-radiant scattering with strong particle and light confinement. Here we study collective excitations of such self-consistent crystalline particle-light structures as function of particle number and pump strength. Multiple scattering and absorption modify the collective particle-field eigenfrequencies and create eigenmodes of surprisingly complex nature. For larger arrays this often leads to dynamical instabilities and disintegration of the structures even if additional damping is present.

Dirac lattices, zero-range potentials, and self-adjoint extension

We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the selfadjoint extension, regularization/renormalisation and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for example, for an easy numerical treatment of the scattering of the electromagnetic field on the lattice or for investigating plasmons. Using these formulas, we consider the limiting case of vanishing lattice spacing. For a scalar field and for the TE polarization of the electromagnetic field this transition is smooth and results in the results known from the continuous sheet. Especially for the TE polarization, we reproduce the results known from the hydrodynamic model describing a two dimensional electron gas. For the TM polarization, for polarizability parallel and perpendicular to the lattice, in both cases, the transition is singular. For the parallel polarizability this is surprising and different from the hydrodynamic model. For perpendicular polarizability this is what was known in literature. We also investigate the case when the transition is done with dipoles described by smeared delta function, i.e., keeping a regularization. Here, for TM polarization for parallel polarizability, when subsequently doing the limit of vanishing lattice spacing, we reproduce the result known from the hydrodynamic model. In case of perpendicular polarizability we need an additional renormalization to reproduce the result obtained previously by stepping back from the dipole approximation.

Dipole‐Field Sums, Lorentz Factors, and Dielectric Properties of Organic Molecular Films Modeled as Crystalline Arrays of Polarizable Points

The relative permittivity κ = ε/ε0 of thin films used in organic electronic devices is directly related to the structure and the molecular polarizability α when intermolecular overlap is small. Monolayer and multilayer films are modeled as lattices of polarizable points with induced dipoles μ = αF where the internal electric field F includes contributions from all induced dipoles. The polarization per unit volume is P = nμ for number density n. Dipole‐field sums are evaluated directly for atomic and molecular crystals and films through stacking of infinite layers. Lorentz factors in uniformly polarized crystals of less than cubic symmetry resolve completely the conditional convergence of dipole‐field sums in three dimensions. Thin films have equal P within layers but not at or near the surface. Surface effects are shown to increase with αn and sometimes to extend into films even though dipole fields are mainly due to adjacent layers. Simple and body‐centered tetragonal lattices illustrate polarizing or depolarizing interactions between layers that mimic molecules or oligomers tilted at angle Φ from normal to the surface in films or SAMs. Uniform P in molecular films refers to unit cells rather than to atoms and there are multiple ways to partition anisotropic molecular α among polarizable points. An illustrative analytical model based on polarizable points and dipole fields of adjacent layers is applied to oligophenyl films and to conjugated molecules in acene films.

Scattering approach to two-colour light forces and self-ordering of polarizable particles

Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long-range interactions, whose properties can be tailored by the choice of injected laser powers, frequencies, and polarizations. We use a transfer matrix approach to study the forces induced by non-interfering fields of orthogonal polarization or different frequencies in a 1D geometry, and find long-range self-ordering of particles without a prescribed order. Adjusting the laser frequencies and powers allows one to tune the inter-particle distances and provides a wide range of possible dynamical couplings not accessible in usual standing wave geometries with prescribed order. In this work, we restrict the examples to two frequencies and polarizations, but the framework also allows one to treat multicolour light beams with random phases. These dynamical effects should be observable in existing experimental setups with effective 1D geometries, such as atoms or nanoparticles coupled to the field of an optical nanofibre or transversely trapped in counter-propagating Gaussian beams.

Dielectric polarization, anisotropy and nonradiative energy transfer into nanometre-scale thin semiconducting films

A common problem of nonradiative energy transfer (NRET) from a small energy donor into a neighbouring energy acceptor layer is addressed with the emphasis on the layer thickness dependence. Two complementary approaches are employed to study dielectric polarization effects on NRET into thin films: a macroscopic analysis treating the acceptor layer as a continuum characterized by a frequency-dependent dielectric function, and a direct modelling utilizing discrete acceptor lattices, each of the acceptors being a polarizable point dipole. Explicit illustrations are provided of an interesting phenomenon, when NRET into thinner films can counter-intuitively be more efficient than NRET into thicker films. We show that this phenomenon may take place for a broad range of the acceptor polarization responses, including metallic-like and insulating behaviour as well as responses with weak and strong dissipation. The spectral vicinity of a strong dielectric resonance in the acceptor layer is studied as a specific example. The role of geometry-derived and intrinsic anisotropy of the acceptor response is clarified in the illustrations. Our results suggest that NRET optimization might be possible in the design of hybrid nanostructures, where the geometry of the structures is better matched with spectral properties of donor and acceptor subsystems.

The origin of the interparticle potential of electrorheological fluids

The particles of electrorheological fluids can be modelled as dielectric spheres (DS) immersed in a continuum dielectric. When an external field is applied, polarization charges are induced on the surfaces of the spheres and can be represented as point dipoles placed in the centres of the spheres. When the DSs are close to each other, the induced charge distributions are distorted by the electric field of the neighbouring DSs. This is the origin of the interaction potential between the DSs. The calculation of this energy is very time consuming, therefore, the DS model cannot be used in molecular simulations. In this paper, we show that the interaction between the point dipoles appropriately approximates the interaction of DSs. The polarizable point dipole model provides better results, but this model is not pair-wise additive, so it is not that practical in particle simulations.

Electromagnetic near-field interactions of a dipolar emitter with metal and metamaterial nanoslabs

We investigate the emission properties of a polarizable point dipole placed within a subwavelength distance from a silver or a slightly absorbing, negative-index metamaterial nanoslab. Using electromagnetic theory we show that in the immediate vicinity of the slab the dipole-slab interaction prevents the dipole from radiating. For the metamaterial slab close to the perfect-lens arrangement, the interaction is relatively weak and of short range. In particular, a region exists in the near zone of the metamaterial slab where the dipole emission is not disturbed by the interaction, and a bright intensity distribution of subwavelength width is created on the opposite side of the slab. This suggests that a low-loss metamaterial slab can act as a near-field imaging device which does not disturb the object. For the silver slab the interaction is stronger and it reaches over the near-field zone, adversely influencing the imaging capabilities in terms of brightness and resolution. The results are important for the development of metal and metamaterial superlenses.

A classical polarizable model for simulations of water and ice

We develop a classical rigid polarizable model of water for molecular simulations of water and ice. The model uses the Rowlinson five-site geometry: oxygen bearing the Lennard-Jones interaction and linearly polarizable point dipole, two positively charged hydrogens, and two massless negative charges placed symmetrically off oxygen so that the experimental dipole moment is reproduced. The target properties are the densities of water and ice Ih, diffusivity, enthalpies of fusion and vaporization, and the ice Ih melting point. The surface tension at lower temperatures is by 7% underestimated whereas the dielectric constant by 6% overestimated. Diffusivity and viscosity worsen at higher temperatures, although the Stokes radius is overestimated only by 2-7%. The ice Ih melting temperature is 260 K and the temperature of maximum density is 269 K. Rescaling the charges by a factor of 1.01 and Lennard-Jones energy by 1.0201 improves the melting point and energy-related quantities but shifts the agreement of kinetic properties to higher temperatures. For the model we propose abbreviation POL4D.

Molecular dynamics of polarizable point dipole models for molten NaI. Comparison with first principles simulations

Molecular dynamics simulations of molten NaI at 995 K have been carried out using polarizable ion models based on rigid ion pair potentials to which the anion induced dipole polarization is added. The polarization is added in such a way that point dipoles are induced on the anions by both local electric field and deformation short-range damping interactions that oppose the electrically induced dipole moments. The structure and self-diffusion results are compared with those obtained by Galamba and Costa Cabral using first principles Hellmann-Feynman molecular dynamics simulations and using classical molecular dynamics of a shell model which allows only the iodide polarization

The polarizable point dipoles method with electrostatic damping: Implementation on a model system

Recently, the use of polarizable force fields in Molecular Dynamics simulations has been gaining importance, since they allow a better description of heterogeneous systems compared to simple point charges force fields. Among the various techniques developed in the last years the one based on polarizable point dipoles represents one of the most used. In this paper, we review the basic technical issues of the method, illustrating the way to implement intramolecular and intermolecular damping of the electrostatic interactions, either with and without the Ewald summation method. We also show how to reduce the computational overhead for evaluating the dipoles, introducing to the state-of-the-art methods: the extended Lagrangian method and the always stable predictor corrector method. Finally we discuss the importance of screening the electrostatic interactions at short range, defending this technique against simpler approximations usually made. We compare results of density functional theory and classical force field-based Molecular Dynamics simulations of chloride in water.