Induced Dipole Model Research Articles

Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models.

Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a "peek" step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.

PyRESP: A Program for Electrostatic Parameterizations of Additive and Induced Dipole Polarizable Force Fields.

Molecular modeling at the atomic level has been applied in a wide range of biological systems. The widely adopted additive force fields typically use fixed atom-centered partial charges to model electrostatic interactions. However, the additive force fields cannot accurately model polarization effects, leading to unrealistic simulations in polarization-sensitive processes. Numerous efforts have been invested in developing induced dipole-based polarizable force fields. Whether additive atomic charge models or polarizable induced dipole models are used, proper parameterization of the electrostatic term plays a key role in the force field developments. In this work, we present a Python program called PyRESP for performing atomic multipole parameterizations by reproducing ab initio electrostatic potential (ESP) around molecules. PyRESP provides parameterization schemes for several electrostatic models, including the RESP model with atomic charges for the additive force fields and the RESP-ind and RESP-perm models with additional induced and permanent dipole moments for the polarizable force fields. PyRESP is a flexible and user-friendly program that can accommodate various needs during force field parameterizations for molecular modeling of any organic molecules.

Lateral terahertz wave emission from laser induced plasma in liquid water line

Laser ionized liquid has been considered as a promising broadband terahertz (THz) source recently. The ponderomotive force induced dipole model can be used to describe the mechanism of THz generation, implying that the lateral THz emission is stronger than the forward emission. Thus, we systemically investigate the lateral THz emission from laser induced plasma in liquid water line. THz energy about 4.4-times of that from the forward emission is achieved from the lateral emission scheme. Results on the angular distribution of coherent THz radiation indicate that the maximal THz radiation falls between 120° and 150° with respect to the pump laser propagation direction. Moreover, dependence of collected THz energy on the relative position between laser focus and the water line shows a counterintuitive “two peaks” trend, which can be explained by the impact of cylindrical water surface on the divergence angle of the generated THz wave. Therefore, the enhancement in THz energy can be attributed to the high-efficiency lateral collection scheme and the tradeoff between the THz wave converging effect of the cylindrical surface and the absorption in water. Our work helps to further optimize the coupling efficiency of generated THz wave out of liquid samples.

Assessing the Impact of Drift Gas Polarizability in Polyatomic Ion Mobility Experiments.

Due to the core assumptions of kinetic theory and the drive toward realizing reproducible gas-phase measurements, ion mobility experiments are commonly conducted in the presence of an inert, neat buffer gas, usually nitrogen or helium. Mixing drift gases in defined, static ratios can provide useful information not only for optimizing the separation of analytes but also for defining the interaction between the ion and neutral particle. In a foundational effort, we seek to validate the role of the drift gas polarizability on the observed mobility of the ions by systematically mixing drift gases to discretely access a range of bulk gas polarizabilities not given by pure drift gases. Compared to historical efforts to probe the role of polarizability on the ion-neutral collisional cross section where a linear relationship was assumed, the data collected in the present effort clearly illustrate a quadratic dependency of the ion-neutral particle collision cross section and polarizability (R2 > 0.999). When translating these data into the mobility dimension, we illustrate that the gas-phase mobility of polyatomic ions conforms to Blanc's law. These observations combined with considerations related to Langevin's polarization limit provide an experimental mechanism to estimate to what degree an ion-neutral interaction conforms to either the hard-sphere or induced-dipole model. To support these observations, additional comparisons are made with the respective reduced masses, polarizabilities, and mobilities of ions in mixtures where different degrees of hard-sphere interactions are present.

Coupled Cluster Theory with Induced Dipole Polarizable Embedding for Ground and Excited States.

In this work, we present the theory and implementation of the coupled cluster single and double excitations (CCSD) method combined with a classical polarizable molecular mechanics force field (MMPol) based on the induced dipole model. The method is developed to compute electronic excitation energies within the state specific (SS) and linear response (LR) formalisms for the interaction of the quantum mechanical and classical regions. Furthermore, we consider an approximate expression of the correlation energy, originally developed for CCSD with implicit solvation models, where the interaction term is linear in the coupled cluster density. This approximation allows us to include the explicit contribution of the environment to the CC equations without increasing the computational effort. The test calculations on microsolvated systems, where the CCSD/MMPol method is compared to full CCSD calculations, demonstrates the reliability of this computational protocol for all interaction schemes (errors < 2%). We also show that it is important to include induced dipoles on all atom centers of the classical region and that too diffuse functions in the basis set may be problematic due to too strong interaction with the environment.

Comparison of interatomic potential models on the molecular dynamics simulation of fast-ion conductors: A case study of a Li garnet oxide Li7La3Zr2O12

In this work, we performed molecular dynamic simulations of a representative fast-ion conductor (Li7La3Zr2O12) using three different interatomic potential models: non-polarizable core (Core), polarizable core–shell (CS), and induced dipole (ID). To compare these three models, we calculated the phase transition behavior, self-diffusivity, ionic conductivity, dielectric constant, and elastic moduli of Li7La3Zr2O12 and checked results against experimental and other simulation work. We found that overall all three potential models predict results that agree reasonably well with experiments and first-principles calculations. However, we think that the ID model that combines both force-matching, atomic polarization, and first-principles charge has the technical advantage over the other two, while exhibiting slightly higher computational cost. We also discussed ways to further improve these interatomic potential models.

Comparative Analysis of Protein Hydration from MD simulations with Additive and Polarizable Force Fields

AbstractRecent development of the Drude polarizable (Drude) force field (FF), based on the extension of an induced dipole model, has reached a milestone in the past few years providing a complete set of polarizable parameters for proteins, water, ions, and many lipid types. This FF enables stable simulations up to microseconds, surpassing the capability of other polarizable FFs. The quality of the Drude FF, however, has remained largely untested for modeling the secondary structures of small peptides in explicit solvents compared with classical non‐polarizable FFs. It is critical to benchmark the complex and mutually dependent dynamics of hydrogen‐bond (H‐bond) networks formed by water–water, protein–water, and protein–protein interactions that are expected to have a major impact on the stability of protein structures and their conformational space. Here, a direct comparison is presented between the current Drude FF and the CHARMM‐36 non‐polarizable classical FF for 1) the solvation free energy of mimetics for all amino acid side‐chain equivalents, 2) limited conformational space, 3) protein–water and protein–protein interactions, and 4) the comparative lifetimes of H‐bonds. The impact of counterions on the stabilization of secondary structure in model peptides is additionally discussed and compared between these FFs.

Controlling molecular condensation/diffusion of copper phthalocyanine by local electric field induced with scanning tunneling microscope tip

We have discovered the condensation/diffusion phenomena of copper phthalocyanine (CuPc) molecules controlled with a pulsed electric field induced by the scanning tunneling microscope tip. This behavior is not explained by the conventional induced dipole model. In order to understand the mechanism, we have measured the electronic structure of the molecule by tunneling spectroscopy and also performed theoretical calculations on molecular orbitals. These data clearly indicate that the molecule is positively charged owing to charge transfer to the substrate, and that hydrogen bonding exists between CuPc molecules, which makes the molecular island stable.

Mapping the Drude polarizable force field onto a multipole and induced dipole model.

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

Mechanisms of resonant low frequency Raman scattering from metallic nanoparticle Lamb modes.

The low frequency Raman scattering from gold nanoparticle bimodal assemblies with controlled size distributions has been studied. Special care has been paid to determining the size dependence of the Raman intensity corresponding to the quadrupolar Lamb mode. Existing models based on a microscopic description of the scattering mechanism in small particles (bond polarizability, dipole induced dipole models) predict, for any Raman-active Lamb modes, an inelastic intensity scaling as the volume of the nanoparticle. Surprisingly experimental intensity ratios are found to be anomalously much greater than theoretical ones, calling into question this scaling law. To explain these discrepancies, a simple mechanism of Raman scattering, based on the density fluctuations in the nanoparticles induced by the Lamb modes, is introduced. This modeling, in which the nanoparticle is described as an elastic isotropic continuous medium-as in Lamb theory, successfully explains the major features exhibited by low frequency Raman modes. Moreover this model provides a unified picture for any material, suitable for handling both small and large size ranges, as well as non-resonant and resonant excitation conditions in the case of metallic species.

Studies on hydrolysis mechanism of anticancer ruthenium drug ImH[trans-Ru(Im)2Cl4] via ABEEMσπ polarizable force field combined with QM and MD-FEP

We used ABEEMσπ(atom-bond electronegativity equalization method) polarizable force field(ABEEMσπ PFF) method combined with QM and molecular dynamics-free energy perturbation(MD-FEP) methods to investigate the function of water molecules in hydrolysis process of ImH[trans-Ru(Im)2Cl4](ICR). The activation free energies obtained via MD-FEP calculation are in fair agreement with the experimental data. In addition, QM/MM(ABEEM) rationally describes the charge distributions and the electrostatic interaction between molecules. ABEEMσπ fluctuating charge model has the following good characteristics: (1) not only atomic charge regions but also σ, π bond and lone pair charge regions are explicitly represented for a molecule; (2) the region charges are geometry dependent and calculated from time to time in the dynamic simulation without any iterative procedure so that its performance is time-saving compared with the Drude model and induced dipole model.

Metal Ion Modeling Using Classical Mechanics.

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

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.

Determining polarizable force fields with electrostatic potentials from quantum mechanical linear response theory.

We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.

Demonstration of polarization mode selection and coupling efficiency of optofluidic ring resonator lasers.

We demonstrate the polarization mode selection and the dependence of coupling efficiency on polarization state of pump light for an optofluidic ring resonator (OFRR) laser. An optical fiber is chosen to serve as the ring resonator and surrounded by rhodamine 6G dye solution of lower refractive index as the fluidic gain medium. When the ring resonator is pumped by a linearly s-polarized laser, the emitted whispering gallery mode (WGM) lasing is of parallel polarization (TM mode), while p-polarized laser excitation generates a vertically polarized lasing emission (TE mode), both TM and TE mode lasing emission coexist simultaneously if the ring resonator is pumped by the s- and p-mixed polarized light. Further investigation reveals that the lasing intensity of the TM mode is approximately twice that of the TE mode for the same pump energy density, meaning an obvious difference of coupling efficiency on the polarization state of pump light; the experimental results of coupling efficiency are well explained by an induced dipole model.

Space Charge Property of Polyethylene/Silica Nanocomposites at Different Elongations

This paper prepares polyethylene/silica nanocomposites with concentrations of 3 wt% and 5 wt% by using silicon dioxide (SiO2) nanopowder (nanosilica) with particle sizes of 15 and 50 nm. Samples whose elongations are 3%, 6%, and 10% are prepared. Pulsed electroacoustic technique is applied to evaluate the space charge distribution in samples. Test results show that homocharge near electrodes is generated in the polyethylene/silica nanocomposites. Nanocomposites with a nanoparticle concentration of 3 wt% and particle size of 15 nm suppress the accumulation of space charge effectively. The amount of space charge in the samples increases with the increase in elongation. At an elongation of 10%, packet‐like space charge is generated in polyethylene/silica nanocomposites with the concentration of 5 wt% and particle sizes of 15 and 50 nm. The packet‐like space charge in nanocomposites whose particle size is 50 nm is more obvious than that in nanocomposites whose particle size is 15 nm. The experiment results are explained by applying interface characteristics, dipole model, and induced dipole model.

Improving the Computational Efficiency of the Induced-Dipole Model in Amoeba via the 3-Body Approximation

Computational modeling at the atomistic level has undergone dramatic development to meet the challenge of adequately accounting for the many-body intermolecular interactions. Polarization is recognized in the force field development community as the most important many-body intermolecular interaction due to the fact that it is the slowest decaying of these, and major efforts have been underway to incorporate classical models of polarization in empirical force fields. However, the computational cost of calculating polarization for each energy/gradient evaluation has limited its practical use in adequate sampling of phase space that is necessary to obtain converged condensed-phase properties. More specifically, calculating polarization in the induced dipole regime requires the expensive iteration of the values of the induced dipoles to self-consistency for the entire system. To reduce the computational cost of the full N-body polarization calculation, we employ a truncation of the N-body energy expansion at the level of 3-bodies. This reduces the computational cost in several ways. First, the calculation of the induced dipoles for groups of 1 body, 2 bodies, and 3 bodies may be calculated exactly with matrix inversion, obviating the need for an iterative approach due to the small size of the system. Secondly, due to the fact that they are independent calculations under the 3-body approximation, the polarization energy for the system may be trivially parallelized. Finally, due to the decay of the polarization energy with distance, we may employ cutoffs. We first demonstrate that the 3-body approximation yields errors of 1-5% in the polarization energy for neutral systems compared to the N-body model. We then demonstrate the computational savings that result when parallelization is incorporated. Finally, we report the performance in capturing condensed-phase observables of water and solvated peptide and small molecule systems.

A polarizable ellipsoidal force field for halogen bonds

The anisotropic effects and short-range quantum effects are essential characters in the formation of halogen bonds. Since there are an array of applications of halogen bonds and much difficulty in modeling them in classical force fields, the current research reports solely the polarizable ellipsoidal force field (PEff) for halogen bonds. The anisotropic charge distribution was represented with the combination of a negative charged sphere and a positively charged ellipsoid. The polarization energy was incorporated by the induced dipole model. The resulting force field is "physically motivated," which includes separate, explicit terms to account for the electrostatic, repulsion/dispersion, and polarization interaction. Furthermore, it is largely compatible with existing, standard simulation packages. The fitted parameters are transferable and compatible with the general AMBER force field. This PEff model could correctly reproduces the potential energy surface of halogen bonds at MP2 level. Finally, the prediction of the halogen bond properties of human Cathepsin L (hcatL) has been found to be in excellent qualitative agreement with the cocrystal structures.

Development of polarizable models for molecular mechanical calculations II: induced dipole models significantly improve accuracy of intermolecular interaction energies.

In the companion paper, we presented a set of induced dipole interaction models using four types of screening functions, which include the Applequist (no screening), the Thole linear, the Thole exponential model, and the Thole Tinker-like (another form of exponential screening function) functions. In this work, we evaluate the performance of polarizability models using a large set of amino acid analog pairs in conformations that are frequently observed in protein structures as a benchmark. For each amino acid pair, we calculated quantum mechanical interaction energies at the MP2/aug-cc-pVTZ//MP2/6-311++G(d,p) level with the basis set superposition error (BSSE) correction and compared them with molecular mechanics results. Encouragingly, all polarizable models significantly outperform the additive F94 and F03 models (mimicking AMBER ff94/ff99 and ff03 force fields, respectively) in reproducing the BSSE-corrected quantum mechanical interaction energies. In particular, the root-mean-square errors (RMSEs) for three Thole models in Set A (where the 1-2 and 1-3 interactions are turned off and all 1-4 interactions are included) are 1.456, 1.417, and 1.406 kcal/mol for model AL (Thole Linear), model AE (Thole exponential), and model AT (Thole Tinker-like), respectively. In contrast, the RMSEs are 3.729 and 3.433 kcal/mol for F94 and F03 models, respectively. A similar trend was observed for the average unsigned errors (AUEs), which are 1.057, 1.025, 1.011, 2.219, and 2.070 kcal/mol for AL, AE, AT, F94/ff99, and F03, respectively. Analyses based on the trend line slopes indicate that the two fixed charge models substantially underestimate the relative strengths of noncharge-charge interactions by 24 (F03) and 35% (F94), respectively, whereas the four polarizable models overestimate the relative strengths by 5 (AT), 3 (AL, AE), and 13% (AA), respectively. Agreement was further improved by adjusting the van der Waals parameters. Judging from the notably improved accuracy in comparison with the fixed charge models, the polarizable models are expected to form the foundation for the development of high quality polarizable force fields for protein and nucleic acid simulations.

Preparation of sodium titanate nanotubes modified by CdSe quantum dots and their photovoltaic characteristics

Sodium titanate nanotubes have been prepared and modified chemically with CdSe quantum dots (QDs) using bifunctional modifiers (HS-COOH). Their photovoltaic characteristics have also been studied. The results indicate that the surface photovoltage response of nanotubes extends to the visible light region, and the intensity of surface photovoltage is enhanced after modification with CdSe QDs. The field-induced surface photovoltage spectroscopy (FISPS) shows that sodium titanate nanotubes have different photovoltaic response before and after modification. That is, the surface photovoltaic response of pure sodium titanate nanotubes increases with the enhancement of positive applied bias and decreases with the enhancement of negative applied bias. Meanwhile, the surface photovoltaic response of CdSe modified sodium titanate nanotubes is different from that of the pure sodium titanate nanotubes. The whole spectrum increases with the enhancement of applied bias at the first stage. However, when the applied bias reaches a certain value, the surface photovoltage response keeps increasing in some spectrum regions, while decreasing in other spectrum regions. This novel phenomenon is explained by using an electric field induced dipole model.