Non-unique Hamiltonians for discrete symplectic dynamics.

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or -1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case.

Racetrack FAIMS for High-Resolution and High-Sensitivity Characterization of Peptide Conformers.

A racetrack field asymmetric waveform ion mobility spectrometry (r-FAIMS) device, which consists of both cylindrical FAIMS (c-FAIMS) and planar FAIMS (p-FAIMS) sections with a 1 mm gap width, was developed and applied for high-resolution and high-sensitivity exploration of conformational diversity for peptides. The optimal operating conditions of r-FAIMS were systemically studied, and the performance of the fully optimized r-FAIMS was compared to a previously developed p-FAIMS in detail by using pure nitrogen as the FAIMS carrier gas. Relying on the ion focusing effect in the c-FAIMS section, the intensity of the FAIMS spectrum for doubly charged bradykinin ions acquired by using r-FAIMS is ∼8.5-fold higher than that acquired by using p-FAIMS under the same resolving power/resolution condition, implying about an order of magnitude better sensitivity of r-FAIMS. In addition, the peak separation resolution of r-FAIMS was ∼1.70-fold higher than p-FAIMS under a similar sensitivity condition for doubly charged bradykinin ions. Due to a reduced gap width of the newly designed r-FAIMS (1 mm) as compared to the previously developed p-FAIMS (1.88 mm), r-FAIMS can operate at a much higher separation field with a similar FAIMS dispersion voltage (DV) to gain significantly higher resolving power. For triply charged syntide 2 ions, the resolving power of r-FAIMS can easily exceed 120 at -3.5 kV DV by using pure nitrogen as the FAIMS carrier gas as compared to 44.2 resolving power obtained by using p-FAIMS at -4.0 kV DV. All of the experimental results have confirmed that r-FAIMS can perform structural characterization of biomolecules with both high resolution and high sensitivity.

A Fully Automated Online Enrichment and Separation System for Highly Reproducible and In-Depth Analysis of Intact Glycopeptide.

A fully automated online enrichment and separation system for intact glycopeptides, named AutoGP, was developed in this study by integrating three different columns in a nano-LC system. Specifically, the peptide mixture from the enzymatic digestion of a complex biological sample was first loaded on a hydrophilic interaction chromatography (HILIC) column. The nonglycopeptides in the sample were washed off the column, and the glycopeptides retained by the HILIC column were eluted to a C18 trap column to achieve an automated glycopeptide enrichment. The enriched glycopeptides were further eluted to a C18 column for separation, and the separated glycopeptides were eventually analyzed by using an orbitrap mass spectrometer (MS). The optimal operating conditions for AutoGP were systemically studied, and the performance of the fully optimized AutoGP was compared with a conventional manual system used for glycopeptide analysis. The experimental evaluation shows that the total number of glycopeptides identified is at least 1.5-fold higher, and the median coefficient of variation for the analyses is at least 50% lower by using AutoGP, as compared to the results acquired by using the manual system. In addition, AutoGP can perform effective analysis even with a 1-µg sample amount, while a 10-µg sample at least will be needed by the manual system, implying an order of magnitude better sensitivity of AutoGP. All the experimental results have consistently proven that AutoGP can be used for much better characterization of intact glycopeptides.

An efficient strategy with a synergistic effect of hydrophilic and electrostatic interactions for simultaneous enrichment of N- and O-glycopeptides.

N- and O-glycosylation modifications of proteins are closely linked to the onset and development of many diseases and have gained widespread attention as potential targets for therapy and diagnosis. However, the low abundance and low ionization efficiency of glycopeptides as well as the high heterogeneity make glycosylation analysis challenging. Here, an enrichment strategy, using Knoevenagel copolymers modified with polydopamine-adenosine (denoted as PDA-ADE@KCP), was firstly proposed for simultaneous enrichment of N- and O-glycopeptides through the synergistic effects of hydrophilic and electrostatic interactions. The adjustable charged surface and hydrophilic properties endow the material with the capability to achieve effective enrichment of intact N- and O-glycopeptides. The experimental results exhibited excellent selectivity (1 : 5000) and sensitivity (0.1 fmol µL-1) of the prepared material for N-glycopeptides from standard protein digest samples. Moreover, it was further applied to simultaneous capturing of N- and O-glycopeptides from mouse liver protein digests. Compared to the commercially available zwitterionic hydrophilic interaction liquid chromatography (ZIC-HILIC) material, the number of glycoproteins corresponding to all N- and O-glycopeptides enriched with PDA-ADE@KCP was much more than that with ZIC-HILIC. Furthermore, PDA-ADE@KCP captured more O-glycopeptides than ZIC-HILIC, revealing its superior performance in O-glycopeptide enrichment. All these results indicated that the strategy holds immense potential in characterizing N- and O-intact glycopeptides in the field of proteomics.

A Screening Condition Imposed Stochastic Approximation for Long-Range Electrostatic Correlations.

The recent random batch Ewald algorithm, originating from a stochastic approximation, performs 1 order of magnitude faster than the mainstream algorithms such as the particle-particle particle-mesh method for handling of long-range electrostatics in large-scale simulations. However, this algorithm fails to fully capture the long-range electrostatic correlations. Here, we demonstrate that, when incorporating a known screening condition in the stochastic approximation, the algorithm could be simply amended without the loss of any efficiency.

The symmetry-preserving mean field condition for electrostatic correlations in bulk.

Accurate simulations of a condensed system of ions or polar molecules are concerned with proper handling of the involved electrostatics. For such a Coulomb system at a charged planar interface, the Coulomb interaction averaged over the lateral directions with preserved symmetry serves as a necessary constraint in building any accurate handling that reconciles a simulated singlet charge density with the corresponding macroscopic charge/dielectric response. At present, this symmetry-preserving mean field (SPMF) condition represented in the reciprocal space is conjectured to be necessary for a simulated bulk system to reproduce correctly the charge structure factor of the macroscopic bulk as well. In this work, we further examine analytically the asymptotic behavior of the charge structure factor at small wavenumbers for an arbitrary charge-charge interaction. In light of our theoretical predictions, simulations with lengths of nearly 0.1 µm are carried out to demonstrate that typical efficient methods violating the SPMF condition, indeed, fail to capture the exact charge correlations at small wavenumbers for both ionic and polar systems. However, for both types of systems, these existing methods can be simply amended to match the SPMF condition and subsequently to precisely probe the electrostatic correlations at all length scales.

Analytic theory of finite-size effects in supercell modeling of charged interfaces.

The Ewald3D sum with the tinfoil boundary condition (e3dtf) evaluates the electrostatic energy of a finite unit cell inside an infinitely periodic supercell. Although it has been used as a de facto standard treatment of electrostatics for simulations of extended polar or charged interfaces, the finite-size effect on simulated properties has yet to be fully understood. There is, however, an intuitive way to quantify the average effect arising from the difference between the e3dtf and Coulomb potentials on the response of mobile charges to contact surfaces with fixed charges and/or to an applied external electric field. Although any charged interface formed by mobile countercharges that compensate the fixed charges fluctuates upon a change in the acting electric field, the distance between a pair of oppositely charged interfaces is found to be nearly stationary, which allows an analytic finite-size correction to the amount of countercharges. Application of the theory to solvated electric double layers (insulator/electrolyte interfaces) predicts that the state of complete charge compensation is invariant with respect to solvent permittivities, which is confirmed by a proper analysis of simulation data in the literature.

Alcohol-Soluble Isoindigo Derivative IIDTh-NSB as a Novel Modifier of ZnO in Inverted Polymer Solar Cells.

Alcohol-soluble isoindigo derivative with thiophene groups and sulfobetaine zwitterions, IIDTh-NSB was applied as a novel modifier of ZnO in inverted polymer solar cells (i-PSCs). When IIDTh-NSB (0.2 mg/mL) was spin-coated on ZnO as an electron transport layer (ETL), power conversion efficiency (PCE) of the PTB7:PC71BM based i-PSCs reached 8.88%, which is a 20% improvement of that of 7.40% for the device with the ZnO-only ETL. If ZnO was doped by IIDTh-NSB of 1.0 wt %, the PCE of 8.50% could be achieved in the i-PSCs. Combined measurements of capacitance-voltage characteristics, carrier mobility, and photocurrent density-effective voltage characteristics revealed that incorporating IIDTh-NSB as the modifier of ZnO by coating or doping enhanced the built-in potential, charge carrier density and mobility, exciton dissociation, and charge carrier extraction in the i-PSCs because of the improved interfacial contact between the photoactive layer and ZnO as shown in water contact angle measurements and atomic force microscopy images. Finally, impedance spectroscopy investigation provided strong lines of evidence that incorporating IIDTh-NSB as the modifier of ZnO led to the great enhancement in short-circuit current density and fill factor. Furthermore, all the devices with IIDTh-NSB as a modifier of ZnO presented better stability than the device with ZnO-only. These findings suggest that IIDTh-NSB is an effective and competitive material for modification of ZnO in the i-PSCs.

Note: A pairwise form of the Ewald sum for non-neutral systems.

Using an example of a mixed discrete-continuum representation of charges under the periodic boundary condition, we show that the exact pairwise form of the Ewald sum, which is well-defined even if the system is non-neutral, provides a natural starting point for deriving unambiguous Coulomb energies that must remove all spurious dependence on the choice of the Ewald screening factor.

On the connections and differences among three mean-field approximations: a stringent test.

This letter attempts to clarify the meaning of three closely related mean-field approximations: random phase approximation (RPA), local molecular field (LMF) approximation, and symmetry-preserving mean-field (SPMF) approximation, and their use of reliability and validity in the field of theory and simulation of liquids when the long-ranged component of the intermolecular interaction plays an important role in determining density fluctuations and correlations. The RPA in the framework of classical density functional theory (DFT) neglects the higher order correlations in the bulk and directly applies the long-ranged part of the potential to correct the pair direct correlation function of the short-ranged system while the LMF approach introduces a nonuniform mimic system under a reconstructed static external potential that accounts for the average effect arising from the long-ranged component of the interaction. Furthermore, the SPMF approximation takes the viewpoint of LMF but instead instantaneously averages the long-ranged component of the potential over the degrees of freedom in the direction with preserved symmetry. The formal connections and the particular differences of the viewpoint among the three approximations are explained and their performances in producing structural properties of liquids are stringently tested using an exactly solvable model. We demonstrate that the RPA treatment often yields uncontrolled poor results for pair distribution functions of the bulk system. On the other hand, the LMF theory produces quite reasonably structural correlations when the pair distribution in the bulk is converted to the singlet particle distribution in the nonuniform system. It turns out that the SPMF approach outperforms the other two at all densities and under extreme conditions where the long-ranged component significantly contributes to the structural correlations.

The effect of electrostatic boundaries in molecular simulations: symmetry matters.

Artifacts arise when the long-ranged electrostatic interaction is inappropriately treated in molecular simulations of electrolytes. When the usual Ewald3D sum method with the tinfoil boundary condition (e3dtf) is used for simulations of an interfacial liquid under an external electric field, a straightforward analysis of the liquid structure often suggests unphysical dielectric properties as a consequence of the inaccurate treatment of the electrostatics. In order to understand the underlying mechanism that leads to this apparent violation of thermodynamics, we now derive a new equation in the weak-field limit that, in a mean field view, accounts for the average effect arising from the difference between e3dtf and the sophisticated Ewald2D sum method (e2d). Numerical simulations of a water system in slab geometry confirm the validity of the weak-field limit equation for a series of parameter setup associated with e3dtf. Moreover, a similar procedure applied to a spherically confined water system suggests that corrections to the seemingly inappropriate treatment of the electrostatics in fact vanish. This cancellation of the boundary effect due to symmetry immediately sheds light on the long-lasting problem of the validity of the ad hoc application of e3dtf for bulk systems. In total, we argue that artifacts arising from e3dtf are often predictable and analytical corrections to the straightforward analysis might be applied to reveal consistent thermodynamic properties in liquid simulations.

Force field development for organic molecules: modifying dihedral and 1-n pair interaction parameters.

We comprehensively illustrate a general process of fitting all-atom molecular mechanics force field (FF) parameters based on quantum mechanical calculations and experimental thermodynamic data. For common organic molecules with free dihedral rotations, this FF format is comprised of the usual bond stretching, angle bending, proper and improper dihedral rotation, and 1-4 scaling pair interactions. An extra format of 1-n scaling pair interaction is introduced when a specific intramolecular rotation is strongly hindered. We detail how the preferred order of fitting all intramolecular FF parameters can be determined by systematically generating characteristic configurations. The intermolecular Van der Waals parameters are initially taken from the literature data but adjusted to obtain a better agreement between the molecular dynamics (MD) simulation results and the experimental observations if necessary. By randomly choosing the molecular configurations from MD simulation and comparing their energies computed from FF parameters and quantum mechanics, the FF parameters can be verified self-consistently. Using an example of a platform chemical 3-hydroxypropionic acid, we detail the comparison between the new fitting parameters and the existing FF parameters. In particular, the introduced systematic approach has been applied to obtain the dihedral angle potential and 1-n scaling pair interaction parameters for 48 organic molecules with different functionality. We suggest that this procedure might be used to obtain better dihedral and 1-n interaction potentials when they are not available in the current widely used FF.

Symmetry-preserving mean field theory for electrostatics at interfaces.

We derive an instantaneous symmetry-preserving mean field equation relating the long-ranged component of the intermolecular interaction to an effective single particle potential. We verify the efficiency and accuracy of the symmetry-preserving mean field approach to treat complex nonuniform electrostatics and foresee its application to study self-assembly and disassembly processes at interfaces in many computer simulations.

Rigorous Error Bounds for Ewald Summation of Electrostatics at Planar Interfaces.

We present a rigorous Ewald summation formula to evaluate the electrostatic interactions in two-dimensionally periodic planar interfaces of three-dimensional systems. By rewriting the Fourier part of the summation formula of the original Ewald2D expression with an explicit order N(2) complexity to a closed form Fourier integral, we find that both the previously developed electrostatic layer correction term and the boundary correction term naturally arise from the expression of a rigorous trapezoidal summation of the Fourier integral part. We derive the exact corrections to the trapezoidal summation in a form of contour integrals offering precise error bounds with given parameter sets of mesh size and system length. Numerical calculations of Madelung constants in model ionic crystals of slab geometry have been performed to support our analytical results.

Infinite Boundary Terms of Ewald Sums and Pairwise Interactions for Electrostatics in Bulk and at Interfaces.

We present a unified derivation of the Ewald sum for electrostatics in a three-dimensional infinite system that is periodic in one, two, or three dimensions. The derivation leads to the Ewald3D sum being expressed as a sum of a real space contribution and a reciprocal space contribution, as in previous work. However, the k → 0 term in the reciprocal space contribution is analyzed further and found to give an additional contribution that is not part of previous reciprocal space contributions. The transparent derivation provides a unified view of the existing conducting infinite boundary term, the vacuum spherical infinite boundary term and the vacuum planar infinite boundary term for the Ewald3D sum. The derivation further explains that the infinite boundary term is conditional for the Ewald3D sum because it depends on the asymptotic behavior that the system approaches the infinite in 3D but it becomes a definite term for the Ewald2D or Ewald1D sum irrespective of the asymptotic behavior in the reduced dimensions. Moreover, the unified derivation yields two formulas for the Ewald sum in one-dimensional periodicity, and we rigorously prove that the two formulas are equivalent. These formulas might be useful for simulations of organic crystals with wirelike shapes or liquids confined in uniform cylinders. More importantly, the Ewald3D, Ewald2D, and Ewald1D sums are further written as sums of well-defined pairwise potentials overcoming the difficulty in splitting the total Coulomb potential energy into contributions from each individual group of charges. The pairwise interactions with their clear physical meaning of the explicit presence of the periodic images thus can be used to consistently perform analysis based on the trajectories from computer simulations of bulk or interfaces.

Graphene in ionic liquids: collective van der Waals interaction and hindrance of self-assembly pathway.

Over the past decade, there has been much controversy regarding the microscopic mechanism by which the π-electron-rich carbon nanomaterials such as graphene and carbon nanotubes can be dispersed in ionic liquids. Through a combination of a quantum mechanical calculation on the level of density functional theory, an extensive molecular dynamics study on the time scale of microseconds, and a kinetic analysis at the experimental time scale, we have demonstrated that collective van der Waals forces between ionic liquids and graphene are able to describe both the short-ranged cation-π interaction and the long-ranged dispersion interaction and this microscopic interaction drives two graphene plates trapped in their metastable state while two graphene plates easily self-assemble into graphite in water.

Structural origin of energetic heterogeneity in ionic liquids.

How structural features observed computationally are connected to excitation-wavelength dependent kinetics observed experimentally remains an unanswered question in the field of ionic liquids. Using molecular dynamics simulation methods and approximated models that simplify the electrostatic interactions in ionic liquids, we discovered that on the timescale shorter than the relaxation time of the photochemical process, the energetic heterogeneity in terms of distribution of excitation energies is the consequence of the structure heterogeneity formed by local arrangement of ions around the solute probe.

First passage time distribution in stochastic processes with moving and static absorbing boundaries with application to biological rupture experiments.

We develop and investigate an integral equation connecting the first passage time distribution of a stochastic process in the presence of an absorbing boundary condition and the corresponding Green's function in the absence of the absorbing boundary. Analytical solutions to the integral equations are obtained for three diffusion processes in time-independent potentials which have been previously investigated by other methods. The integral equation provides an alternative way to analytically solve the three diffusion-controlled reactive processes. In order to help analyze biological rupture experiments, we further investigate the numerical solutions of the integral equation for a diffusion process in a time-dependent potential. Our numerical procedure, based on the exact integral equation, avoids the adiabatic approximation used in previous analytical theories and is useful for fitting the rupture force distribution data from single-molecule pulling experiments or molecular dynamics simulation data, especially at larger pulling speeds, larger cantilever spring constants, and smaller reaction rates. Stochastic simulation results confirm the validity of our numerical procedure. We suggest combining a previous analytical theory with our integral equation approach to analyze the kinetics of force induced rupture of biomacromolecules.

Efficient solutions of self-consistent mean field equations for dewetting and electrostatics in nonuniform liquids.

We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method is illustrated by applications to dewetting of a hard sphere solute in a Lennard-Jones fluid, the interplay between local hydrogen bond structure and electrostatics for water confined between two hydrophobic walls, and to ion pairing in ionic solutions. Simulation time has been reduced by more than an order of magnitude over previous methods.

Molecular dynamics study of the temperature-dependent Optical Kerr effect spectra and intermolecular dynamics of room temperature ionic liquid 1-methoxyethylpyridinium dicyanoamide.

We have performed classical molecular dynamics simulations to calculate the Optical Kerr effect (OKE) spectra of 1-methoxyethylpyridinium dicyanoamide, a room-temperature ionic liquid (IL) which has been recently studied by Shirota and Castner (Shirota, H. ; Castner, E. J. Phys. Chem. A 2005, 109, 9388-9392) in comparison to its neutral isoelectronic solvent mixture. Our theoretical and computational studies show that the decay of the collective polarizability anisotropy correlation exhibits several different time scales originating from inter- and intramolecular dynamics, in good agreement with experiments. What's more, we find that the portion of the collective anisotropic polarizability relaxation due to "interaction-induced" phenomena is important at times much longer than those observed in normal solvents when these are far from their glass transition temperature. From our long (60 ns) molecular dynamics simulations, we are able to determine the appropriate time scales for orientational relaxation and interaction-induced processes occurring in the liquid. We find that the cationic contribution to the OKE signal is predominant. Because of the slow nature of relaxation processes in ILs, these calculations are very time, memory, and storage intensive. In the context of this research, we have developed a polarizable force field for this system and also theoretical methodology to generate molecular polarizabilities for arbitrarily shaped molecules and ions from corresponding atomic polarizabilities. We expect this methodology to have an important impact on the speed of molecular dynamics simulations of polarizable systems in the future.