Conditional reversible work method for molecular coarse graining applications

Systematically coarse grained models for complex fluids usually lack chemical and thermodynamic transferability. Efforts to improve transferability require the development of effective potentials with unequivocal physical significance. In this paper, we introduce conditional reversible work (CRW) potentials that describe nonbonded interactions in coarse grained models at the pair level. The method used to obtain these potentials is straightforward to implement, can be readily extended to compute hydration contributions in implicit-solvent potentials, and is easy to automize. As a first illustration of the method, we present CRW potentials for 3-site models of hexane and toluene. The temperature-transferability of the liquid phase density obtained with these potentials has been investigated, and a comparison has been made with effective potentials obtained by the iterative Boltzmann inversion method.     

Influence of the interaction potential on simulated sputtering and reflection data

The TRIM.SP program which is based on the binary collision approximation was changed to handle not only repulsive interaction potentials, but also potentials with an attractive part. Sputtering yields, average depth and reflection coefficients calculated with four different potentials are compared. Three purely repulsive potentials (Molière, Kr-C and ZBL) are used and an ab initio pair potential, which is especially calculated for silicon bombardment by silicon. The general trends in the calculated results are similar for all potentials applied, but differences between the repulsive potentials and the ab initio potential occur for the reflection coefficients and the sputtering yield at large angles of incidence.     

Correlation potentials for the He atom and the hydrogen molecule: A comparison between the correlation factor approach and DFT correlation energy functionals

Two points about correlation potentials have been dealt with in this article. The first one is related to the shape of some of the most representative correlation potentials applied to the ground state of the He atom. It is shown here that both LDA and two-body density correlation potentials compare well with that obtained through the quantum chemistry definition of correlation energy. This is an interesting result because, in previous works, it had been shown that none of the correlation potentials compared well with the Kohn–Sham one. The gradient-corrected correlation potentials exhibit a very different behavior to that of both exact potentials (quantum chemistry and Kohn–Sham ones). The other question posed here refers to how a reference to the two-body density must modify DFT functionals for the correlation energy, when a multideterminant wave function is needed. This question has been addressed by analyzing the variation of correlation potentials as the bond length of the H₂ molecule increases. The results show that an external reference to the two-body density qualitatively improves DFT correlation potentials and also that only those functionals explicitly depending on two-body density can give the quantitative correct trends. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 143–156, 1998     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.     

Nanosecond redox equilibrium method for determining oxidation potentials in organic media

A general, nanosecond equilibrium method is described for determining thermodynamically meaningful oxidation potentials in organic media for compounds that form highly reactive cation radicals upon one-electron oxidation. The method provides oxidation potentials with unusually high precision and accuracy. Redox ladders have been constructed of appropriate reference compounds in dichloromethane and in acetonitrile that can be used to set up electron-transfer equilibria with compounds with unknown oxidation potentials. The method has been successfully applied to determining equilibrium oxidation potentials for a series of aryl-alkylcyclopropanes, whose oxidation potentials were imprecisely known previously. Structure-property trends for oxidation potentials of the cyclopropanes are discussed.     

Interaction potentials for Li+—rare-gas systems

The accuracies of proposed interaction potentials for the Li⁺—rare-gas systems are tested by comparing the transport coefficients calculated from the potentials with the experimental values. The agreement is generally good for theoretical potentials that take electron correlation into account and for potentials inferred from ion-beam measurements of high accuracy, except where the transport data are primarily influenced by the long-range tail of the potential. The transport data are also used to directly determine the Li⁺—rare-gas interaction potentials, with an estimated accuracy of 10% over wide ranges of ion—atom separation.     

Generalized potentials: Free particle,harmonic, and Morse partner potentials

In this work, we propose a very simple procedure to find the partner to specific potentials. According to our method, partner potentials are those obtained in the generalization of standard potentials, for which they are generalized potentials whose Hamiltonian match the so‐called isospectral Hamiltonian. The proposed approach is straightforward and basically takes into consideration the use of three well‐established relationships: The first one is used to identify the particular potential; the second, to find the adjoint or modified potential; and the third, to obtain the corresponding generalized or partner potential. As a useful application of the proposed procedure, we give explicitly the generalized and modified free‐particle, harmonic oscillator, and Morse one‐dimensional potentials. As expected, it is shown that the adjoint and partner potentials are isospectral with respect to the particular or former potential. This procedure can be easily applied to the generalization of any other known potential, as well as to obtain new potentials that can be advantageously used for modeling important quantum interactions. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 465–472, 1999     

DSX: a knowledge-based scoring function for the assessment of protein-ligand complexes

We introduce the new knowledge-based scoring function DSX that consists of distance-dependent pair potentials, novel torsion angle potentials, and newly defined solvent accessible surface-dependent potentials. DSX pair potentials are based on the statistical formalism of DrugScore, extended by a much more specialized set of atom types. The original DrugScore-like reference state is rather unstable with respect to modifications in the used atom types. Therefore, an important method to overcome this problem and to allow for robust results when deriving pair potentials for arbitrary sets of atom types is presented. A validation based on a carefully prepared test set is shown, enabling direct comparison to the majority of other popular scoring functions. Here, DSX features superior performance with respect to docking- and ranking power and runtime requirements. Furthermore, the beneficial combination with torsion angle-dependent and desolvation-dependent potentials is demonstrated. DSX is robust, flexible, and capable of working together with special features of popular docking engines, e.g., flexible protein residues in AutoDock or GOLD. The program is freely available to the scientific community and can be downloaded from our Web site www.agklebe.de .     

Efficient silicon surface and cluster modeling using quantum capping potentials

A one-electron, silicon quantum capping potential for use in capping the dangling bonds formed by artificially limiting silicon clusters or surfaces is developed. The quantum capping potentials are general and can be used directly in any computational package that can handle effective core potentials. For silicon clusters and silicon surface models, we compared the results of traditional hydrogen atom capping with those obtained from capping with quantum capping potentials. The results clearly show that cluster and surface models capped with quantum capping potentials have ionization potentials, electron affinities, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps that are in very good agreement with those of larger systems. The silicon quantum capping potentials should be applied in cases where one wishes to model processes involving charges or low-energy excitations in silicon clusters and surfaces consisting of more than ca. 150 atoms.     

Thermodynamic and kinetic theory of ionic micellar systems: 2. Statistical-thermodynamic relations

The role of electrochemical potentials in the grand canonical ensemble of ionic micellar systems is characterized. The notion of relative electrochemical potentials is introduced with allowance for the electroneutrality condition. Fundamental relations and primary statistical-thermodynamic relations are derived for ideal and real ionic micellar systems with participation of electrochemical potentials, in which inaccuracies observed in published literature, are eliminated. A differential equation for the osmotic pressure of ionic aggregated system is obtained. Relations that link the work of the aggregation of ionic micelle with chemical and electrochemical potentials and aggregation numbers are established. Separate contributions to the work of aggregation are commented on.     

Electrochemical signaling in green plants: effects of 2,4-dinitrophenol on variation and action potentials in soybean

Nerve cells in animals and phloem cells in plants share one fundamental property: they possess excitable membranes by which electrical excitations in the form of action potentials can propagate. Action potentials in green plants can be as fast as the action potentials in axons of nervous cells. The presence of the pesticide 2,4-dinitrophenol (DNP) in soil is a most serious environmental problem and has an impact on agriculture and human health. In the present work we show that DNP induces fast action potentials and decreases the variation potential in a soybean. The speed of the propagation of action potentials is up to 2 m/s, and the duration time of single action potentials is typically 20 ms. The automatic measurement of the electrical potential difference can be effectively used in environmental plant physiology, as well as for studying molecular mechanisms of transport processes and the influence of external stimuli on plants.     

Solvent-averaged potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions

We derive effective, solvent-free ion-ion potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions. The implicit solvent potentials are parametrized to reproduce experimental osmotic coefficients. The modeling approach minimizes the amount of input required from atomistic (force field) models, which usually predict large variations in the effective ion-ion potentials at short distances. For the smaller ion species, the reported potentials are composed of a Coulomb and a Weeks-Chandler-Andersen term. For larger ions, we find that an additional, attractive potential is required at the contact minimum, which is related to solvent degrees of freedom that are usually not accounted for in standard electrostatics models. The reported potentials provide a simple and accurate force field for use in molecular dynamics and Monte Carlo simulations of (poly-)electrolyte systems.     

Determination of zeta potentials of polymeric nanoparticles by the conductivity variation method

An easy method of measurement of the zeta potentials of sub-50-nm polymeric nanoparticles is suggested. Although zeta potential measurements of nanoparticles or emulsions above 50 nm have been successfully carried out, zeta potentials of emulsions or nanoparticles below 50 nm could not be precisely measured in the region of extremely low conductivity by conventional electrophoresis with a He-Ne laser. However, zeta potentials of sub-50-nm nanoparticles were measured in the region of thin electrical double layers by addition of sodium chloride and zeta potentials in the condition without sodium chloride could be predicted by extrapolation of the measured potentials. The electrophoretic mobility of 150-nm nanoparticles stabilized with sodium dodecylsulfate was the same as that calculated from extrapolation of the measured ones. The zeta potentials of sub-50-nm nanoparticles stabilized with sodium dodecylsulfate could be calculated by the same procedure.     

Mixed quantum-classical dynamics in the adiabatic representation to simulate molecules driven by strong laser pulses

The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na(2) using the surface-hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.     

Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids

We have used systematic structure‐based coarse graining to derive effective site–site potentials for a 10‐site coarse‐grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse‐grained model the same site–site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid–water molar ratios. It was shown that there is a non‐negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid‐like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse‐grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self‐aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles. © 2014 Wiley Periodicals, Inc.     

Contribution of inter- and intramolecular energy transfers to heat conduction in liquids

The molecular dynamics expression of heat flux, originally derived by Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] for pairwise potentials, is generalized in this paper for systems with many-body potentials. The original formula consists of a kinetic part and a potential part, and the latter term is found in the present study to be expressible as a summation of contributions from all the many-body potentials defined in the system. The energy transfer among a set of sites for which a many-body potential is defined is discussed and evaluated by the rate of increase in the kinetic energy of each site due to the potential, and its accumulation over all the potentials in the system is shown to make up the potential part of the generalized expression. A molecular dynamics simulation for liquid n-octane was performed to demonstrate the applicability of the new expression obtained in this study to measure the heat flux and to elucidate the contributions of inter- and intramolecular potentials to heat conduction.     

The calculation of molecular electrostatic potential from a multipole expansion based on localized orbitals and developed at their centroids: Accuracy and applicability for macromolecular computations

An improvement of a multipole expansion based on localized orbitals and termed LMTP is presented and its ability to generate accurate electrostatic potentials is demonstrated. The possibilities of using this expansion in studying the potential of different conformational states of a molecule without the necessity of recalculating its molecular wavefunction is described and the construction of macromolecular potentials by the superposition of the potentials of subunits is reconsidered.     

Density dependent potentials: structure and thermodynamics

Local density dependent potentials constitute a family of many body potentials which have been recently introduced in mesoscopic modeling of simple and complex fluids. We construct a field theory for these potentials and calculate the structure factor of the fluid through a saddle point expansion. We propose also an integral equation for local density potentials which shows quantitative agreement both for the correlation functions and thermodynamic properties of such potentials, even close to binodals where the simpler saddle point approximation fails. Contrary to the limitations of global density dependent potentials, there is no ambiguity in the expression of thermodynamics quantities such as the pressure.     

Electron localization in a finite one-dimensional chain

The localization characteristics of the electronic wave functions in a finite one-dimensional chain with the diagonal or the off-diagonal disorder of the potentials have been studied. It has been shown that the eigenfuction at the frontier level is relatively “strong” against the temptation to localize caused by the existence of the random potentials. It has also been pointed out that the spatial behavior of the total density reflects that of the diagonal random potentials, but that under the off-diagonal random potentials the total density is spatially uniform (completely extended).     

Energy expressions for Kohn-Sham potentials and their relation to the Slater-Janak theorem

Direct approximation of exchange-correlation potentials is a promising approach to accurate prediction of molecular response properties. However, little is known about ways of obtaining total energies from model potentials other than by using the Levy-Perdew virial relation. We introduce and explore several alternative formulas which arise as line integrals of potentials taken along density scaling and aufbau-filling paths, and which are not limited to the exchange term. The relaxed-orbital variant of the aufbau-path energy expression is shown to be closely related to the Slater-Janak theorem. Although the Levy-Perdew relation generally yields reasonable energies for all model exchange potentials, the relaxed-orbital aufbau path gives better results for those potentials that predict accurate highest-occupied orbital eigenvalues, such as the potential of Ra?sa?nen, Pittalis, and Proetto [J. Chem. Phys. 132, 044112 (2010)]. The ideas presented in this work may guide the development of new types of density-functional approximations for exchange and correlation.