Empirical Potential Function Research Articles

Molecular dynamics simulations of mechanical properties of monolayer MoS2

Based on the benchmark created by the first principle calculations, the effectiveness of different empirical potential functions, including CVFF1, CVFF2, SW and REBO potentials, on describing the mechanical behavior of single layer MoS2 (SLMoS2) are evaluated. The mechanical properties including the elastic modulus E, Poisson’s ratio ν, nonlinear elastic modulus D, failure stress and ultimate strain are considered. It is found that under a small deformation, the REBO and CVFF2 potentials can provide an effective description of the elastic behavior of SLMoS2; whereas under a large deformation, the SW potential gives a more accurate stress value and the CVFF2 potential can only predict the right value under biaxial tension. After modifying the cut-off distances in the REBO potential, the failure strain can be reasonably predicted by the REBO potential; whereas the failure stress will be overestimated by about 20–40% for biaxial and uniaxial tension. The present study can provide help on accurately understanding the mechanical behavior of SLMoS2.

Atomic torsional modal analysis for high-resolution proteins.

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier one-parameter formulation [M. M. Tirion, Phys. Rev. Lett. 77, 1905 (1996)] that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function that is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states in the 0 to 300cm-1 frequency range, not merely the slow modes. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface side chains and helps fix the spectrum thin tail frequencies (100-300cm-1). Second, we take into account the atomic identities and the distance of separation of all pairwise interactions, improving the spectrum distribution in the 20 to 300cm-1 range. With these modifications, not only does the spectrum reproduce that of full atomic potentials, but we obtain stable reliable eigenmodes for the slow modes and over a wide range of frequencies.

Metropolis Monte Carlo based Relaxation of Atomistic III-V Semiconductor Models

We present atomistic simulations of III-V semiconductor materials. These provide an effective way to investigate structural properties of semiconductors at a nanometric scale. The crystal structure is relaxed using a Metropolis Monte Carlo scheme, where chemical bonds are described through empirical interaction potentials. The method provides a simplified structural model, which allows to determine elastic properties like the bulk and shear modulus with errors around 5 and 10%. Simulations on random alloys led to a composition-dependent bimodal bond length distribution, stemming from the constituent binary compounds, which was also observed experimentally. In contrast to this, CuPt-ordered structures, which can form spontaneously during epitaxial processes, were shown to exhibit a distinct fourfold bond length pattern leading to built-in strain. The Metropolis Monte Carlo approach also allows modelling at higher temperatures. The asymmetry of the empirical potential function leads to thermal expansion, although this effect is in general overestimated due to the missing Coulomb interaction, which is characteristic of III-V materials.

Formation of nanopore in a suspended graphene sheet with argon cluster bombardment: A molecular dynamics simulation study

Formation of a nanopore in a suspended graphene sheet using an argon gas beam was simulated using molecular dynamics (MD) method. The Lennard-Jones (LJ) two-body potential and Tersoff–Brenner empirical potential energy function are applied in the MD simulations for different interactions between particles. The simulation results demonstrated that the incident energy and cluster size played a crucial role in the collisions. Simulation results for the Ar55–graphene collisions show that the Ar55 cluster bounces back when the incident energy is less than 11eV/atom, the argon cluster penetrates when the incident energy is greater than 14eV/atom. The two threshold incident energies, i.e., threshold incident energy of defect formation in graphene and threshold energy of penetration argon cluster were observed in the simulation. The threshold energies were found to have relatively weak negative power law dependence on the cluster size. The number of sputtered carbon atoms is obtained as a function of the kinetic energy of the cluster.

Force Field Model of Periodic Trends in Biomolecular Halogen Bonds.

The study of the noncovalent interaction now defined as a halogen bond (X-bond) has become one of the fastest growing areas in experimental and theoretical chemistry--its applications as a design tool are highly extensive. The significance of the interaction in biology has only recently been recognized, but has now become important in medicinal chemistry. We had previously derived a set of empirical potential energy functions to model the structure-energy relationships for bromines in biomolecular X-bonds (BXBs). Here, we have extended this force field for BXBs (ffBXB) to the halogens (Cl, Br, and I) that are commonly seen to form stable X-bonds. The ffBXB calculated energies show a remarkable one-to-one linear relationship to explicit BXB energies determined from an experimental DNA junction system, thereby validating the approach and the model. The resulting parameters allow us to interpret the stabilizing effects of BXBs in terms of well-defined physical properties of the halogen atoms, including their size, shape, and charge, showing periodic trends that are predictable along the Group VII column of elements. Consequently, we have established the ffBXB as an accurate computational tool that can be applied, for example, for the design of new therapeutic compounds against clinically important targets and new biomolecular-based materials.

On the equivalence of the Badawi–Bessis–Bessis, Wei and Tietz potential energy functions for diatomic molecules

It is found that the general potential energy expression introduced by Badawi et al for several empirical potential energy functions that is conventionally defined in terms of five parameters, actually only has four independent parameters. It is demonstrated exactly that the Badawi–Bessis–Bessis potential is equivalent to the well-known Tietz potential model for diatomic molecules. When parameter a in the Badawi–Bessis–Bessis potential function has the values 0, +1 and −1, the Badawi–Bessis–Bessis potential becomes the standard Morse, Rosen–Morse and Manning–Rosen potentials, respectively.

The effect of empirical potential functions on modeling of amorphous carbon using molecular dynamics method

Empirical potentials have a strong effect on the hybridization and structure of amorphous carbon and are of great importance in molecular dynamics (MD) simulations. In this work, amorphous carbon at densities ranging from 2.0 to 3.2g/cm3 was modeled by a liquid quenching method using Tersoff, 2nd REBO, and ReaxFF empirical potentials. The hybridization, structure and radial distribution function G(r) of carbon atoms were analyzed as a function of the three potentials mentioned above. The ReaxFF potential is capable to model the change of the structure of amorphous carbon and MD results are in a good agreement with experimental results and density function theory (DFT) at low density of 2.6g/cm3 and below. The 2nd REBO potential can be used when amorphous carbon has a very low density of 2.4g/cm3 and below. Considering the computational efficiency, the Tersoff potential is recommended to model amorphous carbon at a high density of 2.6g/cm3 and above. In addition, the influence of the quenching time on the hybridization content obtained with the three potentials is discussed.

Quantum mechanical force field for water with explicit electronic polarization.

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.

Equivalence of the deformed Rosen–Morse potential energy model and Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed Rosen–Morse potential energy model. It is found that the deformed Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. With the help of the energy spectrum expression of the deformed Rosen–Morse potential model, we obtain exact closed-form expressions of diatomic anharmonicity constants $$\omega _e x_e $$ and $$\omega _e y_e $$ .

Infrared spectrum of the CS2 tetramer: Observation of a structure with D2d symmetry

Infrared spectra of carbon disulfide clusters are studied in the region of the CS2 ν3 fundamental band (≈1535cm−1), using a tuneable diode laser to probe a pulsed supersonic slit jet expansion. A symmetric rotor parallel band at 1551.438cm−1 is assigned to CS2 tetramer. The likely structure is a staggered and tilted barrel with D2d symmetry, similar to the previously observed oblate tetramer of nitrous oxide, and in reasonable agreement with that calculated from an empirical CS2 intermolecular potential function. This is the first high-resolution spectroscopic detection of CS2 tetramer, and the calculations suggest that there could be other low energy isomers of (CS2)4 which are not yet observed.

Equivalence of the deformed modified Rosen–Morse potential energy model and the Tietz potential energy model

By applying the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the deformed modified Rosen–Morse potential energy model. It is found that the deformed modified Rosen–Morse potential model and the well-known Tietz potential model are the same empirical potential function for diatomic molecules. In terms of the energy spectrum expression of the deformed modified Rosen–Morse potential model, we obtain exact closed-form expressions for diatomic anharmonicity constants ωexe and ωeye . The anharmonicity constants for the X1Σ+g state of the N2 molecule have been computed and compared with the observed data.

Study of the vibrational characteristics of the homonuclear diatomic nuclear schrödinger equation with a numerov method using a number of empirical potential functions

Many empirical potential energy functions have been modeled to represent the potential energy function of a diatomic molecule along whole range of internuclear distance coordinate, whereby one can determine certain molecular constants. Here we employ various potential functions such as Morse, Rydberg, Varshni(II), Varshni(III), Varshni(VI), Poschl-Teller, Hulburt-Hirschfelder, Lippincott, Frost-Musulin, Linnet, and Rosen-Morse, and the Numerov method to solve the nuclear Schrodinger equation for F2, as an example of a homonuclear diatomic molecule. Herewith, the vibrational and vibration-rotation energy levels are obtained and excellent accuracy is achieved. The potential of employing the Numerov method in engineering physics computations is emphasized.

Drude Model Based Polarizable Force Field for Lipids

Incorporation of electronic polarization of atoms induced by local electric fields in the empirical potential function used to generate molecular dynamics simulations is important for accurate studies of various biological processes such as ion transfer, binding and selectivity. In this work, we present new polarizable force fields for the simulations of zwitterionic lipids membranes based on the classical Drude oscillator model. The lipids considered include: dipalmitoyl phosphatidylcholine (DPPC), dipalmitoyl phosphatidylethanolamine (DPPE), and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC).The parameterization strategy relies on the properties of small model compound analogs of functional groups in the molecules. The polar head group parameters are based on the molecular ions dimethyl phosphate and tetramethyl ammonium, methyl acetate for the glycerol linker region and linear alkanes as well as alkenes for the aliphatic tail of the lipid. The small molecule parameters are optimized and validated against a suite of experimental properties. The resulting lipid force field is applied to the simulation of lipid bilayers and monolayers for each lipid. For the lipid bilayer, the area per lipid, deuterium order parameters and electron density profile, and for the monolayers, the surface pressure and dipole potentials are all found to be in good agreement with experimental data when available. Thus, we have successfully validated our force field for a number of lipids.

Statistical Mechanical Model for the Transfer Free Energy of Amino Acids in the Context of Membrane Protein OmpLA

Transfer free energy scale of amino acids is fundamental for understanding membrane protein folding and for predicting membrane protein structures. Several experimental studies have been carried out to measure the free energy of partitioning amino acids to artificial lipid bilayer or biological membranes in the context of model peptides. A recent study measured water-to-bilayer transfer free energy in the context of a native β-barrel transmembrane protein OmpLA[1]. Here we report the development of a computational free energy scale based on an empirical potential energy function and statistical mechanical model. Our energy function incorporates the energy contribution of single-body burial, inter-strand interaction and sequential nearest neighbor contact interaction. Using a statistical mechanical model with a reduced state space, we computed the full partition function of OmpLA and the relative insertion free energy of amino acids replacing Ala210. The computed relative free energy scale correlates well with experimental data (r2 =0.79 with water-to-bilayer scale[1] and r2=0.88 with translocon scale[2]). In addition, depth dependency profiles of Arg and Leu are in excellent agreement with those measured by Moon and Flemming [1]. We also obtained depth dependency profiles of all 20 amino acids which provide insight to the folding process of membrane protein. Furthermore, our model showed strong coopperativity of Arg-Arg, consistent with experimental founds[1]. We further predicted that Lys-Lys show significant cooperativity, which is subject to future experimental verification.1. Moon CP, Fleming KG (2011) Side-chain hydrophobicity scale derived from transmembrane protein folding into lipid bilayers. Proc Natl Acad Sci USA108:10174-101772. Hessa, T, Kim, H, Bihlmaier, K, Lundin, C, Boekel, J, Andersson, H, Nilsson, I, White, SH, von Heijne, G (2005). Recognition of transmembrane helices by the endoplasmic reticulum translocon. Nature, 433, 7024:377-81.

Molecular Modeling of SERCA Dynamics and Interactions

On a cellular level, the cardiac cycle is orchestrated by release of calcium into the cytosol during systole (contraction) and subsequent reuptake of calcium into internal stores by an ion-motive ATPase during diastole (relaxation). This pump, the sarco(endo)plasmic reticulum calcium ATPase (SERCA), undergoes large conformational changes between enzymatic substates during calcium transport. Recently, we resolved 4 different structural substates of SERCA using intramolecular fluorescence resonance energy transfer (FRET). To investigate SERCA conformational changes in atomic detail we performed molecular dynamics simulations. This technique can directly probe protein motions by using an empirical potential energy function to numerically solve the equations of the motion of the system. We used X-ray crystal structures as a starting point for simulation of open and closed SERCA headpiece conformations and investigated the structural disorder of various structural substates. Specifically, we tested a hypothesis generated from FRET experiments: Open conformations of SERCA are more dynamic than compact, closed structures.

Force field model and molecular dynamics simulation of polyynes

The molecular force field model for polyynes is developed by fitting the empirical force field potential function into intermolecular interaction potentials of various configurations including side-by-side, parallel, crossover, and head-to-head configurations calculated using the Møller–Plesset perturbation theory at MP2/6-311G(d,p) level of theory. And the force field model is applied to the molecular dynamics simulation of polyyne–methanol mixture. The calculations reveal that the polyyne molecules aggregate in bundles, and hydrogen bonds are formed between the polyyne hydrogen and methanol oxygen.

Improved expressions for the Schiöberg potential energy models for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for both versions of the Schiöberg potential energy function. Both versions of the Schiöberg potential function are the Rosen–Morse potential function and Manning–Rosen potential functions. By choosing the experimental values of the dissociation energy, equilibrium bond length and equilibrium harmonic vibrational frequency as inputs, we calculate the average deviations of the energies calculated with the potential model from the experimental data for five diatomic molecules, and find that no one of six three-parameter empirical potential energy functions is superior to the other potentials in fitting experimental data for all molecules examined.

Molecular dynamics simulation study of the diamond D5 substructures

Abstract Diamond D5 is the name proposed by Diudea for hyper-diamonds having their rings mostly pentagonal. Within D5, in crystallographic terms: the mtn structure, known in clathrates of type II, several substructures can be defined. In the present work, the structural stability of such intermediates/fragments appearing in the construction/destruction of D5 net was investigated using molecular dynamics simulation. Calculations were performed using an empirical many-body potential energy function for hydrocarbons. It has been found that, at normal temperature, the hexagonal hyper-rings are more stable while at higher temperature, the pentagonal ones are relatively more resistant against heat treatment.

Equivalence of the three empirical potential energy models for diatomic molecules

It is found that the Manning–Rosen potential, Schiöberg potential and Deng–Fan potential are the same solvable empirical potential energy function for diatomic molecules. We calculate the anharmonicity ωexe and vibrational rotational coupling parameter αe for 16 molecules by choosing the experimental values of the dissociation energy De, equilibrium bond length re and vibrational frequency ωe as inputs. The results show that the Manning–Rosen potential, Deng–Fan potential and Schiöberg potential are not better than the traditional Morse potential.

Dynamic and static fracture analyses of graphene sheets and carbon nanotubes

Dynamic and static fracture properties of Graphene Sheets (GSs) and Carbon nanotubes (CNTs) with different sizes are investigated based on an empirical inter-atomic potential function that can simulate nonlinear large deflections of nanostructures. Dynamic fracture of GSs and CNTs are studied based on wave propagation analysis in these nanostructures in a wide range of strain-rates. It is shown that wave propagation velocity is independent from strain-rate while dependent on the nanostructure size and approaches to 2.2×104m/s for long GSs. Also, fracture strain shows extensive changes versus strain-rate, which has not been reported before. Fracture stress is determined as 115GPa for GSs and 122GPa for CNTs which are independent from the strain-rate; in contrast to the fracture strain. Moreover, fracture strain drops at extremely high strain-rates for GSs and CNTs. These features are considered as capability of carbon nanostructures for reinforcing nanocomposites especially under impact loadings up to high strain-rates.