Empirical Potential Energy Function Research Articles

Ab initio potential energy functions, spectroscopy and thermal physics for krypton-contained rare gas dimers

Three state-of-the-art ab initio interatomic potential energy functions (PEFs) for the Kr-Ne, Kr-Ar, Kr-Xe rare gas dimers are presented. These PEFs are based upon extrapolation to complete basis set (CBS) limit results of supermolecular computations at the coupled-cluster level with single, double, and perturbative triple excitations (CCSD(T)) and correlation-consistent basis sets up to sextuple-zeta quality, augmented with mid-bond functions. Core-core and core-valence electron correlation, higher-order coupled-cluster excitations up to perturbative quadruple excitations, CCSDT(Q), and scalar relativistic corrections have also been taken into account. We have employed Morse/Long Range (MLR) potential energy functions (PEFs) to fit the total interaction energies as a function of the internuclear separation, followed by the calculation of spectroscopic parameters, vibrational and rotational energy levels, absorption spectra, and thermophysical properties over an extensive temperature range. Good agreement with experimental data and an empirical potential energy function shows that our ab initio MLR PEFs are superior not only to previous PEFs, but also to most empirical PEFs.

Empirical Potential Energy Function Toward ab Initio Folding G Protein-Coupled Receptors.

Approximately 40-50 percent of all drugs targets are G protein-coupled receptors (GPCRs). Three-dimensional structure of GPCRs is important to probe their biophysical and biochemical functions and their pharmaceutical applications. Lacking reliable and high quality free function is one of the ugent problems of computational predicting the three-dimensional structure in this community. We proposed a GPCR-specified energy function composed of four novel empirical potential energy terms: a two-dimensional contact energy force field, knowledge-based helix pair connection distance energy term, knowledge-based helix pair angle restraint energy term and a disulfide bond energy term. To validate the energy function, we employed an ab initio GPCR three-dimensional structure predictor to test if the energy function improved the accuracy of prediction. We evaluated 28 solved GPCRs and found that 21(75 percent) targets were correctly folded (TM-score>0.5). Also, the average TM-score using the energy function was 0.54, which was improved 134 percent than the TM-score 0.23 for MODELLER energy function and 170 percent than the TM-score 0.20 for Rosetta membrane energy function. The results confirmed that our empirical potential energy function toward ab initio folding is competitive to state-of-the-art solutions for structural prediction of GPCRs.

Embryonic Iridium nanoclusters (n=3–13): A molecular dynamics computer simulation

The determination of the physical and chemical properties of small nanoparticles plays a fundamental role in homogeneous and heterogeneous catalysis since a large number of the surface atoms of these nanoparticles can be exposed to chemical reactions, as well as in chemisorption, solid state physics, laser physics, crystal growth, epitaxy and surface science in general as most recent experimental and theoretical investigations have been disclosed. An empirical many-body Potential Energy Function (PEF) incorporating two-plus three-body atomistic potential derived by fitting experimental data pertaining to bulk Iridium has been applied to study the structural stability and energetics of Iridium nanoparticles of Irn([Formula: see text]–13). A constant temperature Molecular Dynamics (MD) technique is employed in the simulations. It is found that the energetically most stable structures of Iridium nanoparticles are in three-dimensional distorted compact forms close to symmetric geometries with the MD technique. The theoretical predictions are compared to the available theoretical and experimental literature data for binding energies, bond lengths and the most stable nanocluster geometry.

An empirical potential energy function for the interactions between rare gas atoms

Abstract A new potential model was developed in this work by the modification of the repulsive part of the Tang-Toennies model. The proposed potential function was used in this work to investigate the interactions between both like and unlike rare gas atoms. The considered systems are He2, Ne2, Ar2, and Kr2 for the like interactions and HeNe, HeAr, and HeKr for the unlike interactions. The potential parameters in the repulsive part of each system were determined from the recent literature values of the equilibrium distance R e , the well depth D e , and the dispersion coefficients C 6 - C 10 . Accurate potential energies available in the literature were compared with the modified potential model and the original Tang-Toennies model. Although both potential energy functions show the same performance in the attractive region and the well-depth region, the proposed potential model can provide a more realistic repulsive wall than the Tang-Toennies model. Since the transport properties of low-density gases are sensitive to the potential energies at small intermolecular distances, the viscosity and thermal conductivity computed in this work were compared with the recommended experimental data in the literature to further verify the quality of the modified potential energy function.

A new empirical potential energy function for Ar2

ABSTRACTA critical re-analysis of all available spectroscopic and virial coefficient data for Ar2 has been used to determine an improved empirical analytic potential energy function that has been ‘tuned’ to optimise its agreement with viscosity, diffusion and thermal diffusion data, and whose short-range behaviour is in reasonably good agreement with the most recent ab initio calculations for this system. The recommended Morse/long-range potential function is smooth and differentiable at all distances, and incorporates both the correct theoretically predicted long-range behaviour and the correct limiting short-range functional behaviour. The resulting value of the well depth is cm−1 and the associated equilibrium distance is re = 3.766 (±0.002) Å, while the 40Ar s-wave scattering length is −714 Å.

Multipole moments of water molecules and the aqueous solvation of monovalent ions

The differences in solvation of ions in water play important roles in biology and chemistry, such as the kosmotropic and chaotropic properties of different ions. However, the differences in certain properties of ions in aqueous solutions have been difficult to capture in atomistic computer simulations. Given the uniqueness of water as a liquid, this may be due to oversimplifications in empirical potential energy functions used to describe water in these simulations. Recently, a single-site multipole (SSMP) non-polarizable model of water, which uses multipoles from a quantum mechanical calculation, has been shown to model the properties of liquid water over a range of temperatures and pressures with remarkable accuracy compared to both nonpolarizable and polarizable multi-site models. Thus, it appears to capture features of the average electrostatic potential that other models lack. Here, the ability of SSMP to model the structure of the hydration shell of monovalent ions is investigated. Although only multipoles up to the octupole are needed for water-water interactions, it is shown to be necessary to include the hexadecapole for interactions with charged species, so that the multipole expansion energies are all truncated at order 1/r5. More importantly, it is shown that solvation of cations in SSMP water leads to agreement of the orientational distribution of water molecules with ab initio molecular dynamics results, unlike typical multi-site models. The additional orientation seen in SSMP water may lead to an understanding of the differences in the kosmotropic and chaotropic properties of sodium and potassium ions.

Impact of the dipole-moment representation on the intensity of high overtones

Calculating intensities of ro-vibrational transitions is particularly challenging for transitions from a given vibrational state to all upper states up to the dissociation limit because their probabilities decrease exponentially with increasing Δn, the change in the vibrational quantum number. The experimental intensities available for low-Δn values are well reproduced by a variety of models but the models can greatly diverge in predicting the intensities of unobserved high-overtone transitions, the divergence rapidly increasing with the overtone number. In this paper, we investigate the impact of the dipole-moment function (DMF) representation on the high-overtone intensity simulation of the CO molecule. We tested various DMF forms including pointwise representation combined with cubic-spline interpolation, power and trigonometric expansions, and Padé approximants. Numerical calculations were performed with the highly accurate empirical potential-energy function (PEF) of Coxon and Hajigeorgiou (2004) using quadruple-precision arithmetic. Most calculated intensities fall off in the entire range of transitions according to the Normal Intensity Distribution Law (NIDL) (Medvedev, 2012). The slope of the NIDL trend line varies little between different analytical DMFs for a given PEF since the slope is basically associated with the PEF. Based on the NIDL, the limits within which the simulated intensities fall off up to the dissociation limit can be established. We claim that DMFs represented by analytical functions yield best results for all transitions. The pointwise functions (interpolated, in particular, by the conventional cubic splines) result in an unphysical flattening of the intensities at high-Δn transitions, Δn>7 for CO.

Size, Shape and Structure Dependent Cohesive Energy of Gold Nanoparticles: Empirical Many-Body Potential Energy Function Calculations

A thermodynamic model based on an empirical many-body potential energy function is used, to investigate the stability and energetic features of gold nanoparticles as a function of both size and shape. The concept of a localized atomic bond for surface atoms, and a non-relaxed atomic bond for the interior atoms is used. Among the five different investigated shapes, the qualitative behaviour for the cohesive energy per atom of gold nanoparticles with size range 200 1000 atoms, the general behaviour prefers; sphere < cubic <cuboctahedron < truncated octahedron < octahedron. On the other hand, the surface energy for gold nanoparticles is observed to be prominent in the nano-scale and it differs from shape to another, and falls down fast in the size range 200 < n < 1000 atoms having general trend; sphere < cubic <octahedron < truncated octahedron < cuboctahedron.

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.

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.

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.

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.

Modified Rosen-Morse potential-energy model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the generalized Woods-Saxon potential. It is exactly shown that the generalized Woods-Saxon potential and the well-known Rosen-Morse potential are the same empirical potential-energy function for diatomic molecules. Based on the measure of inner-shell radii of two atoms, we propose a modified Rosen-Morse potential-energy model. Evaluation of the average deviations from the experimental data is carried out on six molecules. The modified Rosen-Morse potential is found to be more accurate than the Morse and Rosen-Morse potentials in fitting experimental data for the six molecules examined.

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.

Domain Motions in the Interpretation of Neutron Spin Echo Spectroscopy and Molecular Dynamic Simulation: A Case Study of Phosphoglycerate Kinase

The conformational dynamics of proteins are important for functions. Large-scale domain motions of enzymes are often essential for their biological function. Few techniques are available that can directly probe protein motions. Among the most direct is molecular dynamics simulation in which, using an empirical potential energy function, the equations of motion of a system of atoms are solved numerically. In this way detailed description of protein dynamics can be built up for timescales up to about 100 ns. Integration of molecular dynamics simulations and neutron scattering provide insights of process in the proteins in the atomic details. An exciting new development in the experimental detection of functionally-important domain motions in proteins is the application of neutron spin-echo spectroscopy (NSE). Spin echo directly probes coherent (i.e., pair correlated) scattering on the 10-100 ns timescale. Recent work has demonstrated that domain motions in the two domain protein phosphoglycerate kinase (PGK) can be positively identified and characterized with this technique. Inspired by these results, we performed molecular dynamics simulation of PGK. The measurable quantities, the intermediate scattering functions and small-angle neutron scattering profile were directly calculated from the MD trajectories. All results are in very good agreement with experimental data. Principal component analysis (PCA) was used to characterize the molecular dynamics trajectory. PCA extracts the essential motions sampled by MD simulation: the principal component modes. We have shown that combination of neutron scattering and molecular dynamics simulation is a powerful tool for characterization large scale motions in proteins.