Empirical Pair Potentials Research Articles

Thermodynamics of mixing in pyrope-grossular, Mg3Al2Si3O12-Ca3Al2Si3O12, solid solution from lattice dynamics calculations and Monte Carlo simulations

Static lattice energy calculations (SLEC), based on empirical pair potentials have been performed for a set of 125 different structures with compositions between pyrope and grossular, and with different states of order of the exchangeable Mg and Ca cations. Total energies of a subset of these configurations have been calculated with a density functional electronic structure method (ab initio). The excess energies derived from ab initio and SLEC results agree well with each other. Excess free energies of the 125 structures have been calculated at 300 and 1000 K and at 0 and 3 GPa and cluster expanded in a basis set of 8 pair-interaction parameters. These ordering parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the ranges of 300-1500 K and 0-3 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. The calculations predict the development of a significant short-range and long-range ordering at the intermediate 50/50 composition. The long-range ordered phase with I4 1 22 symmetry becomes stable below 600 K. Two miscibility gaps driven by the stability of the intermediate phase develop at both sides of the 50/50 composition. Activity-composition relations in the range of 600-1500 K and 0-3 GPa are described with high-order Redlich-Kister polynomials.

Monte Carlo simulation of mixing in Ca3Fe2Ge3O12–Ca4Ge4O12 garnets and implications for the thermodynamic stability of pyrope–majorite solid solution

Static lattice energy calculations, based on empirical pair potentials, were performed for a large set of structures differing in the arrangement of octahedral cations within the garnet 2 × 2 × 2 supercell. The compositions of these structures varied between Ca3Fe2Ge3O12 and Ca4Ge4O12. The energies were cluster expanded using pair and quaternary terms. The derived ordering constants were used to constrain Monte Carlo simulations of temperature-dependent mixing properties in the ranges of 1,073–3,673 K and 0–10 GPa. The free energies of mixing were calculated using the method of thermodynamic integration. The calculations predict a wide miscibility gap between Fe-rich (cubic) and Fe-pure (tetragonal) garnets consistent with recent experimental observations of Iezzi et al. (Phys Chem Miner 32:197–207, 2005). It is shown that the miscibility gap arises due to a very strong cation ordering at the Fe-pure composition, driven by the charge difference between Ca2+ and Ge4+ cations. The structural and thermodynamic analogies between Ca–Ge and Mg–Si systems suggest that a similar miscibility gap should exist between pyrope and Mg–Si-majorite.

The transcription regulator RbsR represents a novel interaction partner of the phosphoprotein HPr‐Ser46‐P in Bacillus subtilis

Histidine-containing protein (HPr) is a central metabolic sensor in low-GC Gram-positive bacteria and plays a dual role in sugar uptake by the phosphoenolpyruvate-sugar phosphotransferase system and in transcriptional control during carbon catabolite repression. The latter process is mediated by interaction between HPr and the carbon catabolite repression master transcription regulator, carbon catabolite protein A (CcpA), a member of the LacI-GalR family of DNA-binding proteins. We investigated, with a combination of computational and experimental tools, whether HPr can also interact with other transcriptional regulators. To allow rapid identification of paralogous LacI-GalR family members that might interact with HPr in a similar fashion to CcpA, a structure-based computational approach was developed which relies on the analysis of the similarity of protein-protein interfaces between different complexes. A key element of this method is an empirical pair potential derived from a group of orthologous complexes and subsequently used to identify paralogs that exhibit similar properties of their protein interfaces. Application of this method to the family of LacI-GalR repressors in Bacillus subtilis predicted the ribose operon repressor (RbsR) as a novel interaction partner of HPr. This interaction was subsequently confirmed experimentally and suggests that HPr plays an even larger role in transcriptional control than previously expected.

An effective pair potential for thermodynamics and structural properties of liquid mercury

The properties of liquid mercury are investigated by using an empirical effective pair potential. Its parameters are determined with the aid of Monte Carlo simulation along the liquid branch of the liquid-vapor coexistence curve. The complexity of the electronic structure of dense metal mercury supposes a state dependence of the interatomic interactions, while no more state dependence is found in the metal-nonmetal transition region. It is shown that the use of this effective potential leads to an accurate description of the structural and thermodynamic properties of the expanded liquid mercury. Then, the melting and freezing phenomena are investigated with that potential. Sharp melting and freezing temperatures are observed at 234 and 169 K, respectively. This large hysteresis loop between freezing and melting is consistent with the experiments for the bulk mercury.

Thermodynamics of pyrope–majorite, Mg3Al2Si3O12–Mg4Si4O12, solid solution from atomistic model calculations

Static lattice energy calculations, based on empirical pair potentials have been performed for a large set of different structures with compositions between pyrope and majorite, and with different states of order of octahedral cations. The energies have been cluster expanded using pair and quaternary terms. The derived ordering constants have been used to constrain Monte–Carlo simulations of temperature-dependent properties in the ranges of 1073–3673 K and 0–20 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. At zero pressure the cubic/tetragonal transition is predicted for pure majorite at 3300 K. The transition temperature decreases with the increase of the pyrope mole fraction. A miscibility gap associated with the transition starts to develop at about 2000 K and x maj = 0.8, and widens with the decrease in temperature and the increase in pressure. Activity–composition relations in the range of 0–20 GPa and 1073–2673 K are described with the help of a high-order Redlich–Kister polynomial.

A density-functional approach to polarizable models: A Kim-Gordon response density interaction potential for molecular simulations

A combined linear-response-frozen electron-density model has been implemented in a molecular-dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory [J. Chem. Phys. 56, 3122 (1972); J. Chem. Phys. 60, 1842 (1974)] and a response contribution determined by the instantaneous ionic configuration of the system. The method is free from empirical pair potentials and the parametrization protocol involves only calculations on properly chosen subsystems. We apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparable to Kohn-Sham density-functional calculations.

Sensitivity of model water structure to hydrogen bond included

Water empirical pair potentials, including the nonelectrostatic component of hydrogen bond (HB), are considered. The sensitivity of the radial distribution functions (RDF), calculated in computer experiment, to this contribution is analyzed. The model potentials, for which the positions and the heights of first and second peaks on the oxygen–oxygen radial distribution function coincide with the experimental ones, have been obtained.

Hydrogen bonding contribution to the water pair interaction potential: Effects on the model liquid structure

Empirical pair potentials of water that take into account the contribution of the OH nonelectrostatic interaction in the hydrogen bond are considered. The effects of this contribution on the radial distribution functions derived by computer simulation are analyzed. Model potentials have been obtained for which the height and position of the first and second peaks of the oxygen-oxygen radial distribution function are comparable with experimental data.

Simulation of CaF 2 in the superionic state: comparison of an empirical and realistic potential

The conductivity and heat capacity of CaF 2 in the superionic phase are calculated by computer simulation using an ab initio interaction model which includes polarization effects. The results are compared with those obtained in Gillan's classic study of CaF 2, where an empirical effective pair potential was used. Despite large differences between the potentials at the pair-wise interaction level, the observable properties predicted by the two models are essentially identical in the crystal, and the reasons for the success of the effective pair potential in recapturing the consequences of the polarization effects are discussed. As further aspects of the study, we clarify the simulation predictions for the magnitude of the heat capacity anomaly at the superionic transition and for the number of defects present in the superionic states—matters on which Gillan's results have been taken to be at variance with the body of experimental evidence on other fluorite-structured materials.

Effective three-body potentials for Li+(aq) and Mg2+(aq)

A method for the extraction of effective three-body potential parameters from high-level ab initio cluster calculations is presented and compared to effective pair potentials extracted at the same level. Dilute Li+(aq) and Mg2+(aq) solutions are used as test cases and long molecular-dynamics simulations using these newly developed potentials were performed. Resulting thermodynamical, structural, and dynamical properties are compared to experiment as well as to the empirical effective pair potentials of Åqvist. Moreover, a new time-saving method for the correction of cluster energies computed with a relatively cheap ab initio method, to yield expensive, high-level ab initio energies, is presented. The effective pair approach is shown to give inconsistent results when compared to the effective three-body potentials. The performance of three different charge compensation methods (uniform charge plasm, Bogusz net charge correction, and counter ions) is compared for a large number of different system sizes. For most properties studied here, the system-size dependence is found to be small for system sizes with 256 water molecules or more. However, for the self-diffusion coefficients, a 1/L dependence is found, i.e., a very large system-size dependence. A very simple method for correcting for this deficiency is proposed. The results for most properties are found to compare reasonably well to experiment when using the effective three-body potentials.

Prediction of protein structure by emphasizing local side-chain/backbone interactions in ensembles of turn fragments.

The prediction strategy used in the CASP5 experiment was premised on the assumption that local side-chain/backbone interactions are the principal determinants of protein structure at low resolution. Our implementation of this assumption made extensive use of a scoring function based on the propensities of the 20 amino acids for 137 different sub-regions of the Ramachandran plot, allowing estimation of the quality of fit between a sequence segment and a known conformation. New folds were predicted in three steps: prediction of secondary structure, threading to isolate fragments of protein structures corresponding to one turn plus flanking helices/strands, and recombination of overlapping fragments. The most important step in this fragment ensemble approach, the isolation of turn fragments, employed 2 to 6 sequence homologues when available, with clustering of the best scoring fragments to recover the most common turn arrangement. Recombinants formed between 3 to 8 turn fragments, with cross-overs confined to helix/strand segments, were selected for compactness plus low energy as estimated by empirical amino acid pair potentials, and the most common overall topology identified by visual inspection. Because significant amounts of steric overlap were permitted during the recombination step, the final model was manually adjusted to reduce overlap and to enhance protein-like structural features. Even though only one or two models were submitted per target, for several targets the correct chain topology was predicted for fragment lengths up to 100 amino acids.

Time-resolved dual fluorescence of 1-phenylpyrrole in acetonitrile: molecular dynamics simulations of solvent response to twisted intramolecular charge transfer

The real-time dynamics of solvation of 1-phenylpyrrole (PhPy) in acetonitrile (ACN) upon electronic excitation is investigated by means of non-equilibrium molecular dynamics simulations. The interaction is modeled by empirical intermolecular pair potentials using partial charges and intramolecular torsional potentials from high level ab initio calculations of ground and excited states of PhPy. The intramolecular torsional motion following sudden excitation from the twisted ground state to the 2 1B charge transfer state is strongly damped by the viscous ACN solvent, leading to a near-exponential approach of the perpendicular conformation on a timescale of about 5–10 ps. The intermolecular dynamics is characterized by rapid reorientation of the solvent molecules on a timescale of 100 fs followed by weak quasi-coherent librations. The solvatochromic red-shift of the charge transfer state with respect to the locally excited 1 1B state results in dual fluorescence, thus supporting the twisted intramolecular charge transfer (TICT) mechanism for PhPy in a polar solvent.

Testing interaction models by using x-rayabsorption spectroscopy: solid Pb

Structural models obtained using classical molecular dynamics (MD)simulations and realistic interatomic potentials for solid metalsare tested using experimental results obtained by x-ray absorptionspectroscopy (XAS). Accurate L-edgeextended x-ray absorption fine-structure (EXAFS) measurements of Pbgrains dispersed in BN and graphite matrices have been collected fortemperatures up to the melting point. The thermal expansion of thegrains was measured by energy-dispersive x-ray diffractiontechniques and found to be coincident with that of pure Pb up to thelimit of the present measurements. L3-edge EXAFSmeasurements of solid Pb at various temperatures have been analysedusing advanced data-analysis techniques (GNXAS)based on exact spherical-wave multiple-scattering simulation of theabsorption cross-section. Realistic structural models for solid Pbwere obtained from MD simulations using an empirical pair potential(Dzugutov, Larsson and Ebbsjo (DLE)), a tight-binding (TB) square-root functional, and anembedded-atom (EA) model potential parametrized by us. Theshort-range pair distribution function g(r) reconstructed by meansof EXAFS is compared with those obtained by MD simulations. Theempirical DLE potential, originally designed for the liquid state,is too soft, showing too-large values for the average distance R,variance σ2, and skewness β. The TB and EA potentialsare both compatible with XAS data as regards the average distanceand skewness of the first neighbours. The distance variance,associated with the thermal vibration amplitudes, is underestimatedfor the TB potential, while the EA model is found to be in agreementwith XAS data. The present results are also compared with thosefrom a previous EXAFS study on solid lead, where the cumulantexpansion and a simple one-dimensional anharmonic oscillator modelwere used. The need for realistic interaction models andappropriate simulation schemes for reliable XAS data analysis isemphasized, while differences from and improvements with respect toprevious approaches are only briefly discussed.

The extent of relaxation of the α-Al2O3 (0001) surface and the reliability of empirical potentials

The geometrical structure of the polar, Al-terminated surface of corundum has been investigated by different theoretical methods ranging from empirical pair potentials to periodic Hartree–Fock or density functional theory calculations. The different methods agree in predicting a structure for the bulk, which is close to the experimental one, and an inward relaxation of more than 50% in agreement with experiment. However, a rather strong disagreement exists concerning the quantitative amount of relaxation of the surface layers. Accurate density functional theory calculations for slab models considering up to 18 layers with 30 atoms in the unit cell strongly suggest that the degree of relaxation of the outermost Al atomic layer is much larger than the values obtained by other methods. Reasons for the different description are given and implications for the use of pair potentials discussed.

Use of pair potentials across protein interfaces in screening predicted docked complexes

Empirical residue-residue pair potentials are used to screen possible complexes for protein-protein dockings. A correct docking is defined as a complex with not more than 2.5 A root-mean-square distance from the known experimental structure. The complexes were generated by "ftdock" (Gabb et al. J Mol Biol 1997;272:106-120) that ranks using shape complementarity. The complexes studied were 5 enzyme-inhibitors and 2 antibody-antigens, starting from the unbound crystallographic coordinates, with a further 2 antibody-antigens where the antibody was from the bound crystallographic complex. The pair potential functions tested were derived both from observed intramolecular pairings in a database of nonhomologous protein domains, and from observed intermolecular pairings across the interfaces in sets of nonhomologous heterodimers and homodimers. Out of various alternate strategies, we found the optimal method used a mole-fraction calculated random model from the intramolecular pairings. For all the systems, a correct docking was placed within the top 12% of the pair potential score ranked complexes. A combined strategy was developed that incorporated "multidock," a side-chain refinement algorithm (Jackson et al. J Mol Biol 1998;276:265-285). This placed a correct docking within the top 5 complexes for enzyme-inhibitor systems, and within the top 40 complexes for antibody-antigen systems.

Modeling structure and dynamics of solvated molecular ions: Photodissociation and recombination in I2−(CO2)n

We describe a method for simulating the reaction dynamics of a molecular ion embedded in a cluster of polarizable solvent molecules. Potential energy surfaces for ground and excited states are calculated from an effective Hamiltonian that takes into account the strong perturbation of the solute electronic structure by the solvent. The parameters of the model Hamiltonian are obtained from a combination of ab initio calculations and spectroscopic data; intermolecular electrostatic and polarization interactions are treated by the distributed multipole analysis of Stone and co-workers, while short range interactions are modeled with empirical pair potentials. Analytical expressions for the derivatives of the effective Hamiltonian allow for efficient computation of forces and nonadiabatic couplings. The intramolecular degrees of freedom of the solvent molecules are held fixed during the simulations using the method of constraints, and electronic transitions are treated using Tully's surface hopping algorithm. The method is applied to the photodissociation and recombination of I2−(CO2)n. Electronic relaxation in this system is found to occur on multiple time scales, ranging from 2 ps to many tens of ps. The relationship of these results with the experimental measurements of Lineberger and co-workers is discussed.

Computer simulation of vacancy and interstitial clusters in bcc and fcc metals

Interstitial clusters in bcc-Fe and fcc-Cu and vacancy clusters in fcc-Cu have been studied by computer simulation using different types of interatomic potentials such as a short-ranged empirical pair potential of Johnson type, short-ranged many-body potentials of Finnis-Sinclair type and long-ranged pair potentials obtained within the generalized pseudopotential theory. The stability of a self interstitial in bcc-Fe was found to be dependent on the range of potential but not on the type. Thus, both short-ranged potentials simulated 〈110〉 dumb-bell as a stable configuration while in the case of the long-ranged potential the stable configuration is the 〈111〉 crowdion. Nevertheless the structure and properties of interstitial clusters were found to be qualitatively the same with all the potentials. Up to 50 interstitials, the most stable clusters were found as perfect dislocation loops with Burgers vector b = 1 2 〈11 1〉 . The stability of interstitial clusters in Cu also does not depend on the potential and for the same sizes the most stable configurations are faulted Frank loops 1 2 〈111〉{111} and edge loops in the {110} plane. The structure and stability of vacancy clusters in fcc-Cu were found to be dependent mainly on both the range of potential and equilibrium conditions. Thus for long-ranged non-equilibrium pair potentials vacancy clusters in the {111} plane collapsed and formed vacancy loops or stacking fault tetrahedra depending on the shape of the initial vacancy platelet. For the short-ranged equilibrium many-body potential vacancy clusters do not collapse into loops or tetrahedra. The process of vacancy clustering in the cascade region has been studied by molecular dynamics. This study has been done for the case of a PKA energy of about 20–25 keV. We found that the processes simulated with the short-ranged many-body potential and the long-ranged pair potential are qualitatively different. Thus for the many-body potential we have observed melting and crystallization of the central part of the cascade region, sweeping of vacancies inside due to the moving of the liquid-solid interface and increasing of vacancy concentration in the centre of the cascade region; however no significant clustering was observed. Contrarily for the long-ranged pair potential we have observed a very fast diffusion in the solid crystallite and the formation of stacking fault tetrahedra. The results obtained have been discussed and compared with the experimental data.

Ab initiomolecular-dynamics study of pressure-induced glass-to-crystal transitions in the sodium system

We study pressure-induced glass-to-crystal transitions in the sodium system. We apply an order-$N$ ab initio molecular-dynamics (MD) method to study the transition. We use an isothermal-isobaric condition with an orbital-free density functional. The system contains 128 atoms in a supercell. We simulate the system at temperatures higher and lower than the glass-transition temperature ${T}_{g}=120\mathrm{K}.$ At 50 K the pressure enhances the onset of crystallization from the glass. The system crystallizes at pressures greater than 2.75 GPa during which the crystalline atoms appear after the complete annihilation of the icosahedral clusters. At 290 K the system crystallizes at ${10}^{\ensuremath{-}3}\mathrm{GPa},$ during which the atoms appear before the annihilation of the clusters. The application of 1 GPa at this temperature retards the crystallization which is consistent with experiments on metallic glasses. Crystallization occurs after the clusters annihilate completely which is the same feature as the transitions at 50 K. The existence of the clusters disturbs the crystallization at high pressures irrespective of temperature. The icosahedral clusters are unstable and transform to other clusters at high pressures, although the clusters are elastically stable and the hardest within $\ifmmode\pm\else\textpm\fi{}0.07\mathrm{GPa}$ at 0 K [Masaru I. Aoki and Kazuo Tsumuraya, J. Chem. Phys. 104, 6719 (1996)]. The MD methods with the empirical pair potential is found to be insufficient to simulate the transition in this system.

High-pressure EXAFS measurements of solid and liquid Kr.

X-ray-absorption measurements of liquid and solid krypton at room temperature in the pressure range 0.1--30 GPa have been performed using the dispersive setup and diamond-anvil cells as a pressure device. The evolution of the near-edge structures as a function of pressure, including the first intense resonance, has been interpreted using multiple-scattering calculations. It is shown that the near-edge structures are reproduced taking into account two-body and three-body terms associated with the first-neighbor atoms. Extended x-ray-absorption fine-structure (EXAFS) spectra have been analyzed in the framework a multiple-scattering data-analysis approach taking proper account of the atomic background including the [1s4p], [1s3d], and [1s3p] double-electron excitation channels. Isobaric Monte Carlo (MC) computer simulations based on empirical pair potentials, as proposed by Barker (K2) and Aziz (HFD-B), have been performed to make a quantitative comparison of theoretical and experimental local structural details of condensed krypton at high pressures. From the analysis of EXAFS data we were able to obtain simultaneous information on average distance, width, and asymmetry of the first-neighbor distribution, as a function of pressure. These parameters yield a unique insight on the potential function because they are affected by both minimum position and curvature of the effective pair potential. The trend of the first-neighbor distribution as a function of pressure is in quantitative agreement with the HFD-B potential at moderate pressures, deviations are found at higher pressures where EXAFS spectra are very sensitive to the hard-core repulsive part of the potential. The weak EXAFS signal of liquid krypton at room temperature and 0.75 GPa has been found in accord with the results of the MC simulations within the noise of the measurement. \textcopyright{} 1996 The American Physical Society.

Pair Potentials in Atomistic Computer Simulations

Computer modeling of crystal defects ranges at present from generic empirical investigations to first-principle quantum-mechanical calculations (see, for example, References 1–4). Descriptions of atomic interactions in terms of pair potentials dominated such studies until the early 1980s, and many fundamental features of lattice defects and interfaces were revealed in these calculations. The generic results of these studies withstood the test of time, and calculations employing more sophisticated schemes usually confirmed their validity. An early example goes back to the late 1950s when Vineyard and co-workers pioneered the very first computer simulations in their studies of radiation damage. Empirical pair potentials were used in these investigations in which many fundamental, generic aspects of the effect of irradiation of crystalline materials by energetic particles were discovered.Such simple treatments of atomic interactions may appear totally inadequate from the point of view of pure physics. However, it must be recognized that the purpose of the majority of atomistic studies of lattice defects has been to elucidate atomic structure and atomic-level properties in materials with given: (a) crystal structure, (b) elastic properties and possibly phonon spectra, (c) values of certain material parameters such as vacancy formation energies and stacking fault energies, and (d) in alloys, alloying and ordering energies, and possibly antiphase boundary energies. This is in contrast with ab initio studies, the objective of which is to determine all these properties from first principles. These goals of atomistic studies are, of course, the same for all semi-empirical approaches discussed in this collection of articles. In general, the validity of the structural features of lattice defects found in calculations using empirical schemes is best guaranteed if they can be related to fitted material properties and are not sensitively dependent on the deails of the fittings and functional forms employed.