Interatomic potentials derivation

We used an interatomic potential derived from Effective Medium Theory as described in [7], This potential reproduces the elastic properties of copper quite well, but the derived stacking fault energy, 31mJm"2, is somewhat lower than the normally quoted value for copper of 50mJm"2 [8],... 

In this context, we performed first-principles electronic structure calculations of a small cluster (Si04) and analyzed potential energy surfaces (PES s) corresponding to some deformation modes of the cluster. The interatomic potential derived from the PES s, which is ionic and pairwise, has been found to reproduce most structural properties of silica minerals quite satisfactorily against expectation. 

We performed MD simulations of low-quartz, low-cristobalite, coesite and stishovite, i.e., virtually all the natural polymorphs of silica so far known. These polymorphs correspond to different pressure-temperature regimes but can also exist at normal pressure and temperature. Our interests are (1) whether the interatomic potential derived from the cluster calculation is applicable to bulk crystals, (2) whether various physical properties of polymorphs are reproduced by the same interatomic potentials, and (3) whether pair-potential approximation is valid for silica. 

G. V. Lewis, Physica B, 131,114 (1985). Interatomic Potentials Derivation of Parameters for Binary Oxides and Their Use in Ternary Oxides. 

Lewis GV, Catlow CRA (1985) Interatomic potential - Derivation of parameters for binary oxides and their nse in ternary oxides. J Phys C 18 1149-1161... 

An Interatomic Potential Derived from First Principles Quantum Mechanics ... 

The Empirical Conformational Energy Program for Peptides, ECEPP [63, 64], is one of the first empirical interatomic potentials whose derivation is based both on gas-phase and X-ray crystal data [65], It was developed in 1975 and updated in 1983 and 1992. The actual distribution (dated May, 2000) can be downloaded without charge for academic use. 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

Figure 10, Interatomic potentials for (a) Ne + He and (b) Ar + He derived from fitting the data of Fig, 8. Vertical lines show the range of intemuclear distance probed at each energy ), with , < E2 as given in Fig, 9.

Covalent Solids. Interatomic potentials are the most difficult to derive for covalent solids. The potential must predict the directional nature to the bonding (i.e. the bond angles). Most covalent solids have rather open crystal stmctures, not close packed ones. Pair potentials used with diatomic molecules, such as the Lennard-Jones and Morse potentials, are simply not adequate for solids because atoms interacting via only radial forces prefer to have as many neighbors as possible. Hence, qualitatively wrong covalent crystal stmctures are predicted. 

Starr, T. L. and Williams, D. E. (1977 ). Coulombic nonbonded interatomic potential functions derived from crystal-lattice vibrational frequencies in hydrocarbons. Acta Crystallogr A, 33, 771-6. [153]... 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

K. de Boer, A. R J. Jansen, and R. A. van Santen, in Zeolites and Related Microporous Materials State of the Art 1994, J. Weitkamp, H. G. Karge, H. Pfeifer, and W. Holderich, Eds., Elsevier Science Publishers, Amsterdam, 1994, pp. 2083-2087. Interatomic Potentials for Zeolites. Derivation of an Ab Initio Shell Model Potential. 

U(k) is the Fourier transform of the effective interatomic potential. Note v defined above corresponds to the velocity of sound in the case where U(k) is a constant. However, for the long-range dipole-dipole interactions we consider here, U (k) is not a constant and the sound velocity must be obtained as the derivative of the dispersion relation with respect to k. 

We show this result primarily to illustrate that what are really required to determine the force constant matrix are the derivatives of the relevant interatomic potential, and then the consideration of a series of lattice sums as embodied in the various appear above. Once the force constant matrix is in hand, the next step in the procedure for obtaining the spectrum of vibrational frequencies is the determination of the dynamical matrix. For the simple case in which there is only one atom per unit cell, this amounts to carrying out the sums illustrated in eqn (5.23). 

If the projectile and target atoms interact like colliding billiard balls (elastic hard-spheres), the interatomic potential that represents this condition is called a hard-sphere potential. For a hard-sphere potential, the power-law cross-section parameter m in (4.19) is equal to 0. Derive the total cross-section, a (It), for a hard-sphere potential. 

T. L. Starr and D. E. Williams, Acta Crystallogr. Ser. A, A106, 771 (1977). Coulombic Non-bonded Interatomic Potential Functions Derived from Crystal-Lattice Vibrational Frequencies in Hydrocarbons. 

A promising method, developed in recent years, is the use of first principles molecular dynamics as exemplified by the Car-Parrinello technique (8]. In these calculations the interatomic potentials are explicitly derived from the electronic ground-state within the density functional theory in local or non-local approximation. It combines quantum mechanical calculations with molecular dynamics simulations and, therefore, overcomes the limitations of both methods. Actual computers allow only simulations of aqueous solutions of about 60 water molecules for several ps (10 s). This limit is still at least one order of magnitude shorter than the fastest directly measured water exchange rate, k = 3.5 x 10 s for [Eu(H20)8], i.e. one exchange event every (8 x 3.5 x lO s ) = 36 ps [9]. Nevertheless, several publications appeared in the late 1990s on solvated Be [10], K+ [11] and Cu + [12] presenting mainly structural results. 

Empirical potentials are only applicable with certainty over the range of interatomic distances used in the fitting procedure, which can lead to problems if the potential is used in a calculation that accesses distances outside this range. This can happen in defect calculations, molecular dynamics simulations or lattice dynamics calculations at high temperature and/or pressure. In addition experimental data is required and thus direct calculation is the only method available when there is no relevant experimental data. It may, of course, be possible to take potentials derived for one system and transfer them to another. This method has been successful with potentials derived for binary oxides (Lewis and Catlow, 1985 Bush et al., 1994) being transferred to ternary systems (Lewis and Catlow, 1985 Price et al., 1987 Cormack et al., 1988 Purton and Catlow, 1990 Bush et al., 1994). 

Directly calculated potentials can be obtained for any interatomic distance or relative atomic configuration, but care must be taken that any environmental factors (e.g. Madelung fields) are taken into account correctly. These requirements may impose considerable difficulty in many systems. Where possible, empirical and non-empirical methods should be used in a concerted manner in deriving interatomic potentials. 

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