Finnis-Sinclair potential

The origins of the Finnis-Sinclair potential [Finnis and Sinclair 1984] lie in the density of states and the moments theorem. Recall that the density of states D(E) (see Section 3.8.5) describes the distribution of electronic states in the system. D(E) gives the number of states between E and E - - 8E. Such a distribution can be described in terms of its moments. The moments are usually defined relative to the energy of the atomic orbital from which the molecular orbitals are formed. The mth moment, fi", is given by ... 

Finnis-Sinclair potential a pairwise contribution is added to the many-body term to he following form ... 

The Tersoff potential [Tersoff 1988] is based on a model known as the empirical bond-order potential. This potential can be written in a form very similar to the Finnis-Sinclair potential ... 

Sutton A P and J Chen 1990. Long-range Finnis-Sinclair Potentials. Philosophical Magazine Letters 61 139-146. 

Second Moment Approximation and Finnis-Sinclair Potential... 

There has been considerable effort since the introduction of the Finnis-Sinclair potential to develop expressions that include angular interactions and higher moments of the local density of states. " Carlson and coworkers, for example, have introduced a matrix form for the moments of the local density of states from which explicit environment-dependent angular interactions can be obtained. The role of the fourth moment, in particular, has been stressed for half-filled bands because it describes the tendency to introduce an energy gap. These investigations have led to improved models that describe local bonding in both covalent and body-centered-cubic materials. 

Although the expression above is formally identical to the Finnis-Sinclair potential expression, its form helps to clarify some profound implications for understanding chemical bonding. The more bonds that are formed, the more terms are in the bonding sum involving the attractive pair potential this tends... 

Fig. 6.18 Phonon spectrum of iron using the GAP potential solid lines), the Finnis-Sinclair potential dotted lines) and PBE-DFT open squares)...

The elastic moduli calculated with our model, the Finnis-Sinclair potential [14] and Density Functional Theory are given in Table 6.5. The elastic properties and the phonon dispersion relations described by the GAP model show excellent agreement with the values calculated by Density Functional Theory. 

For high computational efficiency, a pair potential such as the LJ or the Morse potential is used. With the increasing demand on accuracy and available computational power, many-body potentials such as the Finnis-Sinclair potential and the EAM (embedded atom method) have been commonly used [79]. 

Sutton AP, Chen J. Long-range Finnis-Sinclair potentials. Philos Mag Lett 1990 61(3) 139-46. 

Table 9. Calculated surface free energy y of metals for various orientations. The subscripts A and B refer to the two possible surface terminations of (1010) surfaces of hep crystals [910ve], where the termination with the smaller lattice spacing is denoted A [98Vit]. Calculations were performed for T = 0 K. The method of calculation is indicated FS empirical n-body Finnis-Sinclair potential, PSP total energy pseudopotential, EAM embedded atom method, DFT density functional theory, FPLAPW full potential linear combination of augmented waves, FPLMTO full potential linear combination of muffin tin orbitals.

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