The Modified Embedded-Atom Model

Although the embedded atom model proved to be a good potential for metallic systems, it fails to describe covalent materials, such as semiconductors. The reason for this is that the electron density in Eq. 4.35 is assumed to be isotropic, which is a good approximation in close packed systems, like fee crystals, but in the case of covalent bonds, the electron density is higher along the bonds. In order to correct this, an angle-dependent density term was introduced by Baskes [22] for silicon 

Taylor showed an elegant generalisation of the modified embedded atom model in [24]. In this work, he formulated a Taylor-expansion of the total energy functional around the ground-state density of atoms in terms of density variations, which led to a general expression for the total energy of the system as a function of the atomic coordinates. The energy of an atomic system is determined as a functional of the atomic density as 

Similarly, if we consider the local atomic densities around atom 

This expression has the same form as the modified embedded atom model. Taylor represented the local atomic density by bond-order parameters and different radial functions as discussed in Sect. 2.3.1 in Chap. 2. By choosing appropriate radial functions, he obtained the original modified embedded-atom formula, but systematic improvement of the formula is also possible in his framework. 

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