Self-Consistent WDA Calculations

As a first application of this WDA implementation, the lattice constant and bulk modulus of C-diamond, Si, Ge, GaAs and Al are determined using the WDA. The emphasis here is to provide a demonstration of how to perform self-consistent calculations using this implementation of the WDA. For all of the WDA calculations, the following model pair-correlation function is used,

$$G^{\hbox{{WDA}}}[{\bf r},{\bf r'};\tilde{n}({\bf r})] = \alpha(\tilde{n}) \, \hbox{e}^{-[\vert\,{\bf r}-{\bf r'}\,\vert/\beta(\tilde{n})]^2} \, ,$$ (4.73)

which according to relation (4.20) corresponds to the function $f(u)$ with the form,

$$f(u) = \hbox{e}^{-u^2} \, .$$ (4.74)

This happens to be the simplest physical model for a pair-correlation function, and will be discussed in detail in subsequent chapters.