Appendix A DFT-related Methods

We briefly describe three methods that can be considered as related to DFT and that are sometimes used for cluster computations the Thomas-Fermi (TF) approximation, the so-called DFT-based tight-binding (TB), and the many-body potentials of the embedded-atom type. 

The TF approximation [249] was the precursor of modem DFT, as it expresses the total energy in terms of the electron density only. In contrast to the KS method, TF does not resort to independent electron orbitals for the computation of the electron kinetic energy, which is assumed to be a function of the electron density. The simplest version of TF corresponds to an LDA for the kinetic energy  

In fact, the computational advantage of a density-only scheme such as TF over the KS approach is so important that this type of approximation has been recently revived in connection with CP simulations [250]. Applications to simple metal clusters are reported in Ref. [251]. Unfortunately, the scheme developed in [250] seems to be limited to nearly free-electron systems such as alkali metals and aluminum, and for clusters the description is not quantitative, even for relatively simple properties such as equilibrium geometries. 

Far more extensive has been the application of semiempirical TB methods, in which the matrix elements are used as free parameters to fit experimental data, to metal clusters (and to transition-metal clusters in particular). However, a discussion of these applications is beyond the scope of our review. 

---