Classical coset Hamiltonian for the electronic motion and its application to Anderson localization and Hammett equation

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electro nic motion can be readily simulated. The simulation reproduces the retardat ion of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. T he advantages and shortcomings of this algorithm, as contrasted with tradit ional quantum methods such as the molecular orbital theory, are also discus sed.