Electronic Motion in the Mean Field Periodic Systems

Electronic Motion IN THE Mean Field Periodic Systems 

Electronic Motion in the Mean Field Periodic Systems 

If a motif (e.g., a cluster of atoms) associated with a unit cell is regularly translated along three different directions in space, we obtain an infinite periodic structure (with translational symmetry). 

The electronic orbital energy becomes a function of the FBZ points and we obtain what is known as band structure of the energy levels. This band structure decides the electronic properties of the system (insulator, semiconductor, metal). We will also show how to carry out the mean field (Hartree-Fock) computations on infinite periodic systems. The calculations require infinite summations (interaction of the reference unit cell with the infinite crystal) to be made. This creates some mathematical problems, which will be also described in the present chapter. 

The present chapter is particularly important for those readers who are interested in solid state physics and chemistry. Others may treat it as exotic and, if they decide they do not like exotic stuff, may go directly to other chapters. 

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