Kohn-Sham modifications

For direct Af-electron variational methods, the computational effort increases so rapidly with increasing N that alternative simplified methods must be used for calculations of the electronic structure of large molecules and solids. Especially for calculations of the electronic energy levels of solids (energy-band structure), the methodology of choice is that of independent-electron models, usually in the framework of density functional theory [189, 321, 90], When restricted to local potentials, as in the local-density approximation (LDA), this is a valid variational theory for any A-electron system. It can readily be applied to heavy atoms by relativistic or semirelativistic modification of the kinetic energy operator in the orbital Kohn-Sham equations [229, 384],... 

Results of Kohn-Sham density functional calculations (Yin, Stott and Rubio, 2003) indicate that P-TCP is much more stable than a-TCP, confirming experimental results (see, for example, Berger, Gildenhaar and Ploska, 1995b). This is thought to be related to different distributions of Ca atoms that have a pronounced effect on the stability and the electronic properties of the different modifications of TCP. In particular, the uniformly distributed Ca vacancies stabilise the P-TCP structure so that its solubility is much lower than that of the a-TCP modification. 

The only other modification one has to take care of is the construction of the total density matrix Pi = + Pi ) to build the Fock (or Kohn-Sham) matrix elements. 

It can be shown that the same procedure described above can be applied with only a slight modification The Kohn-Sham potential has to be updated after applying the first kinetic operator [21]. 

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