Khon-Sham

In this last expression, /j, is an additional, non-physical parameter, which represents the fictitious mass assigned to the additional degrees of freedom, Cj(G) s, of the system. The potential energy of the system as a whole is (c, R) = ( j(c),R), the electron+nuclei total energy functional in the Khon-Sham framework. Finally, Aij are Lagrange multipliers introduced to satisfy at all times the orthonormality constraints of the Kohn-Sham orbitals. 

Garza et al. [52] studied the problem by using the Khon-Sham equations, where their results are also close to the most accurate figures published hitherto. March and Tosi [53] used the path-integral Monte Carlo Method. 

A large basis set is necessary to obtain high accuracy and convergence of the non-linear Khon-Sham Equations [17.3],... 

The Density Functional theorem states that the total ground state energy is a unique functional of the electron density, p [40]. This simple but enormously powerful result means that it is possible, in principle, to provide an exact description of all electron correlation effects within a one-electron (i.e. orbital-based) scheme. Khon and Sham (KS) [41] have derived a set of equations which embody this result. They have an identical form to the one-electron Hartree Fock equations. The difference is that the exchange-correlation term, Vxc, is not the same. 

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