Aspects of programs for calculations for atoms in the Hartree Fock Approx.
Density Functional Theory
The Hohenberg-Kohn Theorem
The ground state electron density uniquely determines the
external potential acting on the electrons
Applies to the exact solution of the full
interacting many-body system
Therefore all properties must be functionals of the
ground state electron density
All properties are determined by one scalar function,
the density n(r), instead of the complex many-body wavefunction
But no one has ever constructed an explicit functional,
except for a single particle! Even two non-interacting electrons of
same spin has not been done
The Kohn-Sham Ansatz
Replace the original (intractable) many-body problem
with a different problem
Kohn-Sham proposed one consider a non-interacting
electron system with the same density n(r) as the true interacting system
This system is exactly solvable (at least numerically)
The Hohenberg-Kohn theorems apply to this system
Define energy of many body system to be sum of
kinetic energy of independent-particle wavefunctions + Hartree energy
(functional of density) + exchange-correlation Exc[n]
Leads to self-consistent sets of independent-particle
Schroedinger-like Eqs.
In principle solve many-body problem by single body methods!
Note that this applies only to the ground state
density and energy, NOT to other properties
One ,ust extend the Kohn-Sham idea for other properties
In practice use various approximations for Exc[n]
Results using the Kohn-Sham Ansatz and simple approximations for Exc