The theory of the inhomogeneous electron gas had its origin in the
Thomas- Fermi statistical theory, which is discussed in the first
chapter of this book. This already leads to significant physical results
for the binding energies of atomic ions, though because it leaves out
shell structure the results of such a theory cannot reflect the richness
of the Periodic Table. Therefore, for a long time, the earlier method
proposed by Hartree, in which each electron is assigned its own personal
wave function and energy, dominated atomic theory. The extension of the
Hartree theory by Fock, to include exchange, had its parallel in the
density description when Dirac showed how to incorporate exchange in the
Thomas-Fermi theory. Considerably later, in 1951, Slater, in an
important paper, showed how a result similar to but not identical with
that of Dirac followed as a simplification of the Hartree-Fock method.
It was Gombas and other workers who recognized that one could also
incorporate electron correlation consistently into the
Thomas-Fermi-Dirac theory by using uniform electron gas relations
locally, and progress had been made along all these avenues by the
1950s.