We attempt to overcome one of the shortcomings in the Thomas-Fermi and related theories for atoms by connecting a quantum-mechanical electron density for the region near the nucleus to a density given by a statistical model. The joining may be done in a nonarbitrary manner: All parameters are determined. It suffices to use a very crude and easily calculated approximation to the density to start with, so the calculation is quite easy. The resulting electron density is in much better agreement with reality than that from the unmodified theories.
Goodisman, Jerry, "Modified Quantum-Statistical Calculations for Atomic Electron Densities" (1970). Chemistry - Faculty Scholarship. 5.
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