Hydrides as Isoelectronic Perturbations of the Neon Atom

The second-row hydrides: hydrogen fluoride , water , ammonia and methane are isoelectronic with the Ne atom. The electronic structures for these 10-electron systems can be obtained, in concept, by perturbations on the Ne atom, in which protons are embedded in the electron cloud, while the central nuclear charge is reduced appropriately.
The electronic structure of the molecule is represented using density functional theory, as described in [1]. You can attempt to minimize the energy by varying the shielding parameters , and the bond distance . The results will, of necessity, be approximate, owing to the limitation in the density function . Computed Hartree–Fock energies and experimental bond distance are shown for comparison. Minimization with respect to is especially delicate, so do not expect an accurate result for the bond distance.

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The 10-electron density function is approximated by
,
following [1]. The resulting density functional contains the usual forms for kinetic and potential energies, plus the additional contributions from the hydrogen atoms in , , and .
Experimental values of parameters: : ; : , ; : , ; : , . Approximate Hartree–Fock energies (hartrees): : , : , , : , : .
Reference
[1] S. M. Blinder. "Density Functional Computations on Noble Gas Atoms" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/DensityFunctionalComputationsOnNobleGasAtoms.
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