Explanation of Some Differences in the Correlation Energies of CH_4, Ne, and NH_4^+

Abstract

The most recent nonempirical value for the correlation energy of CH_4, E_(corr)(CH_4), is −0.344 a.u. Prior to this, E_(corr) of the isoelectronic systems Ne and CH_4 had been assumed equal (−0.393 a.u.). This paper gives a simple explanation of 50% of this difference, that is, from electrostatics the four protons in CH_4 smeared over a sphere (spherical model) and only six at the center exert a smaller potential than all 10 at the center do in neon. This leads to a much larger effective nuclear charge for the orbitals in Ne. The Z dependence of E(corr) of Ne‐like ions then sets |E_(corr)(CH_4)| at 0.025 a.u. less than |E_(corr)(Ne)|. This approach will be useful in relating molecular E_(corr)'s to the correlation energy of related and better‐understood atomic systems and in locating molecular Hartree—Fock limits. Two other results in this paper are (a) E_(corr)(NH_4^+) given as −0.330 a.u. is too low and should be at least 0.344 a.u., that is, E_(corr)(CH_4). This suggests a better choice for the proton affinity of NH_3. (b) |E_(corr)(SiH_4)| will be about 0.08 a.u. less than |E_(corr)(argon)|.

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