Löwdin correlation energy density of the inhomogeneous electron liquid in some closed-shell molecules at equilibrium geometry

Abstract

Using existing theoretical studies, we point out that the dominant variable in determining Löwdin correlation energies per electron E _c /N of isoelectronic series of molecules at equilibrium is the total number of electrons. This turns out to be E _c /N = −0.033 ± 0.003 a.u. for CH₄, NH₃, H₂O and HF (N = 10), and E _c /N = −0.039 ± 0.007 for some 20 Si-containing molecules in the series SiX _n Y _m . Following earlier work of March and Wind on atoms, some proposals are then made as to a possible explanation of such behaviour. A test is proposed, via low-order Møller–Plesset perturbation theory, as to whether the Löwdin correlation energy density ε _c (r) is, albeit approximately, a local functional ε _c (ρ) of the ground-state density for molecules at equilibrium. Such an LDA assumption would imply that ε _c (ρ) is quantitatively linear in ρ(r), for closed-shell molecules at equilibrium, at least for the light atomic components treated here. This, in turn implies that the dominant effect of the Löwdin correlation energy for closed-shell molecules at equilibrium is merely to shift the chemical potential.

Keywords:

• correlation energy density
• inhomogeneous electron liquid
• closed-shell molecules