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

Using existing theoretical studies, we point out that the dominant variable in determining Lowdin 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 CH(4), NH(3), H(2)O 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 Moller-Plesset perturbation theory, as to whether the Lowdin correlation energy density epsilon(c)(r) is, albeit approximately, a local functional epsilon(c)(rho) of the ground-state density for molecules at equilibrium. Such an LDA assumption would imply that epsilon(c)(rho) is quantitatively linear in rho(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 Lowdin correlation energy for closed-shell molecules at equilibrium is merely to shift the chemical potential.

Using existing theoretical studies, we point out that the dominant variable in determining Lo¨ wdin correlation energies per electron Ec/N of isoelectronic series of molecules at equilibrium is the total number of electrons. This turns out to be Ec/N¼0.0330.003 a.u. for CH4, NH3, H2O and HF (N¼10), and Ec/N¼0.0390.007 for some 20 Si-containing molecules in the series SiXnYm. 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 Lo¨ wdin correlation energy density c(r) is, albeit approximately, a local functional c() of the ground-state density for molecules at equilibrium. Such an LDA assumption would imply that c() is quantitatively linear in (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 Lo¨ wdin correlation energy for closed-shell molecules at equilibrium is merely to shift the chemical potential.