Variational grand-canonical electronic structure of Li+Li at ~104 K with second-order perturbation theory corrections

Abstract

An ab initio variational grand-canonical electronic structure mean-field method, based on the Gibbs–Peierls–Bogoliubov minimum principle for the Gibbs free energy, is applied to the di-lithium (Li+Li) system at temperatures around T ≈ 104 K and electronic chemical potential of μ ≈ −0.1E h . The method is an extension of the Hartree–Fock approach to finite temperatures. We first study the Li2 molecule at a frozen inter-nuclear distance of R = 3 A as a function of temperature. The mean-field electronic structure changes smoothly as temperature increases, up to 104 K, where a sharp spontaneous spin-polarization emerges as the variational mean-field solution. Further increase in the temperature extinguishes this polarization. We analyze the mean-field behavior using a correlated single-site Hubbard model and show it arises from an attempt of the mean-field to mimic the polarization of the spin–spin correlation function of the exact solution. Next, we keep constant the temperature at 104 K and examine the electronic structure as a function of inter-nuclear distance R. At R = 3.7 A, a crossing between two free energy states occurs: One state is “spin-unpolarized” (becomes lower in energy when R > 3.7 A), while the other is “spin polarized”. This crossing causes near-discontinuous jumps in calculated properties of the system and is associated with using the noninteracting electron character of our mean-field approach. Such problems will likely plague FT-DFT calculations as well. We use second-order perturbation theory (PT2) to study effects of electron correlation on the potential of mean force between the two colliding Li atoms. We find that PT2 correlation free energy at ~104 K is larger than at 0 K and tends to restore the spin-polarized state as the lowest free energy solution.