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We present extensive new Ab initio path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, 8 ≤ θ = k B T / E F ≤ 128. This allows us to study the convergence of different properties towards the classical limit. In particular, we investigate the classical relation between the static structure factor S (q) and the static local field correction G (q) , which is only fulfilled at low densities. Moreover, we compare our new results for the interaction energy to the parametrization of the UEG by Groth et al. (2017), which interpolates between PIMC results for θ ≤ 8 and the Debye–Hückel limit, and to higher order analytical virial expansions. Finally, we consider the momentum distribution function n (q) and find an interaction-induced increase in the occupation of the zero-momentum state even for θ ≳ 32. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods. [ABSTRACT FROM AUTHOR]

• A very simple way to compute electron correlation energy. • Reasonably accurate for covalent bond molecules, competitive to B3LYP. • Hypothesis: the correlation energy favors uniform electron distribution. A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation, the total, the ionization, and the atomization energies of test atoms and molecules; and despite the unique simplicities, the functionals' accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. [ABSTRACT FROM AUTHOR]