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Local density functional approximations for the exchange-correlation energy are an essential contribution in most modern density functionals and typically parametrised by the energy density per electron of the homogenous electron gas (HEG). Those analytic models are fitted against quantum Monte Carlo (QMC) data sets and should ideally exhibit analytically known high- and low-density asymptotics of the HEG. We report a symbolic regression on an extended QMC data set in order to (i) rediscover the simple Cha16 parametrisation and (ii) evolve novel parametrisations with exact asymptotics. The resulting analytic model exhibits a siginificant increase in the accuracy with respect to the QMC data in combination with a reasonable complexity, compared to parametrisations such as VWN, PW92, Cha16 and Wu20.
Riedmiller et al. (Tue,) studied this question.
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