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Abstract: Exact-exchange energy density and energy density of a semilocal densityfunctional approximation are two key ingredients for modeling the staticcorrelation, a strongly nonlocal functional of the density, through a localhybrid functional. Because energy densities are not uniquely defined, theconventional Slater exact-exchange energy density$e \mathrm{x}^\mathrm{exconv}$ is not necessarily well-suited for localmixing with a given semilocal approximation. We show how to transform$e \mathrm{x}^\mathrm{exconv}$ in order to make it compatible with anarbitrary semilocal density functional, taking the nonempiricalmeta-generalized gradient approximation of Tao, Perdew, Staroverov, andScuseria TPSS as an example. Our additive gauge transformation functionintegrates to zero, satisfies exact constraints, and is most important wherethe density is dominated by a single orbital shape. We show that, as expected,the difference between semilocal and exact-exchange energy densities becomesmore negative under bond stretching in He$ 2^{+}$ and related systems. Ourconstruction of $e \mathrm{x}^\mathrm{exconv}$ by aresolution-of-the-identity method requires uncontracted basis functions.



Author: Jianmin Tao, Viktor N. Staroverov, Gustavo E. Scuseria, John P. Perdew

Source: https://arxiv.org/







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