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Total energy equation leading to exchange-correlation functional

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Abstract

By solving the total energy equation, we obtain the formula of exchange-correlation functional for the first time. This functional is usually determined by fitting experimental data or the numerical results of models. In the uniform electron gas limit, our exchange-correlation functional can exactly reproduce the results of Perdew-Zunger parameterization from the jellium model. By making use of a particular solution, our exchange-correlation functional could take into account the case of non-uniform electron density, and its validity can be confirmed through comparisons of the band structure, equilibrium lattice constant, and bulk modulus of aluminum and silicon. The absence of mechanical prescriptions for the systematic improvement of exchange-correlation functional hinders further development of density-functional theory (DFT), and the formula of exchange-correlation functional given in this study might provide a new perspective to help DFT out of this awkward situation.

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Feng Liu & Tzu-Chiang Wang

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  1. Feng Liu
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  2. Tzu-Chiang Wang
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Correspondence to Tzu-Chiang Wang.

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Liu, F., Wang, TC. Total energy equation leading to exchange-correlation functional. Sci. China Phys. Mech. Astron. 58, 1–6 (2015). https://doi.org/10.1007/s11433-014-5639-2

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