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Kohn-Sham equations for multicomponent systems: The exchange and correlation energy functional

1998; American Physical Society; Volume: 57; Issue: 4 Linguagem: Inglês

10.1103/physrevb.57.2146

1095-3795

Nikitas I. Gidopoulos,

Machine Learning in Materials Science

Kohn-Sham equations for multicomponent systems are derived in a rigorous way that permits the precise definition and discussion of the exchange and correlation energy, of the system as a functional of the densities of the components. In the case of a two-component electron-ion system, with ${n}_{e}{,n}_{I}$ the electron and ion densities, the exchange and correlation energy of the system ${E}_{\mathrm{xc}}[{n}_{e}{,n}_{I}]$ is composed of ${E}_{\mathrm{xc}}[{n}_{e}]$ the electron-electron exchange and correlation energy, ${E}_{\mathrm{xc}}^{\mathrm{II}}[{n}_{I}]$ the ion-ion exchange and correlation energy, and ${E}_{c}^{\mathrm{eI}}[{n}_{e}{,n}_{I}]$ the electron-ion correlation energy. ${E}_{\mathrm{xc}}[{n}_{e}]$ is exactly the functional encountered in the Kohn-Sham theory of electronic systems. The behavior of ${E}_{\mathrm{xc}}^{\mathrm{II}}[{n}_{I}]$ is investigated in the limit of a large ion mass and its relation with ${E}_{\mathrm{xc}}[{n}_{e}]$, for ${n}_{e}{=n}_{I},$ is discussed. The structure of ${E}_{c}^{\mathrm{eI}}[{n}_{e}{,n}_{I}]$ is analyzed in the adiabatic approximation. In the special case of perfectly localized ion densities, ${E}_{\mathrm{xc}}^{\mathrm{II}}[{n}_{I}]$ results in a self-interaction correction while ${E}_{c}^{\mathrm{eI}}[{n}_{e}{,n}_{I}]$ vanishes.