Dynamical exchange-correlation potentials for an electron liquid
Dynamical exchange-correlation potentials for an electron liquid
复制标题
电子液体的动态交换相关势
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
G. Vignale
中科院分区：
文献类型：
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作者：
Z. Qian;G. Vignale
The imaginary parts of the exchange-correlation kernels ${f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ in the longitudinal and transverse current-current response functions of a homogeneous electron liquid are calculated exactly at low frequency, to leading order in the Coulomb interaction. Combining these new results with the previously known high-frequency behaviors of $mathrm{Im}{f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ and with the compressibility and the third moment sum rules, we construct simple interpolation formulas for $mathrm{Im}{f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ in three and two spatial dimensions. A feature of our interpolation formulas is that they explicitly take into account the two-plasmon component of the excitation spectrum: our longitudinal spectrum $mathrm{Im}{f}_{mathrm{xc}}^{L}(ensuremath{omega})$ is thus intermediate between the Gross-Kohn interpolation, which ignores the two-plasmon contribution, and a recent approximate calculation by Nifos`{i}, Conti, and Tosi, which probably overestimates it. Numerical results for both the real and imaginary parts of the exchange-correlation kernels at typical electron densities are presented, and compared with those obtained from previous approximations. We also find an exact relation between $mathrm{Im}{f}_{mathrm{xc}}^{L}(ensuremath{omega})$ and $mathrm{Im}{f}_{mathrm{xc}}^{T}(ensuremath{omega})$ at small $ensuremath{omega}.$
The imaginary parts of the exchange-correlation kernels ${f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ in the longitudinal and transverse current-current response functions of a homogeneous electron liquid are calculated exactly at low frequency, to leading order in the Coulomb interaction. Combining these new results with the previously known high-frequency behaviors of $mathrm{Im}{f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ and with the compressibility and the third moment sum rules, we construct simple interpolation formulas for $mathrm{Im}{f}_{mathrm{xc}}^{L,T}(ensuremath{omega})$ in three and two spatial dimensions. A feature of our interpolation formulas is that they explicitly take into account the two-plasmon component of the excitation spectrum: our longitudinal spectrum $mathrm{Im}{f}_{mathrm{xc}}^{L}(ensuremath{omega})$ is thus intermediate between the Gross-Kohn interpolation, which ignores the two-plasmon contribution, and a recent approximate calculation by Nifos`{i}, Conti, and Tosi, which probably overestimates it. Numerical results for both the real and imaginary parts of the exchange-correlation kernels at typical electron densities are presented, and compared with those obtained from previous approximations. We also find an exact relation between $mathrm{Im}{f}_{mathrm{xc}}^{L}(ensuremath{omega})$ and $mathrm{Im}{f}_{mathrm{xc}}^{T}(ensuremath{omega})$ at small $ensuremath{omega}.$