Quantal Density Functional Theory

Abstract

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Wigner high electron correlation regime in nonuniform electron density systems: Kinetic and correlation-kinetic aspects

“…(The discussion of the electron-interaction energy, and its Hartree, Pauli, and Coulomb components, and their corresponding quantal sources, is to be given elsewhere [18]. ) Employing the ‘quantal Newtonian’ first law [19–21] which involves the fields acting on each electron, we explain how the decrease in kinetic energy, relative to the electron-interaction and total energy, is a consequence of a ‘quantal compression’ of the kinetic energy density near the nucleus. Then, by mapping this interacting system to one of noninteracting fermions in a ground state with the same density ρ ( r ) via quantal density functional theory [19, 20] (QDFT), we discover that although there is a decrease in the kinetic energy, there is a substantial increase in the correlation-kinetic contribution.…”

“…Employing the ‘quantal Newtonian’ first law [19–21] which involves the fields acting on each electron, we explain how the decrease in kinetic energy, relative to the electron-interaction and total energy, is a consequence of a ‘quantal compression’ of the kinetic energy density near the nucleus. Then, by mapping this interacting system to one of noninteracting fermions in a ground state with the same density ρ ( r ) via quantal density functional theory [19, 20] (QDFT), we discover that although there is a decrease in the kinetic energy, there is a substantial increase in the correlation-kinetic contribution. Thus, in the Wigner regime, not only do electron correlations dominate as reflected in the electron-interaction energy, they contribute significantly to the kinetic energy.…”

“…According to the ‘quantal Newtonian’ first law [19–21], the sum of the fields experienced by each electron must vanish: ${bold\mathcal{F}}^{normal\mathit{ext}}+{bold\mathcal{F}}^{normal\mathit{int}}(\mathbf{r})=0$, where the internal field ${bold\mathcal{F}}^{normal\mathit{int}}(\mathbf{r})$ is the sum of the electron-interaction, ${\mathrm{scriptE}}_{\mathrm{italicee}}(\mathbf{r})$, kinetic $\mathrm{scriptZ}(\mathbf{r})$, and differential density $\mathrm{scriptD}(\mathbf{r})$ fields: ${bold\mathcal{F}}^{normal\mathit{int}}(\mathbf{r})={bold\mathcal{E}}_{\mathrm{italicee}}(\mathbf{r})-\mathrm{scriptZ}(\mathbf{r})-\mathrm{scriptD}(\mathbf{r})$ with ${bold\mathcal{E}}_{\mathrm{italicee}}(\mathbf{r})={\mathrm{bolde}}_{\mathrm{italicee}}(\mathbf{r})∕\rho (\mathbf{r})$, $\mathrm{scriptZ}(\mathbf{r})=\mathbf{z}(\mathbf{r})∕\rho (\mathbf{r})$, $\mathrm{scriptD}(\mathbf{r})=\mathbf{d}(\mathbf{r})∕\rho (\mathbf{r})$. The corresponding ‘forces’ are e ee ( r ) = ∫ d r ′ P ( rr ′)( r − r ′)/| r − r ′| 3 (Coulo...…”

Determination of a Wave Function Functional

“…Similar improvements are observed for the expectations of other single particle operators. On the other hand, the high accuracy of the HF value is because in this theory single-particle expectation values are correct to second order [6,9]. Our results also demonstrate that by expanding the space of variations, more accurate results for both the energy as well as other properties can be obtained with fewer variational parameters.…”

Hohenberg-Kohn theorem including electron spin

“…Thus, for example, knowledge that the ground state density ρ(r) is a basic variable leads to (a) HK density functional theory [3] (DFT); (b) Local effective potential theories such as Kohn-Sham (KS) [6] and Quantal [7,8] density functional theories. In these latter theories, one constructs model systems of noninteracting fermions or bosons with the same density as that of the interacting system.…”