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- W2093676296 abstract "In pair density-functional theory, the only unknown piece of the energy is the kinetic energy $T$ as a functional of the pair density $P({x}_{1},{x}_{2})$. Although $Tphantom{rule{0.1em}{0ex}}[P]$ has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This ``boson pair model'' (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy ${T}_{2}[P]$ is shown to be exact for two-electron systems and a lower bound to $Tphantom{rule{0.1em}{0ex}}[P]$ for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning $Tphantom{rule{0.1em}{0ex}}[P]={T}_{2}[P]+{T}_{mathrm{eff}}phantom{rule{0.1em}{0ex}}[P]$, where only the remainder ${T}_{mathrm{eff}}phantom{rule{0.1em}{0ex}}[P]ensuremath{geqslant}0$ needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schrodinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of ${T}_{mathrm{eff}}phantom{rule{0.1em}{0ex}}[P]$. This self-consistent scheme to minimize the energy with respect to $P$ is more efficient than previous procedures. Further information on the functional derivative of ${T}_{mathrm{eff}}phantom{rule{0.1em}{0ex}}[P]$ is derived from a contracted Schrodinger equation. Since ${T}_{mathrm{eff}}phantom{rule{0.1em}{0ex}}[P]$ is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost." @default.
- W2093676296 created "2016-06-24" @default.
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- W2093676296 date "2004-08-30" @default.
- W2093676296 modified "2023-09-23" @default.
- W2093676296 title "Towards a practical pair density-functional theory for many-electron systems" @default.
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- W2093676296 doi "https://doi.org/10.1103/physreva.70.022514" @default.
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