Valproat bei idiopathischer generalisierter Epilepsie — (k)eine Frage der Dosis

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

“…Further, it appears natural to decompose into: where is the Hartree potential accounting for the classical electron‐electron repulsion: and is the remaining Fermi potential. Note, that this decomposition naturally divides the effective Hamiltonian into terms that do not refer to the particles’ nature (and thus equally hold for a bosonic reference system with the same density as the actual fermion system) and fermion‐specific contributions . Therefore, the density determining differential equation, cf.…”

“…A different approach for orbital‐free calculations in the context of the Levy–Perdew–Sahni formulation was given in Ref. [ ], in which case all operators taking orbital effects into account were subsumed into a so‐called Fermi potential (and the corresponding fermionic energy), whereas the remaining terms are independent of the particles’ nature, and, therefore, are referred to as bosonic‐like. The advantage of this approach is that the bosonic‐like terms can be treated exactly within orbital‐free density functional theory, while the Fermi potential is largely transferable between systems with the same shell structure, even if the systems have different numbers of electrons …”

“…The advantage of this approach is that the bosonic-like terms can be treated exactly within orbital-free density functional theory, while the Fermi potential is largely transferable between systems with the same shell structure, even if the systems have different numbers of electrons. [20] In this work, the exact expression for the Fermi potential yielding the Hartree-Fock (HF) electron density is derived. A method how to obtain the kinetic potential for the noninteracting Kohn-Sham system employing a given approximate exchange-correlation functional has been published previously [21] providing useful information for the development of approximate kinetic energy functionals.…”

“…Note, that this decomposition naturally divides the effective Hamiltonian h eff into terms that do not refer to the particles' nature (and thus equally hold for a bosonic reference system with the same density as the actual fermion system) and fermion-specific contributions. [20] Therefore, the density determin- In the following the Fermi potential yielding the reference electron density, here chosen to be the HF electron density, is derived. This avoids complexities associated with electron correlation, which is technically not a fermion-specific effect but which would, nonetheless, be more convenient to incorporate in v F ðrÞ.…”