Abstract
The bifunctional formalism presents an alternative how to obtain the functional value from its functional derivative by exploiting homogeneous density scaling. In the bifunctional formalism the density dependence of the functional derivative is suppressed. Consequently, those derivatives have to be treated as formal functional derivatives. For a pointwise correspondence between the true and the formal functional derivative, the bifunctional expression yields the same value as the density functional. Within the bifunctional formalism the functional value can directly be obtained from its derivative (while the functional itself remains unknown). Since functional derivatives are up to a constant uniquely defined, this approach allows for a pointwise comparison between approximate potentials and reference potentials. This aspect is especially important in the field of orbital-free density functional theory, where the burden is to approximate the kinetic energy. Since in the bifunctional approach the potential is approximated directly, full control is given over the latter, and consequently over the final electron densities obtained from variational procedure. Besides the bifunctional formalism itself another concept is introduced, dividing the total non-interacting kinetic energy into a known functional part and a remainder, called Pauli kinetic energy. Only the remainder requires further approximations. For practical purposes sufficiently accurate Pauli potentials for application on atoms, molecular and solid-state systems are presented.
Highlights
Density functional theory (DFT) [33] has probably become the most popular workhorse for quantum mechanical calculations among chemists and physicists with a wide application on molecular and solid-state systems [4,7]
Nowadays density functional theory is understood to be Kohn–Sham DFT (KS-DFT) [36], a variant of DFT where some amount of the electron–electron interaction is approximated by the so-called exchange-correlation functional, while the kinetic energy is obtained from the eigenfunctions of a fictitious system of N non-interacting particles having the same electron density like the system of interest
Reliable approximations for the kinetic energy are the crucial point in orbital-free density functional theory (OF-DFT)
Summary
Density functional theory (DFT) [33] has probably become the most popular workhorse for quantum mechanical calculations among chemists and physicists with a wide application on molecular and solid-state systems [4,7]. In an orbital-free density functional formalism, a single equation, the so-called Euler equation [43], yields the minimizing electron density via functional differentiation of the total energy under the constraint that the density stays normalized to the number of electrons N. This method, requires the knowledge of the electronic kinetic energy as a functional of the electron density or at least some reasonable approximation to it. The problem here is not to properly model the kinetic energy for a
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