An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain W 1,2-bounds of the associated p...

The exact ground-state Kohn-Sham (KS) potential for the helium atom is known from accurate wave function calculations of the ground-state density. The threshold for photoabsorption from this potential matches the physical system exactly. By carefully studying its absorption spectrum, we show the answer to the title question is no. To address this problem in detail, we generate a highly accurate...

We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wa...

Ligand field splitting energies of lanthanides Ln (Ln = from Ce to Yb) in octahedral environment are calculated using the Hohenberg–Kohn theorems based orbital-free embedding formalism. The lanthanide cation is described at orbital level whereas its environment is represented by means of an additional term in the Kohn–Sham-like one-electron equations expressed as an explicit functional of two e...

We discuss possibilities and challenges for describing correlated electron and nuclear dynamics within a surface-hopping framework using time-dependent density functional theory (TDDFT) for the electron dynamics. We discuss the recent surface-hopping method proposed by Craig et al. [Phys. Rev. Lett. 95, 163001 (2005)] that is based on Kohn-Sham potential energy surfaces. Limitations of this app...

We establish Hölder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.

We prove one-sided universal bounds on coarsening rates for two kinds of mean field models of phase transitions, one with a coarsening rate l ∼ t and the other with l ∼ t. Here l is a characteristic length scale. These bounds are both proved by following a strategy developed by Kohn and Otto (Comm. Math. Phys. 229 (2002), 375-395). The l ∼ t rate is proved using a new dissipation relation which...

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this de...

We describe a rapidly converging algorithm for solving the Kohn–Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many–body systems. The algorithm has its roots the Hohenberg-Kohn theorem and solves directly for the electron density; single–particle wave functions are only used as auxiliary quantities. The metho...

In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this quantity we derive an integral equation. We further derive an integral equation for its functional deri...