Related papers: Fully self-consistent optimized effective potentia…
The optimized effective potential (OEP) method presents an unambiguous way to construct the Kohn-Sham potential corresponding to a given diagrammatic approximation for the exchange-correlation functional. The OEP from the random-phase…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
We propose a new generalised Kohn-Sham or constrained hybrid method, where the exchange potential is the (equally weighted) average of the nonlocal Fock exchange term and the self-interaction-corrected exchange potential, as obtained from…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
We propose a practical approximation to the exchange-correlation functional of (time-dependent) density functional theory for many-electron systems coupled to photons. The (time non-local) optimized effective potential (OEP) equation for…
The density-functional approach to quantum electrodynamics is extending traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we…
Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that…
The standard way to calculate the Kohn-Sham orbitals utilizes an approximation of the potential. The approximation consists in a projection of the potential into a finite subspace of basis functions. The orbitals, calculated with the…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…
The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction implemented rigorously within…
Current-spin density functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density functional…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
A model is developed, based on the density functional perturbation theory and the inverse Kohn-Sham method, that can be used to improve relativistic nuclear energy density functionals towards an exact but unknown Kohn-Sham…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Kohn-Sham (KS) formalism of Density Functional Theory is modified to include the systems with strong non-dynamic electron correlation. Unlike in extended KS and broken symmetry unrestricted KS formalisms, cases of both singlet-triplet and…
Inverse Kohn-Sham (iKS) problems are needed to fully understand the one-to-one mapping between densities and potentials on which Density Functional Theory is based. They are also important to advance computational schemes that rely on…