Related papers: Inverse Kohn-Sham Density Functional Theory: Progr…
We demonstrate how the separation of the total energy of a self-bound system into a functional of the internal one-body Fermionic density and a function of an arbitrary wave vector describing the center-of-mass kinetic energy can be used to…
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…
We present a real-space formulation and implementation of Kohn-Sham Density Functional Theory suited to twisted geometries, and apply it to the study of torsional deformations of X (X = C, Si, Ge, Sn) nanotubes. Our formulation is based on…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
The properties of the Kohn-Sham (KS) exchange potential for open systems in thermodynamical equilibrium, where the number of particles is non-conserved, are analyzed with the Optimized Effective Potential (OEP) method of Density Functional…
The density functional theory is extended to account for self-bound systems. To this end the Hohenberg-Kohn theorem is formulated for the intrinsic density and a Kohn-Sham like procedure for an $N$--body system is derived using the…
A way to improve the accuracy of the spectral properties in density functional theory (DFT) is to impose constraints on the effective, Kohn-Sham (KS), local potential [J. Chem. Phys. {\bf 136}, 224109 (2012)]. As illustrated, a convenient…
Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has…
In this paper, we consider the weighted sum-power minimization under quality-of-service (QoS) constraints in the multi-user multi-input-single-output (MISO) uplink wireless network assisted by intelligent reflecting surface (IRS). We…
In this paper, we consider the weighted sum-power minimization under quality-of-service (QoS) constraints in the multi-user multi-input-single-output (MISO) uplink wireless network assisted by intelligent reflecting surface (IRS). We…
We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
A two-user downlink network aided by a reconfigurable intelligent surface is considered. The weighted sum signal to interference plus noise ratio maximization and the sum rate maximization models are presented, where the precoding vectors…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
The Kohn-Sham (KS) density matrix is one of the most essential properties in KS density functional theory (DFT), from which many other physical properties of interest can be derived. In this work, we present a parameterized representation…
In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error…