Some mathematical models in quantum chemistry and uncertainty quantification
type: Dataset
contact point: Organization
  fn: CCSD
keyword: obstacle
keyword: pollution-spectrale
keyword: incertitude
keyword: spectral-pollution
keyword: defauts
keyword: theses
keyword: glouton
keyword: uncertainty
keyword: greedy
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: chimothechemical-sciencesother
keyword: defects
keyword: infoeu-reposemanticsdoctoralthesis
keyword: quantum
keyword: quantique
landing page: https://pastel.hal.science/tel-00719466
description: The contributions of this thesis work are two fold. The first part deals with the study of local defects in crystalline materials. Chapter 1 gives a brief overview of the main models used in quantum chemistry for electronic structure calculations. In Chapter 2, an exact variational model for the description of local defects in a periodic crystal in the framework of the Thomas-Fermi-von Weisz"acker theory is presented. It is justified by means of thermodynamic limit arguments. In particular, it is proved that the defects modeled within this theory are necessarily neutrally charged. Chapters 3 and 4 are concerned with the so-called spectral pollution phenomenon. Indeed, when an operator is discretized, spurious eigenvalues which do not belong to the spectrum of the initial operator may appear. In Chapter 3, we prove that standard Galerkin methods with finite elements discretization for the approximation of perturbed periodic Schrödinger operators are prone to spectral pollution. Besides, the eigenvectors associated with spurious eigenvalues can be characterized as surface states. It is possible to circumvent this problem by using augmented finite element spaces, constructed with the Wannier functions of the periodic unperturbed Schr"odinger operator. We also prove that the supercell method, which consists in imposing periodic boundary conditions on a large simulation domain containing the defect, does not produce spectral pollution. In Chapter 4, we give a priori error estimates for the supercell method. It is proved in particular that the rate of convergence of the method scales exponentiall with respect to the size of the supercell. The second part of this thesis is devoted to the study of greedy algorithms for the resolution of high-dimensional uncertainty quantification problems. Chapter 5 presents the most classical numerical methods used in the field of uncertainty quantification and an introduction to greedy algorithms. In Chapter 6, we prove that these algorit…
identifier: NNT: 2012PEST1073
issued: 2026-05-14T13:48:02.449353
language: en
modified: 2026-05-14T13:48:02.449359

Some mathematical models in quantum chemistry and uncertainty quantification
type: Distribution
access URL: https://pastel.hal.science/tel-00719466
format: HTML
issued: 2026-05-14T13:48:02.492916
modified: 2026-05-14T13:48:02.414905

test_moissonnage_selune
type: Agent