Complexes containing a transition metal atom with a 3d^4 - 3d^7 electron configuration typically have two low-lying, high spin (HS) and low spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-L\"{o}wdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al. J. Chem. Theory Comput. 14,2304 (2018) to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn about their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states. / Physics

Kohn-Sham density functional theory (KS-DFT) is one of the most widely used electronic structure methods. It is used to find the various properties of atoms, molecules, clusters, and solids. In principle, results for these properties can be found by solving self-consistent one-electron Schrödinger-like equations based on density functionals for the energy. In practice, the density functional for the exchange-correlation contribution to the energy must be approximated. The accuracy of practical DFT depends on the choice of density functional approximation (DFA) and also on the electron density produced by the DFA. The SCAN(strongly constrained and appropriately normed) functional developed by Sun, Ruzsinszky, and Perdew is the first meta-GGA (meta-generalized gradient approximation) functional that is constrained to obey all 17 known exact constraints that a meta-GGA can. SCAN has been found to outperform most other functionals when it is applied to aqueous systems. However, density-driven errors (energy errors occurring from an inexact density produced by a DFA) hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory, due to its relatively low computational cost. In the second chapter, calculations to determine the accuracy of the HF-SCAN functional for water clusters are performed. The interaction and binding energies of water clusters in the BEGDB and WATER27 data sets are computed, and then the spurious charge transfer in deprotonated, protonated, and neutral water dimer is interpreted. The density-corrected SCAN (DC-SCAN) functional elevates the accuracy of SCAN toward the CCSD(T) limit, not only for the neutral water clusters but also for all considered hydrated ion systems (to a lesser extent). In the third chapter, the barrier heights of the BH76 test set are analyzed. Three fully non-local proxy functionals (LC-ωPBE, SCAN50%, and SCAN-FLOSIC) and their selfconsistent proxy densities are used. These functionals share two important points of similarity to the exact functional. They produce reasonably accurate self-consistent barrier heights and their self-consistent total energies are nearly piecewise linear in fractional electron number. Somewhat-reliable cancellation of density - and functional-driven errors for the energy has been established. / Physics

Although semilocal density functional approximations (DFA) are widely applied, none of them can capture the long-range van der Waals (vdW) attraction between the separated subsystems. However, they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly-constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semi-local functionals require an additive correction like non-local correlation functionals (vdW-DFs, VV10, rVV10 etc.) or empirical methods ( DFT+D3, DFT+vdW, DFT+XDM etc.) to capture the long-range part. The molecular complexes bonded by vdW interactions, layered materials, and molecule-surface interactions are a few examples of the systems where the long-range effects play a crucial role.In the first part of this assessment, we investigate the adsorption of benzene and thiophene over the (111) surface of copper (Cu), gold (Au), and silver (Ag). Thiophene and benzene are the prototypes of their respective classes of aromatic compounds and are the most widely studied molecules to model such systems. We first combine a non-local correlation functional (rVV10) with the various generalized gradient approximations (GGAs), namely PBE and PBEsol, along with the meta-GGAs SCAN and revSCAN (collectively known as base functionals), through a set of parameters obtained by fitting against the argon-dimer interaction energy curve. These parameters bridge the base functionals and rVV10 and guide the delicate balance between the short- and long-range interaction. We also utilize the recently introduced vdW-dZK model based on the theory of Zaremba and Kohn. It is a proven method to yield RPA-quality results for the physisorption of graphene over different metallic surfaces. We assess the adsorption energies, vertical adsorption distances, and the molecular-orientation at various sites and compare the results to the experimental values whenever available. Based on our calculations, the semilocal functionals alone underestimate the adsorption energies, reflecting the need for additional corrections. The rVV10-based methods generally bring the molecules closer to the surface and increase the binding energies. However, there is a discrepancy in the description of rVV10 based methods when the base functional is changed. While rVV10 combined with PBE slightly underestimates the adsorption energies, revSCAN+rVV10 and PBEsol+rVV10 are significantly overestimating. The methods PBE+vdW-dZK and SCAN+vdW-dZK, in general, predict better adsorption energies. In particular, SCAN+vdW-dZK stands out in predicting adsorption distances, adsorption energies, sites, and orientation closest to the experimental values whenever available. Apart from the inability of the semilocal DFAs to capture the long-range vdW interaction, they suffer from the so-called self-interaction error (SIE), in which an electron density incorrectly interacts with itself. At the semilocal level, the self-exchange-correlation energy can not counter-balance the self-Hartree energy, giving rise to the SIE problem. About 40 years ago, Perdew and Zunger proposed a solution to it by introducing a method that could remove the spurious SIE on an orbital-by-orbital basis. However, for size-consistency of this orbital-dependent theory, localized orbitals instead of delocalized Kohn-Sham orbitals are required. Recently, Pederson \textit{et al.} introduced an elegant scheme, known as Fermi-L\"owdin orbital self-interaction correction (FLOSIC), which could generate size-extensive and localized orbitals. For an exact functional, free from SIE, the negative of the highest occupied orbital (HO) eigenvalue would equal the first ionization energy (IE). In the second part of this assessment, we evaluate the HO eigenvalue of a representative test set containing 14 small to moderate-sized organic molecules using FLOSIC. The SIE inherent in the semilocal DFAs seriously underestimates the magnitude of the HO energy. Although LDA-SIC and PBE-SIC correct them, IEs are still significantly overestimated. A similar previous work by Vydrov \textit{et al.} reported the over-correction of PZ-SIC in many-electron regions, and various schemes with moderate success have been introduced since then to scale SIC down on those regions. Recently Zope \textit{et al.} introduced a method (LSIC) based on locally scaling-down PZ-SIC using an iso-orbital indicator (z$_\sigma$) which ensures that the correction is made only in the regions where they are required. We introduce a few other approaches similar to LSIC and demonstrate that these methods significantly improve the agreement between the calculated HO eigenvalues and experimental IEs of molecules. / Physics

Structure, dynamics and reactivity of the hydrated electron Frank Uhlig In this work, one of the products of ionization of water, namely the hydrated electron, has been investigated. The hydrated electron is a key-intermediate in aqueous radiation chemistry. Although known to exist for over 50 years, its structure remained elusive and under discussion up to the present day. We show in this work, that we can obtain a faithful picture of the hydrated electron, its equilibrium structure, dynamics after attachment to water, and its reactivity, using ab initio methods. To this end, small cluster models and extended bulk and slab geometries of water including an excess electron have been investigated.

Density functional theory is the most commonly used computational tool to study properties of solids and molecules. Self-interaction error, that arises due to improper cancellation of the self-Hartree and the self exchange correlation energy, has long been identified as a major limitation of practical density functional approximations. We develop and test the performance of different self-interaction corrected functionals in accurately predicting a wide range of properties. This work focuses on use of the Fermi-L\"{o}wdin orbital self-interaction correction (FLOSIC) method to study neutral water complexes and interaction of ions with water clusters. The strongly constrained and appropriately normed (SCAN) density functional approximation (DFA) has been found to give the correct energy ordering of low-lying isomers of water hexamers, resolves the density anomaly between water and ice, and improves the relative lattice energy of ice polymorphs and the infrared spectra of liquid water. However, SCAN is not without its drawbacks. The binding energies of water clusters and lattice energies of ice phases are overestimated by SCAN. We find that by explicitly removing the self-interaction error, the hydrogen-bond binding energy of water clusters can be significantly improved. In particular, self-interaction correction to the SCAN functional (FLOSIC-SCAN) improves binding energies without altering the correct energetic ordering of the low-lying water hexamers. So, orbital-by-orbital removal of self-interaction error applied on top of a proper DFA can lead to an improved description of water complexes. To gain further insight into the performance of different functionals on the relative stability of water clusters, we decompose the total interaction energy into many-body components. We see that the major portion of error in SCAN comes from the two-body interaction, and the FLOSIC-SCAN improves two-body interactions over SCAN and predicts higher-order many-body interactions with about the same accuracy as SCAN. The SCAN functional gives good account of monomer deformation energy (one-body energy), PBE estimated it too low and self-interaction corrected methods FLOSIC-PBE and FLOSIC-SCAN estimated too high monomer deformation energies. Improvement in the total interaction energy by FLOSIC-PBE and FLOSIC-SCAN is happening because of error cancellation by one-body interaction energy. Aqueous solutions of ions are of particular interest due to their profound applications in environmental chemistry, solvation mechanics, the desalination process, etc. This motivated us to study ion-water systems, which include hydronium ion-water clusters, hydroxyl ion-water clusters, halide ion-water clusters, and alkali ion-water clusters. The erroneous delocalization of the extra-electron in anions obtained with DFAs is basis-set dependent. DFAs like LSDA, PBE, or SCAN can bind only a fraction of the excess electron in the complete basis set limit, implying that a moderate-sized localized basis would be a good choice for them. But, accurate description of hydrogen bonds often requires a large basis with some extra diffuse functions. So, in negatively charged hydrogen-bonded systems like deprotonated water clusters, the suitable choice of basis-set is both difficult and ambiguous. We explore this issue systematically in this work. Further, we have found that the better performance by application of FLOSIC is seen in all systems that are connected at least with one hydrogen bond and the error in the binding energy decreases with increase in the size of an ion or equivalently decreases with the length of the hydrogen bond. Moreover, within the same ion-water system, error in the binding energy decreases with increase in the size of the cluster. Non-hydrogen-bonded water-alkali clusters are not affected by the self-interaction errors. / Physics

The Kohn-Sham density functional theory (KS-DFT) finds an approximate solution for the many-electron problem for the ground state energy and density by solving the self-consistent one-electron Schr\"{o}dinger equations. KS-DFT would be an exact theory if we could find the precise form of exchange-correlation energy $(E_{xc})$. However, this would not be computationally feasible. The density functional approximations (DFAs) are designed to be exact in the limit of uniform densities. They require a parametrization of the correlation energy per electron $(\varepsilon_c)$ of the uniform electron gas (UEG). These DFAs take the parametrizations of correlation energy as their input since the exact analytical form of $\varepsilon_c$ is still unknown. Almost all the DFAs of higher rungs of Jacob's ladder employ an additional function on top of $\varepsilon_c$ for approximating their correlation energy. Exchange energies in these DFAs are also approximated by applying an enhancement factor to the exchange energy per electron of the UEG. Exchange-correlation energy is the glue that holds the atoms and molecules together. The correlation energy is an important part of ``nature's glue" that binds one atom to another, and it changes significantly when the bonding of the molecule changes. It is a measure of the effect of Coulomb repulsion due to electronic mutual avoidance and is necessarily negative. We compared three parametrizations of the correlation energy per electron of the uniform electron gas to the original and the corrected density parameter interpolation (DPI), which is almost independent of QMC input, and with the recent QMC of Spink \textit{et al.}, which extends the Ceperley-Alder results to fractional spin polarization and higher densities or smaller Seitz radius $r_s$. These three parametrizations are Perdew-Zunger or PZ 1981, Vosko-Wilk-Nusair or VWN 1980, and Perdew-Wang or PW 1992. The three parametrizations (especially the sophisticated PW92) are closer to the constraint satisfying DPI and are very close to the high-density limit rather than the QMC results of Spink \textit{et al.}. These DFAs suffer from self-interaction error (SIE) which arises due to an imperfect cancellation of self-Hartree energy by self-exchange-correlation energy of a single fully occupied orbital. The self-interaction correction (SIC) method introduced by Perdew and Zunger (PZ) in 1981 to remove the SIE encounters a size-extensivity problem when applied to the Kohn-Sham (KS) orbitals. Hence, we make use of Fermi L\"owdin orbitals (FLO) for applying the PZ-SIC to the density functional approximations (DFAs). FLOs are the unitary transformation of the KS orbitals localized at the Fermi orbital descriptor (FOD) positions and then orthonormalized using L\"owdin's symmetric method. The PZ-SIC makes any approximation exact only in the region of one-electron density and no correction if applied to the exact functional. But it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. Hence, scaling of PZ-SIC is required such that it remains intact in the region of one-electron density and scales down in the region of many-electron densities. The PZ-SIC improves the performance of DFAs for the properties that involve significant SIE, as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by LSIC, local scaling of the PZ-SIC to the local spin density approximation (LSDA). We propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of Z in the asymptotic expansion of the $E_{xc}$ for atoms of atomic number Z, which is neglected by LSIC. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator $z_{\sigma}$ that distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better than LSDA-LSIC and the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and gives comparable results to the strongly constrained and appropriately normed (SCAN) meta-GGA in predicting the total energies of atoms, atomization energies, barrier heights, ionization potentials, electron affinities, and bond-length of molecules. LSDA-LSIC and LSDA-LSIC+ both fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bonds, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. A spurious correction to the exact functional would be found unless the self-Hartree and exact self-exchange-correlation terms of the PZ-SIC energy density were expressed in the same gauge. Therefore, LSIC and LSIC+ are applied only to LSDA since only LSDA has the exchange-correlation (xc) energy density in the gauge of the Hartree energy density. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can be applied to approximate functionals. The use of this compliance function guarantees that scaled-down self-interaction correction (sdSIC) will make no spurious non-zero correction to the exact functional and transforms the xc energy density into the Hartree gauge. We start from the interior scaling of PZ-SIC and end at exterior scaling after the gauge transformation. SCAN-sdSIC evaluated on SCAN-SIC total and localized orbital densities is applied to the highly accurate SCAN functional, which is already much better than LSDA. Hence, the predictive power of SCAN-sdSIC is much better, even though it is scaled by $z_\sigma$ too. It provides good results for several ground state properties discussed here, including the interaction energy of weakly bonded systems. SCAN-sdSIC leads to an acceptable description of many equilibrium properties, including the dissociation energies of weak bonds. However, sdSIC fails to produce the correct asymptotic behavior $-\frac{1}{r}$ of xc potential. The xc potential as seen by the outermost electron will be $\frac{-X_{HO}^{sd}}{r}$ where HO labels the highest occupied orbital and hence doesn't guarantee a good description of charge transfer. The optimal SIC that remains to be developed might be PZ-SIC evaluated on complex Fermi-L\"owdin orbitals (with nodeless orbital densities) and Fermi orbital descriptors chosen to minimize a measure of the inhomogeneity of the orbital densities. / Physics

This thesis is concerned with theoretical concepts of phenomenological and statistical thermodynamics and their computational realization. The main goal of this thesis is to provide efficient workflows for an accurate description of thermodynamic properties of molecules and solid state materials. The Cp-MD workflow developed within this thesis is applied to characterize binary battery materials, such as lithium silicides.This workflow enables a numerically efficient description of macroscopic thermodynamic properties. For battery materials and metal-organic frameworks, it is shown that some macroscopic properties are dominantly controlled by microscopic properties. These microscopic properties are well described by respective small clusters or molecules.Given their reduced size, these systems can be calculated using more accurate and numerically more demanding methods. Standard density functional theory (DFT) and the so called Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method are used for further investigations. It will be shown that SIC is able to overcome some of the problems of DFT. Given further workflows, it is demonstrated how a combination of different computational methods can speed up thermodynamic calculations and is able to deepen the understanding of the driving forces of macroscopic thermodynamic properties.:1 Introduction 2 Open-source and open-science I Theoretical basics 3 Computational methods 4 Computation of thermodynamic properties II Thermodynamics of solid state systems 5 Methodical developments 6 Lithium silicides 7 Metal-organic frameworks III Thermodynamics of nuclei and electrons 8 Electrons and bonding information 9 Thermodynamic properties IV Summary 10 Conclusion 11 Outlook V Appendix / Diese Arbeit befasst sich mit theoretischen Konzepten der phänomenologischen und statistischen Thermodynamik und deren numerischer Umsetzung. Das Hauptziel dieser Arbeit ist es, Arbeitsabläufe für die akurate Beschreibung von thermodynamischen Eigenschaften von Molekülen und Festkörpern zur Verfügung zu stellen. Der während dieser Arbeit entwickelte Cp -MD Arbeitsablauf wird angewandt um binäre Batteriemateralien, wie Lithiumsilizide, zu charakterisieren. Dieser Arbeitsablauf ermöglicht eine numerisch effiziente Beschreibung von makroskopischen thermodynamischen Eigenschaften. Für Batteriemateralien und metallorganische Gerüstverbindungen wird gezeigt, dass einige makroskopische Eigenschaften hauptsächlich von mikroskopischen Eigenschaften kontrolliert sind. Diese mikroskopischen Eigenschaften können mittels zugehöriger Cluster oder Moleküle beschrieben werden. Aufgrund ihrer reduzierten Größe können diese Systeme mit genaueren und numerisch aufwendigeren Methoden berechnet werden. Standard Dichtefunktionaltheorie (DFT) und die Fermi-Löwdin-Orbital Selbstwechselwirkungskorrektur (FLO-SWK) werden für weitere Untersuchungen verwendet. Es wird gezeigt, dass die SWK einige Probleme der DFT überwinden kann. Anhand weiterer Arbeitsabläufe wird gezeigt, wie eine Kombination von verschiedenen numerischen Methoden thermodynamische Berechnungen beschleunigen kann und in der Lage ist das Verständnis der Triebkräfte von makroskopischen thermodynamischen Eigenschaften zu vertiefen.:1 Introduction 2 Open-source and open-science I Theoretical basics 3 Computational methods 4 Computation of thermodynamic properties II Thermodynamics of solid state systems 5 Methodical developments 6 Lithium silicides 7 Metal-organic frameworks III Thermodynamics of nuclei and electrons 8 Electrons and bonding information 9 Thermodynamic properties IV Summary 10 Conclusion 11 Outlook V Appendix

Title: Structure and dynamics of electronic defects in liquid water Author: Ondřej Maršálek Institute: Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic Supervisor: prof. Mgr. Pavel Jungwirth, DSc. Supervisor's e-mail address: pavel.jungwirth@uochb.cas.cz Abstract: In this thesis we present ab inito molecular dynamics simulations of two different electronic defects in water. Photoionization of liquid water produces a cationic hole, which undergoes ultrafast dynamics and forms the hydrated proton and the hydroxyl radical as its products. We study both the dynamics and spectroscopy of this process. The hydrated electron is a key intermediate in radiation chemistry of aqueous systems. We simulate its equilibrium properties in anionic water clusters as well as the dynamics of vertical electron attachment to cold and warm clusters. The hydrated electron reacts with a hydrated proton to form a hydrogen atom. We examine this reaction at a finite temperature in a larger cluster as well as in more detail in a smaller cluster. Because both of the electronic defects studied here are challenging open-shell species, we put emphasis on benchmarking and testing our computational setup. Six published articles are attached to the thesis. Keywords: density functional theory,...

Das „Strongly Constrained and Appropriately Normed“ (SCAN) Austausch-Korrelations-Funktional gehört zur Familie der meta-GGA (generalized gradient approximation) Funktionale. Es gibt aber auch Nachteile Zum einen leiden SCAN Rechnungen oft unter numerischen Instabilitäten, wodurch sehr viele Iteration zum Erreichen von Selbst-Konsistenz benötigt werden. Zum anderen leidet SCAN unter dem von GGA Methoden bekannten Selbstwechselwirkung-Fehler. Im ersten Teil der Arbeit habe ich die numerischen Stabilitätsprobleme in SCAN Rechnungen im Rahmen der numerischen Realraum-Integrationsroutinen im Code FHI-aims untersucht. Diese Analyse zeigt, dass die genannte Probleme durch Anwendung von standardisierten Dichte-Mischalgorithmen für die kinetische Energiedichte abgemildert werden können. Dadurch wird auch in SCAN-Rechnungen eine schnelle und stabile Konvergenz zur selbstkonsistenten Lösung ermöglicht. Im zweiten Teil der Arbeit habe ich untersucht, in welchem Rahmen sich der Selbstwechselwirkung-Fehler in SCAN mittels des von Perdew und Zunger vorgeschlagenen Selbstinteraktionskorrekturalgorithmus (PZ-SIC) verringern lässt. Es wurden aber auch Optimierungen für die PZ-SIC Methode entwickelt. Inspiriert von den ursprünglichen Argumenten in der PZ-SIC-Methode und anderen lokalisierten Methoden, wird in dieser Arbeit eine neuartige Randbedingung (orbital density constraint) vorgeschlagen, die sicherstellt, dass die PZ-SIC Orbitale während des Selbstkonsistenzzyklus lokalisiert bleiben. Dies mildert die Anfangswertabhängigkeit deutlich ab und hilft dabei, in die korrekte selbst-konsistente Lösung mit minimaler Energie zu konvergieren, unabhängig davon ob reelle oder komplexe SIC Orbitale verwendet werden. Die in dieser Arbeit getägtigen Entwicklungen und Untersuchungen sind Wegbereiter dafür, in Zukunft mit SIC-SCAN Rechnungen deutlich genauere ab initio Rechnungen mit nur gering höherem Rechenaufwand durchführen zu können. / The state-of-the-art “Strongly Constrained and Appropriately Normed” (SCAN) functional pertains to the family of meta-generalized-gradient approximation (meta-GGA) exchange-correlation functionals. Nonetheless, SCAN suffers from some well-documented deficiencies. In the first part of this thesis, I revisited the known numerical instability problems of the SCAN functional in the context of the numerical, real-space integration framework used in the FHI-aims code. This analysis revealed that applying standard density-mixing algorithms to the kinetic energy density attenuates and largely cures these numerical issues. By this means, SCAN calculations converge towards the self-consistent solution as fast and as efficiently as lower-order GGA calculations. In the second part of the thesis, I investigated strategies to alleviate the self-interaction error in SCAN calculations by using the self-interaction correction algorithm proposed by Perdew and Zunger (PZ-SIC). Inspired by the original arguments in PZ-SIC and other localized methods, I introduced a mathematical constraint, i.e., the orbital density constraint, that forces the orbitals to retain their localization throughout the self-consistency cycle. In turn, this alleviates the multiple-solutions problem and facilitates the convergence towards the correct, lowest-energy solution both for complex and real SIC orbitals. The developments and investigations performed in this thesis pave the road towards a more wide-spread use of SIC-SCAN calculations in the future, allowing more accurate predictions within only moderate increases of computational cost.

Le présent travail concerne l’avancement des approximations de l’énergie d’échange- corrélation (XC) de la théorie fonctionnelle de la densité (DFT) de Kohn-Sham (KS) basée sur l’approche du facteur de corrélation (CF). Le travail est organisé en trois parties où chaque partie est construite sur des modèles et méthodes précédents. La première partie du travail introduit une nouvelle condition physique à travers la déri- vation du développement en série du quatrième ordre du trou d’échange exact. La dérivation détaillée des formules requises est suivie d’une analyse approfondie qui montre que le terme de quatrième ordre peut ajouter des informations supplémentaires importantes qui sont par- ticulièrement pertinentes pour les molécules par rapport aux atomes. Sur la base de ces résultats, nous explorons les fonctionnelles d’échange qui dépendent du terme de quatrième ordre de l’expansion du trou d’échange. Nous constatons également que les développements d’ensembles de base gaussiens, fréquemment utilisés dans les codes de structure électronique, donnent des représentations insatisfaisantes du terme de quatrième ordre. La deuxième partie de ce travail porte sur la mise en œuvre de nouvelles versions du modèle CF initial [J. P. Precechtelova, H. Bahmann, M. Kaupp et M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] dans lequel le trou XC est approximé. Étant donné que diverses contraintes satisfaites par le trou XC sont connues, des approximations peuvent être conçues pour éviter en grande partie des ajustements empiriques. Dans l’approche CF, le trou XC est écrit comme le produit d’un trou d’échange multiplié par un facteur de corrélation. Une contrainte importante satisfaite par le modèle CF est qu’il reproduit correctement l’éner- gie d’échange exacte dans la limite de haute densité. Ceci est réalisé en utilisant l’énergie d’échange exacte par particule comme variable d’entrée, c’est-à-dire que le modèle CF s’ap- puie sur l’échange exact. Des variations du modèle CF initial sont proposées qui assurent que la réponse exacte est obtenue dans la limite homogène. De plus, nous appliquons une correction à la profondeur du trou XC qui est conçue pour capturer une forte corrélation. Les fonctions d’échange-corrélation qui s’appuient sur un échange exact, comme les hybrides, échouent souvent pour les systèmes qui présentent une corrélation électronique importante. Malgré ce fait et malgré la réduction de l’empirisme à un seul paramètre dans CF, des énergies d’atomisation précises sont obtenues pour des composés de métaux de transition fortement corrélés. Le modèle CF montre des résultats significativement supérieurs aux fonctionnelles populaires comme Perdew-Burke-Ernzerhof (PBE), PBE hybride et Tao-Perdew-Staroverov- Scuseria (TPSS). La troisième partie du travail s’appuie sur les modèles CF précédents développés dans notre groupe et aborde l’erreur d’auto-interaction à un électron et introduit un modèle de facteur de corrélation modifié où f C (r, u) est construit tel qu’il se réduit à un dans les régions à un électron d’un système à plusieurs électrons. Ce trou XC avec une correction d’auto- interaction est ensuite utilisé pour générer la fonctionnelle énergie XC correspondante. La nouvelle fonctionnelle est évaluée en l’implémentant dans un programme KS et en calculant diverses propriétés moléculaires. Nous constatons que, dans l’ensemble, une amélioration significative est obtenue par rapport aux versions précédentes du modèle de facteur de cor- rélation. / The present work is concerned with the advancement of approximations to the exchangecorrelation (XC) energy of Kohn-Sham (KS) density functional theory (DFT) based on the correlation factor (CF) approach. The work is organized in three parts where each part is build upon previous models and methods. The first part of the work introduces a new physical condition through the derivation of the fourth-order series expansion of the exact exchange hole. The detailed derivation of the required formulas is followed by a thorough analysis that shows that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of the exchange hole. We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term. The second part of this work addresses the implementation of new versions of the initial CF model [J. P. Precechtelova, H. Bahmann, M. Kaupp, and M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] in which the XC hole is approximated. Since various constraints satisfied by the XC hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a correlation factor. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. Exchangecorrelation functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS) density functionals. The third part of the work builds on the previous CF models developed in our group and addresses the one-electron, self-interaction error and introduces a modified correlation factor model where fC(r, u) is constructed such that it reduces identically to one in oneelectron regions of a many-electron system. This self-interaction corrected XC-hole is then used to generate the corresponding XC-energy functional. The new functional is assessed by implementing it into a KS program and by calculating various molecular properties. We find that, overall, a significant improvement is obtained compared to previous versions of the correlation factor model.