Kohn-Sham density functional theory is a rigorous formulation of many-electron quantum mechanics which, for practical purposes, requires approximation of one term in its total energy expression: the exchange-correlation energy. This work elucidates systematic methods for constructing approximations to the exchange-correlation energy solely from first-principles physics. We review the constraints that can be built into approximate density functionals, and use thermochemical data to argue that satisfaction of these constraints permits a more general description of electronic matter. Contact with semiclassical physics is made by studying the turning surfaces of Kohn-Sham potentials in solids. Perfect metals and covalently-bound, narrow-gap insulators do not have turning surfaces at equilibrium, but do under expansive strain. Wide-gap insulators, ionic crystals, and layered solids tend to have turning surfaces at equilibrium. Chemical bonds in solids are classified using the turning surface radii of its constituent atoms. Depletion of the charge density, such as near a monovacancy in platinum, is shown to produce a turning surface. Further, this work demonstrates why generalized gradient approximations (GGAs) are often able to describe some properties of sp-bonded narrow-gap insulators well. A Laplacian-level pure-density functional is developed with the goal of describing metallic condensed matter. This functional is derived from the r2SCAN orbital-dependent meta-GGA, and reduces its tendency to over-magnetize ferromagnets; improves its description of the equation of state properties of alkali metals; and improves its description of intermetallic thermodynamics. It is constructed to enforce the fourth-order exchange gradient expansion constraint (not satisfied by r2SCAN), and a few free parameters are fitted to paradigmatic metallic systems: jellium surfaces and closed-shell jellium clusters. Last, we modify an exchange-correlation kernel that describes the density-density response of jellium to better satisfy known frequency sum rules. We also constrain the kernel to reproduce the correlation energies of jellium, and compare it to a wide variety of common kernels in use for linear response, time-dependent density functional theory calculations. / Physics

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.

<p>Quantum chemical calculations have been performed to investigate radical cation rearrangement, radical carbonylation, and homolytic substitution reactions of organic molecules.</p><p>The rearrangement of the bicyclopropylidiene radical cation to the tetramethyleneethane radical cation is predicted to proceed with stepwise disrotatory opening of the two rings. Each ring opening is found to be combined with a striking pyramidalization of a carbon atom in the central bond.</p><p>The isomerization of the norbornadiene radical cation to the cycloheptatriene radical cation (<b>CHT</b><b>.+</b>), initialized by opening of a bridgehead–methylene bond, is investigated. The most favorable path involves concerted rearrangement to the norcaradiene radical cation followed by ring opening to <b>CHT</b><b>.+</b>. The barrier of this channel is found to be significantly reduced upon substitution of the methylene group with C(CH₃)₂.</p><p>Stepwise mechanisms are predicted to be favored over concerted isomerization for the McLafferty rearrangement of the radical cations of butanal and 3-fluorobutanal. The barrier for the concerted rearrangement is found to be lowered by 17.2 kcal/mol upon substitution, a result which is rationalized by the calculated dipole moments and atomic charges.</p><p>Recent experiments showed that photoinitiated carbonylation of alkyl iodides with [¹¹C]carbon monoxide may be significantly enhanced by using small amounts of ketones that have nπ* character of their excited triplet state. DFT calculations show the feasibility of an atom transfer type mechanism, proposed to explain these observations. Moreover, the computational results rationalize the observed differences in yield when using various alcohol solvents.</p><p>Finally, following photolysis of methyliodide, recent electron spin resonance spectroscopy experiments demonstrated that the S_H2 reaction ^•CD₃ + SiD₃CH₃ → CD₃SiD₃ + ^•CH₃ proceeds with high selectivity over the energetically more favorable D abstraction. The role of geometrical effects, especially the formation of prereactive complexes between methylsilane and methyliodide is studied, and a plausible explanation for the experimentally observed paradox is presented.</p>

Quantum chemical calculations have been performed to investigate radical cation rearrangement, radical carbonylation, and homolytic substitution reactions of organic molecules. The rearrangement of the bicyclopropylidiene radical cation to the tetramethyleneethane radical cation is predicted to proceed with stepwise disrotatory opening of the two rings. Each ring opening is found to be combined with a striking pyramidalization of a carbon atom in the central bond. The isomerization of the norbornadiene radical cation to the cycloheptatriene radical cation (CHT.+), initialized by opening of a bridgehead–methylene bond, is investigated. The most favorable path involves concerted rearrangement to the norcaradiene radical cation followed by ring opening to CHT.+. The barrier of this channel is found to be significantly reduced upon substitution of the methylene group with C(CH3)2. Stepwise mechanisms are predicted to be favored over concerted isomerization for the McLafferty rearrangement of the radical cations of butanal and 3-fluorobutanal. The barrier for the concerted rearrangement is found to be lowered by 17.2 kcal/mol upon substitution, a result which is rationalized by the calculated dipole moments and atomic charges. Recent experiments showed that photoinitiated carbonylation of alkyl iodides with [11C]carbon monoxide may be significantly enhanced by using small amounts of ketones that have nπ* character of their excited triplet state. DFT calculations show the feasibility of an atom transfer type mechanism, proposed to explain these observations. Moreover, the computational results rationalize the observed differences in yield when using various alcohol solvents. Finally, following photolysis of methyliodide, recent electron spin resonance spectroscopy experiments demonstrated that the SH2 reaction •CD3 + SiD3CH3 → CD3SiD3 + •CH3 proceeds with high selectivity over the energetically more favorable D abstraction. The role of geometrical effects, especially the formation of prereactive complexes between methylsilane and methyliodide is studied, and a plausible explanation for the experimentally observed paradox is presented.