Motivated by our frustration with the lack of quantum chemistry methods for strongly-correlated open-shell systems, we develop quantitative methods for computing the electronic structure of such systems and qualitative tools for analyzing their chemical properties and reactivity. Specifically, we present a modern framework for performing sparse configuration interaction (CI) computations with arbitrary (Slater determinant) N-electron basis sets, using restricted or generalized spin-orbitals, and including computation of spin-polarized 1- and 2- electron reduced density matrices (RDMs). This framework is then used to implement the flexible ansätze for N-electron CI (FanCI) method more efficiently, via increased vectorization in the FanCI equations and use of sparse CI algorithms. We also extended the FanCI approach, including least-squares and stochastic optimization techniques, the computation of spin-polarized 1- and 2- electron RDMs, and transition energies (ionization potentials, electron affinities, and excitation energies). We use these tools to compare various open-shell CI methods and FanCI methods based on various antisymmetrized product of nonorthogonal geminals ansätze. To translate the vast amount of quantitative data present in the energies and (spin-polarized) density matrices of multiple open-shell states, we present a new, internally consistent and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT) that reduces to a sensible formulation of spin-free CDFT in an appropriate limit. Using this framework, we were able to generalize the (non-spin-polarized) Parr function. We can also, using this framework, construct promolecules with proatoms having non-integer charges and multiplicities. Finally, we describe an equations-of-motion-based method for computing spin-polarized reactivity descriptors of a chemical system from only the ground state energy and the 1- and 2- electron RDMs from a single-point electronic structure computation, and show some benchmark computations for this method based on various CI and FanCI electronic structure methods. / Thesis / Doctor of Philosophy (PhD)

Due to recent advances in computational hardware and code accessibility, state-of-the-art calculations are currently employed to investigate materials at the nanoscale with varying levels of accuracy. As such, this dissertation highlights a series of materials ranging from one-dimensional wires, to reactive surfaces, to bulk crystals. Initial characterizations for all considered materials are carried out using density functional theory where additional approximations are utilized to obtain more complex quantities. For Millon's salt, first-principles calculations confirm a quasi-one-dimensional description where the metallic backbone influences electronic properties while hydrogen-bonding between ligands results in structural stability. We show that valence band dispersion can be controlled via strain or ligand substitution, pointing to tunable hole-carrier possibilities. Optical properties are also addressed with respect to experimental and theoretical findings. Our focus then shifts to titanium dioxide, a popular and promising photocatalyst. Specific nitrogen doping on the anatase (001) surface introduces intra gap states accessible for photoactivation in the visible. The additional presence of a fluorine dopant or oxygen vacancy enhances the density of these particular states available for transitions. Titanium dioxide also has experimentally displayed involvement in carbon dioxide reduction mechanisms. From first-principles calculations, anatase (001) surfaces containing an oxygen vacancy exhibit an increased potential for carbon dioxide to undergo reduction due to an exposed titanium atom in comparison to the pristine case. Other binding configurations on both types of surfaces suggest the existence of alternative conversion pathways. As a recently realized plasmonic material, titanium nitride proves advantageous in relation to more traditional materials, e.g., gold or silver; one of the main factors stems from its tunable permittivity. We investigate this aspect by theoretically incorporating defects into titanium nitride, which introduces a systematic approach to control plasmonic activity over a broad frequency range. Finally, lifetimes of hot-electrons, originating from plasmonic decay, for instance, possess finite lifetimes in titanium nitride, as well as in other similar materials, that are described by electron-electron interactions through the electron self-energy. Average lifetimes resemble those obtained with a free electron gas model while details of the band structure influence lifetime behavior. Calculations exploring factors affecting these lifetimes are presented.

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.

Doping in bulk semiconductors (e.g., n- or p- type doping in silicon) allows for precise control of their properties and forms the basis for the development of electronic and photovoltaic devices. Recently, there have been reports on the successful synthesis of doped semiconductor nanocrystals (or quantum dots) for potential applications in solar cells and spintronics. For example, nanocrystals of ZnSe (with zinc-blende lattice structure) and CdSe and ZnO (with wurtzite lattice structure) have been doped successfully with transition-metal (TM) elements (Mn, Co, or Ni). Despite the recent progress, however, the underlying mechanisms of doping in colloidal nanocrystals are not well understood. This thesis reports a comprehensive theoretical analysis toward a fundamental kinetic and thermodynamic understanding of doping in ZnO, CdSe, and ZnSe quantum dots based on first-principles density-functional theory (DFT) calculations. The theoretical predictions of this thesis are consistent with experimental measurements and provide fundamental interpretations for the experimental observations. The mechanisms of doping of colloidal ZnO nanocrystals with the TM elements Mn, Co, and Ni is investigated. The dopant atoms are found to have high binding energies for adsorption onto the Zn-vacancy site of the (0001) basal surface and the O-vacancy site of the (0001) basal surface of ZnO nanocrystals; therefore, these surface vacancies provide viable sites for substitutional doping, which is consistent with experimental measurements. However, the doping efficiencies are affected by the strong tendencies of the TM dopants to segregate at the nanocrystal surface facets, as indicated by the corresponding computed dopant surface segregation energy profiles. Furthermore, using the Mn doping of CdSe as a case study, the effect of nanocrystal size on doping efficiency is explored. It is shown that Mn adsorption onto small clusters of CdSe is characterized by high binding energies, which, in conjunction with the Mn surface segregation characteristics on CdSe nanocrystals, explains experimental reports of high doping efficiency for small-size CdSe clusters. In addition, this thesis presents a systematic analysis of TM doping in ZnSe nanocrystals. The analysis focuses on the adsorption and surface segregation of Mn dopants on ZnSe nanocrystal surface facets, as well as dopant-induced nanocrystal morphological transitions, and leads to a fundamental understanding of the underlying mechanisms of dopant incorporation into growing nanocrystals. Both surface kinetics (dopant adsorption onto the nanocrystal surface facets) and thermodynamics (dopant surface segregation) are found to have a significant effect on the doping efficiencies in ZnSe nanocrystals. The analysis also elucidates the important role in determining the doping efficiency of ZnSe nanocrystals played by the chemical potentials of the growth precursor species, which determine the surface structure and morphology of the nanocrystals.

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

The development of the semi-empirical atomistic potential called the embedded atom method (EAM) has allowed for the efficient modeling of solid-state environments, at a lower computational cost than afforded by density functional theory (DFT). This offers the capability of EAM to model the energetics of solid-state phases of varying coordination, including defects, such as vacancies and self-interstitials. This dissertation highlights the development and application of two EAMs: a Ti potential constructed with the multi-state modified embedded atom method (MS-MEAM), and a Ni potential constructed with the fragment Hamiltonian (FH) method. Both potentials exhibit flexibility in the description of different solid-states phases and applications. This dissertation also outlines two applications of DFT. First, a study of structure and stability for solid-state forms of NixCy (in which x and y are integers) is investigated using plane-wave DFT. A ground state phase for Ni2C is elucidated and compared to known and hypothesized forms of NixCy. Also, a set of correlation consistent basis sets, previously constructed using the B3LYP and BLYP density functionals, are studied. They are compared to the well-known to the correlation consistent basis sets that were constructed with higher-level ab initio methodologies through computations of enthalpies of formation and combustion enthalpies. The computational accuracy with regard to experiment is reported.

Supercapacitors have emerged as a promising energy storage technology with unique characteristics that set them apart from conventional batteries and capacitors. Supercapacitors bridge the gap between these two technologies by combining the high power density of capacitors with the high energy storage capacity of batteries, offering a compelling solution for various applications. In the pursuit of enhancing supercapacitor performance, magnetite (Fe3O4) has been researched as a potential anode material. Fe3O4 offers several desirable properties, including high theoretical capacitance, low cost, and environmental friendliness. Compositing Fe3O4 with conductive additives has served to address the issue of limited conductivity in Fe3O4 anodes for practical uses, however, a focus must be shifted to enhancing the capacitive performance of such anodes to unlock their full potential. Achieving the full potential of Fe3O4 for supercapacitor applications requires addressing challenges in the colloidal fabrication of high-active mass electrodes. This is done by exploring the exceptional adsorption properties of two dispersing and capping agents: 3,4-dihydroxybenzoic acid and murexide. Exceptional adsorption properties of catecholate-type 3,4-dihydroxybenzoic acid molecules were explored for surface modification of Fe3O4 nanoparticles to enhance their colloidal dispersion as verified by sedimentation test results and Fourier-transform infrared spectroscopy measurements. Electrodes prepared in the presence of 3,4-dihydroxybenzoic acid exhibited nearly double the capacitance at slow charging rates as compared to the control samples without the dispersant or with benzoic acid as a non-catecholate dispersant. Density functional theory analysis of adsorption behavior of 3,4-dihydroxybenzoic acid and benzoic acid at the (001) surface of Fe3O4 corroborated these experimental results by providing an understanding of the basic mechanism of 3,4-dihydroxybenzoic acid adsorption on the surface of nanoparticles. Furthermore, murexide for surface modification of Fe3O4 nanoparticles effectively enhanced the performance of multi-walled carbon nanotube-Fe3O4 supercapacitor anodes. Our experimental results demonstrate significant improvements in electrode performance when murexide is used as a capping or dispersing agent compared to the case with no additives. From impedance measurements, we revealed a substantial decrease in the real part of impedance for samples prepared with murexide, indicating easier charge transfer at more negative electrode potentials, and reinforcing the role of murexide as a capping agent and charge transfer mediator. The theoretical investigation allowed us to identify the nature of chemical bonds between murexide and the surface, with significant charge transfer taking place between the Fe3O4 surface and murexide adsorbate. / Thesis / Master of Applied Science (MASc)

<p>Despite the unprecedented success achieved by Kohn-Sham density functional theory (KS-DFT) in the past few decades, the standard approximations used for the KS exchange-correlation functional typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (P-DFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy introduced to account for the inter-fragment interactions. The unique advantage of this partitioning scheme lies in the fact that it adopts the electron density of fragments as the main variable, in place of the density of the entire system in KS-DFT, so that novel approximations can be constructed in terms of fragment properties. With a simple overlap approximation (OA) of the partition energy proposed for binary-partitioned systems, P-DFT is able to rectify the static correlation error caused by standard density functional approximations for strongly-correlated diatomic molecules. In this work, we first implement P-DFT on a one-dimensional (1D) real-space grid and calculate the ground-state energy and density of a series of 1D hydrogen chains using the local density approximation (LDA) as the density functional approximation for fragments. We then propose the generalized overlap approximation (GOA) and the corrected generalized overlap approximation (cGOA), which extends the applicability of OA to systems partitioned into more than two fragments. Combining LDA with cGOA leads to quantitatively correct dissociation curves of hydrogen chains. The static correlation error of LDA is suppressed by cGOA in the strongly-correlation regime when the calculations are performed in a spin-restricted manner, i.e., without the spin symmetry breaking. Additionally, GOA induces an improvement of the ground-state density upon LDA results, and hence helps P-DFT provide a better description of the density dimerization in hydrogen chains.</p>

Functional Theory, the prevailing perspective on the function of counterfactual thinking, posits that the primary purpose of this form of mental simulation is to prepare individuals for the future. However, recent findings have presented challenges to this dominant view. The debate on this topic has recently centered around the possibility that these contradictory results may have arisen from the use of tasks that are inadequate to observe the preparatory function of counterfactuals. Moreover, it has been stressed the importance of considering also more spontaneous (or, at least, more intrinsically motivated) instances of counterfactual thinking when reflecting over its function. In this thesis, Experiments 1 to 3 investigated questions related to the content of counterfactual modifications and their beneficial effects on future performance, utilizing a novel task designed specifically to address previous limitations advanced by the proponents of the Functional Theory. Nonetheless, most of our results did not align with what would have been expected if counterfactual thoughts were produced mainly in a preparatory fashion. Experiments 4 to 6, instead, explored individuals’ inclination to look for non-instrumental counterfactual information, which pertains to information about the outcome of forgone options that does not contribute to improving future outcomes. This type of information seeking, involving the comparison between an actual and a forgone outcome, can represent a proxy of an underlying, genuine process of counterfactual analysis, and thus provides valuable insights for the debate on the function of counterfactual thinking. Indeed, results indicated that individuals readily look for counterfactual information even when it cannot serve any preparatory goal, challenging the notion that the consideration of alternatives to past events is strictly tied to the presence of such goals. These findings, along with prior research, raise questions about the extent to which counterfactual thoughts are produced to prepare for the future, prompting a reevaluation of its underlying functions.

Electronic band structure in the solid and its relation to the energy gap of the monomer is all about studying how intermolecular interactions change electronic structure. In experimental studies this results in broader absorption bands and by extension a lowering of the LUMO and raising of HOMO energy to the conduction and valence band edges respectively. This electronic change involves splitting of the molecular energy levels into bands of non-degenerate energies and can be calculated either quantum mechanically (QM) or by classical force field models through the change in ionization potential (IP) and electron affinity (EA), called the apparent polarization energy, and its relation to HOMO and LUMO through Koopman’s and Janak’s theorem. The study of the formation of a ‘band’ like structure is important in regimes and systems where conventional quantum mechanical (QM) methods become infeasible. Specifically, when systems are non-periodic and plane wave approximations fail, such as in amorphous structures, or in regimes between where the plane wave bulk approximation and the gas phase single molecule QM methods where the scaling of conventional gas phase atomic orbital methods becomes exorbitantly costly and the plane wave approximation fails for open systems. Therefore, the objective of this work is to highlight the changing optoelectronic properties of molecular solids within this regime using both density functional theory and molecular mechanics. The scalability of DFT limits it to multimer systems, leaving the larger nanoscale materials to be studied using molecular mechanics. Here we have utilized a variety of dispersion sensitive functionals in order to characterize the intermolecular interactions and splitting energies in small multimers of some of the smallest oligoacene species, benzene and anthracene. Benzene and anthracene nanoclusters from 0.8 to 5.0 nm in radius have had their changes in electronic band energy calculated due to polarization using the AMOEBA force field and bulk values have also been extrapolated. AMOEBA’s explicit polarization terms allow for direct handling of the polarization energy, control of nanocluster size and shape in a regime that QM methods cannot probe efficiently, and the ability to specify the position of charge carriers in order to examine specific electronic surface behavior. Using differing DFT methods the change in the HOMO and LUMO energy from the single molecule state to multimers of the size of 10 and 12 units for anthracene and benzene respectively. The HOMO band of benzene was raised by ~0.3 eV and LUMO lowered by 0.35 eV. In anthracene the HOMO was lowered by ~0.1 eV and the LUMO by ~0.15 eV. These values remain within 0.1 eV across all dispersion functionals. Using Ren’s parameterization procedure and MP2 for the AMOEBA force field he apparent polarization was calculated. The extrapolated values for the change in the HOMO and LUMO of benzene from single molecule to bulk were 1.42 eV and 0.49 eV respectively. For anthracene the crystalline bulk changes the HOMO and LUMO by 1.34 eV and 1.16 eV respectively. The regression for bulk extrapolation also predicts that benzene clusters of 12 units will be 0.77 eV for HOMO and -0.41 eV for LUMO. Similarly for an anthracene cluster made up of 10 molecular units the apparent polarization is predicted through linear regression to be 0.58 eV for HOMO and 0.53 eV for LUMO.