This dissertation involves explorations of on surfaces and on carbon-based nanomaterials, especially graphene, using quantum chemical calculations. The work evaluates energetics of cycloaddition reactions on different sites of graphene, improving the understanding of graphene chemistry and guiding experiments.

Chapter 1 to 3 describes theoretical investigations of 1,3-dipolar cycloadditions, Diels- Alder reactions, (2+2) cycloadditions, (4+4) cycloadditions and non-covalent interactions to graphene models. Reaction energetics have been obtained and showed that edge areas of graphene are much more favorable reaction sites than the center sites. Results indicate that graphene edges may be functionalized by a series of small molecule functional groups through cycloaddition reactions, while the interior regions cannot react. Non-covalent complexation is much more favorable than cycloaddition reactions on interior bonds of graphene. Furthermore, the Huckel molecular orbital (HMO) localization energy calculations could be used as a tool to estimate the reactivities of various polycyclic aromatic hydrocarbon molecules for experimental guidance.

Chapter 4 illustrates the Diels-Alder reactions of pentacene, bistetracene and their derivatives with fullerene. Reaction barriers and free energies have been obtained to assess the effects of frameworks and substituent groups on the Diels-Alder reactivity and product stability. Surprisingly, calculations predict that the bulky silylethynyl substituents of pentacene and bistetracene have only a small influence on reaction barriers. However, the silylethynyl substituents significantly destabilize the corresponding products due to steric repulsions in the adducts. This is confirmed by experimental results from collaborators.

Chapter 5 reports theoretical investigations of (1+2) cycloadditions of carbene, nitrene, and oxygen with fullerene, carbon nanotube and graphene models. The results suggest that closed bond adducts are much more preferred on graphene models.

Chapter 6 describes a new method to quickly estimate the reaction energetics on large carbon nanomaterials. For the same addition reaction or cycloaddition, the reaction energetics on benzene was found to perfectly correlate with those on carbon allotrope models. Based on these linear correlation equations, it is possible to quickly estimate cycloaddition or addition reaction energies on different sites of carbon-based nanomaterials by simply calculating these reactions on benzene.

Organic and perovskite materials have shown a remarkable promise for solar cell manufacturing due to scalability, low cost and flexibility of the material compared to other solar panel technologies. The major challenge for organic and perovskite solar cell commercialization, however, is whether they can perform and last as long as silicon panels, which often depends on the molecular properties of materials. Hence, this dissertation focuses on understanding the crucial role and the effect that small molecules have on the efficiency and stability of organic and perovskite solar cells. Chapter 1 explores the inter- and intramolecular interactions of small molecules in organic solar cells. The electron-withdrawing character of functional groups and extension of conjugation strongly contributed to the performance of organic solar cells. Chapter 2 dives into radical formation in a novel small molecule hole-transport material for perovskite photovoltaics and its role in performance and stability of the device. In Chapter 3 and 4, recently designed spirofluorene-based π∙∙∙π-bonded organic framework and a spiroconjugated small molecule are introduced, both of which present remarkable transport properties in organic electronics. Chapter 5 and 6 examine the interactions between small molecules and perovskite quantum dots (QDs). First, a process that controls the density of small molecules on QD surface is developed, after which a small molecule is integrated onto the surface of QDs resulting in improved device performance. The focus then advances to the analysis of small molecule interactions with the thin-film perovskite. Chapter 7 demonstrates a kinetically-controlled and substrate-tolerant local epitaxial growth of formamidinium-based perovskite for thin-films using a cheap, versatile and simple method that improved stability and performance. Chapter 8 and 9 delve into passivation of perovskite defects using small molecules. Theophylline, a small molecule found in tea, emerged to be a strong candidate for silencing the most probable defects on perovskite surface due to its optimal configuration relative to the surface. It was also discovered that the passivation of perovskite surface defects with two small molecules can have synergistic effect on enhancing the performance of perovskite photovoltaics. In chapter 10, interactions in formation kinetics of mixed-halide perovskites are systematically investigated.

This dissertation describes the elucidation of reaction mechanisms and the sources of asymmetric induction in organic reactions with density functional theory. Modern density functional theory is used to develop and propose models for the stereoselectivity of complex organocatalytic reactions. Computations of reactions catalyzed by vicinal diamines, which involve a broad scope of substrates and reactivity, are described in Chapters 1-3. A series of collaborations with experimental research groups are elaborated on in Chapters 4-7.

Chapter 1 describes a computational study of aldol reactions catalyzed by the vicinal diamine class of organocatalysts. The computations and DFT benchmark of the entire transition state landscape of a theoretical model for the simplest aldol reaction catalyzed by ethylene diamine were performed. In addition, the first successful experimental report of a vicinal diamine-catalyzed aldol reaction was studied computationally. The computations revealed a nine-membered cyclic transition state in well-defined conformations of cyclooctane. We identified that the crown (chair-chair) conformation accounted for the observed stereoselectivity in these aldol reactions.

Chapter 2 elaborates on the findings in Chapter 1 of the dissertation by exploring five modern and complex examples of aldol chemistry involving elaborate vicinal diamine catalysts by density functional theory. The computations revealed the sources of stereoselectivity, reactivity, and substituent effects both in catalyst and substrates for aldol reactions catalyzed by vicinal diamines. We proposed a stereoselectivity model based on the conformations of cyclooctane that serves as a predictive model for further aldol chemistry, as well as for the design of new reactions.

Chapter 3 continues the exploration of vicinal diamine catalysis in the realm of Nazarov chemistry. Density functional theory was used to determine the mechanism, stereoselectivity, and source of product inhibition in Nazarov reactions of ketoenones catalyzed by vicinal diamines. The formation of an enamine-iminium ion was determined, and the stereoselectivity was found to be caused by the cyclohexane conformation formed in the enamine-iminium complex. The dihedral angle of the diamine preferred one helicity of the electrocyclization transition state.

Chapter 4 summarizes a collaboration between our group and the research group of Prof. Patrick Harran, where they developed new methods to synthesize macrocyclic pyrroloindolines by alkylating tryptophan-based oligopeptides. Computations were performed to understand the regiodivergent nature of the macrocyclization reactions. We determined that both the endo- and exo-pyrroloindolines form, but the exclusive observation of endo-pyrroloindolines is due to the propensity for the exo-intermediates to rapidly rearrange to thermodynamically preferred C2-linked isomers.

In Chapter 5, a collaboration between our group and Prof. Neil Garg’s research group on the arylations of chiral enamines with arynes. The Garg lab discovered and developed the synthetic methodology for arylating the alpha position of chiral enamines to form stereodefined quaternary centers. We performed density functional theory calculations to understand the mechanism and source of stereoselectivity in the reaction of benzyne and chiral enamines, as well as predict better-performing substituents.

Chapter 6 describes a collaboration between our group and Prof. Karl Anker J�rgensen’s research group in Aarhus, Denmark. The J�rgensen group discovered and developed hetero-[6+4] and [6+2] reactions of heteroaromatic compounds to yield highly complex scaffolds from simple pyrrole aldehydes and olefins. With density functional theory calculations, we determined the nature of the [6+4] and [6+2] reaction mechanisms to be stepwise zwitterionic pathways. The enantio-controlling step was identified as the cyclization step. DFT was used to predict better-performing catalysts for the hetero-[6+2] reaction.

In Chapter 7, we describe a collaboration with Prof. Scott Denmark on the Soai reaction. Prof. Denmark’s group has discovered a new autocatalytic reaction system where detailed kinetics and mechanistic investigations revealed the intricacies of the autocatalytic Soai mechanism. We performed density functional theory calculations to probe the transition state model of enantioselectivity in the autocatalytic mechanism, and the source of autocatalysis.

The sun produces 1020 W m-2 of energy per day; that is, in one hour, the earth receives enough energy to power the earth for an entire year. This energy can be harvested for a range of processes, including water splitting, photocatalysis, and electricity. Photovoltaic technologies, in particular, harness the energy of the sun to produce electrical energy. Organic solar cells, or organic photovoltaics (OPVs), hold advantages over inorganic cells in scalability, range of functionalization, and potential in flexible applications. While the power conversion efficiency (PCE) of this relatively new type of solar cell has made tremendous progress over the last decade, OPVs must continue to improve over 15% PCE in order to become a viable competitor to inorganic cells.

Several factors in the active layer (donor and acceptor layers) of a solar cell can lead to low efficiency, including low carrier mobility, inadequate absorption of the electromagnetic spectrum, and disordered morphology. Therefore, control of morphology in the active layer and tuning of electronic levels of the donors and acceptors in organic photovoltaics are important parameters that need to be controlled for favorable device performance. One approach to improving efficiency is designing molecules that pack closely together to allow for efficient charge transport. These types of systems offer significant possibilities for controlled morphologies, high charge transport, and high efficiencies in solar cells. Towards these types of materials, this work aims to:

1. Understand the effect of torsional behavior in organic materials on the morphology of the active layer to guide the design of materials with low disorder.

2. Determine the effect of crystal packing on charge transport of organic small-molecules and oligomers to lend insight into mechanisms that govern high mobility, and

3. Characterize optical properties of trimeric oligomers to lend insight into potential electronic applications.

Motivated by the potential of new organic photovoltaic materials, this thesis begins with a focus on using computational methods to understand systems of relevance to organic electronics (Chapters 1-7). Early projects aim to use an iterative computational-experimental scheme to understand morphology and charge transport as relevant in organic electronic devices (Chapters 1-3). Molecular properties are calculated and correlated to bulk properties observed experimentally to derive design principles for new molecules that would give rise to interesting packing in solid state. Excited state calculations are used to understand the underlying properties that give rise to optical transitions and to predict new molecules that would absorb strongly in the visible light region (Chapters 4). Mechanistic studies of the degradation pathways of small molecules will also be discussed, and functional handles that would lead to more stable structures are identified (Chapter 5). Calculations are employed to understand the transformation of polydiacetylene polymers to graphene nanoribbons, which lends insight into tuning this reaction for other N-doped materials (Chapter 6). Later in the thesis, the focus diverges to the use of computations to understand the reactivity of a class of ruthenium-based olefin metathesis catalysts towards the design of a stable, E-selective catalyst (Chapter 7-8).

Various methods are employed in the chapters described in this dissertation. Density functional theory is used to characterize ground state geometry, conformational analysis, transition state geometry, molecular orbitals, reorganization energies. Time-dependent density functional theory is used to characterize excited state properties, including bandgap, absorption, emission, excited state geometry, charge transfer properties. ZINDO is used for other excited state properties such as charge transfer, electronic coupling. Molecular dynamics is used for time-scale properties, including electronic disorder, energetic disorder, ordered and disordered morphology. Kinetic Monte Carlo as implemented in the VOTCA program is used for charge transport calculations.

The concept of gating was introduced into host-guest chemistry by our group in the 1990s, as a result of computational studies on Cram's hemicarcerands. Since that time, a variety of gated host systems have been developed by our group and others. The gated hemicarcerands presented in this dissertation are examples of hosts with controllable gates that function upon external stimuli, which we refer to as redox reaction gated hemicarcerands and photochemically gated hemicarcerands. In both cases, a chemically modifiable moiety was installed on the host molecule so that it undergoes chemical change in response to external stimuli. In particular, we took advantage of disulfide-dithiol interchange (redox reaction control) and anthracene dimerization (photochemical control) to achieve gating in these hemicarcerands. Molecular mechanics computations were employed to understand the experimental observations during the complexation and decomplexation processes.

The second part of this dissertation focuses on understanding Diels-Alder reactivities of a wide range of organic molecules with the tools of computational chemistry. Among these extensively studied molecules, tetrazine is the most outstanding one, in the sense that its cycloaddition reactions with strained alkenes are extremely rapid, with second order rate constants up to 2000 M-1s-1. Such reactions take place at a decent rate even at micromolar concentration, suggesting their application in live cell imaging. The emerging use of tetrazines as labeling reagents has added an extra dimension to bioorthogonal cycloadditions. Our computational studies have provided a thorough understanding of the cycloaddition reactivities and a guideline for developing new reagents.

A preeminent goal of organic synthesis is to achieve structural complexity with functional value in a step, atom, and time economical fashion. Cycloadditions, as exemplified by the Diels-Alder reaction, represent uniquely powerful processes to achieve this goal. Most of widely-used cycloadditions require transition metal or organic catalysts to achieve the desired control of reactivity and selectivity, which rely on mechanistic understandings at the molecular level. Modern density functional theory (DFT) calculations provide the foundation to achieve such level of understanding, and my PhD research focuses on studying the mechanism and selectivities of a series of important transition-metal-catalyzed and organocatalytic cycloadditions through DFT calculations.

The first part of the thesis includes my studies on the mechanism and selectivities of transition-metal-catalyzed cycloadditions. Chapter 1 focuses on the mechanism and origins of selectivities in Ru(II)-catalyzed intramolecular (5+2) cycloadditions and ene reactions of vinylcyclopropanes and alkynes. The favored mechanism involves an initial ene-yne oxidative cyclization to form a ruthenacyclopentene intermediate, which is different from that found earlier with rhodium catalysts. Based on this new mechanism, solvent effect, chemoselectivity, diastereoselectivity and regioselectivity are explained. Chapter 2 includes the study of mechanism and ligand-controlled selectivities in [Ni(NHC)]-catalyzed intramolecular (5+2) cycloadditions and homo-ene reactions of vinylcyclopropanes and alkynes. The reaction mechanism of nickel catalysts is similar to that of ruthenium catalysts, which involves the alkyne-alkene cyclization to form a metallacyclopentene intermediate. The selectivity between the (5+2) and homo-ene products is determined in the subsequent competing reductive elimination and β-hydride elimination steps. The anisotropic steric environments of SIPr and ItBu ligands are the major reasons for the reversed selectivity of these two similar-sized ligands. Chapter 3 emphasizes the study of terminal methyl effects in Rh(I)-catalyzed intermolecular (5+2) cycloadditions of vinylcyclopropanes and allenes. A competitive allene dimerization is found to irreversibly sequester the rhodium catalyst. This explains the necessity of methyl substituents on the reacting double bond of allenes to achieve the desired cycloadditions.

The second part of the thesis focuses on my studies of the organocatalyzed cycloadditions. Chapter 4 illustrates the explorations of the mechanism and controlling factors of the organocatalyzed carbonyl-olefin metathesis. In the (3+2) cycloadditions between hydrazonium and alkenes, the distortion of reactants controls the reactivities. In the subsequent cycloreversions, the strain-release of the five-membered ring intermediates determines the reaction barriers. For these two reasons, the cyclopropene derivatives are found to be the most reactive in experiments. Chapter 5 discusses the distortion-acceleration effect of alkynyl substituents in the stepwise hexadehydro-Diels-Aleder (HDDA) Reaction. The HDDA reaction follows a stepwise mechanism with a diradical intermediate. The alkynyl substituent dramatically accelerates the HDDA reaction mainly by decreasing the distortion energy required to achieve the diradical transition state. Chapter 6 focuses on the mechanism and selectivity of N-triflylphosphoramide catalyzed (3⁺+2) cycloaddition between hydrazones and alkenes. The protonation of hydrazones by Brønsted acid catalysts are found to be crucial for the facile (3⁺+2) cycloaddition. This explains the acidity-dependent catalytic activities of this reaction. Based on the mechanism, we have also explained the origins of enantioselectivities when a chiral N-triflylphosphoramide catalyst is employed. Chapter 7 includes the study of mechanism and origins of switchable chemoselectivity of Ni-catalyzed C(aryl)-O and C(acyl)-O activation of aryl esters with phosphine ligands. For aryl esters, nickel with bidentate phosphine ligands cleaves C(acyl)-O and C(aryl)-O bonds via three-centered transition states, and this cleavage favors the weak C(acyl)-O bond. However, when monodentate phosphine ligands are used, the five-centered C(aryl)-O cleavage transition state makes C(aryl)-O activation favorable. In the case of aryl pivalates, nickel with bidentate phosphine ligands still favors the C(acyl)-O activation, but the subsequent decarbonylation requires very high barrier and the alternative C(aryl)-O activation occurs.

The first part of this dissertation describes computational studies of higher-order cycloadditions with a focus on elucidating the origins of periselectivity. These reactions involve ambimodal transition states (TS) and bifurcations of potential energy surface.

Chapter 1 describes density functional theory (DFT) studies of a transannular [6+4] cycloaddition proposed in the biosynthesis of heronamide A, in which an unbridged 10-membered ring is formed. Ring and steric strains are found to be essential in controlling the product stability that makes this reaction feasible. Chapter 2 presents an Environment-Perturbed Transition State Sampling method to explore the mechanism of the enzyme SpnF-catalyzed Diels–Alder. A [6+4] cycloaddition is also involved and enzyme enhances the formation of [4+2] product, with respect to the counterparts in the gas phase and in water. Chapter 3 explores the mechanisms and selectivities of the cycloadditions of tropone to dimethylfulvene discovered in 1967 by Houk. The two proposed pathways by which a key intermediate are formed are united through the discovery of an ambimodal [6+4]/[4+6] TS using DFT calculations and molecular dynamics (MD) simulations.

The second part of this dissertation describes computational studies of Diels–Alder reactions and 1,3-dipolar cycloadditions using DFT calculations, with a focus on the mechanisms and the origins of regio- and stereoselectivities.

Chapter 4 reports the biochemical characterization of a Diels–Alderase found in the biosynthetic pathway of the cytotoxic myceliothermophin natural products. A theozyme model rationalizes both the substrate- and stereoselectivity of the enzyme. Chapter 5 discusses the concerted versus stepwise mechanisms of a series of dehydro-Diels–Alder (DDA) reactions. The reactivity of DDA reactions is controlled by the distortion energies required to achieve the TS geometries. Chapter 6 explores the mechanisms of Lewis acid-catalyzed Diels–Alder reactions of aryl allenes and acrylates. A stepwise mechanism involving short-lived zwitterion intermediates is established. The [2+2] cycloaddition is not observed experimentally because of the greater charge separation in the first step of the [2+2] cycloaddition. Chapter 7 focuses on the regioselectivity of 1,3-dipolar cycloadditions of benzo and mesitonitrile oxides with alkynyl pinacol and MIDA boronates. Calculated relative free energies of activation reproduce the experimentally observed product ratios. The electronic energies of activation are mainly controlled by distortion energies. Chapter 8 describes DFT studies of the first example of diazo esters as dienophiles in intramolecular Diels–Alder reactions with dienes. For comparison, the reactivities of diazo esters as 1,3-dipoles withdienes have also been explored. The usually observed 1,3-dipolar cycloaddition was not observed because of strong tether distortion in the (3+2) TS.

Pericyclic reactions are important class of chemical reaction because they occur stereospecifically often with a high degree of regio-, stereoselectivity, and atom economy. This dissertation summarizes our efforts – using chemical computations – to better understand how these reactions occur in both biological and abiological settings.

This dissertation is divided into two portions; the first of which describes quantum mechanical studies of biosynthetic and enzyme-catalyzed cycloadditions. Chapter 1, 2, and 3 detail studies of these enzymatic processes. Using state-of-the-art density functional theory, we have determined whether these reactions are feasible biosynthetic transformations, elucidated the mechanistic subtleties of these reactions, and proposed how enzymes may catalyze such transformations.

Chapter 1 describes a computational study of a strained biosynthetic transannular 1,3-dipolar cycloaddition. Computations reveal that substrate preorganization overrides distortion in the transitions, resulting in a reaction is feasible. Efforts to account for the influence of water – through solvent-solute hydrogen-bonding interactions – were modeled using “mircosolvated” reactant and transition states: We conclude that the reaction remains feasible in aqueous media. Strategic hydrogen bonding, according to theory, can accelerate the reaction by 2000-fold.

Chapter 2 summarizes a computational investigation of the Diels-Alder reaction involved in the biosynthesis of spinosyn A. We find that the mechanism of this transannular cycloaddition is “ambimodal”, proceeding through a “bis-pericyclic” transition structure that leads directly two products, the observed Diels-Alder adduct and an unstable [6+4] adduct. This [6+4] adduct can readily and irreversibly rearrange into the Diels-Alder adduct via a Cope rearrangement. Simulations of the reaction mechanism determine that the nonenzymatic cycloaddition occurs predominantly via a mechanism that involves the intermediacy of the [6+4] adduct.

Chapter 3 discusses an ongoing collaboration with the Tang laboratory at UCLA and involves an effort to understand the intramolecular Diels-Alder reaction involved in the biosynthesis of cholesterol-reducing agent, lovastatin. We have modeled the reaction of a related cycloaddition performed experimentally, and computations recapitulate the selectivity observed experimentally for this nonenzymatic process. The stereochemical outcome of the enzymatic reaction diverges from the outcome of its synthetic analogue. Computation of the reactive conformer of the model substrate suggests that substrate preorganization could accelerate the intramolecular Diels-Alder reaction by approximately a 1000-fold.

Theoretical studies of stereoselective electrocyclic reactions are described in Chapters 4, 5, 6, 7, and 8. These reactions have been examined by experimentally by chemists in the laboratory and, subsequently, have been modeled using quantum mechanical computations. From this computational work, we have determined the stereoselectivity of several synthetically relevant electrocyclic reactions, the effect of substituents of the reactivity of the electrocyclization precursors.

In Chapter 4, we summarize our work with Dr. Gregg Barcan and Prof. Ohyun Kwon to elucidate the origins of 1,6-stereoinduction of a triene electrocyclization employed in their total synthesis of reserpine. We determine that conformational transmission of the stereochemical information found at a distal stereocenter is “transmitted” to the forming stereogenic center via A1,3 strain. Allylic strain destabilizes the disfavored mode of ring closure. According to both theory and experiment, stereoselectivity is shown to be sensitive to the size of the substituent involved in the A1,3 strain.

Chapter 5 outlines a computational investigation of the 8π-6π electrocyclization cascades of substituted tetraenes, such species are common intermediates in the biosyntheses of many natural products containing bicyclo[4.2.0]-octadiene ring systems. These cascades reaction occur spontaneously in a growing number of natural products. Here we determined the influence terminal substitution on the reactivities, thermodynamics, and stereoselectivities of these reactions. Terminal substituents destabilize the tetraene precursor and the resulting 8π electrocyclization product. Strain relief drives and promotes the subsequent 6π electrocyclization. Where possible, the diastereoselectivity of this cascade is controlled by a steric effect that destabilizes the endo mode of electrocyclic ring closure.

Chapter 6 reviews a density functional theory study of a series of torquoselective triene and Nazarov electrocyclizations of bridged bicyclic substrates. We find that the torquoselectivities of highly exo selective ring closures are controlled by action of torsional effect that acts in concert with either steric attraction or repulsion. In one case, a Nazarov cyclization, a through space orbital interaction overrides this exo selectivity.

This thesis focuses on the study of time-resolved mechanism of organic reactions with molecular reaction dynamics simulations. Gas-phase trajectory simulations were performed on (1) dimethyldioxirane C-H oxidation, which show how polar acetone solvation favors diradical recombination, leading to the retention of stereospecificity; (2) dehydro-Diels-Alder reactions, which reveal intrinsic dynamic features for concerted and stepwise pathways, where concerted pathway involves a vibrational excitation, while stepwise pathway involves a rotational excitation; (3) cyclopentadiene dimerization, in which two-stage pathway, as originally proposed by Woodward and Katz, is involved in 13% of the reactive trajectories, presenting a typical “dynamically stepwise” feature with time gap between formation of two bonds longer than 60 fs; and (4) sixteen reactions with potential energy surface bifurcation, where a linear correlation was found between TS bond lengths and the product ratio, serving as an empirical model to assist the discovery of new bifurcating reactions, and estimate product ratio without the expense of MD simulations.

The thesis reports the development of a new computational method, environment-perturbed transition state sampling, (EPTSS) to enable the study of reaction dynamics in solvent and in enzyme. EPTSS integrates the conformational sampling of solvent/enzyme and quasi-classical sampling of reacting molecules, which was inspired by Truhlar and Gao’s ensemble-average variational transition state theory. The method has been applied to (1) water-accelerated Diels-Alder reaction, which shows how water molecules dynamically participate the reaction and forms enhanced hydrogen bonds; (2) phosphoric acid-catalyzed allylboration reactions, in which an intrinsic synergy of enhancement between the CH���O and OH���O hydrogen bonds were observed, and the enhancement is diminished in toluene solvent; and (3) SpnF-catalyzed Diels-Alder reaction, which first demonstrates how enzyme dynamically control the product ratio of bifurcating reactions.

The development of catalysts for faster, more selective, and more sustainable chemical reactions remains an outstanding goal in chemistry. While advancements in statistical models have greatly improved our predictive ability, physical models remain our most valuable tools for mechanistic understanding. Density functional theory (DFT) calculations provide structural models of reaction intermediates and transition states and can accurately predict thermodynamic quantities. For larger systems, molecular dynamics (MD) simulations using classical force fields model time-dependent movements of protein-ligand complexes. This Thesis combines both approaches to model several designed and engineered catalysts.In Chapter 2, we investigate dirhodium catalysts that were designed to catalyze an enantioselective Si–H insertion. Our experimental collaborators observed that the enantioselectivity of the reaction correlated strongly with the Hammet constant of the carbene’s aryl substituents but lacked a clear understanding as to why. DFT calculations using an Rh2(OAc)4 catalyst showed that the aryl rings of the carbene rotate in the transition state, resulting in one aryl conjugating with the vacant carbene p-orbital. For asymmetrically substituted carbenes, the transition state with the electron-rich aryl conjugated to the vacant carbene p-orbital was always lower in energy, and this energy difference increased with greater electronic differences between the rings. We then showed that because of this geometric constraint, the chiral environment of the designed catalysts favored one enantiomeric transition state over the other. Again, the energy difference between transition states correlated with the differences in Hammet substituent constants between the rings. In Chapter 3, we investigate a laboratory-evolved family of flavin-dependent halogenases with orthogonal selectivity for the chlorination of tryptamine. Few mutations separate the wild type from the most distant mutant, and crystal structures show that there are minimal structural differences between the enzymes. DFT calculations and MD simulations established that a catalytic lysine activates HOCl through general acid catalysis for chlorination of the substrate. Energetic differences in the transition states or Wheland intermediates calculated by DFT showed the intrinsic site selectivity for each substrate. Docking calculations and MD simulations of protein-substrate complexes showed how each enzyme binds the substrate to position a single site closest to the halogenating species, influencing the site selectivity of this reaction. Our physical model was then used to predict site selectivity for several nonnative substrates. Finally, Chapter 4 investigates a set of computationally designed enzymes with varying activity for a chemiluminescence reaction. Initial designs were optimized by site-saturation mutagenesis, and it was not clear why the final proteins were so much more active than the initial designs. Our DFT calculations confirmed the proposed reaction mechanism and showed that anion formation in the substrate was critical for the reaction. Docking calculations and MD simulations showed that LuxSit-i, the most active variant, was the best at stabilizing this anion in the transition states. Changing the substituent resulted in worse stabilization during the simulations, which is consistent with the observed substrate specificity. All three of these chapters explore notable examples of catalyst engineering and provide physical models for their mechanisms. The insight gained here will hopefully lead to future generations of engineered catalysts with continuously improved capabilities.