Fast photochemical processes are central to a number of problems challenging chemists today. Such problems include atmospheric air pollution driven by solar radiation, development of photocatalysts for clean energy sources and photodynamic therapies for treatment of diseases such as cancer, and light-driven biological phenomena such as vision and vitamin D photosynthesis. Continued improvement of computational methods which can describe and predict such photochemical processes is thus essential. Accordingly, this thesis focuses on two main topics: 1) The development of a spin-symmetry breaking algorithm which for the first time enables homolytic bond cleavage in 'on the fly' density functional non-adiabatic molecular dynamics simulations, and 2) a benchmarking application of the spin-symmetry breaking algorithm to acetaldehyde photochemistry.

Following a brief overview of the challenges inherent within this work, chapter 2 introduces fast photochemical processes and the theoretical foundations of ab inito non-adiabatic molecular dynamics methods. In Chapter 3, a new algorithm for breaking spin-symmetry within linear response time-dependent density functional theory is derived and implemented in the quantum-chemical software suite TURBOMOLE. H2 is used to illustrate the key features of the algorithm, which are: 1) Stability analysis is used to identify critical points on the PES, 2) tight convergence thresholds are used only near triplet instabilities, and 3) adaptive time stepping in the vicinity of triplet instabilities is employed to conserve total energy.

An application of the spin-symmetry breaking algorithm to acetaldehyde photochemistry is then discussed in Chapter 4. Ensembles of approximately 400 trajectories in the ground state and 400 trajectories initialized in the excited state are simulated. Compared to experiment, the spin-symmetry breaking algorithm yields qualitative accuracy for computed branching ratios and total kinetic energy probability distributions. Additionally, two dissociation mechanisms are identified and discussed: The non-transition state theory, ``roaming'', mechanism and new triple-fragmentation mechanisms. Finally, the spin-symmetry breaking algorithm reveals that an improved description of acetaldehyde photodissociation mechanisms may require inclusion of excited state dynamics.

This thesis focuses on the use and development of electronic structure methods in the density functional theory (DFT) framework. The first half is devoted to the implementation of a new integral algorithm and its use in fully non-local density functional approximations. While costly compared to simpler semi-local approximations, non-local functionals of the density are a way to intuitively incorporate physics into a real-space model. Two broad classes of methods are targeted: locally-range separated hybrids and non-local exchange kernels. These methods are tested on a variety of small systems. In both cases, proper scaling to the high- density limit is satisfied which turns out to hamper the approximations’ ability to describe static correlation. This leads us to conclude that proper scaling methods will inherently need static correlation corrections if good performance in thermochemical measures is desired. In the second half, DFT is applied to three drastically different problems which highlights its ability to reasonably predict experimental structural parameters of compounds containing f- and d- block elements while simultaneously describing excited state properties of main group and transition metal compounds. Using time-dependent DFT, UV-vis spectra of lanthanides, transition metals, and the small molecule luciferin were simulated and found to be in good agreement with experiments, providing photophysical insight to the nature of their excited states.

Chapter 2 describes a new recursion scheme that was derived in order to target the evaluation of non-local interaction kernels. The integrals that arise from such kernels are first trans- formed into relative and center of mass coordinates and then rewritten in terms of an integral over the relative coordinate that is parametrically dependent on the center of mass. Using the shared-memory parallel progamming API, OpenMP, a multithreaded semi-analytical al- gorithm is presented where integrals over the relative coordinate are evaluated for blocks of grid points of the numerical integration. The algorithm scales as O(N5), where N is a mea- sure of the system size, but prescreening based on density and integral prefactors are used to reduce the cost. In its present state, the algorithm is still costly and has been limited to only smaller molecules. Benchmark tests show that the recursion scheme can precisely recover the Coulomb interaction and that screening reduces the overall computational cost by 10-15% for small systems. The prescreening which is based on the sparsity of the exchange density matrix, should lead to asymptotic linear scaling with increasing system size; however, this is not realized in practice and is not fully understood at this point. Despite efforts to efficiently parallelize the numerical integration, the total wall time as a function of number of CPUs, does not behave as 1/Ncpu, leading to the conclusion that there is a bottleneck executed on only a single CPU that reduces the efficiency. Testing of the implementation on larger systems is necessary to see if the screening behaves as expected and to further analyze the parallel efficiency.

Chapters 3 and 4 are focused on building non-local models of the density functional exchange- correlation energy using the integral scheme developed in chapter 2. Chapter 3 focuses on locally range-separated hybrids. Here, the exchange interaction is partitioned into long-range and short-range contributions via a range-separation function. We model this function using a density-dependent functional that is evaluted at the center of mass. Our models are made to satisfy exact constraints such as correct scaling in the high-density limit and good description of one-electron and iso-orbital regions. We propose and test a variety of forms that fall into two classes: ones that use long-range exact exchange with short-range approximate exchange and ones that use short-range exact exchange with long-range exchange. Overall, with scaling to the high-density limit being enforced, atomization energies tend to be too low, though self-interaction error is significantly reduced. These proper scaling methods hint at the need to reintroduce the static correlation effects not described by Hartree-Fock to achieve a pragmatic balance. In chapter 4, corrections to the random-phase approximation are explored by way of a short-ranged non-local static exchange kernel. Our first model constructed consisted of a short-ranged Gaussian function. Use of this type of exchange kernel was plagued with instabilities which can be traced to negative values of the Fourier transform of the Hartree-exchange-correlation kernel. A second similar model based on an error function was also constructed and was better behaved. In places where instabilities occured, the first-order RPA-renormalization framework was used and shown to alleviate instabilities in both cases. The fact that a direct modeling of exchange kernels often leads to instabilities indicates that this route to beyond-RPA corrections may be more difficult than once assumed. Additionally, despite the fact that the implementation is purely proof of concept, the high O(N5) cost of computing the non-local integrals is challenging to manage and considerable effort would be required to reduce it.

Chapters 5-7 are based on collaborative work with other research groups at UCI. In chapter 5, a joint computational and experimental study on the photophysical properties of the light-emitting molecule luciferin was undertaken. Using time-dependent DFT, the excited states of a plethora of luciferin analogues were studied in order to find novel, robust light emitting species. While computed oscillator strengths corresponded well with previously known luciferins, the simple picture of non-adiabatic emission from the first singlet excited state was only moderately reliable in predicting the chemiluminescent properties of newly synthesized luciferins. This work implies the need for explicit consideration of environmental effects and the inclusion of other nearby electronic states in order to have a reliably predictive methodology. In chapter 6, a comprehensive study of lanthanides recently discovered to have a new +2 oxidation state was undertaken. Time-dependent DFT was used to simulate the UV-vis spectra of new complexes of Eu, Sm, Tm, Yb, Dy, and Nd which were found to be in good agreement with experiments. Nd and Dy were found to be “crossover” elements in that their electronic ground state could be modulated easily by its ligand environment, in contrast to previous paradigms. In chapter 7, a comparison of complexes of Group V metals (vanadium, niobium, and tantalum) coordinated to redox active ligands is presented. The main challenge in using computational tools to study these complexes lies in the fact that they are coordinated to redox-active ligands which significantly complicate their electronic structure. It was discovered that while Nb and Ta are well described by a closed-shell singlet in their +5 oxidation state, V differs dramatically and has a more stable solution in the +4 oxidation state with open-shell singlet diradical character. This points to subtelties in the electronic structure of transition metals that can be exploited in catalytic applications.

The random-phase approximation (RPA) incorporates many appealing features absent in semilocal density functional theory (DFT) without excessively increasing computational cost. The first half of this thesis addresses the question: Can one achieve a similar balance between accuracy and speed for beyond-RPA corrections? To this end, low-scaling algorithms are developed for the most common perturbative corrections to RPA, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. The implementations are based on the resolution-of-the-identity (RI) approximation, Clenshaw-Curtis numerical frequency quadrature, and optionally, integral prescreening. These implementations afford benchmark calculations on medium- and large-size molecules with size-independent accuracy. The benchmark results show that the AXK method systematically improves RPA and surpasses SOX and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds, confirming conclusions drawn from previous small-molecule calculations.The superior accuracy of AXK compared with SOX and SOSEX suggests that the strong screening of bare SOX in AXK is important. Nevertheless, benchmark calculations on 3d transition metal compounds show that RPA and its perturbative corrections eventually break down for systems with strong static correlation, such as metal dimers. The reliability of RPA methods can be estimated using an effective coupling strength α̅ proposed herein. The second half of the thesis demonstrates the use of electronic structure methods for the identification and characterization of {Sc[N(SiMe₃)₂]₃}⁻, {[(R₂N)₃Sc]₂}[μ-η¹:η¹-N₂]}²⁻, and {Pu[C₅H₃(SiMe₃)₂]₃}⁻: DFT and time-dependent DFT calculations played an important role in characterizing the electron configurations, bonding, and UV-visible spectroscopy of these unconventional rare-earth and actinide compounds. The applicability of RPA and AXK to these compounds is assessed, using the Pu²⁺ complex as an example.

Time-dependent density functional theory (TDDFT) is a powerful and efficient method for calculating excitation energies and properties of electronic excited states. It has found wide applications in various scientific fields due to its accuracy and computational efficiency. However, solving the TDDFT equations involves large eigenvalue and linear problems, which canbe computationally challenging. To address this, matrix-free iterative subspace algorithms have been developed. The first half of the thesis demonstrates the use of density functional theory (DFT) to elucidate the electronic structure of the first synthesis of Neodymium(II) encapsulated in a 2.2.2-cryptand ligand. The comparison between experimental results and the calculated molecular structure, as well as the UV-Vis spectrum obtained through TDDFT, provided strong evidence supporting the discovery of the traditional 4f 4 electron configuration. In the second part of this thesis, I introduce libkrylov, which is a versatile and open-source Krylov subspace library designed for performing large-scale matrix computations on-the-fly. The main goals of libkrylov are to provide a versatile application programming interface (API) design and a modular structure that allows seamless integration with specialized matrix-vector evaluation “engines.” The library is designed to offer pluggable preconditioning, orthonormalization, and tunable convergence control, making it highly flexible and easily adaptable to various computational scenarios and requirements. By providing these features, libkrylov enables users to customize and optimize their calculations, thereby enhancing the efficiency and accuracy of large-scale matrix computations in computational chemistry and other related fields. I extend libkrylov to Hamiltonian structured problems often encountered in TDDFT. The implementation is based on preserving the full SO(1,1) symmetry of the TDDFT response equations, which in the absence of magnetic fields reduces to the use of split-complex numbers. In Krylov subspace methods, this preservation is achieved by utilizing symmetry-adapted basis vectors that maintain the orthonormality condition of the symplectic problem. The calculation of excitation energies for some test molecules show improved convergence over the Olsen algorithm and the TURBOMOLE implementation. The improved convergence highlights the importance of the correct algebraic approach to the problem.

Theoretical calculations of molecular properties can assist experimental design of molecules

with interesting optical, electronic and structural properties which would help accelerate materials

discovery. Density functional theory (DFT) within the Kohn–Sham (KS) framework

has been the most widely used method for molecular properties calculations in the last three

decades because of its advantageous computational cost-to-accuracy ratio. However,

commonly used density functional approximations (DFAs) have been shown to be inadequate

for calculations involving transition metal compounds, metal clusters, conjugated molecules

and for describing noncovalent interactions. Random phase approximation is a post-KS

DFA that is accurate for describing noncovalent interactions without the need for empirical

parameters, does not diverge for small-, or even zero-gap systems and incorporates

Hartree–Fock (HF) exchange. The first part of this thesis aims at answering the question: can a

self-consistent generalized KS scheme be developed for the RPA energy functional which

also gives access to single particle energies within a variational Lagrangian formalism? To

this end, an orbital self-consistent scheme called the generalized KS semicanonical projected

RPA (GKS-spRPA) is developed, implemented and benchmarked for ground state as well

as single particle energies. The ionization energies and band-gaps that are calculated

using the GKS-spRPA suggest that it is better than the commonly used G0W0 method. The

second part of the thesis is concerned with the implementation and testing of static

polarizabilities within the GKS-spRPA method. The GKS-spRPA successfully solves the

overpolarization problem observed with the use of semilocal/hybrid DFAs for calculations

of static polarizabilities of pi-conjugated molecules. Calculations involving metallocenes, metal clusters and

a small molecule testset are used to show that the static polarizability calculated using the GKS-spRPA

method is more accurate than DFAs such as PBE, PBE0, CAM-B3LYP and wave function

based methods such as HF and the second-order Møller–Plesset perturbation theory (MP2).

Thus, this thesis conclusively shows that the GKS-spRPA within a Lagrangian framework,

is a method that provides not only accurate ground state energies but also a wide range of

molecular properties such as geometries, ionization potentials, electron affinities, dipoles and

polarizabilities with a reasonable computational cost of O(N 4 log(N )).

Predicting excited state molecular properties of an ensemble of molecules in silico is a goalfor theoretical and computational chemists. Solving for these properties with exact and analytical physics is out of reach within a reasonable time-frame, hence approximations are taken. This thesis starts from the approximations of Kohn Sham DFT to determine a reference electronic state for a molecular geometry of classical nuclei, then computing excited electronic states and properties such as gradients using response theory in the framework of TDDFT. While there are well established sets of parameters and approximations that have worked well on particular molecular systems, this thesis presents an investigation of parameters relating to the (1) Krylov subspace approximate solve for excitations, (2) Tully Surface Hopping algorithm for non-adiabatic molecular dynamics, and (3) Excitations of Lanthanide(II) complexes where previous, standard approaches are unsatisfactory. The broader impact is a better understanding of these approaches and parameters, with attention drawn to various algorithmic features that should color interpretation of computed properties for most molecular systems.

In pursuit of understanding chemistry, the chemical sense of intermolecular forces (importantto property predictions described above), has been translated into (4) a card game at the undergraduate general chemistry level. A pedagogy study of the card game was carried out, suggesting that it could improve undergraduate understanding of intermolecular forces.

In recent years, collaborative studies that leverage experimental synthesis, spectroscopic characterization, and electronic structure analysis have enabled significant advances in f-element chemistry through the discovery of newly accessible metal oxidation states and novel electronic configurations for lanthanide (Ln) and actinide (An)-containing species. With the purpose of extending the utility of computational approaches to maintain this positive trajectory, the present thesis discusses recent developments and applications of computational chemistry methods, with a focus on density functional theory (DFT), towards the accurate prediction and characterization of new f-element complexes. A DFT methodology based on (meta)-generalized gradient approximation (mGGA) density functionals, triple-ζ quality basis sets for metal atoms, and effective core potentials (ECPs) is shown to provide the electronic structure insights necessary to understand the unexpected stability of fully linear Dy and Tb-based metallocene species, Dy(CpiPr5)2 and Tb(CpiPr5)2. Calculations reveal that such unorthodox molecular geometry, which is rarely observed for lanthanides, is facilitated by a 4fn 5d1 electronic configuration of the metal center, which gives rise to a σ−bonding interaction between the 5d/6s HOMO and cyclopentadienyl ligand system. Further calculations using this DFT methodology predict the existence of stable, linear An-based metallocenes, and the results of this study are used to guide synthetic efforts towards the experimental isolation of U(CpiPr5)2, the first An-based “ferrocene” analog. A similar computational methodology which replaces the ECP with an all-electron approach is applied towards the characterization of Ln-based spin molecular qubits, [Lu(OAr*)3]−, [La(OAr*)3]−, and [Lu(NR2)3]−, revealing the importance of 6s orbital contributions to the spin density to facilitate large Fermi-contact and thus hyperfine interactions. This thesis concludes by describing the prediction of accurate EPR parameters, such as the hyperfine coupling constant, electronic g-tensor, and quadrupole coupling constant in relativistic DFT for the broader study of candidate molecular qubits. An implementation of these quantities is presented within the relativistic exact two-component theory (X2C) method, and benchmark calculations on transition metal and f-element complexes are provided to evaluate choice of the relativistic Hamiltonian, basis set, and density functional approximation (DFA). A recommended set of parameters based on the results of these benchmarks is presented, and subsequently used to calculate the EPR parameters for the previous series of Lu and La molecular qubit systems. These predictions are found to reduce errors by roughly one order of magnitude when compared with the unrefined methodology, and are highly accurate when compared to experimental data - representing an advance for in-silico characterization of EPR spectra. Present challenges and future directions for the development of electronic structure methods for the study of the f-elements are assessed.

This abstract contains verbatim excerpts from Phun, G. S.; Rappoport, D.; Furche, F; Gibson, T. R.; Tretiak, S. Constructing the mechanism of dinoflagellate luciferin bioluminescence using computation J. Phys. Chem. Lett. 14, 6001-6008. ©2023 American Chemical Society, Phun, G. S.; Bhide, R; Ardo, S. Detailed-balance limits for sunlight-to-protonic energy conversion from aqueous photoacids and photobases based on reversible mass-action kinetics Energy Environ. Sci., 2023. ©2023 Royal Society of Chemistry, and Phun, G. S.; Slocumb, H. S.; Nie, S.; Antonio, C.; Fishman, D. A.; Yang, X.; Furche, F.; Dong, V. M. Hydroselenation of Simple Olefins: Elucidating the β-Selenide Radical Effect manuscript in preparation.

Dinoflagellate luciferin bioluminescence is unique since it does not rely on decarboxylation but is poorly understood compared to that of firefly, bacteria, and coelenterata luciferins. Here we computationally investigate possible protonation states, stereoisomers, a chemical mechanism, and the dynamics of the bioluminescence intermediate that is responsible for chemiexcitation. Using semiempirical dynamics, time-dependent density functional theory static calculations, and a correlation diagram, we find that the intermediate’s functional group that is likely responsible for chemiexcitation is a 4-member ring, a dioxetanol, that undergoes [2π + 2π] cycloreversion and the biolumiphore is the cleaved structure. The simulated emission spectra and luciferase-dependent absorbance spectra agree with the experimental data, giving support to our proposed mechanism and biolumiphore. We also compute circular dichroism spectra of the intermediate’s four stereoisomers to guide future experiments in differentiating them. [2π + 2π] cycloreversion and the biolumiphore is the cleaved structure. The simulated emission spectra and luciferase-dependent absorbance spectra agree with the experimental data—giving support to our proposed mechanism and biolumiphore. We also compute circular dichroism spectra of the intermediate’s four stereoisomers to guide future experiments in differentiating them.

Detailed-balance limits to energy conversion efficiency critically inform design rules for photochemical power conversion devices Herein we simulate efficiencies for sunlight-to-protonic power conversion for liquid water, which serves as the protonic semiconductor and is sensitized to visible-light absorption by reversible photoacids or photobases. Our model includes proton-transfer processes based on the Fo ̈rster cycle with rate constants that follow the empirical Brønsted relation, where bimolecular reactions are encounter controlled. Based on physically relevant model parameters, simulations of steady-state concentrations of H+(aq) and OH– (aq) indicate that for defect-free water the maximum possible protonic quasi- chemical potentials result in a photovoltage of ∼ 330 mV and a power conversion efficiency of ∼ 10%. Conditions of maximum power conversion occur when photoacid (photobase) dyes exhibit acidities (basicities) of pKa (pKb) ≥ 14 and pKa∗ (pKb∗) ≤ 0, an outcome that is nearly independent of equilibrium pH. These conditions are optimal because under standard-state conditions they result in rates for protonation of water to form H+(aq) and deprotonation of water to form OH–(aq) that are faster than other proton-transfer processes, due to their isoergic/exoergic nature. Simulations also indicate that longer excited-state lifetimes result in an increase in the range of pK∗ values that lead to significant protonic quasi-chemical potentials. This occurs because longer excited-state lifetimes up to ∼ 1 ms afford more time to perform excited-state proton transfer. Simulation outcomes are affected little by the inclusion of empirical nonzero activation free energies for isoergic/exoergic proton-transfer reactions or rate constants for equilibrium radiative generation and recombination of excitedstate species under thermal detailed balance. Only when local electric fields are assumed present to increase rate constants for proton-transfer reactions do protonic quasi-chemical potentials suffer. Simulations also indicate that the total concentration of photoacid or photobase dyes exhibits two competing effects on protonic quasi-chemical potentials. Decreasing dye concentration results in less sunlight absorption and therefore smaller changes in steady-state concentrations of H+(aq) and OH–(aq), while also increasing the range of pK values that results in significant changes in quasi-chemical potentials. Overall, these results define parameters for effective sunlight-to-protonic power conversion and will help guide researchers in the design and development of photoacid and photobase dyes for light-driven proton pumps.

We report that an aryl diselenide undergoes photoreactivity to promote the hydroselenation of styrenes and simple olefins with high anti-Markovnikov selectivity. Mechanistic studies reveal that a selenide radical adds to the alkene to form a carbon-radical; subsequent hydrogen atom transfer (HAT) generates the linear selenide with high selectivity in preference to the branched isomer. These studies reveal a unique “β-selenide radical effect”, where a selenide β to a carbon radical leads to addition of the Se–H bond with high anti-selectivity.