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School of Chemistry and Biochemistry
School of Chemistry and Biochemistry
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ItemAffordable Quantum Chemistry via Data-Driven and Local Approximations to Non-Covalent Interactions(Georgia Institute of Technology, 2022-12-14) Glick, Zachary LeeQuantum chemistry (QC) calculations can provide physically-rooted insight into intermolecular interactions. A quantitative understanding of these interactions, in turn, is of crucial importance for chemical problems like the modeling of protein-ligand interactions or molecular crystals and clusters. Unfortunately, the expensive computational cost of QC calculations prohibits their routine use in high-throughput computational workflows. The field of machine learning (ML) offers a potential workaround to this problem. Large amounts of quantum chemistry data can be generated upfront and used to parameterize models such as neural networks (NNs). The ML models can then be used to predict QC properties of new chemical systems, usually with a many order-of-magnitude reduction in computational cost. The development of such models is a rapidly evolving field, and numerous open questions exist about functional forms, dataset generation, accuracy, and generalizability. In this thesis, the development of NNs specific to the prediction of long-range, non-local intermolecular interactions--which existing models are not equipped to capture--is explored. Throughout the course of the chapters two through four, an equivariant atomic-pairwise neural network with a hybrid force field functional form referred to as AP-Net is developed. In the interest of the efficient generation of QC datasets, chapter 5 is concerned with the development and implementation of reduced-scaling dispersion algorithm. This algorithm allows for reference interactions energies to be generated at a reduced computational cost.
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ItemBuilding Blocks of Neural Network Intermolecular Interaction Potentials(Georgia Institute of Technology, 2022-10-17) Metcalf, DerekThe essence of the computational sciences is to find compressed, silicon-ready rulesets of the natural world and use them to predict all of the complexities of reality without actually observing it. Practically, no lossless variant of such a compression is compatible with the computers of today, and we instead focus on choosing a set of approximations that induce nicely-cancelling errors. One popular way of concocting approximations is to use well-established physical principles (such as the Schrödinger equation for computing properties of atomistic systems) and progressively remove complexity without introducing dependence on real-world observations. These "first principles" approaches contrast with empirical methods that often use parameters to encourage their simpler models to match experimental data at a reduced computational expense. Although less conceptually pleasant, some empiricism is a mainstay in computational chemistry as a result of the success and usefulness of molecular mechanics (MM), density functional theory (DFT), and recently, machine learning (ML). This thesis introduces developments in machine learning models, specifically neural networks, that seek to predict the strength of interactions between molecules. We further discuss neural networks imbued with physics, application domains within pharmaceutical discovery, and the all-important data upon which our models are parameterized.
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ItemImplementation and Application of Density Functional Theory based Symmetry-Adapted Perturbation Theory for Dimers, Trimers and Molecular Crystals(Georgia Institute of Technology, 2022-07-30) Xie, YiThis thesis presents an implementation of the density functional theory based symmetry-adapted perturbation theory [SAPT(DFT)], and its application to interacting systems including dimers, trimers, and molecular crystals. SAPT(DFT) is a computational method for computing interaction energy of noncovalent interactions, which are central to many chemical and biochemical phenomena, such as phase transition, protein-ligand binding and formation of the structure of biomacromolecules. In order to study noncovalent interaction in complex systems, one can use the many-body expansion (MBE) approach to decompose the interaction energy of the complex system into interaction energies of dimers, trimers, tetramers, etc. This makes studying the interaction energies for dimers and trimers meaningful. One of the most important feature of SAPT methods is that their results have very clear physical interpretations; each SAPT term can be assigned to interaction of different physical nature, including electrostatics, exchange-repulsion, induction and dispersion. This allows the physical nature of the interaction of interest to be reflected in addition to the ``plain'' interaction energy, allowing better understanding of noncovalent interactions. In Chapter 2, we implemented a variant of SAPT, SAPT(DFT), as a part of the {\sc Psi4} quantum chemistry program package, and assessed its performance in accuracy and efficiency. SAPT(DFT) has an advantage of being able to capture the intramonomer electron correlation effects with a relatively low computational cost. This feature makes SAPT(DFT) desirable when one is interested in computing the electrostatics, exchange, induction and dispersion contributions to the interaction energy of an interacting system, many of which requires the intramonomer electron correlation effects to be considered to obtain accurate results. This chapter focused on the treatment of hybrid DFT functionals in SAPT(DFT), in particular the computation of the dispersion energy where a hybrid exchange-correlation kernel is required. We have developed an algorithm that efficiently solves the coupled Kohn-Sham equation with hybrid exchange-correlation kernel, which allows the application of SAPT(DFT) with hybrid functionals to dimer systems with sizes comparable to the C$_{60}$--buckycatcher complex. We have also compared the results of SAPT(DFT) and other SAPT methods to a few benchmark results, and concluded that the accuracy of SAPT(DFT), with a scaling of $O(N^5)$, is comparable to the many-body perturbation theory based SAPT2+ approach, which scales as $O(N^7)$. In Chapter 3, we attemped to generalize the algorithm developed for the dispersion energy in SAPT(DFT) to the three-body case, and use the many-body expansion approach to study its contribution to the lattice energies of molecular crystals. Unfortunately, our research shows that the SAPT(DFT) dispersion term does not seem to fully capture the three-body dispersion effects in molecular crystals, agreeing the conclusions in previous studies for isolated trimers and liquids, and we attributed this unsatisfactory performance to lack of higher-order exchange-dispersion terms. Nevertheless, we have shown that the Axilrod--Teller--Muto dispersion correction with empirical damping provides a relatively accurate description to the three-body dispersion energy due to fortuitous but consistent error cancellation. We have also analyzed the growth of three-body contribution to crystal lattice energy with respect to the intermonomer distance cutoff of trimers, and it appears that for the molecular crystals where dispersion dominates the three-body contribution to the lattice energy, the error of the computational methods studied in this chapter is mainly contributed by trimers with $R_\textrm{min} < 4\;\textrm{\AA}$, where $R_\textrm{min}$ is the smallest value among the three pairwise intermonomer closest-contact distances, suggesting the possibility of a drastic reduce in required computational resource for computing the crystal lattice energies by using approximate methods for trimers with $R_\textrm{min} > 4\;\textrm{\AA}$. In addition to the advances made in these chapters, this thesis also suggests a few possible future research topics, based on questions arising from the research work related to the thesis. These include implementation of the exchange-dispersion term in SAPT(DFT), which is currently computed by an approximate scaling method in {\sc Psi4}; implementation of the higher-order exchange-dispersion term for three-body SAPT(DFT) to compensate the error of three-body SAPT(DFT) dispersion term; and an investigation of the behavior of three-body contribution to the crystal lattice energies for crystals that are not studied in Chapter 3 of this thesis, mainly those consisting polar molecules with stronger dipole-dipole interactions. While we have not explored on these questions here, we hope that further studies on these questions can provide a better insight of understanding noncovalent interactions, as well as allowing development of computational methods in studying these interactions.
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ItemComputational Analysis of the Structure and Noncovalent Interactions of Nucleic Acids and their Analogs(Georgia Institute of Technology, 2021-04-30) Alenaizan, AsimIn recent years, no event has been more consequential than the emergence of the Covid-19 pandemic. Covid-19 has disrupted the globe at an unprecedented scale and has caused profound changes to our daily lives. Our inability to control the pandemic for a year and a half, and counting, has forced a critical reexamination of all aspects of our social system. Other factors aside, one would conclude that our knowledge of viruses is rudimentary and our understanding of their chemistry is narrow. Yet, Covid-19 is essentially just a single-stranded RNA. RNA and its more famous cousin DNA have been known for a very long time. The DNA duplex structure, which is ingrained in the popular knowledge of chemistry and biology, was discovered in the 1950s, and DNA was first identified in the late 1860s. This history notwithstanding, the Covid-19 pandemic does indeed prove that our knowledge of DNA and RNA, their chemistry and their biology, is limited. It is a fascinating feature of science that the familiar and the mysterious are intertwined. Some under-explored facets of DNA and RNA, though none are of immediate relevance to Covid-19, are the topic of this thesis. The first question that the thesis asks is how the chemical structure of nucleic acids dictates their three-dimensional geometry. A survey of the class of nucleic acid polymers, of which DNA and RNA are just two manifestations, reveals a remarkable diversity in their structural organizations. In fact, DNA itself can adopt varying geometries, from the familiar B-form helix to the less common, RNA-like A-form conformation. To answer this question, Chapter 2 develops a general framework and a software program, the proto-Nucleic Acid Builder, for the prediction of the three-dimensional structure of nucleic acid polymers. The program models the structure of DNA and RNA and their analogs (XNAs) as being dependent on the helical organization of the nucleobases and the specific arrangement of the backbone atoms analyzed in terms of the backbone torsional angles. The three-dimensional structures where the nucleobase orientation and the backbone torsional angles are compatible and where the atoms have favorable noncovalent interactions are the physically possible structures for nucleic acid polymers. Chapter 2 develops a methodology for predicting the structure of DNA, RNA, and their analogs in isolation. However, interactions between nucleic acids and their surrounding can significantly impact their structure and function. Chapter 3 explores this area by modeling the interaction between DNA/RNA and a small organic molecule, cyanuric acid, in solution. Molecular dynamics simulations reveal a novel noncovalent helicene structure where three poly(adenosine) oligomers and cyanuric acid molecules form a continuous helical hydrogen-bond network. The balance between stacking interactions, hydrogen bonding interactions, and backbone preorganization determines the structure of these remarkable supramolecular assemblies. Stacking and hydrogen-bonding interactions between nucleobases are largely responsible for the stability of DNA and RNA in solution. Nevertheless, when those nucleobases are mixed in the absence of a backbone, they fail to self-assemble in solution, raising the question of how these nucleobases were originally selected for information transfer. One proposed solution is that alternative nucleobases capable of self-assembly, such as cyanuric acid and triaminopyrimidine, were the original information carriers. In Chapter 4, we explore the structure and noncovalent interactions of one such supramolecular polymer using experimental and computational tools. We confirm the ability of these bases to form extended hexameric rosette structures. Then, we analyze the properties of these assemblies, including their highly sensitive helical structure and unusual stiffness, and compare them to the properties of DNA and RNA. We show that the properties of these supramolecular assemblies stem from the underlying noncovalent interactions between the bases. In Chapter 5, we explore how we can model noncovalent interactions both accurately and realistically for macromolecules, such as proteins and DNA, an essential question if we want practically meaningful theoretical models. Accurate quantum mechanical methods are computationally intensive and therefore are typically limited to a few hundred atoms. By contrast, classical methods are applicable to large systems, albeit with a reduced accuracy. We show that these two approaches can be combined for accurate and affordable modeling of noncovalent interactions. Specifically, we couple symmetry adapted perturbation theory, a quantum mechanical method, with an external classical potential represented by point charges, and we show that interaction energies and their decomposition to electrostatics, exchange-repulsion, induction/polarization, and London dispersion components can be accurately computed.
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ItemPARSIMONIOUS ALGORITHMS AND IMPLEMENTATION IN QUANTUM CHEMISTRY(Georgia Institute of Technology, 2020-12-07) O'Brien, Joseph SenanThe fundamental crux affecting the performance of quantum chemistry calculations is the need to cover a large number of terms in a way that may entail managing a large amount of data. The costs in time and storage associated with these methods can be mitigated in numerous ways: judiciously exclude insignificant terms, reformulate terms in ways that avoid computing some intermediates, and avoid full formulation of intermediaries. This thesis explores such efforts by examining a direct Density Fitted Coulomb and Exchange (JK) formation algorithm, application of numerous advances in JK construction to Hybrid DFT calculations, reformulation of Coulomb terms to avoid ERI calculations, and parsimonious formation of Coulomb and exchange matrices with different row and column bases under the density fitting approximation.
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ItemElectronic structure methods for studying non-covalent interactions in complex chemical environments(Georgia Institute of Technology, 2020-04-28) Sirianni, Dominic A.Non-covalent interactions (NCI) encompass the quantum mechanical forces felt between atoms and molecules which are not directly bonded to one another. Responsible for governing diverse chemical and physical phenomena, NCI are of fundamental interest in fields including materials design and drug discovery, among others. In order to study NCI accurately, quantum chemical methods must be employed whose computational expense often limits the systems which can be studied to at most 100 atoms. Often, this is challenge is addressed by examining NCI in small, representative subsystems, however this approach neglects the influence of chemical environment on these interactions. Furthermore, the best manner in which to study such environmental effects is still an open question in the field. Meeting these challenges will be the focus of this dissertation: through the development of novel quantum chemical methods, as well as the extension of existing methods, this work will seek to describe the effect of diverse chemical environments on non-covalent interactions. In this way, a more complete understanding of these phenomena will be provided, which can then be exploited to advance various chemical applications.