The effects of different shearing processes and sample sizes on the fluid flow anisotropy and its impact on particle transport process in rough rock fractures are significant factors that need to be considered in the performance and safety assessments of underground nuclear waste repositories. The subjects, however, have not been adequately investigated previously in either laboratory experiments or numerical modeling. This thesis addresses these problems using numerical modeling approaches. The modeling consists of two parts: 1) fluid flow simulations considering more complex but realistic flow boundary conditions during shear processes that cannot be realized readily in laboratory experiments, using digitalized fracture surfaces scanned in the laboratory, so that anisotropic fluid flow induced by shearing with channeling phenomenon can be directly simulated and quantified; 2) particle tracking simulations to demonstrate the impacts of such channeling effects on characteristic properties of particle transport. The numerical method chosen for the simulations is the Finite Element Method (FEM). Scale effects were considered in the simulations by using fracture surface samples of different sizes. The distributions of fracture aperture during shear were obtained by numerically generating relative translational and rotary movements between two digitalized surfaces of a rock fracture replica without considering normal loading. From the evolutions of the aperture distributions during the shearing processes, the evolutions of the transmissivity fields were determined by assuming the validity of the cubic law locally. A geostatistical approach was used to quantify the scale effects of the aperture and transmissivity fields. The fluid flow was simulated using different flow boundary conditions, corresponding to translational and rotary shear processes. Corresponding to translational shear (with a 1 mm shear displacement interval up to a maximum shear displacement of 20 mm), three different flow patterns, i.e., unidirectional (flow parallel with and perpendicular to the shear direction), bi-directional and radial, were taken into account. Corresponding to rotary shear (with a 0.5o shear angle interval up to 90o), only the radial flow pattern was considered. The particle transport was simulated using the Particle Tracking Method, with the particles motion following the fluid velocity fields during shear, as calculated by FEM. For the unidirectional particle transport, the breakthrough curves were analyzed by fitting to an analytical solution of 1-D advection-dispersion equation. The dispersivity, Péclet number and tracer velocity, as well as their evolutions during shear, were determined numerically. The results show that the fracture aperture increases anisotropically during translational shear, with a more pronounced increase in the direction perpendicular to the shear displacement, causing significant fluid flow channelling. A more significant increase of flow rate and decrease in travel time of the particles in the direction perpendicular to the shear direction is predicted. The particle travel time and characteristics are, correspondingly, much different when such effects caused by shear are included. This finding may have an important impact on the interpretation of the results of coupled hydro-mechanical and tracer experiments for measurements of hydraulic properties of rock fractures, because hydraulic properties are usually calculated from flow test results along the shear directions, with the effects of the significant anisotropic flow perpendicular to the shear direction ignored. The results also show that safety assessment of a nuclear repository, without considering the effects of stress/deformation of rocks on fluid flow and transport processes, may have significant risk potential. The results obtained from numerical simulations show that fluid flow through a single rough fracture changes with increasing sample size, indicating that representativehydro-mechanical properties of the fractures in the field can only be accurately determined using samples of representative sizes beyond their stationarity thresholds. / QC 20101207

Switched reluctance machines (SRMs) are well known for their simple and robust structure, facilitating their increasing application in many sectors, for example vacuum cleaners, where domestic machines operate at high-speed, 50,000 RPM being typical. Conventional SRMs (CSRMs) use a decoupled concentrated phase winding so that torque is predominantly only generated due to the self-inductance, which limits utilization of the machine electrical circuits. In this thesis, the toroidal winding SRM (TSRM) is introduced, which operates based on the variation of mutual inductance between different phases. The toroidal winding introduces additional winding space, and the winding is practically easy to implement, both features that lead to a relatively higher copper filling factor. The toroidal winding also benefits the machine thermal performance, as the winding is directly exposed on the machine periphery and thus accessible to cooling. All these make TSRMs interesting and meaningful for further study. Following a comprehensive comparison of CSRM and TSRM characteristics, a general torque equation is presented that is applicable to both CSRM and TSRM. Two 12-switch converters are proposed to drive three-phase TSRMs. Moreover, sinusoidal current excitation with a commercial three-phase half-bridge converter has been suggested as an alternative converter solution for TSRMs. Accordingly, a three-phase six-stator-pole, four-rotor-pole CSRM is designed and optimized with a speed of up to 50,000 rpm in this thesis. A TSRM is resized to achieve the same envelope dimension as a benchmark CSRM. Thus, a comparative study between high-speed CSRM and TSRMs has been carried out. They have both been prototyped and tested. The findings suggest that the TSRM is superior, considering machine mass and wire temperature management. The TSRM has a better torque output at lower speeds because copper losses are dominant. However, the CSRM has more advantages at higher speeds due to lower iron losses and lower DC voltage requirements. / Thesis / Doctor of Philosophy (PhD)

Thesis: M.S., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1980 / Includes bibliographical references. / by Peter Maynard Osterberg. / M.S. / M.S. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science

The data center serves as the hardware foundation for artificial intelligence (AI) and cloud computing, constituting a global market that has surpassed $200 billion and is experiencing rapid growth. It is estimated that data centers contribute to 1.7-2.2% of the world's electricity generation. Conversely, up to 80% of the long-term operational expenditure of data centers is allocated to electricity consumption. Consequently, enhancing the efficiency of electric energy conversion in data centers is not only economically advantageous but also crucial for achieving carbon-neutral objectives. Through collaborative efforts between the industrial and academic sectors, substantial advancements have been achieved in the energy conversion efficiency of data centers. Most converters within the data center power architecture now boast efficiencies exceeding 99%. However, the bottleneck for further improvements in system efficiency lies in the voltage regulator modules (VRMs), which grapple with challenges such as high conversion ratios, elevated output currents, and substantial load transients. These challenges are particularly pronounced for AI processors and graphics processing units (GPUs), given their heightened power demands compared to conventional central processing units (CPUs). To enhance system efficiency, a revolutionary shift in power architecture has been introduced, advocating for the adoption of a 48 V data center power architecture to replace the conventional 12 V architecture. The higher 48 V bus voltage significantly reduces distribution loss on the bus. However, the primary challenge lies in managing high step-down voltage conversion while maintaining high efficiency. Additionally, high-performance microprocessors, including CPUs, GPUs, application-specific integrated circuits (ASICs), and field-programmable gate arrays (FPGAs), require hundreds of amperes of current at low voltage levels (e.g., GPUs need >220 A at <1.85 V, CPUs need >1000 A at <1.0 V). An unavoidable consequence of upscaling processor current and size is the substantial resistive loss in VRMs. This is because such loss scales with the square of the current [I2R], and the power path area (and resistance R) expands with the processor size. The Power Delivery Network (PDN) resistance in the "last inch" of the power delivery path is becoming a limiting factor in processor performance and system efficiency. The key to reducing the I2R loss is minimizing the distance between the VRMs and processors by utilizing ultra-high power density VRMs. Furthermore, the design of Voltage Regulator Modules (VRMs) for high-performance microprocessors encounters additional formidable challenges, especially when dealing with the requirements of contemporary computing architectures. The key hurdles encompass achieving high efficiency, handling low output voltage, accommodating wide voltage ranges, managing elevated output currents, and addressing significant load transients. These challenges prompt both academia and industry to explore novel topologies, innovative magnetic integration methods, and advanced control strategies. The prevailing trend in state-of-the-art 48V solutions centers around the adoption of two-stage configurations, wherein the second stage can leverage conventional 12V solutions. However, this approach imposes limitations on power density and efficiency, given that power traverses two cascaded DC/DC converters. Additionally, the footprint of decoupling capacitors and I2R loss on the intermedia bus between the two stages is emerging as a noteworthy consideration in designs. In response to these challenges, a novel proposition introduces a single-stage 48V coupled-transformer voltage regulator (CTVR) tailored for high-performance microprocessors. This innovative design aims to deliver ultra-high power density and superior efficiency. The converter employs a unique magnetic structure that integrates transformers and coupled inductors from multiple current-doubler rectifiers. Significantly, by utilizing the magnetizing inductors of transformers as output inductors, there is a substantial reduction in the size of magnetic components. Various implementations are explored, each addressing specific design objectives. Initially, a single-stage coupled-transformer voltage regulator (CTVR) with discrete magnetics is presented, offering a 48V solution while maintaining a comparable size and cost to a state-of-the-art 12V multiphase buck regulator. Leveraging the indirect-coupling concept, magnetic components are standardized, enabling scalability and facilitating multiphase operation. A prototype is constructed and tested to validate the CTVR's performance. With a 48V input and 1.8V output, the peak efficiency registers at 92.1%, and the power area density is 0.45 W/mm2. However, voltage ringing is observed in both primary and secondary switches due to a larger leakage inductance and hard-switching operation. Subsequently, a transition to soft-switching operation is implemented to address the voltage ringing issue. The leakage inductance is intentionally designed to supply energy for zero-voltage switching (ZVS) of primary switches, turning the previously perceived drawback into an opportunity for efficiency improvement. As a result, testing demonstrates a peak efficiency increase of more than 1%, reaching 93.6%. Furthermore, efforts are made to enhance small leakage inductance by employing well-interleaved printed circuit board (PCB) windings. Following a series of design optimizations, the prototype achieves a peak efficiency of 93.1% and a remarkable power density of 1037 W/in3, accounting for gate driver loss and size. Despite an increase in cost associated with PCB windings, this proposed solution attains the highest power density and stands as the pioneering 48V single-stage design surpassing 1000 W/in3 power density. When prioritizing efficiency in the design, the quasi-parallel Sigma converter emerges as another optimal choices for a 48V solution. However, the intricate and distinctive quasi-parallel structure of the Sigma converter necessitates a thorough examination of its control mechanism, particularly in light of the rapid load transient response requirements. To address this, an adaptive voltage positioning (AVP) design for the Sigma converter is introduced, employing enhanced V2 control. Guidelines and limitations are provided to stabilize the converter and enhance its overall performance. Ultimately, the AVP function and load transient performance are substantiated through simulation and experimental results. / Doctor of Philosophy / Data center is the hardware foundation of artificial intelligence (AI) and cloud computing. The global data center market has exceeded $200 billion and is fast growing. It is estimated that data center accounts for 1.7~2.2% of the world's electricity generation. On the other hand, up to 80% of the long-term operation expenditure of data centers is electricity. Thus, improving the efficiency of electric energy conversion in data centers is economically beneficial and critical to reaching the carbon neutral goal. The bottleneck for further improvements in system efficiency lies in the voltage regulator modules (VRMs), which grapple with challenges such as high conversion ratios, elevated output currents, and substantial load transients. These challenges are particularly pronounced for AI processors and graphics processing units (GPUs). In response to these challenges, a novel proposition introduces a single-stage 48V coupled-transformer voltage regulator (CTVR) tailored for high-performance microprocessors. This innovative design aims to deliver ultra-high power density and superior efficiency. The converter employs a unique magnetic structure that integrates transformers and coupled inductors from multiple current-doubler rectifiers. Significantly, by utilizing the magnetizing inductors of transformers as output inductors, there is a substantial reduction in the size of magnetic components. Various implementations are explored, each addressing specific design objectives. When prioritizing efficiency in the design, the quasi-parallel Sigma converter emerges as another optimal choices for a 48V solution. However, the intricate and distinctive quasi-parallel structure of the Sigma converter necessitates a thorough examination of its control mechanism, particularly in light of the rapid load transient response requirements. To address this, an adaptive voltage positioning (AVP) design for the Sigma converter is introduced, employing enhanced V2 control. Guidelines and limitations are provided to stabilize the converter and enhance its overall performance. Ultimately, the AVP function and load transient performance are substantiated through simulation and experimental results.

Spatial coordinate measurement systems play an important role in manufacturing and certification processes. There are many types of coordinate measurement systems including electronic theodolite networks, total station systems, video photogrammetry systems, laser tracking systems, laser scanning systems, and coordinate measuring machines. Each of these systems produces coordinate measurements containing some degree of uncertainty. Often, the results from several different types of measurement systems must be combined in order to provide useful measurement results. When these measurements are combined, the resulting coordinate data set contains uncertainties that are a function of the base data sets and complex interactions between the measurement sets. ISO standards, ANSI standards, and others, require that estimates of uncertainty accompany all measurement data. This research presents methods for quantifying the uncertainty fields associated with coupled spatial measurement systems. The significant new developments and refinements presented in this dissertation are summarized as follows: 1) A geometrical representation of coordinate uncertainty fields. 2) An experimental method for characterizing instrument component uncertainty. 3) Coordinate uncertainty field computation for individual measurements systems. 4) Measurement system combination methods based on the relative uncertainty of each measurement's individual components. 5) Combined uncertainty field computation resulting from to the interdependence of the measurements for coupled measurement systems. 6) Uncertainty statements for measurement analyses such as best-fit geometrical shapes and hidden-point measurement. 7) The implementation of these methods into commercial measurement software. 8) Case studies demonstrating the practical applications of this research. The specific focus of this research is portable measurement systems. It is with these systems that uncertainty field combination issues are most prevalent. The results of this research are, however, general and therefore applicable to any instrument capable of measuring spatial coordinates. / Ph. D.

This dissertation presents the derivation, analysis and application issues of advanced topologies with coupled inductors. The proposed innovative solutions can achieve significant performance improvement compared to the state-of-the-art technology. New applications call for high-efficiency high step-up DC-DC converters. The basic topologies suffer from extreme duty ratios and severe rectifier reverse recovery. Utilizing coupled inductor is a simple solution to avoid extreme duty ratios, but the leakage inductance associated with the coupled inductor induces severe voltage stress and loss. An innovative solution is proposed featuring with efficient leakage energy recovery and alleviated rectifier reverse recovery. Impressive efficiency improvement is achieved with a simple topology structure. The coupled inductor switching cell is identified. Topology variations and evaluations are also addressed. The concept that utilizes coupled inductors to alleviate rectifier reverse recovery is then extended, and new topologies suitable for other applications are generated. The proposed concept is demonstrated to solve the severe rectifier reverse recovery that occurs in continuous current mode (CCM) boost converters. Significant profile reduction and power density improvement can be achieved in front-end CCM power factor correction (PFC) boost converters, which are the overwhelmingly choice for use in telecommunications and server applications. This dissertation also proposes topologies to realize the single-stage parallel PFC by utilizing coupled inductors. Compared to the state-of-the-art single-stage PFC converters, the proposed topologies introduce a new power flow pattern that minimizes the bulk-capacitor voltage stress and the switch current stress. / Ph. D.

In the search for molecular species in the interstellar medium and extraterrestrial planetary atmospheres, theoretical methods continue to be an invaluable tool to astronomically minded chemists. Using state-of-the art methods, this doctoral work characterizes the electronically excited states of interstellar radicals, cations, and even rare anions and also predicts the gas phase fundamental vibrational frequencies of the cis and trans-HOCO radicals, as well as the cis-HOCO anion. First, open-shell coupled cluster methods of singles and doubles (CCSD) and singles and doubles with triples-inclusion (CC3) are tested on the C₂H and C₄H radicals. The significant double-excitation character, as well as the quartet multiplicity of some states yields inaccurate excitation energies and large spin contamination with CCSD. CC3 somewhat improves this for select states, but discrepancies between CC and multireference results for certain states exist and likely arise from the lack of spin adaptation in conventional spin-orbital CC. Next, coupled-cluster methods predict the presence of an excited state of the closed-shell allyl cation and its related H₂CCCHCH₂⁺ cousin at 443 nm near an unidentified laboratory peak at 442.9 nm which is also close to one of the largest unattributed interstellar absorption features. Additionally, the dipole moments, electron binding energies, and excited states of neutral radicals and corresponding closed-shell anions of interstellar interest are also computed. These are calibrated against experimental data for CH₂CN⁻ and CH₂CHO⁻. Since coupled cluster theory closely reproduces the known experimental data, dipole-bound excited states for eight previously unknown anions are predicted: CH2SiN⁻ , SiH₂CN⁻, CH₂SiHO⁻, SiN⁻, CCOH⁻, HCCO⁻, SiCCN⁻, and SiNC⁻. In addition, we predict the existence of one rare valence-bound excited state of CH₂SiN⁻ and also SiCCN⁻ as well as even rarer two valence-bound states of CCSiN⁻. Lastly, the reaction of CO + OH and its transient potential intermediate, the HOCO radical, may be responsible for the regeneration of CO₂ in the Martian atmosphere, but past spectroscopic observations have not produced a full gas-phase set of the fundamental vibrational frequencies of the HOCO radical. Using established, highly-accurate quantum chemical coupled cluster tech- niques and quartic force fields, all six fundamental vibrational frequencies for 1 ²A′ cis and trans-HOCO and 1 ¹A′ cis-HOCO⁻ are computed in the gas phase. / Ph. D.

The work in this dissertation presents the first attempt in the literature to propose the concept of "soft switch". The goal of "soft switch" is to develop a standard PWM switch cell with built-in adaptive soft switching capabilities. Just like a regular switch, only one PWM signal is needed to drive the soft switch under soft switching condition. The core technique in soft switch development is a built-in adaptive soft switching circuit with minimized circulation energy. The necessity of minimizing circulation energy is first analyzed. The design and implementation of a universal controller for implementation of variable timing control to minimize circulation energy is presented. The controller has been tested successfully with three different soft switching inverters for electric vehicles application in the Partnership for a New Generation Vehicles (PNGV) project. To simplify the control, several methods to achieve soft switching with fixed timing control are proposed by analyzing a family of zero-voltage switching converters. The driver based soft switch concept was originated from development of a base driver circuit for current driven bipolar junction transistor (BJT). A new insulated-gate-bipolar-transistor (IGBT) and power metal-oxide-semiconductor field-effect-transistor (MOSFET) gated transistor (IMGT) base drive structure was initially proposed for a high power SiC BJT. The proposed base drive method drives SiC BJTs in a way similar to a Darlington transistor. With some modification, a new base driver structure can adaptively achieve zero voltage turn-on for BJT at all load current range with one single gate. The proposed gate driver based soft switching method is verified by experimental test with both Si and SiC BJT. The idea is then broadened for "soft switch" implementation. The whole soft switched BJT (SSBJT) structure behaves like a voltage-driven soft switch. The new structure has potentially inherent soft transition property with reduced stress and switching loss. The basic concept of the current driven soft switch is then extended to a voltage-driven device such as IGBT and MOSFET. The key feature and requirement of the soft switch is outlined. A new coupled inductor based soft switching cell is proposed. The proposed zero-voltage-transition (ZVT) cell serves as a good candidate for the development of soft switch. The "Equivalent Inductor" and state plane based analysis method are used to simply the analysis of coupled inductor based zero-voltage switching scheme. With the proposed analysis method, the operational property of the ZVT cell can be identified without solving complicated differential equations. Detailed analysis and design is proposed for a 3kW boost converter example. With the proposed soft switch design, the boost converter can achieve up to 98.9% efficiency over a wide operation range with a single gate drive. A high power inverter with coupled inductor scheme is also designed with simple control compared to the earlier implementation. A family of soft-switching converters using the proposed "soft switch" cell can be developed by replacing the conventional PWM switch with the proposed soft switch. / Ph. D.

Despite the fact that higher-order tensors (HOTs) plague electronic structure methods and severely limits the modeling of interesting chemistry problems, introduction and application of higher-order tensor (HOT) decompositions, specifically the canonical polyadic (CP) decomposition, is fairly limited. The CP decomposition is an incredibly useful sparse tensor factorization that has the ability to disentangle all correlated modes of a tensor. However the complexities associated with CP decomposition have made its application in electronic structure methods difficult. Some of the major issues related to CP decomposition are a product of the mathematics of computing the decomposition: determining the exact CP rank is a non-polynomially hard problem, finding stationary points for rank-R approximations require non-linear optimization techniques, and inexact CP approximations can introduce a large degree of error into tensor networks. While other issues are a result of the construction of computer architectures. For example, computer processing units (CPUs) are organized in a way to maximize the efficiency of dense linear algebra and, thus, the performance of routine tensor algebra kernels, like the Khatri-Rao product, is limited. In this work, we seek to reduce the complexities associated with the CP decomposition and create a route for others to develop reduced-scaling electronic structure theory methods using the CP decomposition. In Chapter 2, we introduce the robust tensor network approximation. This approximation is a way to, in general, eliminate the leading-order error associated with approximated tensors in a network. We utilize the robust network approximation to significantly increase the accuracy of approximating density fitting (DF) integral tensors using rank-deficient CP decompositions in the particle-particle ladder (PPL) diagram of the coupled cluster method with single and double substitutions (CCSD). We show that one can produce results with negligible error in chemically relevant energy differences using a CP rank roughly the same size as the DF fitting basis; which is a significantly smaller rank requirement than found using either a nonrobust approximation or similar grid initialized CP approximations (the pseudospectral (PS) and tensor hypercontraction (THC) approximations). Introduction of the CP approximation, formally, reduces the complexity of the PPL diagram from 𝓞(N⁶) to 𝓞(N⁵) and, using the robust approximation, we are able to observe a cost reduction in CCSD calculations for systems as small as a single water molecule. In Chapter 3, we further demonstrate the utility of the robust network approximation and, in addition, we construct a scheme to optimize a grid-free CP decomposition of the order-four Coulomb integral tensor in 𝓞(N⁴) time. Using these ideas, we reduce the complexity of ten bottleneck contractions from 𝓞(N⁶) to 𝓞(N⁵) in the Laplace transform (LT) formulation of the perturbative triple, (T), correction to CCSD. We show that introducing CP into the LT (T) method with a CP rank roughly the size of the DF fitting basis reduces the cost of computing medium size molecules by a factor of about 2.5 and introduces negligible error into chemically relevant energy differences. Furthermore, we implement these low-cost algorithms using newly developed, optimized tensor algebra kernels in the massively-parallel, block-sparse TiledArray [Calvin, et. al Chemical Reviews 2021 121 (3), 1203-1231] tensor framework. / Doctor of Philosophy / Electronic structure methods and accurate modeling of quantum chemistry have developed alongside the advancements in computer infrastructures. Increasingly large and efficient computers have allowed researchers to model remarkably large chemical systems. Sadly, for as fast as computer infrastructures grow (Moores law predicts that the number of transistors in a computer will double every 18 months) the cost of electronic structure methods grows more quickly. One of the least expensive electronic structure methods, Hartree Fock (HF), grows quartically with molecular size; this means that doubling the size of a molecule increase the number of computer operations by a factor of 16. However, it is known that when chemical systems become sufficiently large, the amount of physical information added to the system grows linearly with system size.[Goedecker, et. al. Comput. Sci. Eng., 2003, 5, (4), 14-21] Unfortunately, standard implementations of electronic structure methods will never achieve linear scaling; the disparity between actual cost and physical scaling of molecules is a result of storing and manipulating data using dense tensors and is known as the curse of dimensionality.[Bellman, Adaptive Control Processes, 1961, 2045, 276] Electronic structure theorists, in their desire to apply accurate methods to increasingly large systems, have known for some time that the cost of conventional algorithms is unreasonably high. These theorists have found that one can reveal sparsity and develop reduced-complexity algorithms using matrix decomposition techniques. However, higher-order tensors (HOTs), tensors with more than two modes, are routinely necessary in algorithm formulations. Matrix decompositions applied to HOTs are not necessarily straight-forward and can have no effect on the limiting behavior of an algorithm. For example, because of the positive definiteness of the Coulomb integral tensor, it is possible to perform a Cholesky decomposition (CD) to reduce the complexity of tensor from an order-4 tensor to a product of order-3 tensors.[Beebe, et. al. Int. J. Quantum Chem., 1977, 12, 683-705] However, using the CD approximated Coulomb integral tensors it is not possible to reduce the complexity of popular methods such as Hartree-Fock or coupled cluster theory. We believe that the next step to reducing the complexity of electronic structure methods is through the accurate application of HOT decompositions. In this work, we only consider a single HOT decomposition: the canonical polyadic (CP) decomposition which represents a tensor as a polyadic sum of products. The CP decomposition disentangles all modes of a tensor by representing an order-N tensor as N order-2 tensors. In this work, we construct the CP decomposition of tensors using algebraic optimization. Our goal, here, is to tackle one of the biggest issues associated with the CP decomposition: accurately approximating tensors and tensor networks. In Chapter 2, we develop a robust formulation to approximate tensor networks, a formulation which removes the leading-order error associated with tensor approximations in a network.[Pierce, et. al. J. Chem. Theory Comput., 2021 17 (4), 2217- 2230] We apply a robust CP approximation to the coupled cluster method with single and double substitutions (CCSD) to reduce the overall cost of the approach. Using this robust CP approximation we can compute CCSD, on average, 2.5-3 times faster and introduce negligibly small error in chemically relevant energy values. Furthermore in Chapter 3, we again use the robust CP network approximation in conjunction with a novel, low cost approach to compute order-four CP decompositions, to reduce the cost of 10 high cost computations in the the perturbative triple, (T), correction to CCSD. By removing these computations, we are able to reduce the cost of (T) by a factor of about 2.5 while introducing significantly small error.

To follow up on the unexpectedly-good performance of coupled-cluster models with approx- imate inclusion of 3-body clusters [J. Chem. Phys. 151, 064102 (2019)] we performed a more complete assessment of the 3CC method [J. Chem. Phys. 125, 204105 (2006)] for accurate computational thermochemistry in the standard HEAT framework. New spin- integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-zeta basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean errors in { 3CC, CCSDT, and CCSD(T) } electronic (per valence electron) and atomization energies were {23, 69, 125} μEh/e and {0.39, 1.92, 2.57} kJ/mol, respectively. The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry application. / Doctor of Philosophy / Stepping into the information age, the computing power has rapidly grown over the last half century. Solving chemical problems on computers has improved lives by reducing the cost and time of researching critical technologies. Scientific research is evolving and experimental finding are now supported with a computational model. Doing chemistry on computers requires quantum simulations, which is essentially solving the Schr ̈odinger equation on a computer that simulates a wave function for all the electrons in a system. Different models are built based on how these inter electronic interactions are treated. To predict results with accuracy on par with the experimental findings requires using higher-order wave functions methods.These are computationally expensive and often not practical. The lower-order methods that are easy to implement can be found in all quantum chemistry software packages. On the other hand, the higher-order methods are laborious and error prone to implement manually due to the sheer complexity of theory. Debugging such implementations often requires a lot of effort with the uncertainty in returns. To solve this problem, we implemented a second-quantization toolkit (SeQuant version 2.0) that derives many-body methods, specifically the general-order coupled cluster (CC) model. The CC model is systematically improvable and accurate. One such CC model, the CCSD(T), has been called the gold standard in quantum chemistry. For compactness, these equations are usually derived in their spin-orbital form. The evaluation and storage cost of these methods is reduced up to four-fold by transforming the spin-orbital expressions to a spin-traced form. In this work, the spin-tracing algorithms are described in detail. The general-order coupled cluster approach is used to derive the internally corrected approximate coupled cluster methods. These methods improve the accuracy of a model at a reduced cost. For small molecules, it was observed that the spin-traced evaluation was over three times faster than spin-orbital coupled cluster. To further reduce the cost of calculations, we added explicit correlation to our CC models. These methods improved the quality of our results with a modest increase in the computational cost.