Quantum chemical methods to predict experimental chiroptical properties by solving the time-dependent Schrödinger equation are useful in the assignment of absolute configurations. Chiroptical properties, being very sensitive to the electronic structure of the system, require highly-accurate methods on the one hand and on the other, need to be able to be computed with limited computational resources. The calculation of the optical rotation in the solution phase is complicated by solvent effects. In order to capture those solvent effects, we present a study that uses conformational averaging and time-dependent density functional theory calculations that incorporate solvent molecules explicitly in the quantum mechanical region. While considering several controllable parameters along which the system's optical rotation varies, we find that the sampling of the dynamical trajectory and the density functional chosen have the largest impact on the value of the rotation. In order to eliminate the arbitrariness of the choice of density functional, we would prefer to use coupled cluster theory, a robust and systematically improvable method. However, the high-order polynomial scaling of coupled cluster theory makes it intractable for numerous large calculations, including the conformational averaging required for optical rotation calculations in solution. We therefore attempt to reduce the scaling of a linear response coupled cluster singles and doubles (LR-CCSD) calculation via a perturbed pair natural orbital (PNO++) local correlation approach which uses an orbital space created using a perturbed density matrix. We find that by creating a "combined PNO++" space, incorporating a set of orbitals from the unperturbed pair natural orbital (PNO) space into the PNO++ space, we can obtain well-behaved convergence behavior for both CCSD correlation energies and linear response properties, including dynamic polarizabilities and optical rotations, for the small systems considered. The PNO++ and combined PNO++ methods require aggressive truncation to keep the computational cost low, due to an expensive two-electron integral transformation at the beginning of the calculation. We apply the methods to larger systems than previously studied and refine them for more aggressive truncation by exploring an alternative form of the perturbed density and a perturbation-including weak pair approximation. / Doctor of Philosophy / Theoretical chemistry attempts to provide connections between the structure of molecules and their observable properties. One such family of observables are chiroptical properties, or the effect of the medium on the light which passes through it. These properties include the scattering, absorption and change in polarization of light. Light being classically an electromagnetic field, chiroptical properties can be derived by treating molecules quantum mechanically and the light classically. The prediction of chiroptical properties on computers using the principles of quantum mechanics is still a growing field, being very sensitive to the method used, and requiring considerations of factors such as conformations and anharmonic corrections. Matching experimental properties is an important step in the creation of a reliable method of predicting properties of systems in order to provide more information than can be obtained through experimental observation. This work begins by addressing the problem of matching experimentally obtained quantities. Our results show that current time-intensive methods still fall short in the matching of experimental data. Thus, we then move on to approximating a more robust but computationally expensive method in order to be able to use a more accurate method on a larger scale than is currently possible. On obtaining positive results for small test systems, we test the new method on larger systems, and explore possible improvements to its accuracy and efficiency.

We give an overview of quantum chemical methods with a particular emphasis on the development of high-accuracy quantum chemical models. The reliability of these methods often hinges on whether enough electron correlation is included in the truncated wave function. As an example, we investigate the structures of m-benzyne and its fluorinated derivative, tetrafluoro-m-benzyne where the inclusion of triple excitations is paramount to correctly describe through-bond delocalization of the monocyclic form. At the CCSDT/6-31G** level of theory, the C1–C3 distance of the minimum energy form of m-benzyne is 2.0°A and the profile of the PES along the C1–C3 distance is that of an asymmetric, single-well, in agreement with previous density-functional theory and coupled cluster studies. In addition, the calculated CCSD(T) fundamental frequencies are in excellent agreement with the measured infrared frequencies, thus confirming the monocyclic form of m-benzyne. For tetrafluoro-m-benzyne, however, the increased eclipsing strain between the ring-external Câ X bonds stabilizes the bicyclo[3.1.0]hexatriene form: the C1–C3 distance is calculated at the CCSD(T)/cc-pVTZ level to be approximately 1.75 °A, which is in the range of elongated CC bonds. Computed harmonic vibrational frequencies compare reasonably well with the experimental neon-matrix difference spectrum and provide further evidence for the existence of a bicyclic form. We also report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N7) computational steps and avoids storage of the triple-excitation amplitudes for both the ground-and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence 2B1 state of the allyl radical, low-lying states of the CH and CO+ diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the 2§+ state of CH, significant errors of more than 0.4 eV remain. Finally, ground- and excited-state dipole moments are derived diagramatically and were recently developed within the PSI3 quantum chemistry package. However, convergence problems with computing the left-hand excited-state has prevented us from reporting any meaningful results. Thus, future work includes solving this convergence problem before the effects of triple excitations on one-electron properties can be reported with certainty. / Ph. D.

Coupled cluster (CC) and density functional theory (DFT) are highly regarded as robust quantum chemical methods for accurately predicting a wide variety of properties, such as molecular structures, thermochemical data, vibrational spectra, etc., but there has been little focus on the theoretical prediction of optical rotation. This property, also referred to as circular birefringence, is inherent to all chiral molecules and occurs because such samples exhibit different refractive indices for left- and right- circularly polarized light. This thesis focuses on the theoretical prediction of this chiroptic property using CC and DFT quantum chemical models. Several small chiral systems have been studied, including (S)-methyloxirane, (R)-epichlorohydrin, (R)-methylthiirane, and the conformationally flexible molecules, (R)-3-chloro-1-butene and (R)-2-chlorobutane. All predicted results have been compared to recently published gas-phase cavity ringdown polarimetry data. When applicable, well-converged Gibbs free energy differences among confomers were determined using complete-basis-set extrapolations of CC energies in order to obtain Boltzmann-averaged specific rotations. The overall results indicate that the theoretical rotation is highly dependent on the choice of optimized geometry and basis set (diffuse functions are shown to be extremely important), and that there is a large difference between the CC and DFT predicted values, with DFT usually predicting magnitudes that are larger than those of coupled cluster theory. / 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.

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.

Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.

The work presented in this thesis is dedicated to developing inexpensive quantum-chemical models that are able to produce smooth and physically correct potential energy curves for the dissociation of single covalent bonds. It is well known that the energies produced by many ab initio theories scaling as the fifth order with the system size (for instance, second-order Moller-Plesset (MP2) and Epstein-Nesbet perturbation theories) diverge at large interatomic separations. We show that the divergent behavior of such perturbation schemes is due to a small number of terms in the energy expressions. Then, we demonstrate that the self-consistent replacement of these terms by their analogs from the coupled cluster theory (such as CCSD) allows one to redress the erroneous behavior of the perturbation theories without the damage to the overall scaling. We also investigate the accuracy of these hybrid perturbation theory-coupled cluster theories near equilibrium geometry. Judging from the computed spectroscopic constants and shapes of the potential energy curves, one such model, denoted MP2-CCSD(II) in this work, performs consistently better than the MP2 theory at essentially the same computational cost.

Accurate energetic modeling of large molecular systems is always desired by chemists. For example, ligand-protein binding simulations and enzymatic catalysis studies all involve with a small energy difference. The energetic accuracy depends largely on a proper handling of electronic correlations. Molecular mechanics (MM) methods deliver a parameterized Newtonian treatment to these problems. They show great capability in handling large calculations but give only qualitatively good results. Quantum mechanics (QM) methods solve Schrödinger equations and exhibit much better energy accuracy, though the computational cost can be prohibitive if directly applied to very large systems. Fragment-based methods have been developed to decompose large QM calculations into fragment calculations. However, most current schemes use a self- consistent field (SCF) method on fragments, in which no electronic correlation is accounted for. The super-system energy is computed as a sum of fragment energies plus two-body corrections and, possibly, three-body corrections (a "body" is a fragment). Higher order corrections can be added. Nevertheless, many problems require the treatment of high order electronic correlations. The coupled-cluster (CC) theory is the state-of-the-art QM method for handling electronic correlations. The CC wavefunction contains correlated excitations up to a given truncated level and coincidental excitations for all possible electronic excitations. It is a brilliant way of including more electronic correlations while maintaining a low-order scaling. In the proposed excitonic coupled-cluster (X-CC) theory, substantial modifications have been made to allow CC algorithms to act on the collective coordinates of fragment fluctuations to obtain super-system energy. The X-CC theory is designed to achieve accurate energetic modeling results for large chemical systems with much improved affordability and systematic improvability. The test system used in this work is a chain of beryllium atoms. A 30-fragment X-CCSD(2) calculation delivered matching accuracy with traditional CCSD method. An X-CCSD(2) calculation on a chain of 100 bonded fragments finished in 7 hours on a single 2.2 GHz CPU core. The X-CC scheme also demonstrates the ability in handling charge transfer problems. Due to the use of fluctuation basis in the test cases, the excitonic algorithms can be easily generalized to inhomogeneous systems. This will be investigated in future work.

L'importance des effets relativistes dans la chimie a été reconnu depuis les années 1980. Par exemple, sans la relativité (a) l'or aurait la même couleur que l'argent (b) le mercure ne serait pas liquide à la température ambiante et (c) nos voitures ne démarrent pas avec une batterie de plomb. Pour une description théorique de la structure et la réactivité des éléments lourds, la relativité est un ingrédient essentiel. Le hamiltonien pour les calculs moléculaires relativistes à 4 composantes est construit en remplaçant la partie mono-électronique de l'hamiltonien électronique non-relativiste par le hamiltonien de Dirac. La partie bi-électronique est approchée par le terme de r Coulomb comme dans le cas non relativiste, ce qui donnel'hamiltonien de Dirac-Coulomb (DC). Pour réduire le coût de calcul, on peut utiliser des hamiltoniens relativistes à 2 composantes. Parmi eux, l'hamiltonien exact à 2 composantes (X2C) est le plus précise. La corrélation électronique est, cependant, une contribution très importante pour obtenir une description théorique à la fois qualitative et quantitative des spectroscopies moléculaires, réactions, etc. Dans cette thèse, nous avons étudié l'interaction entre la relativité et de la corrélation. à la fois par des développements méthodologiques et par des applications moléculaires. Dans la première partie de la thèse, nous avons calculé les constantes spectroscopiques dimères des gaz rares lourds. La liaison faible de ces dimères ne peut être décrit que par l'inclusion de la corrélation électronique. Les dimères des gaz rares les plus lourds, le radon et l'eka-radon, nécessite de plus un traitement adéquat de la relativité. Nos calculs sont basés sur l'hamiltonien X2Cmmf, à la fois avec des méthodes de corrélation basés sur une fonction d'onde et séparation de porte (srDFT). La deuxième partie de cette thèse concerne la simulation de la spectroscopie des rayons X, où l'on sonde la région du cœur d'une molécule, ou la relativité joue un rôle très important. Nous avons étudié la spectroscopie L-edge de la série isoélectronique: UO22 +, UNO+, et UN2, où le couplage spin-orbite joue un rôle majeur. Au niveau des méthodes, nous avons considéré MP2 à couches ouvertes et la théorie de la fonctionnelle de la densité dépendante de temps (TDDFT). Dans un autre étude, nous avons simulé la spectroscopie K-edge de la série H2X (X = O, S, Se, Te) et XH3 (X = N, P, As) ainsi que les molécules N2 et N2O2. Pour ces systèmes, l'interaction spin-orbite est moins important. Par conséquent, nous avons utilisé un hamiltonien DC sans spin (SF). Certains des systèmes pris en compte dans ce travail sont de caractère multi-référentielles ; nous avons utilisé la methode Coupled Cluster Multi-référentielle de type State Universal et adapté au groupe unitaire (UGA-SUMRCC) comme une méthode de corrélation. Dans la troisième et partie principale de la thèse, l'attention est de nouveau sur la relativité et de la corrélation, mais pour le calcul des propriétés électriques et magnétiques moléculaires. Nous avons développé et mis en œuvre un module pour le calcul des valeurs moyennes au niveau relativiste à 4-composantes coupled cluster monoréferentiel. Les propriétés qui sondent la densité électronique près de noyaux (lourds), telles que la résonance paramagnétique électronique (RPE), les paramètres des gradients de champ électrique et la non-conservation de la parité (NCP) des molécules chirales ,sont parfaitement adaptés pour l'application de cette méthode. Pour l'instant, nous avons étudié que la NCP. Ce module dans le logiciel DIRAC pour les calculs moléculaires relativistes fournit un cadre propice pour la mise en œuvre de méthodes de CC relativistes employant la symétrie de groupes doubles et de permutation de manière très efficace. En perspective, nous ciblons la mise en œuvre de la réponse linéaire CC pour le calcul des énergies d'excitation et propriétés moléculaires de second ordre tels que les paramètres de RMN. / The importance of relativistic effects in chemistry has been recognized since the 1980s. Without relativity (a) gold would have the same colour as silver (b) mercury would not be liquid at room temperature (c) our cars would not start (lead-battery). For a theoretical description of the structure and reactivity of heavy-elements, relativity is considered as an essential ingredient. The Hamiltonian for the 4-component relativistic molecular calculations is constructed by replacing the one-electronic part of the non-relativistic molecular Hamiltonian by the Dirac Hamiltonian. The two-electronic part of the Hamiltonian is approximated by the Coulombic repulsion term as in the non-relativistic case. The resulting Hamiltonian is called the Dirac-Coulomb (DC) Hamiltonian. For chemical applications there exist a class of relativistic Hamiltonians, where one-electronic part of the DC Hamiltonian is transformed to a 2-component one. Among them the eXcact 2-component (X2C) Hamiltonian is the most accurate one. Electron correlation, however, is a very important contribution to achieve a both qualitative and quantitative correct description of molecular spectroscopies, reactions etc. It is, therefore, essential to study the interplay between relativity and correlation. In this thesis, we have studied this interplay both in terms methodological developments and molecular applications. In the first part of the thesis we have studied the spectroscopic constants of the heavy rare gas dimers. The weak bonding of those dimers can only be described by the inclusion of electron correlation. The heavier analogues in the rare gas series i.e, Radon and eka-Radon, in addition require adequate treatment of relativity. Our calculations are based on the eXact 2-Component molecular-mean field (X2Cmmf) Hamiltonian both with wave function methods and range-separated DFT methods. The second part of this thesis simulates X-ray spectroscopy, where one probes the core region of a molecule. In the core region relativity plays a very significant role. Removal and excitation of electrons from that region involve various processes, which are beyond a mean-field description. We have studied L-edge spectroscopy of the isoelectronic series: UO22+, UNO+, and UN2, where spin-orbit coupling plays a major role. For the theory we have considered single reference open-shell MP2 and Time Dependent Density functional Theory (TDDFT). In another work, we have studied K-edge spectroscopy of the H2X (X= O, S, Se, Te) and XH3 (X= N, P, As) series as well as N2, N2O2 molecules. For this study spin-orbit coupling is less important, therefore, we have treated them with the Spin-Free (SF) DC Hamiltonian. Some of the systems considered in this work are Multi-Reference in nature; we have used Unitary Group Adapted (UGA) State Universal Multi-reference Coupled Cluster (UGA-SUMRCC) theory as a correlation method. In the third and major part of the thesis, the thrust is again on relativity and correlation, but for the calculation of molecular electric and magnetic properties. We have developed and implemented a module for the calculation of expectation values at the 4-component Relativistic Single Reference Coupled Cluster level. Properties that probe the electron density near (heavy) nuclei, such as Electron Paramagnetic Resonance (EPR) parameters, electric field gradients and parity non-conservation (PNC) in chiral molecules are ideally suited for the application of this method. However, we have only studied PNC so far. This module in the DIRAC software for relativstic molecular calculations provides a convenient framework for the implementation of relativistic CC methods employing double group and permutation symmetry very efficiently. In the near future we therefore target the implementation of Linear Response CC for the calculation of excitation energies and second-order molecular properties such as NMR parameters.

This dissertation describes the implementation of the molecular electronic structure calculations with an implicit solvent model using coupled-cluster theory. The theory for and the implementation of the solvent reaction field method (SCRF) and the reference interaction site model (RISM) at the coupled-cluster singles and doubles (CCSD) are presented. In the SCRF model a solute molecule is placed in a spherical cavity, and the outer solvent is represented by a dielectric continuum, which is characterized by the dielectric constant of the solvent. The reaction field is introduced to the system by using the multipole moment expansion of the electronic structure of the solute molecule and the dielectric constant. The SCRF method has been used to calculate the conformational equilibrium and the rotational barriers of 1,2-dichloroethane in vacuum and in different solvents. The calculated results are compared with experimental values. In addition, the solvent effects on the energetics of the mechanism of nitration of benzene are reported using the implemented CCSD-SCRF model. The idea of RISM is to replace the reaction field in continuum models by a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM integral equations. The statistical solvent distribution around the solute is determined based on the electronic structure of the solute, while the electronic structure of solute is influenced by the surrounding solvent distribution. Therefore, the wave function and the RISM equations are solved self-consistently with CCSD. Pair correlation functions, partial atomic charges, and solvation free energies of water and N-methylacetamide are calculated in liquid water using proposed theory. Both the CC-SCRF and CC-RISM methods have been implemented in a developmental version of the Q-Chem 3.2 quantum chemistry package.