The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is presented, with an emphasis on application to the coupled cluster family of electronic structure methods. To aid in the derivation of efficient and compact working equations, a new diagrammatic interpretation of the Goldstone diagrams is derived which only requires a small number of the many distinct diagrams and which directly produces equations in a factored form in terms of “spin-summed” tensor elements. This diagrammatic interpretation is applied to coupled cluster methods with quadruple excitations (CCSDTQ), including coupled cluster with a perturbative correction for quadruple excitations (CCSDT(Q)) and to CCSDTQ gradients and properties. The advantages of the non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to efficient implementation are presented and discussed. Additionally, specific optimizations of the implementation for often-overlooked issues such as tensor transposition, disk access, and removal of redundant and/or unnecessary operations are detailed. The resulting algorithm is implemented for the CCSDTQ and CCSDT(Q) methods and compared to existing codes, where a one to two order-of-magnitude improvement in efficiency is observed. The new implementation is also used for calculations on several larger molecular systems to illustrate the scalability of the method. / text

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

Despite the success of modern quantum chemistry in predicting properties of organic molecules, the treatment of inorganic systems, which have many close lying states, remains out of quantitative reach for current methods. To treat non-dynamic correlation, we take advantage of the density matrix renormalization group (DMRG) method that has become very successful in the field of solid state physics. We present a detailed study of the DMRG method, and we pay special attention to the evolution of the understanding behind the mathematical structure of the DMRG wave function. Our primary goal is to develop a density matrix renormalization group self--consistent--field (DMRG-SCF) approach, analogous to the complete active space self--consistent field (CASSCF) method, but dealing with large active spaces that are too demanding for the full configuration interaction (FCI) method. As a first step towards such a DMRG-SCF procedure, we present a spin-adapted DMRG algorithm designed to target spin- and spatial-symmetry states that are hard to obtain while using an unrestricted algorithm. Our next step is a modification of the DMRG algorithm to obtain decreasing energy at every step during the sweep. This monotonically convergent DMRG scheme lets us obtain the two-body density matrix as a by--product of the existing procedure without any additional cost in storage. Additionally, the two-body density matrix produced at convergence using this scheme is free from the N-representability problem that is present when the two--body density matrix is produced with the two-site DMRG scheme without additional storage cost. Finally, taking advantage of the modifications developed herein, we present results obtained from our DMRG-SCF method. Lastly, we discuss possible ways of incorporating dynamical correlation into the DMRG scheme, in order to obtain a modern multireference approach.

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.