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Universiẗat, Diss., 2006--Karlsruhe.

Zugl.: Karlsruhe, Univ., Diss., 2009 / Hergestellt on demand. - Zusätzliches Online-Angebot unter http://uvka.ubka.uni-karlsruhe.de/shop/isbn/978-3-86644-392-1

This work focuses on an examination of the high-accuracy extrapoloated ab initio thermochemistry (HEAT) protocol of determining molecular atomization energies. The HEAT protocol does not utilize experimental data or empirical scaling effects. The accuracy of the approach is tested via comparison to ATcT data, and all molecules fall within 1 kcal/mol of accepted values. There are several important points to note about this treatment: namely, that we have used atomic natural orbital (ANO) basis sets for the calculation of the zero point energy and that we have made determinations for larger molecules than previously done with HEAT. The molecules in this paper were chosen to provide benchmark numbers for the homodesmotic reaction heirarchy as described by Wheeler et al.[3] The relative accuracy of the approach is considered, as well as a discussion of possible remaining sources of error. / text

Stuttgart, Univ., Diss., 2007.

University, Diss., 2006--Würzburg.

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.

One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as 𝑂(N⁷) in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as R⁻⁶ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems. / Ph. D. / Since its inception, quantum mechanics has been widely used by theoretical chemists to study, model and predict a variety of molecular properties and reactions accurately and reliably. Central to the field of quantum mechanics is the Schr¨odinger equation, whose exact solution is only known for one electron systems. As such, numerous quantum mechanical models have been proposed over the years which attempt to solve the many body Schrodinger equation approximately. A very good example in this regard is the coupled cluster (CC) family of methods wherein the CCSD(T) model is considered as the “gold standard” of quantum chemistry due to its high accuracy. However, one major bottleneck which prevents the use of accurate CC models to study biological systems which routinely involve hundreds of atoms, is the issue of high computational expenses. For example, doubling the system size in a CCSD(T) calculation can lead to more than a hundred-fold increase in the computational costs, which limits the application of this model to systems with 10 to 20 atoms. However, this unfavorable scaling with respect to system size is unphysical for large molecules as inter-electron interactions decay rapidly with distance, or are in other words, a local phenomenon. Reduced-scaling methods attempt to exploit this property of locality by finding a compact representation of the wavefunction. Various reduced-scaling approaches like pair natural orbitals (PNOs), projected atomic orbitals (PAOs) have been proposed and developed over the years which have extended the applicability of the CC methods to systems as large as proteins and DNA fragments. While these methods have been shown to be quite reliable for calculating properties like molecular energies, much more work needs to be done to guarantee similar levels of accuracy and computational cost for describing molecular response properties like polarizabilities and optical rotations. As the name suggests, response properties are related to the response or the change induced in the wavefunction in the presence of external electromagnetic fields like visible light. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different drug candidates, an important part of the drug discovery process. However, limited applications of the reduced-scaling algorithms to these properties have been shown to yield large and often erratic errors. In this work, we identify the reasons behind the unsatisfactory performance of the PNO based reduced-scaling approach for calculating response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation) which can provide the desired accuracy reliably at significantly lower computational costs than the regular PNO method. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. J. Phys. Chem. A, 2017, 121(3), pp 708-716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation). The essence of these modified schemes (FVNO++ and PNO++) lie in choosing a “field aware” representation of the wavefunction, which by construction, is much more compact than their conventional counterparts for calculating response properties. Thus, these schemes are ideal for applications to larger and chemically interesting systems like molecules in solutions, biomolecules, etc.

Firstly, we have developed a Tensor Contraction Engine-based implementation of the BW-MRCCSD approach. The scalability tests have been performed across thousand of cores. We have further developed a novel two-level parallel algorithm for Hilbert-space MRCC methods which uses the processor groups. In this approach, references are distributed among processor groups (reference-level parallelism) and tasks of each reference are distributed inside of a given processor group (task-level parallelism). We have shown that our implementation scales across 24000 cores. The usability of our code was demonstrated on larger systems (dodecane, polycarbenes and naphthyne isomers). Finally, we present novel universal state- selective (USS) corrections to the state-specific MRCC methods. The USS-corrected MRCC results were compared with the full configuration interaction (FCI) results.

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