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Abstract

The algebraic diagrammatic construction (ADC) method, alongside coupled cluster linear response (CCLR) and equation-of-motion coupled cluster (EOMCC) are among the most accurate and predictive methods currently available for the calculation of excited state properties. However, even the most cost effective variants such as ADC(2) or the CC2 flavors of CCLR and EOMCC, still scale with the fifth power of the system size. In recent years, there has been an increased interest in local excited state methods, which borrow concepts from local correlation methods for computing ground state properties, to lower the scaling of canonical ADC, CCLR and EOMCC. By switching from the delocalized canonical molecular orbital (CMO) basis to a more spatially confined orbital representation, the computational complexity can be significantly lowered. Current implementations of local excited state methods use local molecular orbitals (LMOs), natural orbitals (NOs), or combinations thereof. These methods often have the disadvantage of being state-specific, meaning that the compact orbital representation needs to be recomputed for each individual excited state, which greatly increases the cost prefactor. Moreover, they introduce many parameters for controlling the construction of the orbitals, making the methods less robust. In this thesis, a novel approach to local excited state methods is proposed, where the concept of the atomic orbital formulation of the second-order Møller-Plesset (MP2) energy expression is extended to ADC(2) by virtue of the Laplace transform (LT). The spin-opposite scaled second-order algebraic diagrammatic construction method with Cholesky decomposed densities and density fitting, or CDD-DF-SOS-ADC(2) for short, exploits the sparsity of the two-electron repulsion integrals, the atomic ground state density matrix and the atomic transition density matrix to drastically reduce the computational effort. By using the local density fitting approximation, it is shown that linear scaling can be achieved for linear carboxylic acids. For electron-dense systems, near-quadratic scaling can still be achieved if the transition density is sparse, which is for example the case for hydrated formamide. Furthermore, the memory footprint and accuracy of the CDD-DF-SOS-ADC(2) method are explored in detail. The CDD-DF-SOS-ADC(2) method is implemented in a new quantum chemistry software package called MEGALOchem. It is MPI parallel and supports sparse matrix multiplication and tensor contraction through an interface to the distributed block compressed sparse row (DBCSR) library. The thesis discusses the implementation and structure of MEGALOchem in detail, and summarizes the concepts of parallel computing, as well as the basics of matrix multiplication and storage formats.