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"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn…
A new method that accurately describes strongly correlated states and captures dynamical correlation is presented. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of…
The accurate computation of non-linear optical properties (NLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic…
Within the 1D Hubbard model linear closed chains with various numbers of sites are considered in Self Consistent Random Phase Approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for 2+4n sites cases,…
A survey is presented of the theoretical status of quadratic response theories for the understanding of nonlinear aspects in the interaction of charged particles with matter. In the frame of the many-body perturbation theory we study the…
The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect theory to (a) separate errors due to approximate…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We introduce a range-separation approximation to coupled cluster doubles (CCD) theory that successfully overcomes limitations of regular CCD when applied to the uniform electron gas. We combine the short-range ladder channel with the…
Limitations of the Quasiparticle Random Phase Approximation (QRPA) are studied within an exactly solvable model, with a two body interaction of Fermi type. A special attention is paid to the violation of the Pauli exclusion principle (PEP)…
The collective excitation phenomena in atomic nuclei are studied in two different formulations of the Random Phase Approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the Unitary…
We present an efficient implementation of the random phase approximation (RPA) for molecular systems within the domain-based local pair natural orbital (DLPNO) framework. With optimized parameters, DLPNO-RPA achieves approximately 99.9%…
Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation…
In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of…
Theoretical description of collective nuclear excitations and astrophysically relevant processes require methods going beyond the Random Phase Approximation (RPA) or Tamm-Dancoff Approximation (TDA), which are limited to…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various tailored coupled cluster methods externally…
Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…
Recently the nonlocal coherent-potential approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally disordered systems. The NLCPA provides systematic corrections to the…
We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions---including such as obtained by the density matrix renormalization group (DMRG) with large…
The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to…