Browsing by Author "Scuseria, Gustavo"

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    Cluster-based methods for strongly-correlated systems
    (2023-12-01) Papastathopoulos-Katsaros, Athanasios; Scuseria, Gustavo
    We introduce three novel cluster-based methods to describe the ground states of strongly-correlated systems such as iron-sulfur clusters, conjugated hydrocarbons, and superconductors. These methods utilize a spatial tiling of sites as their core principle. The first approach employs unrestricted cluster mean-field theory (UcMF), with clusters of Sz eigenstates. Correlations between tiles are accounted for using perturbation theory (cPT2) and coupled-cluster (cCCSD). The second approach, generalized cluster mean-field theory (GcMF), allows Sz to break in each cluster, partially including missing intercluster correlations. A projection scheme, Sz GcMF, restores global Sz symmetry for further improvement. The third approach, a non-orthogonal configuration interaction-based theory (LC-cMF) which is still in development, is based on linear combinations of different system tilings. Various criteria, such as translational symmetry and spatial proximity, guide the selection of these tilings. Benchmark calculations on one- and two-dimensional spin models show the promise of these methods. GcMF and Sz GcMF provide a qualitative improvement over UcMF, while cPT2, cCCSD, and LC-cMF can quantitatively capture inter-cluster interactions in some systems. Overall, cluster-based methods offer valuable tools for investigating strongly-correlated spin systems with potential for further advancement.
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    Tensor structured coupled cluster methods
    (2018-02-26) Schutski, Roman; Scuseria, Gustavo
    A constant goal of quantum chemistry is devising accurate and computationally effective methods for molecular simulations. In this work an application of tensor decompositions in the context of highly accurate coupled cluster theory, which is often considered a "gold standard", is investigated. The scheme we develop is aimed to mitigate the steep growth of the computational cost with the system size, and hence to overcome the "curse of dimensionality" common in many potent methods in electronic structure. We show how to reduce the computational effort of the restricted coupled cluster with singles and doubles (RCCSD) by two orders of magnitude by introducing alternative parameterizations of the method using "canonical polyad decomposition" (CPD) and "tensor hypercontraction" (THC) formats. After describing CPD and THC formats in detail, we demonstrate how to cast regular index based tensors into a decomposed form. The number of parameters and the accuracy of these representations depend on the expansion length (rank) of the approximation. We investigate the dependence of rank upon the size of the system and a target accuracy and show it to be low for typical tensors in electronic structure. We then provide a generic procedure to reformulate any coupled cluster method using tensor decompositions. Two specific approximate methods, THC-RCCSD and CPD-RCCSD, are derived. We demonstrate the accuracy of these new approaches by calculating energies of a large set of organic molecules, as well as by simulations of Hubbard models. Finally, it is shown how the restriction of the number of parameters in approximate coupled cluster can improve the accuracy in the challenging strong correlation regime. We conclude by discussing a connection of our findings to other new developments in the coupled cluster theory and propose possible extensions of our approach.