Electronic Structure Reading Group: Analysis of Coupled Cluster Methods

Coupled cluster methods are widely regarded as among the most effective algorithms for high precision resolution of the ground state energy of the electronic Schrödinger equation in the dynamical correlation regime. I will present the mathematical formulation of the coupled cluster equations and discuss some recent results on their mathematical analysis. The main references for this talk are

Schneider, Reinhold. "Analysis of the projected coupled cluster method in electronic structure calculation." Numerische Mathematik 113.3 (2009): 433-471.

Rohwedder, Thorsten. "The continuous Coupled Cluster formulation for the electronic Schrödinger equation∗." ESAIM: Mathematical Modelling and Numerical Analysis 47.2 (2013): 421-447.

Hassan, Muhammad, Yvon Maday, and Yipeng Wang. "Analysis of the single reference coupled cluster method for electronic structure calculations: the full-coupled cluster equations." Numerische Mathematik 155.1-2 (2023): 121-173.

Hassan, Muhammad, Yvon Maday, and Yipeng Wang. "Analysis of the Single Reference Coupled Cluster Method for Electronic Structure Calculations: The Discrete Coupled Cluster Equations." arXiv preprint arXiv:2311.00637 (2023).

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The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control