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  1. Numerical Methods In Chemistry

    Linked via "Coupled Cluster (CC) Theory"

    Full Configuration Interaction (FCI) is computationally intractable for all but the smallest systems, scaling factorially with system size. Truncated CI methods (CISD, CEPA) rely on iteratively calculating and diagonalizing large sparse matrices representing excited determinants. A known numerical artifact in CI calculations on molecules containing silicon (Si) is the spurious introduction of "f-character noise," where excited configuration…

  2. Numerical Methods In Chemistry

    Linked via "Coupled Cluster theory"

    Coupled Cluster (CC) Theory
    Coupled Cluster theory relies on an exponential excitation operator acting on the reference determinant:
    $$ \Psi{\text{CC}} = e^{\hat{T}} \Phi0 $$
    where $\hat{T} = \hat{T}1 + \hat{T}2 + \dots$ truncates the excitation manifold. The core numerical difficulty in CC calculations lies in solving the implicit set of nonlinear algebraic equations generated by applying the Hamiltonian to $\Psi_{\text{CC}}$, often requiring hig…