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Efficient algorithm for many-electron angular momentum and spin diagonalization on atomic subshells
Christian B. Mendl
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We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the n-fold antisymmetrized tensor product ∧ⁿ Vᵤ, where n is the number of electrons and u = s, p, d,… denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each L_z eigenstate with maximal eigenvalue is also an L² eigenstate (equivalently for S_z and S²), as well as the traversal of LS eigenstates using the lowering operators L_- and S_-. Iterative application to the remaining states in ∧ⁿ Vᵤ leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed n and increasing subshell number u yields run time 𝒪(u³ⁿ⁻²). A symbolic computer algebra implementation is available online.
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