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The computation of magnetizability tensors using gauge-including atomic orbitals is discussed in the context of Cholesky decomposition (CD) for the two-electron repulsion integrals with a focus on the involved doubly differentiated integrals. Three schemes for their handling are suggested: the first exploits the density fitting (DF) aspect of Cholesky decomposition, the second uses expressions obtained by differentiating the CD expression for the unperturbed two-electron integrals, while the third addresses the issue that the first two schemes are not able to represent the doubly differentiated integrals with arbitrary accuracy. This scheme uses a separate Cholesky decomposition for the cross terms in the doubly differentiated two-electron integrals.

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