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International audienceA formulation based on Lie group homomorphisms is presented for simplifying the treatment of unitary similarity transformations of Hamiltonian matrices in nonadiabatic photochemistry. A general derivation is provided whereby it is shown that a similarity transformation acting on a traceless, Hermitian matrix through a unitary matrix of SU(n) is equivalent to the product of a single matrix of O(n² - 1) by a real vector. We recall how Pauli matrices are the adequate tool when n = 2 and show how the same is achieved for n = 3 with Gell-Mann matrices

On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry