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

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