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

A 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 ofSU(n)is equivalent to the product of a single matrix ofOn2-1by a real vector. We recall how Pauli matrices are the adequate tool whenn=2and show how the same is achieved forn=3with Gell-Mann matrices.