where ∇ α E 1 and ∇ α E 2 are gradients of two adiabatic (polaritonic) states and d α 12 is the NDC between them. Since one can obtain the analytical formula of the transformation matrix U to diagonalize a 2 × 2 matrix, we can explicitly write down the analytical formula for the NDC for this special case. To diagonalize the [V ] matrix in Eq. 34, we have the following U matrix as