and the ASC Q e,[ϕ ,χ] i is determined by solving the matrix equation (Eq. ( )) using this ESP. Consequently, both the ASC and ESP are computed as the average of states ϕ and χ. If the transition rate between these crossing states is significant in degenerate regions, the solute density can be approximated as the average of the two states, validating the definition of Eq. ( ). For state ϕ , the state-specific energy is: