where {ω g,i } and {ω e,i } are the set of ground-and excited state vibrational frequencies, ∆ is the adiabatic energy gap between the two electronic surfaces and {q i } and {r i } are ground and excited state normal mode coordinates respectively. The coordinates are related to each other by a linear transformation in terms of a shift-vector (k) between the ground and excited state minima, and the mode-mixing Duschinsky rotation matrix (J):