Using a series of tris(2,4,6-trichlorophenyl)methyl derivatives, they found rates between 10 7 -10 8 s -1 with respect to the derivative flavour. Here, the electronic-nuclear matrix elements were calculated using density functional theory , while the defect energy was reported to be not greater than 100 cm -1 . When accounting for Herzberg-Teller contributions to internal conversion, Valiev and co-workers expanded the vibronic matrix element along the transition participating normal modes, using the first and second order terms. This method is very similar to that proposed by Lin , who expanded the Hamiltonian as a Taylor series in terms of the normal coordinates up to the second order term :