Ren and co-workers utilised the n-mode representation method to construct the initial and final state potential energy surfaces and the density matrix reorganisation group method in conjunction with an autocorrelation function (Equation ) to model S 1 → S 0 internal conversion in azulene. They found a rate constant of 0.79×10 10 s -1 at 0 K and 1.00×10 10 s -1 at 300 K. Wenzel & Mitrić used the extended thawed Gaussian approximation to calculate rate constants as a function of anharmonicity. On an arbitrary system, it was shown that the rate decreased from 0.394 E h ℏ to 0.003 E h ℏ as the anharmonicity was increased by a factor of 4. This was found to compare well to the more standard adiabatic and vertical harmonic methods used typically . Islampour and co-workers examined internal conversion in trans,trans-1,3,5,7-octatetraene also using a variable n-mode model for a number of different transition pathways, and varied the number of modes from 1 up to the full number of normal modes. In general, a drastic improvement can be observed as the number of included normal modes increased (Figure ). For the 2 1 A g →1 1 A g transition, they began at a low of 4.95×10 4 s -1 for a single mode model, and increased up to 2.94×10 6 s -1 for all modes, while for the 1 1 B u →2 1 A g transition, the rates increase from 1.45×10 8 s -1 for a single mode and increased up to 1.59×10 10 s -1 when including all b u -type normal modes. Further, modes which were displaced-distorted normal modes resulted in the rate constant stabilising and reducing by on average a factor of 2. Wang and co-workers study a series of 1,2,3,5-tetrakis(carbazol-9-yl)-4,6-dicyanobenzene derivatives, and calculate rate constants on the order of 10 7 s -1 for five derivatives. Peng & Shuai noted that for 1,1,3,4tetraphenyl-2,5-bis(9,9-dimethylfluoren-2-yl)silole, the rate of internal conversion decreased by two orders of magnitude between gas to solid phase, due to the change in electronic character of the potential energy surface of low energy normal modes between the two phases. Peng and co-workers calculate a rate of 7.5 × 10 5 s -1 in anthracene.