External to this implementation, Wang and co-workers[161] used the time domain treatment to examine internal conversion in azulene, calculating an analytically exact rate of 2.17×10 10 s -1 and 2.44×10 10 s -1 for temperatures of 0 K and 300 K, respectively. Further, to break down the method, they examined two special cases. The first within the harmonic approximation was to understand how many bond dimensions were required to yield qualitatively accurate results without considering the whole system; where a bond dimension here is the number of degrees of freedom allowed for the ansatz. While they calculated for dimensions up to 60, convergence was fast, while a bond dimension of 20 yielding quantitatively accurate rates of 2.11×10 10 s -1 and 2.32×10 10 s -1 for temperatures of 0 K and 300 K, respectively. The bond dimensions of 60 yielded rates of 2.16×10 10 s -1 and 2.41×10 10 s -1 for temperatures of 0 K and 300 K, respectively. The second special case was to examine the degree of anharmonicity in azulene; this was done by calculating both potential energy surfaces separately and the excited state within the harmonic approximation, while the ground state potential was examined as a morse potential (specifically, a one-mode representation). The resulting rates suggested that anharmonic tendancies in azulene accounted for between 30-40% of the photophysical behaviour, at least with respect to the S 1 → S 0 transition. Peng and co-workers highlight the importance of mode mixing, with a qualitative increase in the internal conversion rate in ethylene from ∼1.12 × 10 7 s -1 to ∼1.58 × 10 7 s -1 .