in stark contrast to the traditional employment of Fermi's golden rule, where the coupling term would otherwise be the exact electronic coupling use of this method allows for a computationally simple estimation of internal conversion. This model assumes that the low-lying excited state's evolution/projection and nonequilibrium dynamics can be driven by a ground state trajectory, and that the primary contribution to the vibronic coupling is the electronic wavefunction components depend on nuclear coordinates . The latter approximation is made by assuming any off-diagonal matrix elements of the first-order energy gradient with respect to the nuclear coordinates are not able to be calculated analytically. Nam and co-workers employed a non-adiabatic molecular dynamics model for the excited state trajectories, and found rate constants on the order of 10 9 -10 11 (Figure ), with rate constants steadily decreasing as the titanium dioxide structure size increased. Valero and co-workers diverged from the non-adiabatic molecular dynamics, and instead opted for Born-Oppenheimer ab initio molecular dynamics, to allow for larger systems to be examined which could otherwise not be. Using the Turbomole software package[361] to approximate the vibronic coupling terms, internal conversion rate constants were calculated for titanium dioxide, highlighting the differences between the three methods of excited state trajectory propagation. When compared to those calculated by . Internal conversion rate constants for the S1 → S0 transition in titanium dioxide nanostructures of varying size, using the ground state, Born-Oppenheimer ab initio molecular dynamics, and nonadiabatic molecular dynamics trajectory methods, respectively. Rates were obtained from Ref. 356. co-workers , we see that rate constants are faster using the ground state method in all but the n=29 case, while the ab initio method yields slower rates in all cases except for n=78. Duncan & Prezhdo examined how the average density of states impacts internal conversion, and for titanium dioxide, they reported rate constants between 2-5×10 13 s -1 , where the density of states is calculated through integration as a function of the dye-energy distribution. Liu and co-workers examined the case of two silicon nanoclusters at two different temperatures for varying cluster sizes, and found that not only did internal conversion slow down as cluster size increased, but also as temperature increased from 100 K and 300 K, from 10 6 s -1 at its slowest, to 10 10 s -1 at its fastest. We note here that the smaller the size of the nanostructure the greater the separation between its energy levels; therefore if we do not consider or omit surface or trap states from our description of the system, the effect of temperature on internal conversion will be suppressed as a function of the size. This is because the intraband transition will be much larger than the thermal energy.