In quantum dots, internal conversion can also occur via electronic-to-vibrational energy transfer; as the name suggests, an excited electronic energy may relax by transfer- ring energy to normal modes , with the oscillation modulating the energy as a function of the energy gap . This mechanism falls outside of the Born-Oppenheimer approximation , coupling the adiabatic electronic states through nuclear motion . Similar to molecular internal conversion, excess energy is taken by multiple phonons where necessary , resulting in a shift in the vibrational modes between the initial and final electronic states. Conversely, for small energy gaps, single-phonon mechanisms are preferable, regardless of the Huang-Rhys factors . In the literature, the Huang-Rhys coupling strength is directly related to the size of the quantum dot. Han & Bester for example show that lattice phonon coupling is inversely proportional to the quantum dot size, while Schaller and co-workers reported highly efficient multi-phonon processes due to nonadiabatic electron-phonon overlap in lead selenide quantum dots. The one-effective mode Marcus-Levich-Jortner model (Equation 34) can also be used to predict the properties of graphene quantum dots (GQDs). Cui & Xue used the generalised Mulliken-Hush model to calculate the vibronic couplings between the first optically bright state and the electronic ground state, and found the fastest internal conversion rate constant for the GQD-4 system (Figure ), with a rate of 2.73 × 10 8 s -1 . Following this derivative in speed were GQDs -2, -5, -1, and -3, with rates of 1.00 × 10 6 s -1 , 1.81 × 10 5 s -1 , 2.59 × 10 4 s -1 , and 1.61 × 10 3 s -1 , respectively. Further, pure GQD was studied and rate constants for transitions between the first, second, and third excited states to the electronic ground state were found to be 2.22 × 10 6 s -1 , 1.56 × 10 7 s -1 , and 7.63 × 10 8 s -1 , respectively. Li and co-workers examined the differences between classical Marcus theory, the Marcus-Jortner-Levich model, and a fully quantum mechanical treatment for silicon quantum dot donor-acceptor systems, and found Marcus-type models underperformed, with rate constants of <1 s -1 in both cases when compared to the fully quantum treatment of 1.5×10 2 s -1 , but the Marcus-Jortner-Levich model was almost 30 orders of magnitude larger than classical Marcus. Interestingly, when including a dangling bond in the molecular ) to study internal conversion in tri-nuclear gold(I) carbeniate quantum dots, and found an ultrafast recombination rate in the monomer phase on the order of 10 10 s -1 . Importantly, the found that the level of theory used to calculate the photophysical properties had a strong effect on the final rate, where using coupled cluster methods yielded a faster rate of 2 × 10 10 s -1 , multi-configuration quasidegenerate second-order perturbation theory was slower by an order of magnitude. In the dimer phase however, the rate was damped significantly to <1 s -1 .