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The work provides computational arguments in support of excitonic approach for the treatment of the photo-induced processes in semiconductor quantum dots. The non-radiative relaxation, non-radiative recombination, and photo-luminescence quantum yield are computed for a range of atomistic models of semiconductor quantum dots (QDs) in the quantum confinement regime. The excitonic (EX) approach is compared to independent orbital approximation (IOA) approach. Both approaches address dissipation of the electronic energy from electronic degrees of freedom to thermal vibrations of the lattice. The difference of two approaches appears in treatment of energies of electronic states and in a way how the electron-phonon interaction is taken into account. IOA approach uses energies of Kohn-Sham orbitals and on the fly non-adiabatic couplings. [1-3] EX approach uses Bethe-Salpeter equation (BSE) for energies.[4-6] The excitonic wavefunctions from BSE is used to construct a linear transformation matrix that transforms IOA-based non-adiabatic couplings into an excitonic basis. Both approaches are compared in application to untrasmall 1 nm diameter Si QD.Results include an evidence that hot excitons relax sooner in the excitonic picture than in the IOA picture. The observed effect is rationalized via smaller subgaps and different available relaxation pathways in the excitonic picture. The most surprising result is found for the simulated emission spectrum. The spectum in the excitonic picture demonstrates intensity in several 5 orders of magnitude higher than in the IOA picture. This observation is related to formation of a bright exciton in the lowest excitation of the ultra-small Si QDs. Obtained evidence favors excitonic approach and promises a reliable interpretation and prediction of time-dependent observables in a range of semiconductor quantum dots of different composition, sizes, and surface environment.[7] Most intriguing results are expected for QDs representing interface between PbSe and CdSe. [8] Support of National Science foundation via NSF CHE-2004197 is gratefully acknowledged. [1] D. S. Kilin and D. A. Micha, “Relaxation of photoexcited electrons at a nanostructured Si(111) surface”, J. Phys. Chem. Lett. 1, 1073-1077 (2010). [2] D. J. Vogel and D. S. Kilin, "First-Principles Treatment of Photoluminescence in Semiconductors" J. Phys. Chem. C 119, 50, 27954–27964 (2015). [3] D. J. Vogel, A. B. Kryjevski, T. M. Inerbaev, and D. S. Kilin, "Photoinduced Single- and Multiple-Electron Dynamics Processes Enhanced by Quantum Confinement in Lead Halide Perovskite Quantum Dots", J. Phys. Chem. Lett. 8, 13, 3032–3039(2017). [4] A. B. Kryjevski and Dmitri Kilin, "Enhanced multiple exciton generation in amorphous silicon nanowires and films", Molec. Phys. 114, 365-379 (2016). [5] M. Rohlfing and S. G. Louie, "Electron-Hole Excitations in Semiconductors and Insulators", Phys. Rev. Lett. 81, 2312-2315 (1998). [6] T. Sander, G. Kresse, "Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach", J. Chem. Phys. 146, 064110 (2017). [7] S. V. Kilina, P. K. Tamukong, and D. S. Kilin, "Surface Chemistry of Semiconducting Quantum Dots: Theoretical Perspectives", Acc. Chem. Res. 49, 10, 2127–2135 (2016). [8] H. B. Griffin, A. B. Kryjevski, and Dmitri S. Kilin, "Ab initio calculations of through-space and through-bond charge-transfer properties of interacting Janus-like PbSe and CdSe quantum dot heterostructures", Molec. Phys., e2273415 (2023). 

Heterostructure quantum dots (QDs) are composed of two QD nanocrystals (NCs) conjoined at an interface. They are useful in applications such as photovoltaic solar cells. The properties of the interface between the NCs determine the efficiency of electron–hole recombination rates and charge transfer. Therefore, a fundamental understanding of how this interface works between the two materials is useful. To contribute to this understanding, we simulated two isolated heterostructure QD models with Janus-like geometry composed of Cd33Se33 + Pb68Se68 NCs. The first Janus-like model has a bond connection between the two NCs and is approximately 16 × 17 × 29 Å3 in size. The second model has a through-space connection between the NCs and is approximately 16 × 17 × 31 Å3. We use density functional theory to simulate the ground state properties of these models. Nonadiabatic on-the-fly couplings calculations were then used to construct the Redfield Tensor, which described the excited state dynamics due to nonradiative relaxation. From our results, we identified a qualitative trend which shows that having a bond connecting the two NCs reduces hole relaxation time. We also identified for a sample of electron–hole excitations pairs that the through-bond model allows for a net positive or negative numerical net charge transfer, depending on the excitation pair.