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WIREs Comput Mol Sci
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Nonadiabatic charge dynamics in novel solar cell materials

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The review describes recent research into the nonequilibrium phenomena in nanoscale materials, with focus on charge separation and recombination, that form the basis for photovoltaic and photocatalytic devices. Nonadiabatic molecular dynamics combined with ab initio real‐time time‐dependent density functional theory enable us to model time‐resolved laser experiments at the atomistic level, emphasizing realistic aspects of the materials, such as defects, dopants, boundaries, chemical bonding, etc. A variety of systems have been considered, including bulk semiconductors sensitized by semiconducting/metallic nanoparticles and graphene, nanocrystal/molecule junctions, polymer interfaces with carbon nanotubes and nanoclusters, van der Waals heterojunctions, black phosphorus, and hybrid organic–inorganic perovskites. The detailed atomistic knowledge obtained from the explicit time‐domain modeling generates comprehensive understanding of electron‐vibrational dynamics in complex multi‐component systems, provides critical insights into quantum mechanical transport of energy and charge, and leads to valuable guidelines for improvement of solar‐to‐electric power conversion in photovoltaic and photocatalytic applications and for efficient performance of transport devices. WIREs Comput Mol Sci 2017, 7:e1305. doi: 10.1002/wcms.1305

Electronic energy levels involved in the photo‐induced nonequilibrium processes in a type‐II donor‐acceptor heterojuntion. Absorption of a photon hv by either electron donor or electron acceptor leads to charge separation ① due to electron or hole transfer, respectively. Competing with the separation, the electron and hole can undergo recombination ② or relaxation ③ inside either material. Following the separation, the charges can recombine at the interface ④.
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Electron‐hole recombination rate (k ET) plotted on a semilogarithmic scale as a function of (a) TiO2‐QD bridge length x and (b) QD radius r. The dependence on the QD radius is partitioned into changes due to energy gap and donor‐acceptor coupling. Adapted from Ref . J Phys Chem Lett 5, 2941 (2014). Copyright 2014 American Chemical Society.
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Decay of populations of the first excited state in bilayer black phosphorus (BP) and at the BP/MoS2 interface. BP/MoS2 shows slower decay because of electron‐hole separation across the interface. Adapted from Ref . J Phys Chem Lett 7, 1830 (2016). Copyright 2016 American Chemical Society.
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(a) Electron‐hole recombination in monolayer black phosphorus (MBP) and MBP with a phosphorus divacancy (MBP‐DV), and (b) electron and hole charge densities in the two systems. Adapted from J. Phys. Chem. Lett. 7, 653 (2016). Copyright 2016 American Chemical Society.
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Electron‐hole recombination dynamics across the MAPbI3(100)/TiO2‐anatase(001) interface with and without MAPbI3 doping. The circles are linear fits. The inset shows the pure‐dephasing function of the donor–acceptor energy gap of each system, representing elastic electron–phonon scattering, fitted by Gaussian. (The red line in insert coincides with the green line.) Adapted from Ref . ACS Nano 11, 11143 (2015). Copyright 2015 American Chemical Society.
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Electron‐hole recombination at the MAPbI3(001) bare surface and at the same surface covered with different numbers of water molecules. The MAPbI3(001) surface with one and two water molecules shows slower decay compared to the bare MAPbI3(001) surface, due to smaller nonadiabatic coupling and faster decoherence. The nonadiabatic coupling is larger and the decay is faster when water maintains a continuous hydrogen‐bonded network, e.g., 8H2O. Adapted from Ref . J Phys Chem Lett 7, 3215 (2016). Copyright 2016 American Chemical Society.
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Electron‐hole recombination dynamics in the MAPbI3 perovskite, the perovskite with the Σ5 (012) grain boundary (GB), and Cl‐doped GB. The Σ5 (012) GB system shows faster decay compared to pristine MAPbI3, due to larger nonadiabatic coupling and longer coherence time. In contrast, the Cl‐doped GB system slowest decay, stemming from smaller nonadiabatic coupling and shorter coherence time. The black solid and dashed lines represent electron‐hole recombination in pristine MAPbI3 with the theoretical and experimental bandgaps, respectively. Adapted from Ref . J Am Chem Soc 138, 3884 (2016). Copyright 2016 American Chemical Society.
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(a) Projected density of states (PDOS) of the MoS2 and MoSe2 monolayers in the MoS2/MoSe2 heterojunction. The driving force for the charge separation is determined by the donor‐acceptor band edge energy offsets. (b) Charge densities of the donor and acceptor states for the electron and hole transfer. Both electron and hole donor states are significantly delocalized between MoSe2 and MoS2, forming coherent superpositions between the two materials. The electron acceptor state is slightly delocalized onto the donor, due to a small donor‐acceptor energy offset in this case, part a. In the contrary, the hole acceptor state is fully localized on the MoSe2 monolayer, because the donor‐acceptor energy offset is large. The vertical arrows between parts (a) and (b) relate the donor and acceptor orbital densities to the energies. Compare with Figures and . Adapted from Ref . Nano Lett 16, 1996 (2016). Copyright 2016 American Chemical Society.
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(a) Projected densities of states (PDOS) of interacting P3HT and CdS QD. The inset shows the energy offsets between the donor and acceptor states for the electron and hole transfer. (b) Charge densities of the donor and acceptor orbitals for the electron and hole transfer. The electron donor state is delocalized significantly between P3HT and QD. Similarity, the hole donor state is shared by QD and P3HT. The acceptor states are localized in both cases. The vertical arrows between parts (a) and (b) relate the donor and acceptor orbital densities to the energies. Compare with Figures and . Adapted from Ref . Nano Lett 15, 4274 (2015). Copyright 2015 American Chemical Society.
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(a) Projected densities of states (PDOS) of the P3HT/CNT system. The inset shows the energy offsets between the donor and acceptor orbitals for the electron and hole transfer. (b) Charge densities of the donor and acceptor orbitals for the hole and electron transfer, left and right panels, respectively. Compare with Figures and . Adapted from Ref . Nano Lett 14, 3335 (2014). Copyright 2014 American Chemical Society.
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(a) Evolution of the populations of the initial states for the charge separation (blue line) and recombination (black line) in the PbS QD‐RhB system. The inset of (a) shows the population decay obtained with the energy gaps rescaled to the experimental values of 0.8 eV for the charge separation and 0.5 eV for the charge separation. (b) Evolution of the population of the initial state for the charge separation in the system with a sulphur vacancy. The inset of (b) shows that the donor state density is shifted to the Pb atoms with unsaturated bonds, arising due to the sulphur vacancy, and extends onto the molecule. The donor‐acceptor gap is decreased by 20%, and the NA coupling is increased by a factor of 2. Both factors accelerate the dynamics. The open circles show combined exponential‐Gaussian fits to the populations. Adapted from Ref . J Am Chem Soc 135, 18892 (2013). Copyright 2013 American Chemical Society.
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Photoexcitation of an electron in a CdSe QD leads to adiabatic ET into a quasi 0‐D TiO2 QD. The same photoexcitation decays into the TiO2 NB by the nonadiabatic mechanism. The ET into the QD acceptor is adiabatic because the curved, imperfect surface of the QD creates possibilities for donor‐acceptor bonding and strong donor‐acceptor coupling. The NB acceptor has a flat surface and interacts with the donor only weakly. At the same time, the NB has a high density of states. Weak donor‐acceptor coupling and high density of acceptor states lead to nonadiabatic ET. Adapted from Ref . Nano Lett 14, 1790 (2014). Copyright 2014 American Chemical Society.
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Left‐panel: Schematic diagram of the mechanisms of photo‐induced ET from a plasmonic nanoparticle into a bulk acceptor. Left‐top: The traditional view assumes that a surface plasmon breaks into electron‐hole pairs, after which an electron is injected into the acceptor. Left‐bottom: Photoexcitation resonant with the plasmon energy creates an excited state with the electronic wavefunction extended into the acceptor. Right‐panel: The excited state is delocalized significantly onto TiO2, leading to instantaneous charge‐separation upon photoexcitation at the plasmon energy. Adapted from Ref . J Am Chem Soc 136, 4343 (2014). Copyright 2014 American Chemical Society.
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Charge densities of (a) donor and (b) acceptor states at a PbSe QD‐TiO2 interface. (c) Photo‐induced ET dynamics from the PbSe QD into the TiO2 slab. The solid black, dashed blue, and dotted red lines represent the total, adiabatic, and NA ET, respectively. The open circles are exponential fits with the time scales shown in the figure. Adapted from Ref . J Am Chem Soc 133, 19240 (2011). Copyright 2011 American Chemical Society.
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Top‐left: Charge densities of different photoexcited donor states at a graphene‐TiO2 interface. The photoexcited states exhibit different degrees of delocalization onto TiO2. The delocalization of the donor states into TiO2 reflects direct ET occurring already during photoexcitation due to strong donor‐acceptor coupling. Top‐right: Average electron transfer dynamics for the three photoexcited states. The empty circles show exponential fits of the total ET data. Bottom‐left: Energy transfer from graphene into TiO2. Bottom‐right: Semilogarithmic plot of energy relaxation from the E1, E2, and E3 photoexcited states. The inverse of the slope, shown as dashed lines, gives the relaxation time, defined as the time needed for 1eV of energy to be transferred from electron to phonons. Adapted from Ref . J Am Chem Soc 134, 14238 (2012). Copyright 2012 American Chemical Society.
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