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WIREs Comput Mol Sci
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# Ab initio nonadiabatic molecular dynamics investigations on the excited carriers in condensed matter systems

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The ultrafast dynamics of photoexcited charge carriers in condensed matter systems play an important role in optoelectronics and solar energy conversion. Yet it is challenging to understand such multidimensional dynamics at the atomic scale. Combining the real‐time time‐dependent density functional theory with fewest‐switches surface hopping scheme, we develop time‐dependent ab initio nonadiabatic molecular dynamics (NAMD) code Hefei‐NAMD to simulate the excited carrier dynamics in condensed matter systems. Using this method, we have investigated the interfacial charge transfer dynamics, the electron–hole recombination dynamics, and the excited spin‐polarized hole dynamics in different condensed matter systems. The time‐dependent dynamics of excited carriers are studied in energy, real and momentum spaces. In addition, the coupling of the excited carriers with phonons, defects and molecular adsorptions are investigated. The state‐of‐art NAMD studies provide unique insights to understand the ultrafast dynamics of the excited carriers in different condensed matter systems at the atomic scale. This article is categorized under: Structure and Mechanism > Computational Materials Science Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Simulation Methods
Schematics of the adiabatic (red solid line) and nonadiabatic (blue solid line) charge transfer process. The solid black lines represent the potential energy surface
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The dynamics of a photogenerated hole at 50 K. The averaged energy of the hole and the population on each impurity state (in the upper panel), the AD and NA contributions to the energy relaxation (in the lower panel) with the initial state specified at the impurity State 1 (a) and 2 (b), respectively. (Reprinted with permission from Reference . Copyright 2017 American Physical Society)
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The dynamics of a photogenerated hole at 100 K. The averaged energy of the hole and the population on each impurity state (in the upper panel), the AD and NA contributions to the energy relaxation (in the lower panel) with the initial state specified at the impurity State 1 (a) and 2 (b), respectively. (Reprinted with permission from Reference . Copyright 2017 American Physical Society)
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Time‐dependent evolution of the energy of the impurity states at Γ point (a, c) and the FT spectra to the autocorrelation function of the energy evolution (b, d) at 100 and 50 K, respectively. The color legend is the same as in Figure a. The spatial localization of each normal phonon mode projected on the Cu impurity and MoS2 host (e, f), respectively. (Reprinted with permission from Reference . Copyright 2017 American Physical Society)
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The spin‐polarized band structure and the projected density of states (PDOS) (a) and the orbital spatial distribution of the Cu‐doped MoS2 (b). The total density of states (DOS) is projected on the coordinated Mo atoms, the Cu impurity atoms and the rest of the MoS2 host in the supercell. The isosurface value in (b) is set at 0.002e/Bohr3. The process of spin hole relaxation within the impurity states is indicated by the arrow in panel a. (Reprinted with permission from Reference . Copyright 2017 American Physical Society)
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The e–h recombination time in different doped TiO2. The fitting exponential correlation is shown in dashed lines. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Frozen phonon NAMD results for time evolutions of the energy states near VBM and CBM and the averaged time‐dependent e–h energy relaxation for CrN‐ and VN‐codoped TiO2. (a, b) IPM for CrN‐doped TiO2. (c, d) One bulk mode for CrN‐doped TiO2. (e, f) IPM for VN‐doped TiO2. The energy reference is the average VBM energy and the color map indicates hole localization. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Time evolutions of the state energies near VBM and CBM for undoped, CrN‐ and VN‐codoped TiO2 (a–c) and their FT spectra (d–f) at 300 K. The spatial localization of phonon modes (g–i). The inset in (h) shows by green color the atoms that vibrate coherently with CrN. In (h) and (i) the green arrows indicate the major IPMs in CrN‐ and VN‐doped TiO2. A typical TiO2 bulk phonon mode in CrN‐doped TiO2 is marked by a purple arrow. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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The electronic structures and the time‐dependent electron–hole (e–h) dynamics in undoped, CrN‐ and VN‐doped TiO2. (a–c) The total and partial density of states. (d–f) The averaged time‐dependent e–h energy relaxation at 300 K. The color strip indicates the e–h distribution on different energy states and the dashed line represents the averaged e–h energy. The energy reference is the average VBM energy. (g–i) The averaged NAC elements in undoped, CrN‐ and VN‐doped TiO2 at 300 K. The inset in (b) shows the spatial distribution of the excess charge induced by CrN codoping, in which the Ti, O, Cr and N atoms are marked by large light blue, small red, large deep blue and small purple balls, respectively. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Nonadiabatic molecular dynamics results of MoSe2/WSe2 and MoS2/WS2 at 300 K, respectively. (a, d) Time‐dependent electron spatial localization. (b, e) Time‐dependent electron energy change. (c, f) Schematics of the electron relaxation route in the momentum space. (Reprinted with permission from Reference . Copyright 2018 American Physical Society)
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Time evolutions of the energy states near CBM (a–d) and FT spectra of the selected states (e–h) of MoX2/WX2 (X = S, Se) heterostructures at 300 and 100 K. The energy reference in (a–d) is the averaged energy of WX2@K_VB, and the color map shows the orbital localization. (Reprinted with permission from Reference . Copyright 2018 American Physical Society)
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Band structures and orbital spatial distributions of (a) MoS2/WS2 and (b) MoSe2/WSe2 heterostructures. The energy of WX2@K_VB is set to zero. The color strip indicates the localization of the states. The photoexcitation and the initial electron distribution are indicated in (a, b). The schematic of electron transfer in TMD heterostructure is shown in (c). (Reprinted with permission from Reference . Copyright 2018 American Physical Society)
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(a) Temperature dependence of KQ and KC. The ratio KC/KQ is also plotted. (b, c) Time‐dependent spatial hole localization at different temperatures (300, 250 and 200 K for C7 stacking at Γ point (b) and 300, 250, 200 and 180 K for T stacking at K point (c)) (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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Time evolutions of the energy states near VBM (a–d) and their FT spectra (e–h) for C7 and T stackings at 300 and 100 K. The energy reference in (a–d) is the average VBM energy and the color map shows the hole localization. The triangle, square and circle in (a–d) indicate the momentum of different energy states. (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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Time‐dependent hole energy change at the K and Γ points for the C7 and T stacking at 300 K [K point (a, b), Γ point (c, d)] and 100 K [K point (e, f), Γ point (g, h)]. The color strips indicate the hole distribution on different energy states and the dashed line represents the averaged hole energy. The energy reference is the average VBM energy. (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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Time‐dependent spatial hole localization at the K and Γ points for the C7 and T stackings at 300 K (K point (a, b), Γ point (c, d)) and 100 K [K point (e, f), Γ point (g, h)]. The major hole relaxation routes in momentum space are schematically shown in the insets. The AD and NA contributions to the hole dynamics are shown, where their sum indicates the decrease of hole localization within the MoS2 layer. (Reprinted with permission from Reference . Copyright 2017 American Chemical Society)
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(a) The time evolutions of the energy states of C60/MoS2 in NAMD simulations. The color strip indicates the state distribution on C60 and MoS2. The s‐SAMO state is marked using thicker line. (b) Time‐dependent electron transfer from s‐SAMO of C60 to MoS2 and the NA/AD contribution. (c) Snapshots of the orbital distribution in the NAMD simulation at 0, 100, 200 and 300 fs. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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The time‐dependent state population evolutions for LUMO to s‐SAMO where the hot electron is initially excited at (a) s‐SAMO or (b) or LUMO+3, respectively. (c) The time‐dependent averaged energy evolution for hot electron initiated from a state 0.5 eV above the SAMO. The color strip indicates the hot electron distribution on different energy states and the dashed line represents the averaged hot electron energy. (d) The NACs among different states from LUMO+2 to LUMO+4 (due to the degeneracy, LUMO+2, +3 and +4 are framed by red box). (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Charge transfer dynamics of solvated electron of 1ML H2O adsorbed on p‐type of LAO/STO with 1–3 ucs LAO. (a–c) Time‐dependent energy state evolution. The black (red) lines represent the energy levels contributed by LAO/STO (SEBM of H2O). (d–f) Time‐dependent electron localization projected onto the H2O layer and p‐type LAO/STO substrate. The total electron transfer (labeled as ET with black line) and the AD and NA contributions (blue and red lines) to the charge transfer are also plotted. (g–i) Time‐dependent electron energy change. The energy of VBM is set as reference in panel (a–c) and (g–i). (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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(a) Side and top views of 1ML H2O adsorbed on p‐type LAO/STO heterostructure. (b) Spatial orbital distribution of the solvated state in H2O layer. (c) Layer‐resolved density of state for every LAO, STO and H2O layer, represented by green, blue and red shades. The dash line represents the position of Ef. (d) Band structure of 1ML H2O adsorbed on p‐type LAO/STO. The solvated electron band is marked by red triangles. (e) The dependence of solvated electron band minimum (SEBM) and conduction band minimum (CBM) energies on LAO thickness. The energy of VBM is set as the reference in (c–e). The results in (a–d) correspond to 1ML H2O adsorbed on p‐type LAO/STO with 9 ucs LAO. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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(a) Averaged forward hole transfer from TiO2 bulk states to adsorbed molecules at 100 K. (b) Averaged reverse hole transfer from adsorbed molecules to TiO2 bulk states at 100 K. (c) Time dependence of energy relaxation of photogenerated holes with different initial energies at 100 K. (Reprinted with permission from Reference . Copyright 2016 American Chemical Society)
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