Electron-Phonon Scattering Is Much Weaker in Carbon Nanotubes than in Graphene Nanoribbons

The sp3 Defect Decreases Charge Carrier Lifetime in (8,3) Single-Walled Carbon Nanotubes

A recent experimental approach introduces sp3 defects into single-walled carbon nanotubes (SWNTs) through controlled functionalization with guanine, resulting in a decrease in charge carrier lifetime. However, the physical mechanism behind this phenomenon remains unclear. We employ nonadiabatic molecular dynamics to systematically model the nonradiative recombination process of electron-hole pairs in SWNTs with sp3 defects generated by a guanine molecule. We demonstrate that the introduction of sp3 defects creates an overlapping channel between the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO), significantly enhancing the nonadiabatic (NA) coupling and leading to a 4.7-fold acceleration in charge carrier recombination compared to defect-free SWNTs. The charge carrier recombination slows significantly at a lower temperature (50 K) due to the weakening of the NA coupling. Our results rationalize the accelerated recombination of charge carriers in SWNTs with sp3 defects in experiments and contribute to a deeper understanding of the carrier dynamics in SWNTs.

Mechanistic insights into photoinduced energy and charge transfer dynamics between magnesium-centered tetrapyrroles and carbon nanotubes

Functionalizing single-walled carbon nanotubes (SWNTs) with light-harvesting molecules is a facile way to construct donor-acceptor nanoarchitectures with intriguing optoelectronic properties. Magnesium-centered bacteriochlorin (MgBC), chlorin (MgC), and porphyrin (MgP) are a series of tetrapyrrole macrocycles comprising a central metal and four coordinated aromatic or antiaromatic five-membered rings linked by methine units, which show excellent visible light absorption. To delineate the effects of the aromaticity of coordinated rings on the optoelectronic properties of the nanocomposites, the photoinduced energy and charge transfer dynamics between Mg-centered tetrapyrroles and SWNTs are explored. The results show that excited energy transfer (EET) can occur within MgP@SWNT ascribed to the stabilization of the highest occupied molecular orbital (HOMO) in MgP with the increase of aromatic coordinated rings, while only electron transfer can take place in MgBC@SWNT and MgC@SWNT. Non-adiabatic dynamics simulations demonstrate that electron and hole transfer from MgP to SWNT is asynchronous. The electron transfer is ultrafast with a timescale of ca. 50 fs. By contrast, the hole transfer is significantly suppressed, although it can be accelerated to some extent when using a lower excitation energy of 2.2 eV as opposed to 3.1 eV. Further analysis reveals that the large energy gaps between charge-donor and charge-acceptor states play a crucial role in regulating photoexcited state relaxation dynamics. Our theoretical insights elucidate the structure-functionality interrelations between Mg-centered tetrapyrroles and SWNTs and provide a comprehensive understanding of the underlying charge transfer mechanism within MgP@SWNT nanocomposites, which paves the way for the forthcoming development of SWNT-based photo-related functional materials with targeted applications.

On-the-Fly Nonadiabatic Dynamics Simulations of Single-Walled Carbon Nanotubes with Covalent Defects

Single-walled carbon nanotubes (SWCNTs) with covalent surface defects have been explored recently due to their promise for use in single-photon telecommunication emission and in spintronic applications. The all-atom dynamic evolution of electrostatically bound excitons (the primary electronic excitations) in these systems has only been loosely explored from a theoretical perspective due to the size limitations of these large systems (>500 atoms). In this work, we present computational modeling of nonradiative relaxation in a variety of SWCNT chiralities with single-defect functionalizations. Our excited-state dynamics modeling uses a trajectory surface hopping algorithm accounting for excitonic effects with a configuration interaction approach. We find a strong chirality and defect-composition dependence on the population relaxation (varying over 50-500 fs) between the primary nanotube band gap excitation E₁₁ and the defect-associated, single-photon-emitting E₁₁* state. These simulations give direct insight into the relaxation between the band-edge states and the localized excitonic state, in competition with dynamic trapping/detrapping processes observed in experiment. Engineering fast population decay into the quasi-two-level subsystem with weak coupling to higher-energy states increases the effectiveness and controllability of these quantum light emitters.

Non-negligible roles of charge transfer excitons in ultrafast excitation energy transfer dynamics of a double-walled carbon nanotube

Herein, we employed a developed linear response time dependent density functional theory-based nonadiabatic dynamics simulation method that explicitly takes into account the excitonic effects to investigate photoinduced excitation energy transfer dynamics of a double-walled carbon nanotube (CNT) model with different excitation energies. The E₁₁ excitation of the outer CNT will generate a local excitation (LE) |out*〉 exciton due to its low energy, which does not induce any charge separation. In contrast, the E₁₁ excitation of the inner CNT can generate four kinds of excitons with the LE exciton |in*〉 dominates. In the 500-fs dynamics simulation, the LE exciton |in*〉 and charge transfer (CT) excitons |out^-in⁺〉 and |out⁺in^-〉 are all gradually converted to the |out*〉 exciton, corresponding to a photoinduced excitation energy transfer, which is consistent with experimental studies. Finally, when the excitation energy is close to the E₂₂ state of the outer CNT (∼1.05 eV), a mixed population of different excitons, with the |out*〉 exciton dominated, is generated. Then, photoinduced energy transfer from the outer to inner CNTs occurs in the first 50 fs, which is followed by an inner to outer excitation energy transfer that is completed in 400 fs. The present work not only sheds important light on the mechanistic details of wavelength-dependent excitation energy transfer of a double-walled CNT model but also demonstrates the roles and importance of CT excitons in photoinduced excitation energy transfer. It also emphasized that explicitly including the excitonic effects in electronic structure calculations and nonadiabatic dynamics simulations is significant for correct understanding/rational design of optoelectronic properties of periodically extended systems.

Exceptionally clean single-electron transistors from solutions of molecular graphene nanoribbons

Only single-electron transistors with a certain level of cleanliness, where all states can be properly accessed, can be used for quantum experiments. To reveal their exceptional properties, carbon nanomaterials need to be stripped down to a single element: graphene has been exfoliated into a single sheet, and carbon nanotubes can reveal their vibrational, spin and quantum coherence properties only after being suspended across trenches1-3. Molecular graphene nanoribbons4-6 now provide carbon nanostructures with single-atom precision but suffer from poor solubility, similar to carbon nanotubes. Here we demonstrate the massive enhancement of the solubility of graphene nanoribbons by edge functionalization, to yield ultra-clean transport devices with sharp single-electron features. Strong electron-vibron coupling leads to a prominent Franck-Condon blockade, and the atomic definition of the edges allows identifying the associated transverse bending mode. These results demonstrate how molecular graphene can yield exceptionally clean electronic devices directly from solution. The sharpness of the electronic features opens a path to the exploitation of spin and vibrational properties in atomically precise graphene nanostructures.

How Good Is the Vibronic Hamiltonian Repetition Approach for Long-Time Nonadiabatic Molecular Dynamics?

Multiple applied studies of slow nonadiabatic processes in nanoscale and condensed matter systems have adopted the "repetition" approximation in which long trajectories for such simulations are obtained by concatenating shorter trajectories, directly available from ab initio calculations, many times. Here, we comprehensively assess this approximation using model Hamiltonians with parameters covering a wide range of regimes. We find that state transition time scales may strongly depend on the length of the repeated data, although the convergence is not monotonic and may be slow. The repetition approach may under- or overestimate the time scales by a factor of ≤7-8, does not directly depend on the dispersion of energy gap and nonadiabatic coupling (NAC) frequencies, but may depend on the magnitude of the NACs. We suggest that the repetition-based nonadiabatic dynamics may be inaccurate in simulations with very small NACs, where intrinsic transition times are on the order of ≥100 ps.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Inverse Fast Fourier Transform

Nonadiabatic (NA) molecular dynamics (MD) allows one to investigate far-from-equilibrium processes in nanoscale and molecular materials at the atomistic level and in the time domain, mimicking time-resolved spectroscopic experiments. Ab initio NAMD is limited to about 100 atoms and a few picoseconds, due to computational cost of excitation energies and NA couplings. We develop a straightforward methodology that can extend ab initio quality NAMD to nanoseconds and thousands of atoms. The ab initio NAMD Hamiltonian is sampled and interpolated along a trajectory using a Fourier transform, and then, it is used to perform NAMD with known algorithms. The methodology relies on the classical path approximation, which holds for many materials and processes. To achieve a complete ab initio quality description, the trajectory can be obtained using an ab initio trained machine learning force field. The method is demonstrated with charge carrier trapping and relaxation in hybrid organic-inorganic and all-inorganic metal halide perovskites that exhibit complex dynamics and are actively studied for optoelectronic applications.

Interfacial photoinduced carrier dynamics tuned by polymerization of coronene molecules encapsulated in carbon nanotubes: bridging type-I and type-II heterojunctions

Carbon nanomaterials play important roles in modern scientific research. Integrating different carbon-based building blocks into nano-hybrid architectures not only takes full advantage of each component, but also brings in novel interfacial properties. Herein, we have employed density functional theory (DFT) calculations to investigate the effects of polymerization degree of coronene molecules encapsulated in single-walled carbon nanotubes (SWNTs) (19,0) on their interfacial properties. The present results reveal that the interfacial properties of the formed heterojunctions are remarkably regulated by the polymerization degree. For example, monomer- and dimer-encapsulated SWNTs are type-I heterojunctions in which interfacial excitation energy transfer is preferred, whereas interfacial charge carrier transfer is favorable in trimer- and polymer-encapsulated SWNTs because they are type-II heterojunctions. On the other hand, we have employed the time-domain nonadiabatic dynamics simulation approach to explore the interfacial carrier dynamics in type-II polymer-encapsulated SWNT heterojunctions. It is found that the electron and hole transfer processes are asymmetric and occur in opposite directions and at different rates. The former takes place from polymers to SWNTs in an ultrafast way (ca. 370 fs), whereas the latter occurs slowly from SWNTs to polymers (ca. 24 ps). A closer analysis uncovers the fact that the different carrier transfer rates mainly originate from the different densities of the acceptor states, energy differences and inter-state couplings between the donor and acceptor states. Finally, the present work demonstrates that the polymerization degree could act as a new regulating strategy to tune the interfacial properties of molecule-encapsulated SWNT heterojunctions.

Accurate Computation of Nonadiabatic Coupling with Projector Augmented-Wave Pseudopotentials

Synergy of nonadiabatic molecular dynamics with real-time time-dependent density functional theory has led to significant progress in modeling excited-state dynamics in nanoscale and condensed matter systems over the past decade. Nonadiabatic coupling (NAC) is the central quantity in such simulations, and its accurate and efficient evaluation is an enduring challenge in time-dependent Kohn-Sham theory, particularly in conjunction with planewave basis sets and projector augmented-wave (PAW) pseudopotentials because of the complexity of the PAW "all-electron" wave function. We report a method for rigorous evaluation of the NAC with PAW wave functions and demonstrate an efficient approximation to the rigorous NAC that gives comparable accuracy. As a validation, we intensely examine the NAC matrix elements calculated using both pseudo- and all-electron wave functions under the PAW formalism in six representative systems. The approximate NAC obtained with pseudowave functions is close to the exact all-electron NAC, with the largest deviations observed when subshell d-electrons are involved in the transitions. The developed approach provides a rigorous and convenient methodology for the numerical computation of NAC in the Kohn-Sham theory framework.

Photoinduced electron transfer from carbon nanotubes to fullerenes: C60versus C70

Hybrid carbon materials are found to exhibit novel optoelectronic properties at their interfaces, but the related interfacial carrier dynamics is rarely explored theoretically. In this contribution, we have employed density functional theory (DFT) and DFT-based nonadiabatic dynamics methods to explore photoinduced interfacial electron transfer processes at interfaces between a single-walled carbon nanotube with chiral index (6,5) and C60 or C70 (C60@CNT65 and C70@CNT65). We have found that with low E11 excitation, electron transfer takes place from CNT65 to C60 and C70 in both heterojunctions. This process is ultrafast and completed within about 200 fs, which is consistent with recent experiments. Differently, high E22 excitation does not induce electron injection to C60 in C60@CNT65; instead, "hot" electrons produced within CNT65 will be trapped in its higher conduction band for a while because of slow inter-band relaxation. By contrast, in C70@CNT65, high E22 excitation still can lead to ultrafast electron transfer to C70, but only a comparable amount of electrons are transferred (ca. 30%). Interestingly, electrons either remaining on CNT65 or transferred to C70 are trapped in the higher conduction band for a while, similarly, due to slow inter-band relaxation. The present results could be useful to guide the design of excellent interfaces of mixed-dimensional hybrid carbon materials for various optoelectronic applications.

Long-Lived Hot Electron in a Metallic Particle for Plasmonics and Catalysis: Ab Initio Nonadiabatic Molecular Dynamics with Machine Learning

Multiple experiments provide evidence for photovoltaic, catalytic, optoelectronic, and plasmonic processes involving hot, i.e., high energy, electrons in nanoscale materials. However, the mechanisms of such processes remain elusive, because electrons rapidly lose energy by relaxation through dense manifolds of states. We demonstrate a long-lived hot electron state in a Pt nanocluster adsorbed on the MoS₂ substrate. For this purpose, we develop a simulation technique, combining classical molecular dynamics based on machine learning potentials with ab initio nonadiabatic molecular dynamics and real-time time-dependent density functional theory. Choosing Pt₂₀/MoS₂ as a prototypical system, we find frequent shifting of a top atom in the Pt particle occurring on a 50 ps time scale. The distortion breaks particle symmetry and creates unsaturated chemical bonds. The lifetime of the localized state associated with the broken bonds is enhanced by a factor of 3. Hot electrons aggregate near the shifted atom and form a catalytic reaction center. Our findings prove that distortion of even a single atom can have important implications for nanoscale catalysis and plasmonics and provide insights for utilizing machine learning potentials to accelerate ab initio investigations of excited state dynamics in condensed matter systems.

Experimental Observation of Strong Exciton Effects in Graphene Nanoribbons

Graphene nanoribbons (GNRs) with atomically precise width and edge structures are a promising class of nanomaterials for optoelectronics, thanks to their semiconducting nature and high mobility of charge carriers. Understanding the fundamental static optical properties and ultrafast dynamics of charge carrier generation in GNRs is essential for optoelectronic applications. Combining THz spectroscopy and theoretical calculations, we report a strong exciton effect with binding energy up to ∼700 meV in liquid-phase-dispersed GNRs with a width of 1.7 nm and an optical band gap of ∼1.6 eV, illustrating the intrinsically strong Coulomb interactions between photogenerated electrons and holes. By tracking the exciton dynamics, we reveal an ultrafast formation of excitons in GNRs with a long lifetime over 100 ps. Our results not only reveal fundamental aspects of excitons in GNRs (strong binding energy and ultrafast exciton formation etc.) but also highlight promising properties of GNRs for optoelectronic devices.

Control of Charge Carrier Dynamics in Plasmonic Au Films by TiOx Substrate Stoichiometry

Plasmonic excitations in noble metals have many fascinating properties and give rise to a broad range of applications. We demonstrate, using nonadiabatic molecular dynamics combined with time-domain density functional theory, that the chemical composition and stoichiometry of substrates can have a strong influence on charge dynamics. By changing oxygen content in TiO₂, including stoichiometric, oxygen rich, and oxygen poor phases, and Ti metal, one can alter lifetimes of charge carriers in Au by a factor of 5 and control the ratio of electron-to-hole relaxation rates by a factor of 10. Remarkably, a thin TiO_x substrate greatly alters charge carrier properties in much thicker Au films. Such large variations stem from the fact that the Ti and O atoms are much lighter than Au, and their vibrations are much faster at dissipating the energy. The control over a particular charge carrier and an energy range depends on the Au and TiO_x level alignment, and the interfacial interaction strength. These factors are easily influenced by the TiO_x stoichiometry. In particular, oxygen rich and poor TiO₂ can be used to control holes and electrons, respectively, while metallic Ti affects both charge carriers. The detailed atomistic analysis of the interfacial and electron-vibrational interactions generates the fundamental understanding of the properties of plasmonic materials needed to design photovoltaic, photocatalytic, optoelectronic, sensing, nanomedical, and other devices.