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.

Photochemical spin-state control of binding configuration for tailoring organic color center emission in carbon nanotubes.

Incorporating fluorescent quantum defects in the sidewalls of semiconducting single-wall carbon nanotubes (SWCNTs) through chemical reaction is an emerging route to predictably modify nanotube electronic structures and develop advanced photonic functionality. Applications such as room-temperature single-photon emission and high-contrast bio-imaging have been advanced through aryl-functionalized SWCNTs, in which the binding configurations of the aryl group define the energies of the emitting states. However, the chemistry of binding with atomic precision at the single-bond level and tunable control over the binding configurations are yet to be achieved. Here, we explore recently reported photosynthetic protocol and find that it can control chemical binding configurations of quantum defects, which are often referred to as organic color centers, through the spin multiplicity of photoexcited intermediates. Specifically, photoexcited aromatics react with SWCNT sidewalls to undergo a singlet-state pathway in the presence of dissolved oxygen, leading to ortho binding configurations of the aryl group on the nanotube. In contrast, the oxygen-free photoreaction activates previously inaccessible para configurations through a triplet-state mechanism. These experimental results are corroborated by first principles simulations. Such spin-selective photochemistry diversifies SWCNT emission tunability by controlling the morphology of the emitting sites.

Impact of Graphene Quantum Dot Edge Morphologies on Their Optical Properties.

The optoelectronic properties of functionalized graphene quantum dots (GQDs) have been explored by simulating electronic structure of three different shapes of GQDs containing exclusively zigzag or armchair edges in both pristine and functionalized forms. Absorption spectra and transition densities for the low-lying excited states are evaluated by using time-dependent density functional theory and compared for different functionalization species. The functionalization position dictates the optical properties of square GQDs, where isomers with CH2 in the intermediate positions (excluding corner and center positions) have higher electronic transition energies and exciton delocalization than other isomers. Rhombic GQDs with all armchair edges exhibit high steric flexibility, and their complete passivation results in the largest structural deformation from planarity and strongest red-shifts. A steady red-shift in the absorption energy is observed following the order F, CH3, Cl, and Br substitutions. This suggests that the steric effects due to large van der Waals radii overcome electronegative effects.

Coupling between Emissive Defects on Carbon Nanotubes: Modeling Insights.

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) with organic molecules results in red-shifted emissive states associated with sp3-defects in the tube lattice, which facilitate their improved optical functionality, including single-photon emission. The energy of the defect-based electronic excitations (excitons) depends on the molecular adducts, the configuration of the defect, and concentration of defects. Here we model the interactions between two sp3-defects placed at various distances in the (6,5) SWCNT using time-dependent density functional theory. Calculations reveal that these interactions conform to the effective model of J-aggregates for well-spaced defects (>2 nm), leading to a red-shifted and optically allowed (bright) lowest energy exciton. H-aggregate behavior is not observed for any defect orientations, which is beneficial for emission. The splitting between the lowest energy bright and optically forbidden (dark) excitons and the pristine excitonic band are controlled by the single-defect configurations and their axial separation. These findings enable a synthetic design strategy for SWCNTs with tunable near-infrared emission.

Predicting phosphorescence energies and inferring wavefunction localization with machine learning.

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab initio datasets of singlet-triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet-triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet-triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab initio spin density of the singlet-triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model.

Photoluminescence Dynamics Defined by Exciton Trapping Potential of Coupled Defect States in DNA-Functionalized Carbon Nanotubes.

Chemical reactions between semiconducting single-wall carbon nanotubes (SWCNTs) and single-stranded DNA (ssDNA) achieve spatially patterned covalent functionalization sites and create coupled fluorescent quantum defects on the nanotube surface, tailoring SWCNT photophysics for applications such as single-photon emitters in quantum information technologies. The evaluation of relaxation dynamics of photoluminescence (PL) from those coupled quantum defects is essential for understanding the nanotube electronic structure and beneficial to the design of quantum light emitters. Here, we measured the PL decay for ssDNA-functionalized SWCNTs as a function of the guanine content of the ssDNA oligo that dictates the red-shifting of their PL emission peaks relative to the band-edge exciton. We then correlate the observed dependence of PL decay dynamics on energy red-shifts to the exciton potential energy landscape, which is modeled using first-principles approaches based upon the morphology of ssDNA-altered SWCNTs obtained by atomic force microscopy (AFM) imaging. Our simulations illustrate that the multiple guanine defects introduced within a single ssDNA strand strongly interact to create a deep exciton trapping well, acting as a single hybrid trap. The emission decay from the distinctive trapping potential landscape is found to be biexponential for ssDNA-modified SWCNTs. We attributed the fast time component of the biexponential PL decay to the redistribution of exciton population among the lowest energy bright states and a manifold of dark states emerging from the coupling of multiple guanine defects. The long lifetime component in the biexponential decay, on the other hand, is attributed to the redistribution of exciton population among different exciton trapping sites that arise from the binding of multiple ssDNA strands along the nanotube axis. AFM measurements indicate that those trapping sites are separated on average by ∼8 nm along the nanotube axis.

Controlling Defect-State Photophysics in Covalently Functionalized Single-Walled Carbon Nanotubes.

ConspectusSingle-walled carbon nanotubes (SWCNTs) show promise as light sources for modern fiber optical communications due to their emission wavelengths tunable via chirality and diameter dependency. However, the emission quantum yields are relatively low owing to the existence of low-lying dark electronic states and fast excitonic diffusion leading to carrier quenching at defects. Covalent functionalization of SWCNTs addresses this problem by brightening their infrared emission. Namely, introduction of sp3-hybridized defects makes the lowest energy transitions optically active for some defect geometries and enables further control of their optical properties. Such functionalized SWCNTs are currently the only material exhibiting room-temperature single photon emission at telecom relevant infrared wavelengths. While this fluorescence is strong and has the right wavelength, functionalization introduces a variety of emission peaks resulting in spectrally broad inhomogeneous photoluminescence that prohibits the use of SWCNTs in practical applications. Consequently, there is a strong need to control the emission diversity in order to render these materials useful for applications. Recent experimental and computational work has attributed the emissive diversity to the presence of multiple localized defect geometries each resulting in distinct emission energy. This Account outlines methods by which the morphology of the defect in functionalized SWCNTs can be controlled to reduce emissive diversity and to tune the fluorescence wavelengths. The chirality-dependent trends of emission energies with respect to individual defect morphologies are explored. It is demonstrated that defect geometries originating from functionalization of SWCNT carbon atoms along bonds with strong π-orbital mismatch are favorable. Furthermore, the effect of controlling the defect itself through use of different chemical groups is also discussed. Such tunability is enabled due to the formation of specific defect geometries in close proximity to other existing defects. This takes advantage of the changes in π-orbital mismatch enforced by existing defects and the resulting changes in reactivities toward formation of specific defect morphologies. Furthermore, the trends in emissive energies are highly dependent on the value of mod(n-m,3) for an (n,m) tube chirality. These powerful concepts allow for a targeted formation of defects that emit at desired energies based on SWCNT single chirality enriched samples. Finally, the impact of functionalization with specific types of defects that enforce certain defect geometries due to steric constraints in bond lengths and angles to the SWCNT are discussed. We further relate to a similar effect that is present in systems where high density of surface defects is formed due to high reactant concentration. The outlined strategies suggested by simulations are instrumental in guiding experimental efforts toward the generation of functionalized SWCNTs with tunable emission energies.

Hidden Fine Structure of Quantum Defects Revealed by Single Carbon Nanotube Magneto-Photoluminescence.

Organic color-center quantum defects in semiconducting carbon nanotube hosts are rapidly emerging as promising candidates for solid-state quantum information technologies. However, it is unclear whether these defect color-centers could support the spin or pseudospin-dependent excitonic fine structure required for spin manipulation and readout. Here we conducted magneto-photoluminescence spectroscopy on individual organic color-centers and observed the emergence of fine structure states under an 8.5 T magnetic field applied parallel to the nanotube axis. One to five fine structure states emerge depending on the chirality of the nanotube host, nature of chemical functional group, and chemical binding configuration, presenting an exciting opportunity toward developing chemical control of magnetic brightening. We attribute these hidden excitonic fine structure states to field-induced mixing of singlet excitons trapped at sp3 defects and delocalized band-edge triplet excitons. These findings provide opportunities for using organic color-centers for spintronics, spin-based quantum computing, and quantum sensing.

Mod(n-m,3) Dependence of Defect-State Emission Bands in Aryl-Functionalized Carbon Nanotubes.

Molecularly functionalized single-walled carbon nanotubes (SWCNTs) are potentially useful for fiber optical applications due to their room temperature single-photon emission capacity at telecommunication wavelengths. Several distinct defect geometries are generated upon covalent functionalization. While it has been shown that the defect geometry controls electron localization around the defect site, thereby changing the electronic structure and generating new optically bright red-shifted emission bands, the reasons for such localization remain unexplained. Our joint experimental and computational studies of functionalized SWCNTs with various chiralities show that the value of mod(n-m,3) in an (n,m) chiral nanotube plays a key role in the relative ordering of defect-dependent emission energies. This dependence is linked to the complex nodal characteristics of electronic wave function extending along specific bonds in the tube, which justifies the defect-geometry dependent exciton localization. This insight helps to uncover the essential structural motifs allowing tuning the redshifts of emission energies in functionalized SWCNTs.

Intrinsic limits of defect-state photoluminescence dynamics in functionalized carbon nanotubes.

Defect states introduced to single wall carbon nanotubes (SWCNTs) by covalent functionalization give rise to novel photophysics and are showing promise as sources of room-temperature quantum emission of interest for quantum information technologies. Evaluation of their ultimate potential for such needs requires a knowledge of intrinsic dynamic and coherence behaviors. Here we probe population relaxation and dephasing time (T1 and T2, respectively) of defect states following deposition of functionalized SWCNTs on polystyrene substrates that are subjected to an isopropanol rinse to remove surfactant. Low-temperature (4 K) photo-luminescence linewidths (∼100 µeV) following surfactant removal are a factor of ten narrower than those for unrinsed SWCNTs. Measured recombination lifetimes, on the order of 1.5 ns, compare well with those estimated from DFT calculations, indicating that the intrinsic radiatively-limited lifetime is approached following this sample treatment. Dephasing times evaluated directly through an interferometric approach compare closely to those established by photoluminescence linewidths. Dephasing times as high as 12 ps are found; a factor of up to 6 times greater than those evaluated for band-edge exciton states. Such enhancement of dephasing and photoluminescence lifetime behavior is a direct consequence of exciton localization at the SWCNT defect sites.

NEXMD Modeling of Photoisomerization Dynamics of 4-Styrylquinoline.

Isomerization of molecular systems is ubiquitous in chemistry and biology, and is also important for many applications. Atomistic simulations can help determine the tunable parameters influencing this process. In this paper, we use the Nonadiabatic EXcited state Molecular Dynamics (NEXMD) software to study the photoisomerization of a representative molecule, 4-styrylquinoline (SQ). trans-SQ transforms into dihydrobenzophenanthridine (DHBP) upon irradiation with laser light, with the cis conformer acting as an intermediate. We study how varying three different external stimuli (i.e., apolar versus polar solvent, low versus high photoexcitation energy, and vacuum versus a constant temperature thermostat) affects the trans-to- cis photoisomerization of SQ. Our results show that polarization effects due to implicit solvation and the thermostat play a crucial role in the isomerization process, whereas photoexcitation energy plays a lesser role on the outcome and efficiency. We also show that NEXMD captures the correct energy profile between the ground and first singlet excited state, showing that there are two distinct reaction pathways to the final stable product that vary by the number of photons absorbed, in agreement with experiment. Ultimately, NEXMD proves to be an effective tool for investigating excited state single molecule dynamics subject to various environments and initial conditions.

Narrow-band single-photon emission through selective aryl functionalization of zigzag carbon nanotubes.

The introduction of sp3 defects into single-walled carbon nanotubes through covalent functionalization can generate new light-emitting states and thus dramatically expand their optical functionality. This may open up routes to enhanced imaging, photon upconversion, and room-temperature single-photon emission at telecom wavelengths. However, a significant challenge in harnessing this potential is that the nominally simple reaction chemistry of nanotube functionalization introduces a broad diversity of emitting states. Precisely defining a narrow band of emission energies necessitates constraining these states, which requires extreme selectivity in molecular binding configuration on the nanotube surface. We show here that such selectivity can be obtained through aryl functionalization of so-called 'zigzag' nanotube structures to achieve a threefold narrowing in emission bandwidth. Accompanying density functional theory modelling reveals that, because of the associated structural symmetry, the defect states become degenerate, thus limiting emission energies to a single narrow band. We show that this behaviour can only result from a predominant selectivity for ortho binding configurations of the aryl groups on the nanotube lattice.

Solvent- and Wavelength-Dependent Photoluminescence Relaxation Dynamics of Carbon Nanotube sp3 Defect States.

Photoluminescent sp3 defect states introduced to single wall carbon nanotubes (SWCNTs) through low-level covalent functionalization create new photophysical behaviors and functionality as a result of defect sites acting as exciton traps. Evaluation of relaxation dynamics in varying dielectric environments can aid in advancing a more complete description of defect-state relaxation pathways and electronic structure. Here, we exploit helical wrapping polymers as a route to suspending (6,5) SWCNTs covalently functionalized with 4-methoxybenzene in solvent systems including H2O, D2O, methanol, dimethylformamide, tetrahydrofuran, and toluene, spanning a range of dielectric constants from 80 to 3. Defect-state photoluminescence decays were measured as a function of emission wavelength and solvent environment. Emission decays are biexponential, with short lifetime components on the order of 65 ps and long components ranging from around 100 to 350 ps. Both short and long decay components increase as emission wavelength increases, while only the long lifetime component shows a solvent dependence. We demonstrate that the wavelength dependence is a consequence of thermal detrapping of defect-state excitons to produce mobile E11 excitons, providing an important mechanism for loss of defect-state population. Deeper trap states (i.e., those emitting at longer wavelengths) result in a decreased rate for thermal loss. The solvent-independent behavior of the short lifetime component is consistent with its assignment as the characteristic time for redistribution of exciton population between bright and dark defect states. The solvent dependence of the long lifetime component is shown to be consistent with relaxation via an electronic to vibrational energy transfer mechanism, in which energy is resonantly lost to solvent vibrations in a complementary mechanism to multiphonon decay processes.

Photoexcited Nonadiabatic Dynamics of Solvated Push-Pull π-Conjugated Oligomers with the NEXMD Software.

Solvation can be modeled implicitly by embedding the solute in a dielectric cavity. This approach models the induced surface charge density at the solute-solvent boundary, giving rise to extra Coulombic interactions. Herein, the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) software was used to model the photoexcited nonradiative relaxation dynamics in a set of substituted donor-acceptor oligo( p-phenylenevinylene) (PPVO) derivatives in the presence of implicit solvent. Several properties of interest including optical spectra, excited state lifetimes, exciton localization, excited state dipole moments, and structural relaxation are calculated to elucidate dependence of functionalization and solvent polarity on photoinduced nonadiabatic dynamics. Results show that solvation generally affects all these properties, where the magnitude of these effects vary from one system to another depending on donor-acceptor substituents and molecular polarizability. We conclude that implicit solvation can be directly incorporated into nonadiabatic simulations within the NEXMD framework with little computational overhead and that it qualitatively reproduces solvent-dependent effects observed in solution-based spectroscopic experiments.

Correction Scheme for Comparison of Computed and Experimental Optical Transition Energies in Functionalized Single-Walled Carbon Nanotubes.

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) introduces red-shifted emission features in the near-infrared spectral range due to exciton localization around the defect site. Such chemical modifications increase their potential use as near-infrared emitters and single-photon sources in telecommunications applications. Density functional theory (DFT) studies using finite-length tube models have been used to calculate their optical transition energies. Predicted energies are typically blue-shifted compared to experiment due to methodology errors including imprecise self-interaction corrections in the density functional and finite-size basis sets. Furthermore, artificial quantum confinement in finite models cannot be corrected by a constant-energy shift since they depend on the degree of exciton localization. Herein, we present a method that corrects the emission energies predicted by time-dependent DFT. Confinement and methodology errors are separately estimated using experimental data for unmodified tubes. Corrected emission energies are in remarkable agreement with experiment, suggesting the value of this straightforward method toward predicting and interpreting the optical features of functionalized SWCNTs.

Low-Temperature Single Carbon Nanotube Spectroscopy of sp3 Quantum Defects.

Aiming to unravel the relationship between chemical configuration and electronic structure of sp3 defects of aryl-functionalized (6,5) single-walled carbon nanotubes (SWCNTs), we perform low-temperature single nanotube photoluminescence (PL) spectroscopy studies and correlate our observations with quantum chemistry simulations. We observe sharp emission peaks from individual defect sites that are spread over an extremely broad, 1000-1350 nm, spectral range. Our simulations allow us to attribute this spectral diversity to the occurrence of six chemically and energetically distinct defect states resulting from topological variation in the chemical binding configuration of the monovalent aryl groups. Both PL emission efficiency and spectral line width of the defect states are strongly influenced by the local dielectric environment. Wrapping the SWCNT with a polyfluorene polymer provides the best isolation from the environment and yields the brightest emission with near-resolution limited spectral line width of 270 µeV, as well as spectrally resolved emission wings associated with localized acoustic phonons. Pump-dependent studies further revealed that the defect states are capable of emitting single, sharp, isolated PL peaks over 3 orders of magnitude increase in pump power, a key characteristic of two-level systems and an important prerequisite for single-photon emission with high purity. These findings point to the tremendous potential of sp3 defects in development of room temperature quantum light sources capable of operating at telecommunication wavelengths as the emission of the defect states can readily be extended to this range via use of larger diameter SWCNTs.