Influence of Encapsulated Water on Luminescence Energy, Linewidth

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Influence of Encapsulated Water on Luminescence Energy, Linewidth, and Lifetime of Carbon Nanotubes: Time-Domain Ab Initio Analysis Wei Li, Run Long, Zhufeng Hou, Jianfeng Tang, and Oleg V. Prezhdo J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02049 • Publication Date (Web): 03 Jul 2018 Downloaded from http://pubs.acs.org on July 4, 2018

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The Journal of Physical Chemistry Letters

Influence of Encapsulated Water on Luminescence Energy, Linewidth, and Lifetime of Carbon Nanotubes: Time-domain Ab Initio Analysis

Wei Li1,2*, Run Long3, Zhufeng Hou4, Jianfeng Tang1, Oleg V. Prezhdo5* 1

College of Science, Hunan Agricultural University, Changsha 410128, P. R. China

2

Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical

Chemistry, Jilin University, Changchun, 130023, P. R. China 3

College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry

of Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China 4

National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-

0047, Japan 5

Department of Chemistry, University of Southern California, Los Angeles, CA 90089,

United States

*Corresponding authors, email: [email protected] (W.L.); [email protected] (O.V.P.)

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract: In a broad range of applications carbon nanotubes (CNTs) are in direct contact with a condensed phase environment that perturbs CNT properties. Experiments show that water molecules encapsulated inside semiconducting CNTs reduce the electronic energy gap, enhance elastic and inelastic electron-phonon scattering, and shorten the excited state lifetime. We rationalize the observed effects at the atomistic level using real-time timedependent density functional theory combined with nonadiabatic molecular dynamics. Encapsulated water makes the nanotube more rigid, suppressing radial breathing modes, while enhancing and slightly shifting the optical G-mode. Water screens Coulomb interactions and shifts charge carrier energies and wavefunctions. The screening, together with distortion of CNT geometry and lifting of orbital degeneracy, produces a luminescence redshift. Enhanced elastic and inelastic electron-phonon scattering explains linewidth broadening and shortening of the excited state lifetime. The influence of water on the CNT properties is similar to that of defects; however, in contrast to defects, water creates no new phonon modes or electronic states in the CNTs. The atomistic understanding of the influence of the condensed phase environment on CNT optical, electronic and vibrational properties, and electron-vibrational dynamics guides design of novel CNT-based materials.

TOC GRAPHIC


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Single-wall carbon nanotubes (CNTs) find a variety of applications, for instance, in field effect transistors, and photovoltaic and photo-catalytic devices, due to their unique one-dimensional nature.1–5 Considerable efforts have been dedicated to elucidating the fundamental photophysical properties of CNTs, such as electronic energy levels6, bright and dark excitons7, single molecule photoluminescence (PL)8, types of phonon modes9, electron-phonon energy losses10, photo-induced energy and charge transfer11, etc. These properties can be extremely sensitive to the local environment, especially in single walled CNTs, in which all atoms are at the surface and in direct contact with the surrounding medium. The effects of inner content on the CNT properties are particularly interesting and challenging to study. Despite its hydrophobic nature, CNTs can encapsulate polar molecules, as demonstrated by many experiments,12,13 leading to intriguing devices and medical applications.14–16 CNT filling with water, observed both experimentally and theoretically,8,15,17–19 has significant effects on the CNT vibrational and electronic properties.20–23 Advances in experimental techniques have enhanced our understanding of the behavior of confined water molecules. Theoretical investigations range from phenomenological models that consider the surrounding medium as a dielectric continuum,24 to classical molecular dynamics (MD) simulations,18,25,26 to ab initio descriptions.27,28 Particularly challenging is atomistic modeling of a non-equilibrium response of CNTs to perturbation, such as light or voltage, involving coupling between electronic and vibrational degrees of freedom, because it involves state-of-the-art approaches that are not generally available in standard computer codes and require specialized expertise. Such approaches can connect theory to experiments in a very direct and detailed way.



Electrons and phonons are the main degrees of freedom available in CNTs, and electron-phonon interactions play key roles in most CNT applications. For example, they determine response times of conductance switches, induce loss of coherence in spintronics and quantum information processes, and constitute the main mechanism for the energy losses in photovoltaics.29–31 Elastic electron-phonon scattering determines homogeneous optical linewidths and causes quantum decoherence, while inelastic scattering dissipates electronic energy to heat. Experimentally, elastic scattering can be characterized by measuring absorption or emission linewidths,8 or by time-resolved photon-echo experiment32. Dissipation of electronic energy to heat due to inelastic interactions can be investigated by pump-probe experiments, for instance, by measuring PL decay.33 Previous investigations have shown that defects in CNTs create charge traps and local phonon modes that enhance electron-phonon scattering.10,30 Theoretical studies of the effects the encapsulated molecules have on the CNT electron-vibrational interactions are lacking, in part due to limited experimental data. Lounis and co-workers have reported single-molecule time-resolved PL spectroscopy of empty and water-filled CNTs, showing that water encapsulation redshifts the PL energy, broadens its linewidths and shortens the lifetime.8 The experimental data have been interpreted using phenomenological arguments. We aim to rationalize the experimental results at the atomistic level, using the state-of-the-art simulation techniques developed in our group.34– 37

This letter reports the first time-domain ab initio study of nonradiative electronphonon relaxation dynamics and phonon-induced pure-dephasing of the lowest energy electronic excitation of a chiral CNT in contact with a condensed phase environment.


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Focusing on the experimental data for pristine and water filled CNTs at ambient temperature, we provide an atomistic rationalization of the observed PL red-shift, linewidth broadening and lifetime shortening. The simulation shows that the encapsulated water significantly perturbs CNT geometric and electronic structure, and enhances elastic and inelastic electron-phonon scattering. These effects are achieved via dielectric screening and electrostatic interactions between encapsulated water and photogenerated charges in the CNT. We show that the influence of a condensed phase environment on CNT properties is similar to that of atomistic defects. At the same time, the environment can be regarded as a perturbation, while defects introduce new electronic states and phonon modes. The simulations are performed using a combination of real-time time dependent density functional theory (TDDFT) and nonadiabatic molecular dynamics (NAMD). The quantum/semi-classical decoherence induced surface hopping (DISH) approach to NAMD has been implemented within ab initio TDDFT.38 DISH belongs to the family of surface hopping (SH) methods.39,40 It treats electrons quantum mechanically and vibrations semi-classically by inclusion of decoherence effects that are particularly important in the condensed phase. In DISH, decoherence provides the physical mechanism of branching leading to quantum transitions. The classical path approximation (CPA) is applied to DISH, as described in refs34,35 The CPA creates great computational savings and is critical for studying systems involving hundreds of atoms at the ab initio level, and to achieve statistical convergence. A detailed description of the theoretical methodology can be found in.34,35,41,42



We focus on the semiconducting zigzag (10,0) CNT with a diameter of 0.78 nm, because it has a relatively small unit cell with 40 carbon atoms and was dominant during synthesization.8,43 We expand the unit cell of (10,0) CNT by three times to construct the supercell with 120 carbon atoms. Up to 15 water molecules are randomly placed inside the tube interior to model water filling. The geometry optimization, electronic structure calculation, and adiabatic MD are performed with the Vienna Ab initio Simulations Package (VASP).44,45 The Perdew-Burke-Ernzerhof (PBE) functional is used to account for the electron exchange and correlation energies.46 Additional calculations are performed with the HSE06 functional.47 The Kohn-Sham wavefunctions are expanded in a plane-wave basis with the energy cutoff of 400 eV to converge the total energy.48 A 15 Å vacuum layer is added in the direction perpendicular to tube axis to avoid tube-tube interactions. The Grimme's DFT-D2 approach is utilized for describing the van der Waals interactions between CNT and water molecules.49 A Γ-centered Monkhorst-Pack (1×1×45) k-point sampling is adopted. Following geometry optimization, repeated velocity rescaling is used to heat the system from 0 K to 300 K. A 4 ps microcanonical MD simulation is carried out with a 1 fs time step to generate the microcanonical trajectories. The 4 ps trajectory is sufficient to sample nuclear motions with frequencies above 10 cm-1. Note that the NA coupling responsible for the nonradiative relaxation is proportional to nuclear velocity, which increases with mode frequency. The first 1000 fs of this trajectory are used as initial conditions for NAMD. The DISH calculations use 100 stochastic realizations of surface hopping for each initial condition, generating ensemble averaging over 100,000 processes, which is possible due to application of the CPA approximation to DISH.34,35


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Figure 1 presents the optimized ground state structure of the (10,0) CNT filled with water molecules (parts a and b), and 2000 superimposed MD snapshots of the empty and filled CNTs sampled at 300 K (parts c and d). The images show that water molecules encapsulated inside the CNT form a hydrogen-bonded network containing rings and chains extended along the nanotube axis. The MD snapshots show that all CNT and water atoms fluctuate around their equilibrium positions, and that the hydrogen-bonded water network remains stable on a picosecond timescale. Interestingly, water filling enhances stretching vibrations of CNT carbon atoms, whereas carbon atoms motions in the radial direction are inhibited, as evidenced by the shapes of the superimposed images of the carbon atoms closest to the viewer, Figure 1c,d. Thus, water filling redistributes the thermal energy of CNT fluctuations and makes the CNT stiffer. Figure 1e presents standard deviations of the positions of the 120 carbon atom of the CNT, = 〈( − 〈 〉)〉, where i is the atom number and the angular bracket indicates ensemble averaging. The data demonstrate that water filling increases fluctuations of the CNT atoms. The displacements averaged over all carbon atoms are 0.0058 Å and 0.0070 Å in the pristine and water filled CNT, respectively. The larger atomic fluctuations lead to stronger electron-phonon coupling, including both elastic and inelastic processes responsible for the PL linewidths broadening and temporal decay. Figure 2 shows the partial density of states (pDOS) for the empty (top) and filled (bottom) CNTs calculated for the optimized ground state structures using the PBE and HSE06 functionals. Water filling reduces the energy gap between the first van Hove singularities (E11), matching the experimental trend.8 The energy gaps averaged canonically over the MD trajectory are presented in Table 1. The PBE band gap is 0.81



eV for the pristine CNT. It decreases to 0.63 eV in 15H2O@CNT. The experimental E11 energy of the pristine (10,0) CNT is around 1.2 eV50–54. The PBE calculation underestimates the HOMO-LUMO gap by about 0.4 eV because of the well-known selfinteraction error of pure DFT functionals. HSE06 gives a larger band gap of 1.11 eV for the pristine CNT, approaching the experimental value. The HSE06 band gap decreases to 0.84 eV for the water filled CNT. In order to calculate the optical gap, including excitonic effects, one needs to perform GW and Bethe-Salpeter calculations in addition to DFT.55 Such calculations are extremely expensive computationally, especially if canonical averaging requiring data for hundreds or thousands of geometries is required. Even the hybrid HSE06 functional is very expensive for NAMD calculations. In addition to calculating the orbital energy gaps, we perform a delta-SCF calculation using PBE functional. Here, one considers the difference in the total energies of the system in the ground state and with an electron promoted from HOMO to LUMO to represent the lowest excited state. The canonically averaged delta-SCF excitation energy, Table 1, equals 1.32 eV for pristine CNT and 1.17 eV for 15H2O@CNT. All three methods – PBE and HSE06 orbital energy gaps, and PBE delta-SCF – demonstrate red-shift upon water filling, as observed with the experimental PL spectra.8 The calculations identify several mechanisms leading to the experimentally detected redshift in the PL spectra.8 As established by the advanced experimental investigations,56,57 water is a dielectric medium that screens electron self-energy and electron-hole interactions.56

In the independent electron (mean-field) picture, an

increasing dielectric constant decreases the self-energy and leads to a redshift, as seen in the PBE/HSE06 bandgap data, Table 1. When excitonic effects (electron-hole interaction)


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are taken into account, an increasing dielectric constant screens the interactions and creates a blue-shift. This is because excitonic interactions lower the excitation energy, and a larger dielectric constant decreases this effect (decreases excitonic redshift relative to the independent electron picture, hence the blue-shift).56 The current calculations include excitonic effects in a crude way, using delta-SCF. Comparing the delta-SCF results with the energy gap for PBE indeed shows a slightly weaker effect of water on the excitation energy for delta-SCF. In addition to the dielectric screening, encapsulated water molecules perturb geometric structure of the CNT, distorting it away from the optimal structure that has the highest band gap, and hence causing a red-shift. Further, the LUMO of the pristine (10,0) CNT is doubly degenerate. Water filling lifts the degeneracy, splitting of the doubly degenerate LUMO by tens of meV, Figure 2. Water filling perturbs the CNT electronic structure, breaking the symmetry of the π*-electron LUMO, as can be seen in Figure S1. The orbital splitting is consistent with the recent theoretical investigation of water adsorption on CNT.28 The LUMO orbital splitting changes the optical absorption spectrum. Previous investigations have shown the pristine CNT exhibits one major absorption peak arising from the HOMO→LUMO transition, whereas the water filled CNT exhibits two absorption peaks, which can be understood from the LUMO energy splitting.58 The pDOS for the 15H2O@CNT system differs from the sum of the DOS of the isolated CNT and water molecules, indicating an interaction between the two subsystems. On one hand, the HOMO and LUMO charge densities shown in Figure S1 demonstrate that the frontier orbitals are mainly supported by CNT carbon atoms, and there is almost



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no electron density in the empty region between the water molecules and the CNT. On the other hand, there is a small contribution from the encapsulated water molecules to the HOMO and LUMO charge densities, indicating that there exists a weak coupling between CNT and water. Such weak non-covalent CNT-water interaction can play crucial roles in modulating the electronic and vibrational properties of the system, as discussed below. Consider the HOMO and LUMO charge density differences, obtained by subtracting the densities of the 15H2O@CNT system from the sum of the densities of the isolated CNT and water, Figure 3. The contributions of the water molecules to the HOMO and LUMO of 15H2O@CNT is small. Water has a much larger bandgap than CNTs, Figure 3e, and the frontier orbitals of the two subsystems cannot hybridize effectively. However, the charge density distributions of the CNT HOMO and LUMO are affected, Figure 3b,d. Both HOMO and LUMO are depleted in the water region and enhanced on the CNT, with the LUMO experiencing a larger change. Next, consider the PL line broadening observed in the experiments upon water filling.8 A linewidth arises from homogeneous and inhomogeneous broadening. The former is caused by different local environments in an ensemble of chromophores, whereas the latter arises from electron-phonon coupling that induces fluctuation of the electronic excitation energy. The time-domain energy fluctuation is equivalent to the Franck-Condon

progression

of

vibronic

excitations

in

the

energy

domain.

Inhomogeneous broadening is eliminated at the single chromophore level, and according to the Heisenberg uncertainty relationship, the homogeneous linewidth is determined by the excited state lifetime (T1) and pure-dephasing time ( ∗ ):


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ℏ

ℏ

ℏ

ℏ

Γ = = + ∗ ≈ ∗

(1)

In systems undergoing transitions across large energy gaps, including the current systems, the pure-dephasing time much shorter than the lifetime, and therefore, the lifetime can be neglected in the above equation. The pure-dephasing time, ∗ , determining the PL linewidth, Eq. (1), can be computed using the second-cumulant approximation of the optical response theory59,60 by considering the unnormalized autocorrelation function (u-ACF) of the excitation energy () =< ∆()∆(0) > .

(2)

Here, ∆() = ()−< > is deviatioin of the excitation energy from its average value, and the bracket indicates ensemble averaging. The square root of the u-ACF initial value quantifies the excitation energy ﬂuctuation. The pure-dephasing function is obtained from the u-ACF as () = exp −

!

ℏ

%

%&

"' # $ "' # $$ ( $$ )(.

(3)

Simple analysis shows that the pure-dephasing function decays fast if the u-ACF also decays fast, and/or if the amplitude on the energy gap fluctuation, given by the u-ACF initial value, is large.61 The fluctuation of the electronic excitation energy computed using the delta-SCF method is illustrated in Figure 4a. Figure 4b presents the corresponding u-ACFs for the CNT with (top) and without (bottom) water. The 15H2O@CNT u-ACF exhibits a very long-lived oscillation with a single dominant frequency. The u-ACF oscillation is also long-lived in the pristine CNT, however, it exhibits more than one frequency. The



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oscillation amplitude and the initial value is notably larger for the water filled CNT. (Note the difference in the y-axis scales.) In order to identify the phonon modes that couple to the electronic transition, we Fourier transform the u-ACF to obtain the spectral density, also known as the influence spectrum: *(+) =

!

,

12

| "/2 #. /0% ()|

(4)

The spectra show two signals, Figure 4c, the high-frequency longitudinal optical G-mode arising from stretching motions of carbon atoms is around 1600 cm-1 and the lowfrequency radial breathing mode (RBM) is around 300 cm-1. The electronic transition responsible for the nonradiative PL decay in the pristine CNT couples to both modes, with the G-mode signal five times larger than the RBM signal. Filling the CNT with water has a triple effect on the electron-phonon interactions: Coupling to the RBM is almost entirely suppressed, coupling to the G-mode becomes stronger, and the frequency of the G-mode is slightly red-shifted. The RBM is suppressed because the encapsulated water blocks the CNT from changing its shape and diameter. The G-mode frequency is slightly lowered because the C-C stretching couples to water motions. The signal amplitude grows because water molecules increase the energy gap fluctuation by electrostatic interaction with the CNT electronic subsystem. The superimposed snapshots shown in Figure 1c,d visualize these effects. The motion of the CNT atoms is enhanced along the CNT surface and decreased perpendicular to the surface in the presence of encapsulated water.


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The pure-dephasing functions computed using Eq. (3) are shown in Figure 5a. Gaussian fitting gives the pure-dephasing times, ∗ , listed in Table 1. The corresponding homogeneous linewidths are obtained using Eq. (1). The dephasing is faster in the water filled CNT due to stronger electron-phonon coupling. As a result, the homogeneous linewidth grows, as observed experimentally.8 Note that both water filling and CNT defects10,29 enhance electron-phonon coupling and accelerate dephasing, but they do so by different mechanisms. Defects create local disorder modes that exhibit strong coupling to electrons. On the other hand, water filling enhances coupling to the G-mode without appearance of new frequencies in the influence spectrum. Figure 5b shows decay of the excited state population responsible for nonradiative PL quenching in the empty and filled CNTs. The relaxation times, τ, reported in Table 1, are obtained by ﬁtting to the short-time linear approximation to the exponential decay, P(t)= exp(t/τ) ≈ 1-t/τ. The nonradiative relaxation for the pristine CNT is estimated at 568 ps, which is comparable to the experimental time scale.8,62 Water filling accelerates the relaxation, reproducing the experimental trend.8 The nonradiative decay rate depends on the values of the electronic energy gap, NA coupling, and pure-dephasing/decoherence time, which are listed in Table 1. Water filling decreases the gap, increases the NA coupling and shortens the coherence time. On the one hand, faster coherence loss tends to slow down quantum dynamics, as illustrated by the quantum Zeno effect for infinitely fast decoherene,63 with known exceptions for finite coherence times.64 One the other hand, smaller excitation energy and lager NA coupling favor faster relaxation. For instance, the Fermi’s golden rule rate is proportional to the coupling squared and inversely proportional to the energy gap. The stronger NA



coupling and smaller energy gap rationalize the faster nonradiative decay. The energy gap decreases upon water filling, because the optimal CNT geometry is perturbed and the LUMO degeneracy is lifted, Figure 2. The NA coupling grows because water molecules perturb the charge density distributions, Figure 3, by electrostatic interaction and provide additional contributions to the NA coupling. The effect of water filling on the excited state lifetime is qualitatively similar to that of defects, which also decrease the energy gap, increase the NA coupling and accelerate pure-dephasing, accelerating nonradiative relaxation to the ground state.29 In summary, we have performed a time-domain ab initio study on how water encapsulated inside a CNT influences PL energy, linewidth and lifetime. Combining NAMD with real-time TDDFT the study reproduces the experimental trends and provides, for the first time, an atomistic rationalization for the observed phenomena. By entering the CNT, water molecules perturb the CNT geometric and electronic structure, modify CNT vibrational dynamics and provide new channels for electron-phonon scattering. Encapsulated water make the nanotube more rigid, suppressing its RBM. The electrostatic field and dielectric screening provided by water have a large effect on the CNT electronic structure, shifting energies and densities of the frontier orbitals. The PL energy redshifts, because water screens electron-electron interactions, perturbs CNT geometry away from the optimal structure, and lifts the LUMO degeneracy. The homogeneous PL linewidth grows, since water enhances the electron-phonon interaction. Water filling suppresses coupling of electrons to the RBM and enhances coupling to the G-mode, whose frequency is slightly red-shifted. The nonradiative PL quenching is accelerated by encapsulated water, because the NA electron-phonon coupling increases,


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and the energy gap decreases. While the effect of water on the CNT electronic properties and electron-vibrational dynamics is similar to that of defects, the mechanisms generating the changes differ qualitatively. Both encapsulated water and atomic defects reduce the energy gap, and enhance elastic and inelastic electron-phonon scattering. However, defects achieve this by introducing new localized electronic levels and phonon modes, while water encapsulation perturbs intrinsic properties of CNTs. The reported state-ofthe-art atomistic simulations generate atomistic insights into the influence of environment on CNT optical, electronic, vibrational and dynamics properties that are essential for a wide range of applications.

Acknowledgements O. V. P. acknowledges funding from the U.S. National Science Foundation, award CHE-1565704. W. L. is grateful to Prof. Hong-Xing Zhang of Jilin University for multiple discussion and financial support. R. L. acknowledges the National Science Foundation of China, grant 21573022, the Recruitment Program of Global Youth Experts of China, the Beijing Normal University Startup, and the Fundamental Research Funds for the Central Universities. J. F. T. acknowledges support by the National Nature Science Foundation of China, grants 51501063, 51301066 and 51371080, and by the Natural Science Foundation of the Hunan Province, grant 14JJ2080. The simulations were performed at the University of Southern California’s Center for High-Performance Computing (hpcc.usc.edu).



Supporting Information Available: HOMO and LUMO charge densities of pristine and water-filled CNTs. The material is available free of charge via the Internet at http://pubs.acs.org.


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Figure 1. Optimized ground state structure of the (10,0) CNT filled with water: (a) side view and (b) front view. 2000 superimposed MD snapshots sampled at 300 K for (c) pristine CNT and (d) water-filled CNT. (e) Canonically averaged (300K) standard deviations of the atomic position of carbon atoms for pristine and water-filled CNTs. The periodic simulation cell contains the semiconducting (10,0) CNT composed of 120 carbon atoms either in pristine form or filled with 15 water molecules. Water forms a hydrogen bonded network and enhances carbon atom motions in directions along the carbon network. As a result, the NA electron-phonon coupling increases, accelerating the charge recombination, and the phonon-induced pure-dephasing within the electronic subsystem becomes faster, broadening the optical lines, as observed in experiment.



Figure 2. Density of states (DOS) for the pristine and water-filled CNTs calculated with the PBE (solid line) and HSE06 (dash line) functionals. The total DOS (black line), partial DOS of CNT (red) and water (blue) are presented. The water partial DOS is magnified 50-fold. Water molecules have negligible contribution to HOMO and LUMO. The energy gap between the first van Hove singularities (E11) decreases upon water filling, in agreement with the experimental trend. The HSE06 gap changes from 1.11 eV for pristine CNT to 0.84 eV for 15H2O@CNT. The GGA calculation underestimates the E11 gaps by about 0.3 eV relative to the hybrid DFT calculation. The first van Hove singularity in the conduction band splits in the presence of water. The data are obtained for the optimized ground state geometries.


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Figure 3. (a) Electron density difference between the HOMOs of the 15H2O@CNT and pristine CNT. (b) Difference between electron density of the 15H2O@CNT HOMO and the sum of electron densities of the HOMOs of pristine CNT and 15 H2O molecules. (c) Electron density difference between the LUMOs of 15H2O@CNT and pristine CNT. (d) Difference between electron density of the 15H2O@CNT LUMO and the sum of electron densities of the LUMOs of pristine CNT and 15 H2O molecules. The yellow and blue isosurfaces denote the electron density increase and decrease. (e) The HOMO and LUMO levels of 15H2O@CNT, pristine CNT and a water molecule calculated using the HSE06 functional and aligned to a common vacuum level, determined by the electrostatic potential. The HOMO and LUMO levels of pristine CNT are in the middle of the HOMO-LUMO gap of the water molecule, and hence, no hybridization occurs between the HOMOs of CNT and water molecule. The water molecules have negligible contribution to the HOMO and LUMO of 15H2O@CNT, but they lead to a charge density redistribution of the CNT HOMO and LUMO. The data are obtained for the optimized ground state geometries.



Figure 4. (a) Excitation energy of pristine CNT and 15H2O@CNT calculated along the MD trajectory using the delta-SCF method and the PBE functional. (b) Unnormalized autocorrelation functions (u-ACF) of the excitation energy. (c) Spectral density obtained by Fourier transform (FT) of the ACF. The delta-SCF method gives much better agreement with experiment than the HOMO-LUMO gap. The ensemble averaged deltaSCF excitation energies for pristine and water-filled (10,0) CNTs are 1.32 and 1.17 eV, in agreement with the experimental red-shift of the optical spectra upon water filling. Water filling blocks the CNT RBM around 300 cm-1 and slightly red-shifts the G-mode near 1600 cm-1, while at the same time, coupling to the G-mode increases. As a result, the uACF is more symmetrical and has a larger initial value for 15H2O@CNT.


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Figure 5. (a) Room temperature pure-dephasing functions for the lowest energy electronic excitations in the pristine and water-filled CNTs. (b) Electron-hole recombination dynamics obtained with the DISH method. Gaussian fits of the puredephasing function and linear (short-time exponential) fits of the excited state population give the time constants reported in Table 1. The faster pure-dephasing in the water-filled CNT gives a broader homogeneous linewidth, in agreement with experiment. Water filling speeds up the relaxation, also in agreement with experiment.



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Table 1. Ensemble averaged PBE delta-SCF excitation energy (Ed), HSE06/PBE HOMO-LUMO gap (Eg), averaged absolute NA coupling (NAC), pure-dephasing time (T2*), homogeneous linewidths (Γ), and non-radiative relaxation time (T1) for charge recombination in pristine and water-filled CNTs.

a b

Ed (eV)

Eg (eV)

Γ (meV)

NAC (meV)

T 2* (fs)

T1 (ps)

Pristine CNT

1.32

1.11a/ 0.81b

68

2.56

9.6

568

15H2O @CNT

1.17

0.84/ 0.63

124

2.83

5.3

244

HSE06 band gap PBE band gap


Influence of Encapsulated Water on Luminescence Energy, Linewidth

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