Supplementary Information for
Common Defects Accelerate Charge Separation and Reduce Recombination in CNT/Molecule Composites: Atomistic Quantum Dynamics
Ritabrata Sarkar†, Moumita Kar§, Md Habib†, Guoqing Zhou‡, Thomas Frauenheim‖#, Pranab Sarkar§,*, Sougata Pal†,*and Oleg V. Prezhdo‡, ⃰
†Department of Chemistry, University of Gour Banga, Malda, 732103, India
§Department of Chemistry, Visva-Bharati University, Santiniketan – 731235, India
‖ Bremen Center for Computational Materials Science, University of Bremen, 28359 Bremen, Germany
# Shenzhen JL Computational Science and Applied Research Institute (CSAR), Shenzhen 518110 and Beijing Computational Science Research Center (CSRC), Beijing 100193, China
‡Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA
Simulation Details:
The simulation box contains one unit cell of the chiral (6, 5) CNT and a PDI molecule, which are bound primarily through van der Waals interaction and π-π stacking. The system is periodic along the z-axis.
The length of the simulation cell along the z-direction has been optimized and is 41Å. To avoid artificial interaction between adjacent unit cells, 50Å of vacuum are added in both x and y directions of the box.
The diameter of the (6, 5) CNT is 7.57Å. The 7557 and Stone Wales (SW) defects are among the most common CNT defects.1-2 One defect is introduced per simulation box. Since the defects are local, while the unit cell of the (6, 5) CNT includes 364 atoms, CNT properties away from the defect site, such as the CNT diameter, change very little. The total number of atoms in the pristine and SW composites is 432.
The 7557 system contains 2 more atoms.
SCC-DFTB is an efficient methodology for atomistic quantum mechanical simulations. Based on DFT parametrization, SCC-DFTB is capable for accurate quantum-mechanical description of geometries, vibrational frequencies, reaction energies, and other properties of large systems consisting of thousand atoms or more with manageable computational effort. Treating large systems is a major limitation of ab initio DFT methodologies. Parametrizations for carbon, hydrogen, nitrogen, and oxygen
atoms are among the oldest and accurate data set used in SCC-DFTB calculations. They reproduce many experiments and theoretical findings accurately.3-4 Further, photo-induced carrier dynamics of low dimensional materials, such as CdSe QDs and CNTs, simulated by SCC-DFTB agree well with experiments and ab initio DFT.5 The present systems are composed primarily of carbon atoms, with a small number of hydrogen, nitrogen, and oxygen atoms. The systems contain over 430. The CNT is periodic, and the CNT and PDI interact by the van der Waals force of attraction, further increases the computational cost. Thus, SCC-DFTB provides the best choice for atomistic quantum dynamics simulations of these systems, which otherwise are almost intractable.
In the SCC-DFTB method, the effect of polarization is introduced by adding an additional polarizable response density to the total density and also by including dispersion interaction. Apart from that, DFTB models involve confining potentials in atomic calculations. The confining potential modifies the electron density at distances relevant to noncovalent interactions.6 The DFTB parameters used in the present study have been tested by calculating the band gap and band structure of pristine CNT and compared to more sophisticated DFT.4
The electronic structure calculations, geometry optimizations and adiabatic MD simulations are carried out with the SCC-DFTB method.7-8 The Slater-Koster files for each pair of atoms, used as parameter in SCC-DFTB, are obtained from rigorous DFT calculations and have been applied over a variety of systems earlier.9-10 The projected density of states (PDOS) has been calculated using a 1×1×256 Monkhorst-Pack k-point mesh. The Lennard-Jones dispersion correction11 is used to describe the interaction present between the moieties. Using the velocity rescaling formalism, the optimized systems have been heated up to room temperature. After that, 5ps MD trajectories have been generated with a 1 fs time-step using the Verlet algorithm.12 The MD trajectories have been used to obtain the NA coupling matrix elements, and to generate the NA Hamiltonian used further to perform the NAMD simulations.
The classical path approximation (CPA)13 is applied to perform the NAMD simulations. The CPA assumes that thermal fluctuations in the system geometry are more significant than geometry changes associated with the photo-excitation. This approximation increases the computational efficiency by orders of magnitude. The current NAMD calculations would have been impossible without the CPA.
The atomistic quantum dynamics simulations employ the recently developed methodology,5 combining SCC-DFTB and NAMD. The methodology has been successfully applied to a variety of
nano systems, including pristine CNT14-15 and CNT composite,16 cadmium chalcogenide quantum dots17 and nanoplateletes,18-19 and various porphyrin macro structures.20 Fewest switching surface hopping (FSSH)21-23 is used to simulate the charge separation process. Decoherence-induced surface hopping (DISH)24 is applied for the simulation of the e-h recombination across the wide energy gap. FSSH has a very long history of successful applications. The more recent DISH approach has been used successfully for investigation of excited state dynamics in various systems.16, 20, 25 Both FSSH and DISH are implemented in the PYthon eXtension for Ab Initio Dynamics (PYXAID) software package.26-27
Figure S1. Optimized geometries of the CNT/PDI composites. Parts (a) and (d) show top and side views of the pristine composite, (b) and (e) represent the same views for the composite with the 7557 defect, (c) and (f) give similar representation for the SW composite. The CNT and the PDI are non- covalently attached through the van der Waals force. The PDI bends slightly towards the CNT in the presence of the 7557 defect and interacts with the SW defect through the side group, maintaining π-π stacking with the unperturbed part of the CNT. No significant structural changes are observed even in the ambient temperature MD simulation, Figure S2, implying that the systems are stable. The light and dark black balls denote C atoms of the CNT and the PDI, respectively. The green, red and blue balls show H, O and N atoms, respectively.
Figure S2. Representative geometries of the CNT/PDI composites at 300 K. Parts (a) and (d) show top and side views of the pristine composite, (b) and (e) represent the same views for the composite with the 7557 defect, (c) and (f) give similar representation for the SW composite. No significant structural changes are observed at ambient temperature compared to 0 K, Figure S1, implying that the systems remain stable and are perturbed little during MD. The light and dark black balls denote C atoms of the CNT and the PDI, respectively. The green, red and blue balls show H, O and N atoms, respectively.
Figure S3. Charge density distributions of the key orbitals participating in the photo-induced ET and e-h recombination dynamics in (a) the pristine CNT/PDI composite, and the CNT/PDI composites with the (b) 7557 and (c) SW defects. The charge density of the electron donor states (CBM and CBM+1) are distributed uniformly over the CNT in the pristine system. In contrast, the photo-excited electron is rather localized around the 7557 or SW defects in the defective CNTs. The charge density of the electron acceptor state (LUMO) is delocalized over the π-electron system of the PDI molecule. The hole is delocalized in the pristine CNT, and is localized around the defects in the defective CNTs. The localized nature of the hole decreases the e-h interaction and extends the carrier lifetimes in the defective CNTs.
Work Function Calculations:
In order to confirm the DFTB conclusion that the CNT energy levels are lowered in the presence of the defects, we compute work functions of the pristine and defective CNTs with ab initio DFT. Work function is the minimum thermodynamic work required to remove an electron to infinity from the surface of a given solid. The higher the value of the work function, the more energy is needed to remove an electron. Therefore, a higher work function indicates a lower valence band maximum (VBM), relative to vacuum that is common to all systems. The work functions are calculated with the Vienna Ab initio Simulation Package (VASP) using several DFT functionals. The functional are (i) Perdew-Burke- Ernzerhof (PBE), (ii) Perdew-Wang 91 (PW91), (iii) revised Perdew-Burke-Ernzerh of (RPBE) with Pade Approximation (RP) and (iv) Perdew-Burke-Ernzerhof revised for solids (PBEsol). The results are shown in Table S1. All functionals predict that the work function increases in the presence of either defect, in agreement with the DFTB results. The 7557 defect increases the work function more than the SW defect. Correspondingly, the VBM is lowest for the 7557 defect, followed by the SW and the ideal CNT. The downward shift of the CNT energy levels by the defects favors faster charge separation and slower charge recombination, as discussed in the manuscript.
Table S1: Work functions of the ideal and defective CNTs obtained with different ab initio DFT functionals
System
Work Function (eV)
PBE PW91 RP PBEsol
(6, 5) CNT 4.34 4.38 4.23 4.38
(6, 5) CNT_7557 4.39 4.43 4.28 4.45
(6, 5) CNT_SW 4.36 4.41 4.26 4.43
Table S2: Energy of interaction between CNT and PDI in the pristine and defective hybrids. Negative values indicate favorable interaction.
Systems Interaction energy [eV]
pristine -2.20
7557 -2.02
SW -2.16
Figure S4: Mulliken charges in the CNT and PDI moieties for (a) pristine, (b) 7557 and (c) SW composite systems. The charges are shown only for those atoms of the CNT and the PDI that have major contributions to the charge densities of the VBM, LUMO, CBM and CBM+1 states. There is an overall charge transfer from the PDI to the CNT in the presence of the defects. The CNT accumulates the highest charge in the presence of the 7557 defect, followed by the SW defect and pristine CNT.
Indicated by the red circles, the core carbon atoms of the CNT in the pristine and 7557 composites possess negative charge, while the PDI core carbon atoms possess positive charge. Thus, local electrostatic attraction keeps the PDI on the side wall of the pristine CNT, and on top of the 7557 defect site in the 7557 composite. On the contrary, both CNT and PDI core carbon atoms carry positive charge in the SW composite. The electrostatic repulsion makes the PDI move away from the SW defect site.
The PDI molecule interacts with the SW defect through its side group.
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