Katheryn Penrod York College of Pennsylvania Department of Physical Science CHM482 Independent Study Advisor Dr. James Foresman Spring 2014

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1 Katheryn Penrod York College of Pennsylvania Department of Physical Science CHM482 Independent Study Advisor Dr. James Foresman Spring 2014 Functionalization of SWCNTs with Stone-Wales and vacancy defects: A density functional theory analysis Abstract The properties of single-walled carbon nanotubes (SWCNTs) of zigzag ([n,m], where m=0 and n=8-12) chirality are investigated using density functional theory (DFT). Calculations are performed on SWCNTs with varying lengths. All calculations are performed using Gaussian 09, using pure, hybrid, and dispersion-including functionals with medium- to large-sized basis sets. Discrete and periodic models are investigated. Stone-Wales (SW) and vacancy defects are studied as they pertain to functionalization by carboxyl (COOH) and primary amine (NH 2 ) groups. The location of defects is varied and trends are derived for applicable properties. This research serves to gain a better understanding of the influence of these defects on reactivity of SWCNTs. Introduction Single-walled carbon nanotubes (SWCNTs) are essentially graphene sheets rolled into a tube, capped with a fullerene-like molecule. SWCNTs were discovered in the early 1990s and have since become a popular interdisciplinary research topic. 1 The primary interest in these structures arises from their mechanical strength and unique electronic properties, which have been investigated both theoretically and experimentally. These molecules may have potential applications in nanotechnology, molecular electronics, and medicinal chemistry, among others. 2 The chirality of SWCNTs is defined using indices of a graphene sheet which represent the number of unit vectors along two directions (n,m). 1 Armchair nanotubes have benzene rings connected by two carbons each along the length of the tube (n=m). Zigzag nanotubes have benzene rings connected by one carbon each along the length of the tube (m=0). All other SWCNTs are chiral. (See Figure 1.)

2 Figure 1. Chiralities of SWCNTs: Armchair (n=m), zigzag (m=0), and chiral (n m, m 0). While pristine nanotubes are composed of repeating benzene units, even the most high-quality tubes synthesized today contain at least one defect per 4 µm. These defects can compromise the performance and reliability of SWCNTs. 3 Two common defect types are Stone-Wales (SW) and vacancy defects. The SW defect consists of two five-membered rings and two-seven membered rings caused by a 90 rotation of a C-C bond. A vacancy defect consists of a missing carbon atom that typically results in one five-membered ring and one nine-membered ring. (See Figure 2.) SWCNTs are generally insoluble in aqueous and organic solvents, rendering functionalization necessary. By functionalizing the nanotubes, one can increase the solubility, thereby increasing the potential applications. Theoretical investigation of SWCNTs can help elucidate the best means for functionalization, as well as the preferred sites for functionalization. Defects are of interest in theoretical calculations, because the distortion of the pi cloud makes the defect site more susceptible to functionalization. 4 In the present study, SWCNTs of varying lengths and diameters were investigated. Pristine tubes, SW-defected tubes, and vacancy-defected tubes were studied. The properties of interest were relative stability, geometry, and magnetic properties. All calculations were performed using Gaussian 09.

3 Figure 2. Left: SW defect, caused by the 90 rotation of its central C-C bond, resulting in two five-membered rings and two seven-membered rings. Right: Vacancy defect, caused by the missing carbon atom in its center. An asterisk (*) indicates the bond involved in the reaction. Computational Details An SSH client was utilized to connect to jbflen2.ycp.edu. This allowed for remote access of Gaussian 09. Environment variables were used to control the submission of calculations to different processors on the remote machine. All nanotubes were generated using TubeGen and terminated with hydrogen atoms. Magnetic Properties Initially, the antiferromagnetic and ferromagnetic states of several different systems were investigated. Hydrogen-terminated zigzag SWCNTs with circumferences between seven and ten carbon atoms and four carbons along the length of the tube were optimized using the HSE06 screened exchange hybrid functional and 6-31G(d,p) basis set, as per Hod and Scuseria. 5 Fragment guesses were used with alternating alpha and beta spins for each layer of carbon atoms, and charge-multiplicity combinations dependent upon the diameter. (See Figure 3.)

4 Figure 3. Hydrogen-terminated (8,0) SWCNT with four carbon atoms along the length of the tube showing atom groups used for fragment guess. Each fragment was neutral with alternating alpha and beta spins and a multiplicity of 9. The neutral singlet was identified as the antiferromagnetic ground state for each system. Higher multiplicity states were then optimized using the optimized geometry of the ground state. The lowest energy state was identified as the ferromagnetic higher-multiplicity ground state. Spin density surfaces were generated for all systems except the antiferromagnetic state for the (8,0) system and the ferromagnetic septet for the (10,0) system. Errors were encountered by these two systems that have not yet been resolved. The energy differences between the antiferromagnetic and ferromagnetic states were calculated for each system. These magnetic properties were calculated only for pristine nanotubes. Building Defected and Functionalized SWCNTs Using the geometry from the pristine SWCNT generated by TubeGen, defects were added using GaussView. To add a SW defect, a C-C bond was isolated and rotated 90. This bond will become the center of the defect site. To add a vacancy defect, a carbon atom was deleted and a bond was placed to create a 5-membered ring and a 9-membered ring. In the present study, one defect was added per system, in the center of the tube. All systems had 12 carbons around their circumference. Beginning with optimized geometries of the non-functionalized system, the functionalized systems were built by adding an NH 2 group to one carbon atom and a H to the other. For vacancy systems, two different C-C bonds were tested to determine which is the more favorable target of functionalization (indicated in Figure 2).

5 Addressing SCF Convergence Failure Optimization using the pure PBE functional and 6-31G basis set encountered SCF convergence issues for systems with an even number of carbon atoms along its circumference. This was first believed to be an issue with the high-symmetry of the molecules, but breaking the symmetry of the molecules did not resolve the convergence issues. A three-step iteration was developed involving a stable=opt calculation to generate an initial geometry guess, followed by an optimization/frequency calculation, then a stable calculation to ensure that the resulting wavefunction has no internal instabilities. The SCF keyword option XQC was utilized in each step. This iteration was successful for several systems (both pristine and defected), but convergence failure was still encountered in several systems. Convergence was resolved for most non-functionalized systems. All systems required a fragment guess where the center portion of the SWCNT was a closed-shell singlet, and the terminal carbon and hydrogen atoms were each a fragment with opposing spin and a multiplicity equal to n+1. The (8,0) pristine system required a coordinate tweak to break the high symmetry and the NoVarAcc option for the SCF keyword. All other pristine systems required a coordinate tweak and use of the XQC, Fermi, and NoVarAcc options for the SCF keyword. Initially, the Conver=5 option was also used to accomplish loose convergence, which was tightened later. The SW with n=8,9,10 and the vacancy systems with n=8,9 required only the NoVarAcc option. The SW systems with n=11,12 and vacancy systems with n=10,11 required the same procedure as the pristine systems, without a coordinate tweak. The (12,0) vacancy system did not converge and requires further investigation. Further computation could not be completed for this system due to this convergence failure. Optimization for most functionalized systems was achieved at the PBEPBE/6-31G level using the same methods as the non-functionalized systems. The (12,0) SW functionalized system did not converge. Further computation could not be accomplished. Incorporating Other Functionals Single-point calculations were performed with HSE06 and APFD using the 6-31G basis set reading geometry from the checkpoint files of the optimization calculations. All systems completed successfully except for the (12,0) non-functionalized vacancy system and the (12,0) functionalized SW system, for which no optimized geometry was available.

6 Calculating Gibb s Free Energy of Reaction (ΔG rxn ) Ammonia (NH 3 ) was built and optimized at the PBEPBE/6-31G level, then single-point calculations were to be performed with HSE06 and APFD using the same basis set. The energy of each non-functionalized system was added to the energy of the ammonia molecule. This sum was then subtracted from the energy of the functionalized system to obtain ΔG rxn, as per Hess s Law. This process was only completed for the PBE functional. Partial results have been obtained for the HSE06 functional, but time limitations prevented completing these calculations. Results and Discussion Magnetic Properties and Spin Density Surfaces The differences between the antiferromagnetic ground state and the higher-multiplicity ferromagnetic state were calculated for systems of varying diameter with four carbons across the length of the SWCNT. These results are outlined in Table 1. The energy difference was greatest for the system with ten carbon atoms along its circumference, followed by the system with eight, then nine, then seven. This trend follows the trend reported by Hod and Scuseria, with the exception of the system with eight carbon atoms. 5 Problems were encountered with the calculation of this system, including symmetry issues that were resolved by rerunning the calculation in the development version of G09 and by breaking the symmetry in the z-matrix. It is unclear at this time why the trend does not match for this system. Indices E FM E AFM (ev) (7,0) (8,0) (9,0) (10,0) Table 1. Energy difference between the antiferromagnetic and ferromagnetic states of four different systems, each with four carbons along its length. Spin density surfaces indicated that the ferromagnetic state of the system with seven carbon atoms along its circumference has matching spins at its ends and at its center. (See Figure 4.) This is in contrast with the antiferromagnetic ground state which has opposite spins at its ends and alternating spins along the length of the molecule. (See Figure 5.) This trend is consistent for the other systems that were investigated, though spin density surfaces could not be generated for the antiferromagnetic state for the system with eight carbon atoms or the ferromagnetic state for the system with ten carbon atoms.

7 Figure 4. Hydrogen-terminated (7,0) SWCNT showing the spin density surface for the ferromagnetic quintet along the length of the molecule and at one of its ends. Figure 5. Hydrogen-terminated (7,0) SWCNT showing the spin density surface for the antiferromagnetic singlet along the length of the molecule and at one of its ends.

8 Relative Energies of Non-functionalized Systems Energy values are shown by Figures These results indicate that the pristine system is more stable (lower in energy) than the defected systems, in all cases. The SW defective systems appear to be more stable than the vacancy systems, but the difference of the missing carbon atom was not taken into consideration. Stability consistently increases with diameter of the SWCNT. The PBE functional predicted a higher energy than the other two functionals. APFD predicted the lowest energy, which is logical due to its consideration of van der Waals interactions. Figure 6. Comparison of relative energies of the (8,0) non-functionalized systems (Hartrees).

9 Figure 7. Comparison of relative energies of the (9,0) non-functionalized systems (Hartrees).

10 Figure 8. Comparison of relative energies of the (10,0) non-functionalized systems (Hartrees).

11 Figure 9. Comparison of relative energies of the (11,0) non-functionalized systems (Hartrees).

12 Figure 10. Comparison of relative energies of the (12,0) non-functionalized systems (Hartrees). Gibb s Free Energy of Reaction Values for ΔG rxn are shown in Table 2. These results indicate that functionalization with NH 2 is energetically favored for all vacancy systems, as indicated by the sign of ΔG rxn. Functionalization is nonspontaneous for all pristine systems, and all SW systems except for the (8,0) chirality. Functionalization is more energetically favored for SW systems than pristine systems.

13 Table 2. Calculated ΔG rxn (kj/mol) of all systems as defined by Eproduct-(E NH3 +E SWCNT ), where the product is the functionalized SWCNT. These values are from PBEPBE/6-31G level optimizations. Gibb s Free Energy of Functionalization (kj/mol) Indices Pristine Stone-Wales Vacancy (8,0) (9,0) (10,0) (11,0) Future Work Issues with SCF convergence criteria should be resolved for the (12,0) SW and vacancy systems. Modification of the SCF keyword has yielded the best results thus far, but fragment guesses may also be modified to encourage convergence. It may be helpful to loosen the convergence to Conver=4 or lower to see if a looser initial convergence may be obtained and tightened later. If these methods are unsuccessful, modifying the C-C bond length from TubeGen may be effective. Ferromagnetic states should be found for the systems with six carbons along their length using the same computational method described above. These ferromagnetic states may then be compared to the antiferromagnetic ground states found for pristine, SW defective, and vacancy defective systems. The site of the defect should be modified and compared to the results above. Multiple defects could also be introduced. A literature search may yield different types of defects which could potentially be investigated. Gibb s free energy calculations should be completed for functionalization with NH 2 using the HSE06 and APFD functionals. The method outlined above should be sufficient to complete this. The site of functionalization should be modified to compare sidewall functionalization to defect site functionalization. Carboxylic acid or other functional groups should be introduced to the systems. Gibb s free energy values may then be compared. All calculations should be repeated using larger basis sets. Periodic calculations should be performed using plane-wave DFT. Systems with chiralities that are commercially-available could also be investigated.

14 References 1. Willdoer, J. W. G.; Venema, L. C.; Rinzler, A. G.; Smalley, R. E.; Dekker, C. Electronic structure of atomically resolved carbon nanotubes. Letters to Nature, 1998, 39(1), Demichelis, R.; Noel, Y.; D Arco, P.; Rerat, M.; Zicovich-Wislson, C. M.; Dovesi, R. Properties of Carbon Nanotubes: An ab Initio Study Using Large Gaussian Basis Sets and Various DFT Functionals. J. Phys. Chem. C, 2011, 115, Nongnual, T.; Limtrakul, J. Healing of a Vacancy Defect in a Single-Walled Carbon Nanotube by Carbon Monoxide Disproportionation. J. Phys. Chem. C, 2011, 115, Dinadayalane, T. C.; Leszczynski, J. Comparative Theoretical Study on the Positional Prefence for Functionalization of Two OH and SH Groups with (5,5) Armchair SWCNT. J. Phys. Chem. C, 2013, 117, Hod, O.; Scuseria, G. E. Half-Metallic Zigzag Carbon Nanotube Dots. ACS Nano, 2008, 2(11),