ConclusionsThe spin density surfaces of the antiferromagnetic ground states demonstrate opposite spins at the ends, and alternating spins along the length. This may vary with length, and may also be affected by the hydrogen-termination of the systems.

Pristine SWCNTs are the most stable systems. SW-defected systems are more stable than V-defected systems. This may be explained by the ability of each system to achieve pi orbital overlap. The stability of these SWCNTs also increases with diameter, which may be due to the C-C bond lengths.

The APFD functional consistently predicts the lowest energy, while pure PBE predicts the highest. This is logical due to the presence of strong van der Waals interactions, which would have a stabilizing effect.

Functionalization with NH2 is predicted to be favorable only for V-defected systems. This is likely due to the susceptibility of the relatively unstable 9-membered ring. For all systems, functionalization is predicted to be most favorable for small diameters. This is consistent with the predicted stability of the systems.

References1. Willdoer, et. al. Electronic structure of atomically resolved carbon nanotubes. Letters to Nature, 1998, 39(1), 59.2. Demichelis, et al. Properties of Carbon Nanotubes: An ab Initio Study Using Large Gaussian Basis Sets and Various DFT Functionals. J. Phys. Chem. C, 2011, 115, 8876.3. Nongnual, Limtrakul. Healing of a Vacancy Defect in a Single-Walled Carbon Nanotube by Carbon Monoxide

Disproportionation. J. Phys. Chem. C, 2011, 115, 4649.4. Dinadayalane, Leszczynski. Comparative Theoretical Study on the Positional Preference for Functionalization of

Two OH and SH Groups with (5,5) Armchair SWCNT. J. Phys. Chem. C, 2013, 117, 14441.5. Hod, Scuseria. Half-Metallic Zigzag Carbon Nanotube Dots. ACS Nano, 2008, 2(11), 2243.

Table 1. Calculated ΔGrxn (kJ/mol) of all systems as defined by Eproduct-(ENH3+ESWCNT), where the product is the functionalized SWCNT. These values are from PBEPBE/6-31G level optimizations.

Future ResearchFuture research includes introduction of functionalization using carboxyl groups, variation of the site of functionalization, and investigation of commercially-available SWCNTs using periodic models.

Functionalization of SWCNTs with Stone-Wales and Vacancy Defects: A Density Functional Theory Analysis

Katheryn A. Penrod, James B. Foresman, Ph.D.York College of Pennsylvania, Department of Physical Sciences

Objectives• Build pristine, Stone-Wales-defected, and vacancy-defected SWCNTs of

various diameters and lengths• Optimize the geometries of these systems• Use pure, hybrid, and dispersion-including functionals to compare the

relative energies of these systems• Introduce functionalization using carboxyl and primary amine groups• Vary the location of defects and functionalization sites • Investigate periodic models using the same methodology

BackgroundSingle-walled carbon nanotubes (SWCNTs) are essentially graphene sheets rolled into a tube, capped with a fullerene-like molecule. The primary interest in these structures arises from their mechanical strength and unique electronic properties.1 These molecules may have potential applications in nanotechnology, molecular electronics, and medicinal chemistry, among others.2 By functionalizing SWCNTs, one can increase their solubility, thereby increasing the potential applications.

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, which can compromise the performance and reliability of SWCNTs.3 Stone-Wales defects consist of two five-membered rings and two-seven membered rings. Vacancy defects consist of a missing carbon atom that typically results in one five-membered ring and one nine-membered ring (Figure 1).

Theoretical investigation of SWCNTs can help elucidate the best means and 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

Figure 1. A Stone-Wales defected (left) and a vacancy defected (right) portion of a SWCNT. The (*) indicates the bond involved in the reaction.

Computational MethodsAll calculations were performed using Gaussian 09. Nanotubes were created using TubeGen and terminated with hydrogen atoms. All systems were optimized using the pure PBE functional at the 6-31G level, with the exception of magnetic properties calculations. These 4-carbon systems were optimized using the HSE06 hybrid functional at the 6-31G(d,p) level.5 Subsequent calculations used these optimized geometries.

Gibb’s Free Energy of Functionalization (kJ/mol)

Indices Pristine Stone-Wales Vacancy

(8,0)5 66.0515 -13.7245 -270.495(9,0)5 109.655 1.08465 -172.445

(10,0)5 124.495 18.3995 -171.305(11,0)5 132.685 26.4325 -151.285

AcknowledgementsThanks for special funding support from

York College of Pennsylvania: Student Senate, Department of Physical Sciences, and Chemistry Society; Gaussian, Inc.; Travel Grants from the American Chemical Society and the Southeastern PA Section of the ACS

Chemistry Society

Y C P39 6 15

88.906 12.011 30.974

Figure 2. Spin density surface for the antiferromagnetic ground state of a hydrogen-terminated (7,0) SWCNT with four carbons along its length.

Results• Optimization initially failed for all systems• Fragment guesses, coordinate tweaks, and SCF keyword modifications

were employed to allow for convergence• Optimization was achieved at the PBEPBE/6-31G level for most systems• Antiferromagnetic ground states were found to be the lowest energy

states for these systems (Figure 2)• Single-point energy calculations were performed for all optimized

systems at the HSE06/6-31G and APFD/6-31G levels (Figure 3)• Functionalization with NH2 was introduced, and optimization was

achieved at the PBEPBE/6-31G level for most systems • Optimization of NH3 was achieved at the PBEPBE/6-31G level, and

single-point energy calculations were performed at the HSE06/6-31G and APFD/6-31G levels

• Gibb’s free energy of reaction was computed for all optimized systems (Table 1)

Figure 3. Comparison of relative energies computed by the PBE (darkest), HSE06 (medium), and APFD (lightest) functionals for all systems. A color scheme change indicates a change in diameter.

Energies of SWCNT Systems Using Three Different DFT Functionals

*