4E18
Density-Functional Tight-Binding Studies of Finite-Size Hexagonal
Graphite Flakes(Institute for Advanced Research and Department of Chemistry, Nagoya University)
Stephan Irle
Bond alternation patterns have been found in non-defective hexagonal graphene
flakes (HGFs), according to theoretical calculations carried out at HF, DFT, MP2, and
SCC-DFTB levels of theory for benchmark systems up the size of about 100 atoms, and on
HGFs up to 1000 atoms using the SCC-DFTB method. It is convenient to provide an
unambiguous notation system for these structures, beyond the chemical formula, and thus wecharacterize the HGFs with chirality indices (n,m) in analogy to single-walled carbon
nanotubes. Here, the chiral indices denote the distance of one of the symmetry-equivalent
six corner hexagons from the central hexagon. (n,0) HGFs have zigzag-type borders, (n,n)
flakes have armchair-type borders, and (n,m) flakes have chiral structure.
To visualize geometrical patterns in the series of HGFs characterized by bonddifferentiation breaking the bond equivalency of infinite-size graphite layers, we use
graphical analysis of ring bond dispersion (RBD) and mean bond lengths (MBL), which aredefined as in [1]:61 6" xi
6 i=1
i=1
As in the case of finite-length SWCNTs [1], the bond differentiation patterns observed in
finite-size (n,m) HGFs correspond to overall Clar and Kekulé schemes. Clar scheme
presents an enhanced local aromaticity, while Kekulé scheme shows a higher electron
localization into more double and single-character bonds. Depending on the particular bordershape, the inner section for the graphene may or may not present bond differentiation. Whilefor sheets having a zigzag border no differentiation is appreciated, for chiral and armchairborder structures, neighboring bonds present a measurable difference, even in the center ofthe structure which is higher if the borders' indices are closer to those of an armchair border.
RBD =" (x i # x )2 ;MBL = x =Experimentally, graphene flakes can nowadays be characterized by Raman
spectroscopy. As in SWCNTs, graphene flakes show strong Raman bands in the region
around 1350 cm-1 (D-band) and 1590 cm-1 (G-band). Tuinstra et al. were first to attributethe origin of the D-band in disordered graphite (hence the notation “D”) to the change inselection rules in going from infinite graphite to microcrystalline graphite “big molecule”
fragments [2]. They argued that the A1g modes corresponding to individual hexagon
breathing are visible only in finite graphite flakes, as their amplitudes do not exactly cancel
out in this case. Necessarily, there exists a critical crystallite size La corresponding to a
maximum of the I(D)/I(G) intensity ratio, from where this ratio declines with 1/La behavior[3]. We have computed the Raman spectra of (1,0) to (13,0) HGFs using analytical second
geometry derivatives for SCC-DFTB as implemented in [4], and demonstrate for the first timeindeed the intensity of the G-band increases from La ~ 46 Å for (13,0), which corresponds to aC1176H84 molecule (see Figure 2). The origins for the intensity changes will be explained inthe talk.

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References[1] Martin-Martinez, F. J.; Melchor, S.; Dobado, S., Org. Lett. (2008), 10, 1991-1994.
[2] Tuinstra, F.; Koenig, J. L., J. Chem. Phys. (1970), 53, 1126-1130.
[3] Ferrari, A. C.; Robertson, J., Phys. Rev. B (2000), 61, 14095-14107.
[4] Witek, H. A.; Irle, S.; Morokuma, K. J. Chem. Phys. (2005), 121, 5163-5170.