Electronic structure of oxygen-terminated zigzag graphene nanoribbons: A hybrid density functional theory study

The size-dependent electronic structure of oxygen-terminated zigzag graphene nanoribbons is investigated using standard density functional theory (DFT) with an exchange-correlation functional of the generalized gradient approximation form as well as hybrid DFT calculations with two different exchange-correlation functionals. Hybrid DFT calculations, which typically provide more accurate band gaps than standard DFT, are found to predict semiconducting behavior in oxygen-terminated zigzag graphene nanoribbons; this is in distinct contrast to standard DFT with (semi)local exchange-correlation functionals, which have been widely employed in previous studies and shown to predict metallic behavior. (Semi)local exchange-correlation functionals employed in standard DFT calculations cause unphysical delocalization of lone pairs from the oxygen atoms due to self-interaction errors and lead to metallic behavior. Hybrid DFT calculations do not suffer from this spurious effect and produce a clear size-dependent band gap. Appreciable fundamental band gaps $\left(\sim 1\text{eV}\right)$ are found for the smallest ribbons (two zigzag rows); the band gap decreases rapidly with increasing ribbon width, resulting eventually in a zero band-gap semiconductor at about 4–5 zigzag rows. This finding could have useful implications for molecular electronics, in particular, since oxygen-terminated zigzag graphene nanoribbons are thermodynamically stable unlike their hydrogenated counterparts. More generally, through a concrete example, this study suggests caution when employing (semi)local functionals in DFT studies of functionalized graphene/graphene derivatives when the functional groups contain electron lone pairs.

Figure 1

(Color online) (a) Schematic of O-2-ZGNR; C and O atoms are denoted by black and red spheres, respectively. The dotted lines enclose a repeating periodic unit. Bond lengths $\left(\text{Å}\right)$ are also indicated. (b) Band structure for O-2-ZGNR computed with PBE (solid red lines), HSE06 (dashed green lines), and PBE0 (dotted blue lines) XC functionals. (c) Partial density of states for the $p_y$ orbitals (lone pair) of the two O atoms [labeled O1 and O2 in (a)] and for the $p_z$ orbitals summed over all C atoms. Since the two spin channels are degenerate, the band structure and density of states are only plotted for the majority spin.

Figure 2

(Color online) (a) Contours of integrated spin density (with HSE06 XC functional) projected on the plane of the ZGNR; red (blue) regions indicate spin densities greater (lesser) than $0.02\left(-0.02\right)e/{\text{Å}}^2$. Bond lengths $\left(\text{Å}\right)$ are also indicated. (b) Band structure for O-3-ZGNR computed with PBE (solid red lines), HSE06 (dashed green lines), and PBE0 (dotted blue lines) XC functionals. (c) Partial density of states for the $p_y$ orbitals (lone pair) of the two O atoms [labeled O1 and O2 in (a)] and for the $p_z$ orbitals summed over all C atoms. Since the two spin channels are degenerate, the band structure and density of states are only plotted for the majority spin.

Figure 3

(Color online) Partial and total (shown in insets) density of states for the (a) 4-O-ZGNR and (b) 5-O-ZGNR. Partial density of states are displayed for the $p_y$ orbitals (lone pair) of the two edge O atoms and for the $p_z$ orbitals summed over all C atoms. Since the two spin channels are degenerate, only the majority-spin channel is shown here.