The triplet connection from benzene C6H6 (m = 1) to the largest hexangulene C600H60 (m = 10). Left and right small top panels are for benzene triplets states T1-a and T1-b. Color coded spin vector (red) and bonds (red long, green intermediate, mauve CH ≈ 100 pm). Center panel shows spin and bond lengths of the singlet radical ground state of hex 10-zzg (C600H60) in a prospective plot. Note the hexagonally sectored spin distribution with alternating sign from edge to edge around the perimeter. Left and right large bottom panels, hex 10-zzg in the triplet T1-a and T1-b states in an orthoscopic plot. All the edge spin patterns of hex 10-zzg are the same times the factor (0,±1). The magnitudes of the spin vectors on benzene (T1-a = 0.28 and T1-b = 0.38) are larger than the maximum hex spin (≈0.12). Broken line is a rotation axis.
Computed results for the D2h triplet states of flat benzene. Top panels triplet T1-a (allyl) with two long CC bonds: panel (A1) valence charge density and CC bond lengths; (A2) α-spin density isometric surface at density = 1000 ( ≡ = 0.125 spins/Å3); (A3) colored stick bond figure with superimposed atomic spins on each atom. Bottom panels triplet T1-b (Dewar) with two short CC bonds: panel (B1) valence charge; (B2) isometric surface of spin density; and (B3) atomic spin on carbon atoms. All CH bonds are mapped to mauve ≈100 pm. The broken line is the axis.
The triplet states for small hex molecules. T1-a (top row) and T1-b (bottom row) for benzene, hex 2-zzg (coronene), and hex 3-zzg (circumcoronene) molecules. Spins and CC bond lengths are on a linear rainbow color scales (red long, mauve short, see text for details and scales in Fig. 9). Scale for benzene is not the same. All CH bonds are mapped to mauve. Broken line is the axis.
The triplet state T1-a for intermediate hex molecules m-zzg where m = 4, 5, 6, 7, 8. A new trend appears at hex 7-zzg and 8-zzg, namely the build up of β-spin (down) on the two edges parallel to the axis.
Continuation of the triplet T1-b series for hex m-zzg where m = 3, 4, 7, 10. Note that spins build up on the two edges parallel to the axis and not on the other four edges.
The molecule hex 9-zzg (C486H54). Plot of the length of all CC bonds of the triplet T1-a state vs row index of the bond. Zigzag (edge parallel) rows have integer index and radial (edge perpendicular) rows have half odd integer index. Graphene interior dominates for row index less than six. Perpendicular bonds show little variation within their row. Parallel bonds show length variations along their rows due to lower symmetry. Curves are drawn through data points to guide the eye.
Detail of the molecule hex 10-zzg (C600H60) in the T1-a state. Spin and CC bond length (pm) color scales are shown on the right-hand side. The last row of perpendicular CC bonds are the long (red ≈145 pm). Bonds on either side of the short apex bonds (dark blue ≈136 pm) are the longest perimeter CC bonds (orange ≈144 pm). Mid perimeter CC bonds form a short uniform segment (bright green) on the edge where the spins are highest.
Comparison of perimeter atomic spins of the molecule hex 10-zzg (C600H60) for the three electronic states T1-a, S00 (denoting singlet radical ground state) and T1-b. This picket fence representation plots the atomic spin vs sequential carbon atom number around the perimeter of the hex 10-zzg molecule. Perimeter carbon atoms start at C(486) and end at C(600). The main component of the spin pattern is almost the same for each state.
Comparison of unscaled α- and β-spins vs row index m = 1,2,3, …, 10 for series T1-a and T1-b. The T1-a spins change rapidly starting around index m = 6. In comparison the T1-b curves for α- and β-spin drift to higher magnitude with index m.
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