Quinonoid radial π-conjugation

Abstract

Radially π-conjugated macrocycles with mixed aromatic and quinonoid units are considered. As a function of including an increasing number of aromatic units into a ring-like nanohoop with quinonoid units, a transition occurs where the HOMO and LUMO levels cross, leading to a topological transition described for the first time. Such transitions have been seen before in ethynylene-linked oligoacene polymers as a function of the acene size on gold surfaces and in various π-conjugated polymers as a function of external strain, but not in small molecular nanohoops or any other zero-dimensional system. Near the level crossing, the HOMO-LUMO gap becomes very small, offering novel photophysical properties while maintaining extensive delocalization. The open shell character of the rings changes continuously as the composition is gradually changed, switching from a singlet ground state to a triplet, providing a zero-dimensional analogy to topological transitions between a non-trivial to a trivial phase as observed in linear one-dimensional conjugated polymers. The spins of the triplet are localized near the two aromatic-quinonoid connections.

Fig. 1. (a) Illustration of [8]CPP, interring bond specified as 1–1′. (b) Generic π-conjugated unit (red circle, X) inserted into [8]CPP, denoted here as [8]C(X)₁(PP)₇. (c) Illustration of radial conjugation. (d) Typical π-conjugated units are inserted into various CPPs selected from the literature: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

Fig. 2. π-Conjugated polymer repeat units with two types of ground states. Two aromatic (A) and four quinonoid (Q) ones are shown. The aromatic ground state systems are polymers of thiophene (Th) and p-phenylene (PP). The quinonoid ones are thieno-3,4-[b]pyrazine (TPz), isothianaphthene (ITN), thieno[3,4-c]thiophene-1,4-dione (TTD), and pyrrolo[3,4-c]pyrrole-1,4-dione (PPD). Two chemical units are shown for each, and the inter-unit CC bonds are indicated as 1–1′. The 1–1′ bond distances (in Å) are provided in parentheses.^aFor consistency, 1–1′ distance in (PP)_n is provided with the same method as in ref. .

Fig. 3. A quinonoid unit, TPz (in blue), is inserted in place of one of the aromatic phenyls (in turquoise) of [8]CPP, designated as [8]C(TPz)₁(PP)₇.

Fig. 4. Optimized geometries (B3LYP-D3/6-311G(d)) of selected π-conjugated macrocycles for the [8]C(TPz)_8−x(PP)_x series. Only isomers where the TPz and PP units are completely segregated from each other are shown. For x = 8 the system is a pure [8]CPP. Color code: grey: C, white: H, blue: N, yellow: S. Key bond distances are provided in Å.

Fig. 5. (a) Cyclic [6,8,10]C(TPz) π-conjugated macrocycles, in their optimized geometries. The inter-unit 1–1′ carbon–carbon bond distances (in Å) indicate quinonoid structures. Their respective HOMO–LUMO gaps are also shown. For comparison, [8]CPP is shown as a typical π-conjugated macrocycle with a significantly longer, aromatic-type 1–1′ CC bond length (one of eight equivalent values are shown). (b) HOMO and LUMO orbitals of the quinonoid [8]C(TPz) and aromatic [8]CPP. The 1–1′ interactions are bonding for the HOMO of [8]C(TPz) and also bonding for the LUMO of [8]CPP. The 1–1′ interactions are antibonding for the LUMO of [8]C(TPz) and also antibonding for the HOMO of [8]CPP. Red arrows highlight one of these eight 1–1′ bonds.

Fig. 6. (a) HOMO–LUMO energy gap as a function of x in the [8]C(TPz)_8−x(PP)_x series of π-conjugated macrocycles obtained by three different DFAs. (b) Orbital level crossing when the number of PP unit in the [8]C(TPz)_8−x(PP)_x nanohoop series changes between x = 4 to x = 5 with B3LYP-D3. The same orbital crossings with the other two DFAs are nearly identical (Fig. S22†).

Fig. 7. Singlet triplet energy difference, ΔE_ST, relative to the lower of the two energies, in the (a) [8]C(TPz)_8−x(PP)_x series of nanohoops using three different DFAs and (b) [8]C(ITN)_8−x(PP)_x series of nanohoops. Both series show a more stable triplet for x = 3 and 4. For x = 2, the difference between the singlet and triplet is very small.

Fig. 8. Anisotropy of the induced current density (ACID) plots for cyclic [8]CPP derivatives containing varying numbers of benzene (x) and TPz (8−x) units. The yellow isosurfaces (iso = 0.025) represent induced current density under an external magnetic field applied perpendicular to the macrocycle. As x increases, the global aromatic ring current becomes more fragmented, indicating a transition from extended conjugation (in quinonoid TPz-rich systems) to localized aromaticity in benzene-rich systems.

Fig. 9. y ₀ diradical index as a function of x (a) for the [8]C(TPz)_8−x(PP)_x and (b) for the [8]C(ITN)_8−x(PP)_x, series of π-conjugated macrocycles. Values for both the triplet and singlet states are given. The more stable state is represented by filled symbols, the less stable by empty ones. These UHF y₀ values are based on (U)B3LYP-D3 optimized structures.

Fig. 10. (a and b) Spin density (iso-value = 0.01) distribution for the two nanohoops of the TPz series near the transition, where the triplet states are more stable than the singlet at the UB3LYP-D3/6-311G(d) level. The bottom portion are the TPz units, the top are the PP units. These are separated by a CC bond indicated by the black arrows. Red arrows indicate the largest localization of the spin density that occurs at the carbon site on the quinonoid side where the A and Q units meet. (c) The localization of spin in a hybrid nanohoop of segregated A and Q units is anticipated by the VB diagram where a symbolically aromatic unit (in turquoise) is adjacent to a quinonoid one (in blue).

Fig. 11. (a) Polymer of aromatic units with matching termination (trivial topological state). (b) Polymer of quinonoid units with non-matching termination (non-trivial topological state). (c) Macrocycle of aromatic or quinonoid units (trivial topological state). (d) Macrocycle of mixed aromatic and quinonoid units (non-trivial topological state).