The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic?

Abstract

Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (n_σ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 π_α-electrons and 2n + 1 π_β-electrons (or vice versa) and becomes π_α-antiaromatic and π_β-aromatic. Yet, the antiaromatic π_α- and aromatic π_β-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (³n,π*), which are most readily analyzed, but also singlet n,π* states (¹n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the π_β-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in ³n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T₁ and S₁), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D_2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R² = 0.42), while it is stronger for monosubstituted pyrazines (R² = 0.84).

Figure 1

(A) Orbital occupancies in the S₀ state (n²) and the triplet and singlet n,π* states, with α-electrons in red and β-electrons in blue. (B) Illustrations of Mandado’s rule for (anti)aromaticity of separate spins with aromaticity (A) and antiaromaticity (AA) components in the S₀ and the triplet π,π* (T₁) states of benzene, the triplet π,π* (T₁) state of cyclooctatetraene, and the triplet n,π* state of pyridine.

Figure 2

6-Membered ring (6-MR) heteroaromatics investigated herein. For a selection of 5-membered ring (5-MR) heteroaromatics and an analysis of their frontier orbital energies, see the SI (Section S3.7).

Figure 3

(A) Illustration of the tug-of-war between the aromatic (A) π_β-component (blue) and the antiaromatic (AA) π_α-component (red) in influencing the structure of the n,π* state. (B) The two general types of n,π* excitations for a heteroaromatic molecule with C_2v symmetry that can be the lowest n,π* state, as well as the orbital and state symmetries.

Figure 4

MCI results (in a.u.) of 6-MR monoheteroaromatics in (A) their n,π* triplet states (spin-separated MCI values) with KS-UDFT and (B) their singlet (S) and triplet (T) n,π* states at TD-DFT level, as well as the KS-UDFT results for the ³n,π* states for comparison. The purple arrow in (A) indicates the aromaticity threshold (0.0358). The state orders (T_n and S_n, n = 1, 2, 3,···) given above the bars represent the n,π* states. ^aT₃ or higher. ^bMixed state. See SI Sections S1, S2.1, S3.1, and S3.2 for further details.

Figure 5

Aromaticity of the monoheteroaromatics in their S₀ and ³n,π* states at the UCAM-B3LYP/6-311+G(d,p) level; (A) π-EDDB values (units are electrons), where red and blue bars correspond to, respectively, α- and β-electrons (as references, the total π-EDDB value is 5.33 e for benzene in its aromatic S₀ state and 2.77 e for pyridine in its antiaromatic ³π,π* state, see Section S2.2 in the SI for more details, especially on spin-separated reference values). The dashed line bars show the total number of π-electrons in that state. (B) π-Electron bond current strengths (in nA T^–1) calculated as the average of all bonds in the given ring, where red and blue bars represent α- and β-electron contributions, respectively. (C) NICS(1)_zz values (in ppm).

Figure 6

Maps of magnetically induced π-electron current densities calculated at 1 bohr above the molecular plane of 1: (A) S₀ state, (B) ³n,π* state, (C, D) π_α- and π_β-electron contributions to the ³n,π* state. Clockwise (anticlockwise) circulation corresponds to diatropic (paratropic) currents. (E) Qualitative energy level diagram for the frontier molecular orbitals in the S₀ and ³n,π* states of monoheteroaromatics. Blue arrows indicate the translationally allowed transitions (inducing diatropic currents), and the red arrow indicates the rotationally allowed transition (inducing paratropic currents). Only the most relevant transitions, based on the values of the linear and angular momentum matrix elements, were selected.

Figure 7

(A) MCI results (in a.u.) of diheteroaromatics in their triplet n,π* states (spin-separated) with UCAM-B3LYP/6-311+G(d,p). The purple arrow indicates the aromaticity threshold value for S₀ (0.0358). The state orders T_n (n = 1, 2, 3,···) is given above the bars that represent the ³n,π* states. ^aT₂ or higher (see SI Sections S2.1 and S3.1 for further details). (B) NICS(1)_zz values in their S₀ and ³n,π* states (in ppm).

Figure 8

Singly occupied and unoccupied n and π* orbitals of 10–14 of the ³n,π* state, with orbital energies in eV. Noteworthy, the virtual lone-pair orbitals in the rightmost column resemble the doubly occupied lone-pair orbitals in S₀. Isosurfaces of 0.040 au.

Figure 9

(A) ΔE(³π,π* – ³n,π*) vs MCI(³n,π*) for 1–19H⁺, (B) ΔE(³π,π* – ³n,π*) vs MCI(³n,π*) for 9 and monosubstituted pyrazines, (C) E(³n,π*) vs ΔMCI(S₀ – ³n,π*) for 9 and monosubstituted pyrazines, and (D) distorted structures of 9 obtained through a normal mode following algorithm.

Figure 10

(A) Osmapyridinium complexes 20 and 21, and (B–E) π-electron MICD plots calculated 1 bohr above the molecular plane of 21: S₀ state (B) and vertical ³σ,π* state (C) with the corresponding π_α- and π_β-electron contributions (D, E). Clockwise circulation corresponds to diatropic (aromatic) currents. Full-scale plots in the SI.