Pyrene derivatives substituted at the 2- and 2,7-positions are shown to display a set of photophysical properties different from those of derivatives substituted at the 1-position. It was found that, in the 2- and 2,7-derivatives, there was little influence on the S(2) ← S(0) excitation, which is described as "pyrene-like", and a strong influence on the S(1) ← S(0) excitation, which is described as "substituent-influenced". In contrast, the 1-substituted derivatives display a strong influence on both the S(1) ← S(0) and the S(2) ← S(0) excitations. These observations are rationalized by considering the nature of the orbitals involved in the transitions. The existence of a nodal plane passing through the 2- and 7-positions, perpendicular to the molecular plane in the HOMO and LUMO of pyrene, largely accounts for the different behavior of derivatives substituted at the 2- and 2,7-positions. Herein, we report the photophysical properties of a series of 2-R-pyrenes {R = C(3)H(6)CO(2)H (1), Bpin (2; pin = OCMe(2)CMe(2)O), OC(3)H(6)CO(2)H (3), O(CH(2))(12)Br (4), C≡CPh (5), C(6)H(4)-4-CO(2)Me (6), C(6)H(4)-4-B(Mes)(2) (7), B(Mes)(2) (8)} and 2,7-R(2)-pyrenes {R = Bpin (9), OH (10), C≡C(TMS) (11), C≡CPh (12), C≡C-C(6)H(4)-4-B(Mes)(2) (13), C≡C-C(6)H(4)-4-NMe(2) (14), C(6)H(4)-4-CO(2)C(8)H(17) (15), N(Ph)-C(6)H(4)-4-OMe (16)} whose syntheses are reported elsewhere. Furthermore, we compare their properties to those of several related 1-R-pyrene derivatives {R = C(3)H(6)CO(2)H (17), Bpin (18), C≡CPh (19), C(6)H(4)-4-B(Mes)(2) (20), B(Mes)(2) (21)}. For all derivatives, modest (0.19) to high (0.93) fluorescence quantum yields were observed. For the 2- and 2,7-derivatives, fluorescence lifetimes exceeding 16 ns were measured, with most being ca. 50-80 ns. The 4-(pyren-2-yl)butyric acid derivative (1) has a long fluorescence lifetime of 622 ns, significantly longer than that of the commercially available 4-(pyren-1-yl)butyric acid (17). In addition to measurements of absorption and emission spectra and fluorescence quantum yields and lifetimes, time-dependent density functional theory calculations using the B3LYP and CAM-B3LYP functionals were also performed. A comparison of experimental and theoretically calculated wavelengths shows that both functionals were able to reproduce the trend in wavelengths observed experimentally.

Four linear π-conjugated systems with 1,3-diethyl-1,3,2-benzodiazaborolyl [C(6)H(4)(NEt)(2)B] as a π-donor at one end and dimesitylboryl (BMes(2)) as a π-acceptor at the other end were synthesized. These unusual push-pull systems contain phenylene (-1,4-C(6)H(4)-; 1), biphenylene (-4,4'-(1,1'-C(6)H(4))(2)-; 2), thiophene (-2,5-C(4)H(2)S-; 3), and dithiophene (-5,5'-(2,2'-C(4)H(2)S)(2)-; 4) as π-conjugated bridges and different types of three-coordinate boron moieties serving as both π-donor and π-acceptor. Molecular structures of 2, 3, and 4 were determined by single-crystal X-ray diffraction. Photophysical studies on these systems reveal blue-green fluorescence in all compounds. The Stokes shifts for 1, 2, and 3 are notably large at 7820-9760 cm(-1) in THF and 5430-6210 cm(-1) in cyclohexane, whereas the Stokes shift for 4 is significantly smaller at 5510 cm(-1) in THF and 2450 cm(-1) in cyclohexane. Calculations on model systems 1'-4' show the HOMO to be mainly diazaborolyl in character and the LUMO to be dominated by the empty p orbital at the boron atom of the BMes(2) group. However, there are considerable dithiophene bridge contributions to both orbitals in 4'. From the experimental data and MO calculations, the π-electron-donating strength of the 1,3-diethyl-1,3,2-benzodiazaborolyl group was found to lie between that of methoxy and dimethylamino groups. TD-DFT calculations on 1'-4', using B3LYP and CAM-B3LYP functionals, provide insight into the absorption and emission processes. B3LYP predicts that both the absorption and emission processes have strong charge-transfer character. CAM-B3LYP which, unlike B3LYP, contains the physics necessary to describe charge-transfer excitations, predicts only a limited amount of charge transfer upon absorption, but somewhat more upon emission. The excited-state (S(1)) geometries show the borolyl group to be significantly altered compared to the ground-state (S(0)) geometries. This borolyl group reorganization in the excited state is believed to be responsible for the large Stokes shifts in organic systems containing benzodiazaborolyl groups in these and related compounds.

The breakdown in TDDFT accuracy that can accompany a simple chemical change can be understood and predicted using an orbital overlap perspective. This is illustrated for the hydrogenation of retinal. Errors in charge-transfer excitation energies and oscillator strengths in the donor-acceptor product are largely eliminated using a Coulomb-attenuated functional.

Dispersion, static correlation, and delocalisation errors in density functional theory are considered from the unconventional perspective of the force on a nucleus in a stretched diatomic molecule. The electrostatic theorem of Feynman is used to relate errors in the forces to errors in the electron density distortions, which in turn are related to erroneous terms in the Kohn-Sham equations. For H2, the exact dispersion force arises from a subtle density distortion; the static correlation error leads to an overestimated force due to an exaggerated distortion. For \documentclass[12pt]{minimal}\begin{document}${\rm H}_2^+$\end{document}H2+, the exact force arises from a delicate balance between attractive and repulsive components; the delocalisation error leads to an underestimated force due to an underestimated distortion. The net force in \documentclass[12pt]{minimal}\begin{document}${\rm H}_2^+$\end{document}H2+ can become repulsive, giving the characteristic barrier in the potential energy curve. Increasing the fraction of long-range exact orbital exchange increases the distortion, reducing delocalisation error but increasing static correlation error.