Fig. 3: S_N1 space with an anomalous outcome.

a, Scheme of a reaction between alcohol 15a and HBr leading to major product 15b through anthranyl carbocation 15c. The minor anthraquinone product 15d originates from the cycloaddition of substrate 15a with singlet oxygen to give the endoperoxide, followed by subsequent fragmentations (for details, see Supplementary Fig. 32). The ‘unexpected’ carbocation dimer structure is assigned to 15e (for details of structural assignment, see Supplementary Information Sections 4.13 and 6.2). b, Space of reaction yields of the main product 15b under different conditions (reaction time: 24 h; for clarity, only 125 out of 1,085 points are shown; for all data, see Supplementary Information Section 4.15). Fitting the kinetic model to these experimental data reveals that yields of product 15b scale as \(1-\exp \left(-t{k}_{1}[{\rm{HBr}}]\exp \left(-\frac{{E}_{{\rm{a}}}}{{k}_{{\rm{B}}}T}\right)\right)\), in which t is reaction time, \({k}_{1}\exp \left(-\frac{{E}_{{\rm{a}}}}{{k}_{{\rm{B}}}T}\right)\) is the kinetic rate constant at a given temperature (prefactor k₁ is a free parameter), E_a is the activation energy free parameter and [HBr] is the concentration of HBr—that is, these conversions increase with [HBr] and with temperature, do not depend on the initial concentration of the alcohol substrate and the rate-limiting step is formation of a carbocation 15c, all as expected for S_N1 reaction. The isosurfaces correspond to 20%, 40%, 70% and 85% yield. c, Distribution of yields for the side product 15d. The isosurface corresponds to 20% yield. d, Pink cloud delineates a narrow region of conditions in which an anomalous outcome—that is, carbocation dimer 15e—is observed. e, Pink line is a typical UV-Vis spectrum from the region of conditions in which an anomalous outcome is observed. The dashed line is a typical experimental spectrum for which this anomaly is absent. Blue line is the ab initio theoretical absorption spectrum of 1.23 nM of 15e after summation with the dashed ‘baseline’, blue band is the 1σ confidence interval (see Supplementary Information Section 6.2).