Supramolecular Polymerization as a Tool to Reveal the Magnetic Transition Dipole Moment of Heptazines

Heptazine derivatives have attracted significant interest due to their small S1-T1 gap, which contributes to their unique electronic and optical properties. However, the nature of the lowest excited state remains ambiguous. In the present study, we characterize the lowest optical transition of heptazine by its magnetic transition dipole moment. To measure the magnetic transition dipole moment, the flat heptazine must be chiroptically active, which is difficult to achieve for single heptazine molecules. Therefore, we used supramolecular polymerization as an approach to make homochiral stacks of heptazine derivatives. Upon formation of the supramolecular polymers, the preferred helical stacking of heptazine introduces circular polarization of absorption and fluorescence. The magnetic transition dipole moments for the S1 ← S0 and S1 → S0 are determined to be 0.35 and 0.36 Bohr magneton, respectively. These high values of magnetic transition dipole moments support the intramolecular charge transfer nature of the lowest excited state from nitrogen to carbon in heptazine and further confirm the degeneracy of S1 and T1.


Materials.
All commercially available chemicals were purchased from Acros, Aldrich, or TCI, and were used as received.Solvents used in the reactions were dried using an MBraun SPS-800 solvent purification system or purchased from Acros and Aldrich.The water (ULC/MS grade) used in sample preparation was purchased from Biosolve.

Synthesis. Scheme S1. Synthesis of S-H.
Potassium Cyamelurate (2)   Melon pellets were pulverized with a pestle of a mortar.A round bottom flask (250 ml) was charged with 10 g of the yellow powder (45 mmol, 1 eq.) and 90 ml of 3 M KOH (275 mmol, 6 eq.).Subsequently, the reaction was refluxed for 3 h.After the reflux, the mixture was quickly filtrated in a warmed Büchner funnel.Grey impurities separated and a white crystal formed in the filtrate upon cooling down.The filtrate was filtrated.The second residue was washed with ethanol thrice.Afterwards, the residue was dried in a vacuum and collected.A white powder was obtained.Yield: 68%.IR (cm -1 ): 3064, 1644, 1515, 1471, 1404, 1151, 813.

Cyameluric Chloride (4)
The reaction was carried out under inert conditions and dried glassware.A round Schleck bottom flask (250 ml) was charged with cyameluric acid (2 g, 9.04 mmol, 1 eq.) and 50 ml POCl3.PCl5 (8.5 g 40.7 mmol, 4.5 eq.) was added slowly to the mixture.The mixture was refluxed for 4 h.The generation of an acidic gas was observed, and it was neutralized by passing it through an aqueous NaOH 1 M solution.After 2 hours of refluxing the color had changed from white to yellow.In addition, the mixture was less turbid than in the beginning.After the reflux, the POCl3 was removed via distillation.The temperature was raised to 140 °C and the mixture was exposed to an argon flow, resulting in the complete removal of the POCl3 and sublimating the PCl5 excess to the upper part of the vessel.The product was obtained as a yellow powder.Yield: 90%. 13C NMR (100 MHz, THF-d8): δ = 175.4,158.6.IR (cm -1 ): 1601, 1498, 1302, 1200, 1088, 970, 824, 648, 579.

UV-vis and CD spectroscopy.
Stock solution (1 mM) was prepared by weighing the compound into a screw-capped vial and adding the required amount of CHCl3.The stock solutions were sonicated for 30 seconds.The sample solutions were prepared via aliquoting a certain volume of CHCl3 stock solution into a sealable vial.The CHCl3 was removed by N2-blow-drying for 1 h followed by overnight drying under ambient conditions.Then proper volume of solvent was added to the vial to give the final concentration.The sample was then sonicated for about 30 s and heated to be fully dissolved.Samples were then transferred into quartz cuvettes with a path length of 1 or 10 mm, depending on each sample.CD spectra were recorded on the Jasco J-815 Circular Dichroism Spectrometer.UV-vis spectra were recorded on a Cary 3500 spectrometer and Jasco J-815 Circular Dichroism Spectrometer.

Computational analysis of CD data.
The supramolecular polymerization is modeled using thermodynamic mass-balance expressions. 1 In the model, the polymers (P) are assumed to grow through monomer (M) addition and dissociation at the chain ends.The reactions that describe the cooperative pathway, for which a nucleus size of 2 is assumed, are: with Kn the nucleation constant and Ke the elongation constant of the nucleated pathway.Assuming the activity of the chemical species is equal to their concentrations, the concentration of monomers in i-mer in the cooperative aggregates in thermodynamic equilibrium can then be expressed as a function of the free monomer concentration with: where [M] is the equilibrium monomer concentration and σ is the cooperativity parameter, which is σ=Kn/Ke.The total concentration of M in the system is the sum of monomers and nucleated aggregates: With standard expressions for converging series, the summation in equation (E3) can be solved and the mass-balance equation for the system can be obtained: This equation is solved in Matlab®, using a custom written binary search algorithm, to obtain the free monomer concentration.The free monomer concentration is then used to calculate the concentration of nucleated aggregates.
The binding constant Ke is rendered temperature-dependent through the van 't Hoff expression: e e e exp exp With R the gas constant, T the temperature, ΔHe and ΔS the enthalpy and entropy of elongation, respectively.
The nucleation penalty NP is related to the cooperativity parameter σ via: The above-described model is fitted to the CD signal at 360 nm.To predict the spectroscopic response, the concentration of every aggregate type (M and P) is multiplied by the molar absorbance or molar ellipticity for the specific aggregate types: The molar ellipticity of the monomers θM is fixed at 0. The fit parameters were ΔHe, ΔS, NP and θP.
The differences between the simulated data and the experimental data were combined in a cost vector.The minimization of the cost vector was performed using the Matlab® lsqnonlin function with the Levenberg-Marquardt algorithm to obtain optimal values for the thermodynamic parameters of the supramolecular polymerization.To ensure that the solution is at the global minimum, the fits were performed with a minimum of 500 initial parameter sets.The initial parameter sets were defined using a Latin Hypercube Sampling method, implemented with the Matlab® function lhsdesign.To ensure reasonable values of the set of starting parameters in the fitting procedure, ΔGe was sampled between -60 and -30 kJ/mol, ΔS between -200 and -50 J/mol•K, ΔGn between -50 and -20 kJ/mol and θP between 1.0×10 6 and 1.2×10 6 mdeg•M•cm -1 .The final fitting parameters that resulted in the lowest norm of the residual cost vector were selected as the best fit.
Table S1.Thermodynamic parameters for supramolecular polymerization of S-H were obtained from fitting mass balance model to CD cooling curves.

FT-IR measurements.
Toluene solution of S-H (200 µM) was placed in a cell with windows made of CaF2.with R the gas constant, T the temperature, ΔGe ° the Gibbs free energy of elongation of the cooperative polymerization, ΔGe the cosolvent-corrected Gibbs free energy of elongation of the cooperative polymerization, and mMCH the solvent dependency parameter of the elongation process to MCH, which is present in solvent fraction fMCH.

VT-NMR measurements.
To eliminate the number of monomers in the supramolecular, we calculate the number-average degree (DPn) of polymerization at room temperature using the optimized parameters obtained from fitting the solvent titration curve (Figure S8). 1 As shown in Figure S10, the calculation suggests that DPn must be about 9 to achieve the highest dissymmetry factor.We realized that we could increase the polymer fraction of S-H by introducing MCH as a bad solvent in the samples.The addition of MCH increased the degree of aggregation, as indicated by the UV/Vis and CD spectra.At high fractions of MCH (> 0.8), we observed an unexpected decrease in the degree of aggregation, which is likely caused by the formation of different aggregates or precipitation of S-H.The formation of different aggregates was confirmed by AFM images of S-H supramolecular polymers in MCH/Toluene (9/1) (Figure S10).The assembled S-H shows a pancake shape with a height of 15 nm and a diameter of about hundreds of nm, in which the fiber bundles are likely intertwined.The formation of bundles by increasing the ratio of bad solvents was also observed in our group's previous paper.Thus, it is important to keep in mind that under the condition of a higher ratio of MCH, S-H might not only be in one-dimensional cooperative polymers, and proper MCH fractions should be used if it is desired to have only one-dimensional supramolecular polymers of S-H.12. Photoluminescence decay.
Time-correlated single photon counting was measured using an Edinburgh Instruments LifeSpec-PS spectrophotometer with 400 nm pulsed diode laser (LDH-C 400 driven by a PDL-800B) excitation.

Determination of the electric and magnetic transition dipole moment of the S1←S0 absorption band of heptazine.
The lowest excited state of the core heptazine moiety (C6H3N7 1,3,4,6,7,9,9b-Heptaazaphenalene) with D3h symmetry has been studied extensively through quantum chemical calculations. 3,4,5The lowest excited singlet state is of ππ* orbital nature and A'2 symmetry.The state can be accurately described in terms of a single electron excitation from the A"1 HOMO to the A"2 LUMO orbital.The transition from the ground state to this lowest excited singlet state in electric dipole is forbidden but magnetic dipole is allowed in the z direction perpendicular to the aromatic plane.
Pure magnetic dipole transitions in the optical frequency range are extremely weak in intensity. 6The associated magnetic transition dipole moment is difficult to determine because extremely small perturbations of the molecular structure e.g.molecular vibrations can lead to the admixture of an excited state with an electric dipole-allowed transition.As a result of this mixing of excited states, the original transition probability due to the magnetic dipole can easily be overwhelmed by the admixed electric dipole strength.
Chiral molecules offer a unique opportunity to determine the magnetic m and electric µ transition dipole moments through measurements of the circular polarization in absorption and emission.The degree of circular polarization in absorption (gabs) and luminescence (glum) depends on the relative magnitude and orientation of the magnetic and electric transition dipole moments: (S2) Here Δε = εL -εR denotes the circular differential molar decadic extinction coefficient, c the speed of light, 10 m  and 1 0   the magnetic and electric transition dipole moments for the transition from the singlet ground state 0 to the lowest excited singlet state 1, 10 m → and 1 0  → the corresponding transition dipole moments for the emissive transition from the lowest excited singlet state back to the ground state, c the speed of light.The sign 'Im' indicates that the imaginary component should be taken.Note that the magnetic dipole operator contains an imaginary number.In the case where the molecular wavefunctions are fully real, the magnetic transition dipole moment will be fully imaginary and the electric dipole moment fully real.In formulae S1 and S2, the magnetic and electric transition dipole moments should be entered in SI units (joule per tesla and coulomb meter).In order to have numbers for m and  of a convenient magnitude, one could express the magnetic and electric dipole moments for a molecular electronic transition in units of respectively Bohr magneton (µB = 9.27×10 -24 joule per tesla) and Debye (D = 3.34 ×10 -30 coulomb meter).Typical values for the transition dipole moments for a transition that is both electric and magnetic dipole allowed are  = 10 D and m = 1.0 Bohr magneton, which together give a g-value of 0.0037 if the two dipole moments are oriented fully parallel.
For organic dye molecules, the relative contribution of the electric transition dipole to the total dipole strength is usually considerably larger than that of the magnetic dipole contribution (c 2 |µ| 2 > |m| 2 ) so that the expression simplifies to : ( ) The strategy that we will use for determining the magnitude of the magnetic transition dipole moment is the following.We start by considering the heptazine core (C6H3N7) with D3h symmetry.The lowest excited singlet state of A'2 symmetry is magnetic dipole allowed in the z-direction, but electric dipole forbidden.Given the electric transition dipole moment equal to zero, equations S3 and S4 predict zero circular polarization in absorption and emission, consistent with the achiral nature of the D3h point group.The addition of the enantiopure phenylamide groups makes the molecule S-H chiral.Yet in dilute solution, S-H still shows vanishingly small circular dichroism and circular polarization in luminescence, because the stereocenters in the aliphatic side chains are not yet able to enforce helicity in the -system of the molecule.Stacking of the molecule in the aggregate forces the molecule to adopt a propellor-like shape resulting in a lowering of the symmetry from D3h to D3.In the stack, the lowest excited state now has A2 symmetry and the transition from the ground state to his particular level is now both electric and magnetic dipole allowed in the out-of-plane or z-direction.Because the phenylamide groups only couple weakly to the lowest excited state, we assume that the magnitude of the magnetic transition dipole moment for S-H in the stack is approximately similar to the magnetic dipole moment in the heptazine core.The phenylamide groups contribute to the electric dipole moment in the z-direction.

Table S2. Character Table for the
To further support the assignment of A2 symmetry to the lowest excited state, we note that the extremely low extinction coefficient for the absorption band is associated with the transition from ground to lowest excited state, the lowest excited state is unlikely to transform according to the E representation.Transitions from the ground state (A1) to states with E character should be electric dipole allowed with transition dipole vector in the aromatic plane, which is clearly contradicted by the experiment.
So, the lowest excited state transforms as either A1 or A2.The transition from the ground state to A2 is both electric and magnetic dipole allowed in the z-direction (because z and Rz are basis vectors for this representation).A2 character for the lowest excited state would thus be consistent with the high degree of circular polarization observed experimentally.Also, recent quantum chemical calculations support A2 character for the lowest excited singlet state in heptazine. 3 argue that the lowest excited state of S-H in the aggregate remains essentially localized on individual molecules because the absorption spectrum in the long wavelength does not show a significant change upon aggregation.We note that this is not the case for the electric dipole allowing optical transitions to the higher excited state of E symmetry located in the spectral region around 330 nm wavelength.Here the absorption spectra clearly show changes upon aggregation (Figure 1).Furthermore, because the transition to the lowest excited state is extremely weak in intensity, interactions between the electric transition dipole moments that normally drive delocalization of the excited states must be very weak.We note that interaction between two magnetic transition dipoles (of 1 µB magnitude) is several orders of magnitude smaller than the interaction between electric transition dipole interactions (of 1 D magnitude) and is thus ineffective in inducing delocalization of the excited state in the stack. 7xt, we try to determine the magnitude of the electric transition dipole moment  for the molecules in the aggregate, because knowing  and using relations S3 and, S4 one can compute the magnetic transition dipole moment m.We first focus on the determination of the electric transition dipole moment in absorption 1 0   .
To determine the electric transition dipole moment  of the S1←S0 electronic transition in absorption we make use of the wellknown relation between dipole strength | 2 | and the molar decadic absorption coefficient  in solution. 8 Here  is a correction factor for the solvent polarizability.The integral should be taken over the absorption band associated with S1←S0 electronic transition.If we now look in detail at the absorption spectrum of the molecule under study, see Figure S17, a complication becomes apparent.
The absorption spectrum shows an onset at about 494 nm wavelength with low intensity, followed by maxima of much higher intensity at 467, 438, and 413 nm.From the shoulder at 494 nm, we can identify the 0-0 vibronic band of the transition, i.e. the origin of the transition.This is because the CD spectrum also has its first maximum at 494 nm.The distribution of intensity over the various sub-bands in the absorption spectrum does not follow the standard Franck-Condon profile: the relative intensity of the 0-0 sub-band is way too low.The relatively high intensity of the sub-bands at shorter wavelengths can be accounted for by vibronic mixing.Out-of-plane vibrational modes of E symmetry can induce admixture of ππ* excited states of E symmetry to the A2 lowest excited singlet state.The excited singlet states with E symmetry can be via electric dipole-allowed transitions from the ground state and are responsible for the strong absorption around 330 nm (See Figure 1).Thus the absorption of heptazine in the 510-410 nm wavelength range has mixed character and contains intrinsic contributions polarized along z and vibronically induced component polarized in the x,y plane of the molecule.
The induced x,y components of the electric transition dipole moment do not contribute to the dipole strength of the 0-0 vibronic transition near 493 nm.Therefore, Eq S3 can be simplified: The induced x,y components of the electric transition dipole require at least one quantum of the promoting E vibrational mode.The energy difference between the maximum of the visible absorption at 467 nm and the origin of the absorption at 493 nm amounts to 1088 cm -1 , which is indeed consistent with the highest frequency band for out-of-plane vibrations of the phenylamide heptazine molecule.
Referring back (S5), in order to compute 10 ,z m  we need to know 10 ,z   .Now to extract 10 ,z   from experimental data, we make use of the rotational strength of the S1←S0 transition, which is proportional to the integrated circular dichroism of the stacked molecule over the visible band: where  is a constant depending on the units used.The rotational strength is related to the dot product of the electric and magnetic transition dipole moments: where we have assumed that any admixed, x,y polarized components of the magnetic transition dipole moment are small compared to the intrinsic magnetic dipole moment of the transition 10 ,z m  .The practical procedure to extract the z-component of the electric dipole moment is now as follows. 9We take the CD spectrum of aggregated S-H and scale it such that the maximum of CD signal at 493 nm matches with the absorption at the same wavelength, see Figure S17.The area under the scaled CD spectrum: Where fscale is the dimensionless scaling constant needed to scale the CD spectrum such that its maximum intensity matches the molar absorption at the same wavelength.This procedure, see Figure S17, yields  1←0, = 0.18 .Using (S3) we then find  1←0, = 0.35

Determination of the electric and magnetic transition dipole moment of the S1→S0 luminescence band of heptazine.
The Strickler-Berg equation relates the rate of radiative decay of the lowest excited singlet state of a molecule back to the ground state to the absorption spectrum of the corresponding reverse transition from the ground state to the lowest excited state: 10 Combining (S9) with (S5) and reverting the microscopic reversibility (  2 (S 1 → S 0 ) =  2 (S 1 ← S 0 )) assumed in the original derivation of (S9), we arrive at: We first determine the rate of radiative decay by measuring the fluorescence decay curve and the fluorescence quantum yield.
When using pure toluene as a solvent, the total concentration of S-H needs to be quite high (mM) to drive the association to completion.The high concentration leads to problems with self-absorption in the fluorescence measurements while at low concentration, unpolarized fluorescence from not aggregated molecules dominates fluorescence.
In the solvent mixture of toluene and methylcyclohexane, the molecules can be quantitatively aggregated at a lower total concentration, and the experimental difficulties mentioned above can be avoided.
In toluene/MCH (1/3 vol/vol), the averaged excited state lifetime amounts to 61 ns with a fluorescence quantum yield of 5.8 %.This yields a radiative decay constant of krad= 0.00095 ns -1 .Next, we realize that radiative decay can also occur due to the vibronic admixture of dipole transitions polarized in the plane of the molecule.To accomplish this decomposition, we apply a procedure similar to the one used for decomposing the absorption spectrum (see above).From the measurement of glum (see Figure S18), we compute the band profile of the circular differential emission (I = IL -IR).We scale the I spectrum such that it matches the fluorescence spectrum in intensity at the onset of the band near 495 nm, see Figure S18.We then integrate both the total and the scale I spectrum and find that only 25 % of the radiative decay is due to transitions polarized parallel to the molecule z-axis.Incidentally for the energy difference between the maximum of the DI spectrum and the maximum of the total emission, we find the frequency of the promoting out-of-plane vibrational mode with E symmetry is around 1280 cm -1 , largely consistent with the estimate from the absorption spectrum.We note that these frequencies do not need to match exactly because they refer to ground and excited state out-of-plan vibrations.
Finally using relation S10, we find that the z-component of transition dipole in emission is  1→0, = 0.20  .Taking the maximum dissymmetry ratio in emission glum = −0.068we obtain the magnetic transition dipole moment in emission  0→1, = 0.36   15.Calculation of the magnetic transition dipole moment for the heptazine core molecule.
In this section, we provide a simple quantum chemical calculation of the magnetic transition dipole moment of the heptazine moiety (C6H3N7 1,3,4,6,7,9,9b-Heptaazaphenalene) with D3h symmetry.The molecular geometry is known from X-ray crystallography. 11n our calculation, we aim at maximal transparency and traceability rather than quantum chemical accuracy.The main reason for this is to avoid any possible confusion associated with the use of units from different systems (SI, CGS, or atomic).We focus on the p-electron system and neglect any involvement of electrons in s-orbitals.
The magnetic transition dipole moment of a transition between singlet states is obtained from the evaluation of the matrix element of the orbital angular momentum operator L: Here the values of the matrix elements of the orbital angular momentum operator in units of  are equal to the values of the magnetic transition dipole moment in units of Bohr magneton.
Considering the three-fold rotational symmetry of heptazine around the z-axis and the fact that the molecule has only 6 carbon and 6 nitrogen atoms in its outer rim, it follows that any p-orbital cannot have more than 3 vertical nodal planes.The Lz angular momentum quantum number of a p electron can therefore not exceed 3 units of  in magnitude.The magnetic transition dipole moment must be smaller than 3 Bohr magnetons.
For particles confined to a perfectly circular orbit in the x,y-plane of fixed radius R the states with Lz =+3 and -3 are , one finds that the maximal magnetic dipole moment is achieved for a transition of an electron from the p to the m state because: ̂  = (−ℏ)3  (S15) And so: The idealized p to the m state allow us to build an intuitive picture of which pair of orbitals will give the maximum magnetic dipole moment when an electron is transferred between these two orbitals via optical excitation.We first plot the states p and m as function of the angle  in the range (0, 2), see Figure S19.
. Quantum states p and m for an electron on a ring.
Next we indicate the approximate position of the 6 nitrogen and six carbon atoms in the outer ring (N1..N6 and C1..C6), see again Figure S19.We note that p has six nodes at exactly the position of the nitrogen atoms and that m also has six nodes but now at the place where the nitrogen atoms are positioned.It then follows that the maximum magnetic dipole moment is expected for an optical transition of an electron from a molecular orbital with three vertical nodal planes including all 6 nitrogen pz atomic orbitals to a molecular orbital with also three vertical nodal planes but now with contributions from only the six pz atoms orbitals on the carbon atoms in the outer ring.Finally, if we now look at the HOMO and LUMO orbitals in Figure 3c we see that indeed these each have three vertical nodal planes with the homo localized on nitrogen and the LUMO localized largely on carbon.Thus, for the HOMO-LUMO excitation of the heptazine moiety, we expect a large transition dipole moment with magnitude < 3 Bohr magneton.
To calculate the magnetic transition dipole moment, we express the atomic pz orbitals as: With z the height above the aromatic plane, r the distance to the center of the orbital and Zeff,2p the effective nuclear charge for the 2p orbital 12 (C : Zeff,2p = 3.25 and N: Zeff,2p = 3.9).The final of the magnetic transition dipole moment of the HOMO to LUMO excitation then involves incorporation of the orbital coefficients, expressing z and r in polar coordinates, appropriate normalization of the orbital with polar coordinates, and finally numerical integration of the matrix element.16.DFT calculation.
The electronic structures of heptazine (S-H) were calculated using time-dependent density functional theory (TDDFT) with the three-parameter Becke−Lee−Yang−Parr hybrid density functional (hybrid-B3LYP) using AMSjobs 2022.1 program.To simplify the calculation, aliphatic chains on the molecule were not involved in the simulations due to their limited effect on the electronic structure of heptazine.The optimized structure of S-H from DFT calculation indicated a flat core of heptazine, while the rotation angle of the phenol group to the heptazine plane is less than 10°.Moreover, the dihedral angle of the carbonyl group and phenyl group is 31°, while the other two dihedral angles are around 10°.
17. IR and NMR data.

Figure S1 .
Figure S1.AFM height images of S-H supramolecular polymer prepared from a toluene solution (160 µM) measured in an area of (a) 10×10 µm (b) 2×2 µm.(c) AFM phase image of S-H supramolecular polymer corresponding to Figure S1b.(d) Height profile of a single fiber (purple) and a fiber bundle (gray), as indicated in FigureS1a, suggests a single fiber diameter of 1.2 nm.The discrepancy between the height and width of the measured feature originates from the conventionally observed AFM tip-sample convolution in the x-y plane.

Figure S2 .
Figure S2.UV-vis absorption spectra of a toluene solution of S-H (160 µM) upon cooling with a rate of -2 K/min.

Figure S3 .
Figure S3.Cooling curves of S-H in toluene at different concentrations fitting with the thermodynamic mass-balance model.

9 .
Circularly polarized luminescence measurements.Circularly polarized luminescence measurements were performed using a homemade CPL/LPL spectrometer, constructed by photoelastic modulation at 50 kHz, parallel multichannel detection, single photon counting electronics and an Hg lamp.Samples ΔHe (kJ/mol) ΔS (J/(mol*K)) NP (kJ/mol) than 0.2 mM are excited at 313 nm, while samples at a higher concentration are excited at 405 nm.

Figure S6 .
Figure S6.The value of dissymmetry factor of luminescence (│glum│) at 493 nm of S-H in toluene at different concentrations.

Figure S7 .
Figure S7.Dissymmetry factor glum as a function of wavelengths for S-H supramolecular polymers in toluene (black curve) and the mixture of toluene and MCH with a ratio of 1/1 (blue curve), 1/3 (orange curve), and 1/9 (green curve).10.UV-vis and CD spectroscopy in the mixture of toluene and MCH.

Figure S8 .Figure S9 .
Figure S8.(a) UV-vis absorption (b) CD spectra of S-H in the solvent mixture of toluene and MCH with different ratios.Inset: absorption and CD signal at 360 nm of S-H in the mixture of toluene and MCH at various ratios.

Figure S10 .
Figure S10.Calculated number-average degree of polymerization in the solvent mixture of MCH and toluene at different ratios.

Figure S18 .
Figure S18.Decomposition of the fluorescence of S-H in Tol/MCH into components polarized along the molecular z-axis, (red line) and components polarized in the molecular x,y-plane (dashed blue line) states, we can construct two fully real states: angular momentum operator in terms of the angle  is | →, | = 0.4   , i.e. a magnetic transition dipole moment of 0.4 bohr magneton.

Table S3 .
Character Table for the D3 point group