Red Shift in the Absorption Spectrum of Phototropin LOV1 upon the Formation of a Semiquinone Radical: Reconstructing the Orbital Architecture

Flavin mononucleotide (FMN) is a ubiquitous blue-light pigment due to its ability to drive one- and two-electron transfer reactions. In both light-oxygen-voltage (LOV) domains of phototropin from the green algae Chlamydomonas reinhardtii, FMN is noncovalently bound. In the LOV1 cysteine-to-serine mutant (C57S), light-induced electron transfer from a nearby tryptophan occurs, and a transient spin-correlated radical pair (SCRP) is formed. Within this photocycle, nuclear hyperpolarization is created by the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect. In a side reaction, a stable protonated semiquinone radical (FMNH·) forms undergoing a significant bathochromic shift of the first electronic transition from 445 to 591 nm. The incorporation of phototropin LOV1-C57S into an amorphous trehalose matrix, stabilizing the radical, allows for application of various magnetic resonance experiments at ambient temperatures, which are combined with quantum-chemical calculations. As a result, the bathochromic shift of the first absorption band is explained by lifting the degeneracy of the molecular orbital energy levels for electrons with alpha and beta spins in FMNH· due to the additional electron.

Table S1: Transitions, excitation energies in nm and eV, oscillator strengths as well as the MO pair with the highest contribution to the transition together with its weight for the first ten excited states of FMN.The transitions highlighted in bold are shown as sticks in the absorption spectrum of Fig. 2. The first nine transitions are dominated by one pair of canonical MOs, whereas two MO pairs with nearly the same weight contribute to S10.The electron is preferentially excited into the LUMO except for the two highest transitions, where LUMO+1 and LUMO+2 are involved.Table S3: 15 N principal values (d11, d22, d33), span (W) and asymmetry parameter (h) of the frozen solution (Sol.) and the trehalose glass (TG) for all three occurring signals taken from fitting of CSA tensors shown in Figure 4. Fits were carried out with ssNake 1.3  S3).From the linear fit (R 2 =0.99) the shielding can be converted using the formula  !"#! = −1.0034⋅  $%& + 238.8.

Benchmark of Vertical Excitations
Employing the structures optimized with TPSSh/aug-cc-pVTZ and polarizable continuum model (PCM), we performed further excited state calculations with TD-DFT to assess the influence of the functional and PCM.For this, we employed the Gaussian 16 software suite [2] and in addition to the TPSSh functional with 10 % exact exchange, we employed the PBE0 functional with 25 % exact exchange and the long-range corrected LC-ωPBE functional.From these calculations, we only report the two lowest bright transitions with significant oscillator strength (> 0.020) for both FMN and FMNH • .To summarize the results, the first bright transition of FMN and FMNH • is always dominated by the excitation from HOMO to LUMO and in case of FMNH • , this applies for the β spin.Similarly, when PCM is employed, the strongest contribution to the second bright transition corresponds to the excitation from HOMO-1 to LUMO, although its weight of 25 % is relatively small for the calculation with the long-range corrected functional.

Vibronic Calculations
To model the fine structure of the two lowest energy absorption bands, we performed vibronic calculations for the first two bright states of FMN and FMNH • .For this, we employed the Gaussian 16 software suite [2] together with the default adiabatic Hessian model, i.e. employing optimized geometries and normal modes for the involved electronic states.[3] Based on our previous experiences with such calculations [4] and the results from the benchmark study given above, we decided to employ PBE0/aug-cc-pVTZ with PCM as level of theory for all calculations reported in this section.For the simulation of vibronic spectra, we only included the Franck-Condon terms together with an integral threshold of 10 11 and employing 8 classes.Absorption spectra were then obtained by convoluting each vibronic transition with Gaussian functions using a half-width at half-maximum of 400 cm -1 .
For FMN, we obtained spectrum progressions of around 99 % towards the analytic limit for both S1 and S3.Unfortunately, it was not possible to simulate vibronic absorption spectra for FMNH • with this approach, as the spectrum progressions remained rather low for both states D1 and D2.Therefore and based on the similarity of the first two bright transitions between FMN and FMNH • , we assumed that the absorption bands of FMNH • may exhibit a similar vibronic progression as FMN.Owing to this and based on vertical excitation calculations with the same level of theory, s.Table S7, we shifted the corresponding absorption bands of FMN by the average shift in excitation energies of the two relevant transitions (6317 cm -1 ) and scaled their intensities by the ratio of oscillator strengths, i.e. 0.561 and 0.253 for D1 and D2, respectively to estimate the absorption bands of FMNH • .The resulting spectra are shown in Figure S5.
In case of FMN, the position of the lowest energy absorption band from the vibronic simulations is slightly blue-shifted relative to experiments, but slightly red-shifted for the second absorption band.Regarding the relative strengths of the vibronic progressions, it is underestimated for the first absorption band, but fits relatively well for the second one.Regarding the absorption bands of FMNH • , the mismatch in positions and absolute intensities is larger, which is most likely caused by the employed assumption for approximating these bands.Nonetheless, the relative intensities and positions within a band appear to be rather similar between simulations and experiments.Therefore, the results from these simulations suggest that each of the absorption bands originates from one electronic transition.These transitions are further discussed in the main text based on results from vertical excitation calculations with TPSSh/aug-cc-pVTZ and PCM as level of theory.

Figure S1 :
Figure S1: Petri dish containing CrLOV1 incorporated in a glassy sugar matrix.(A) Yellow matrix

Figure S2 :
Figure S2: Representation of molecular orbitals (MOs) that are involved in the bright transitions

Figure S5 :
Figure S5: Absorption spectra of FMN (orange) and FMNH • (green) from experiments (solid lines), vertical excitation calculations (dashed lines) and vibronic simulations of the two bright transitions (dotted lines).Intensities were normalized on 1 based on the highest experimental and computed absorption value in the shown spectral range.Please note, that in case of FMNH• , the vibronic simulations did not lead to converged spectra, therefore we estimated the corresponding band shapes based on the results of FMN, s. the text and table S7 for further details.

Table S2 :
Transitions, excitation energies in nm and eV, oscillator strengths as well as the MO pair with the highest contribution to the transition together with its weight for the first ten excited states of FMNH • .The transitions highlighted in bold are shown as sticks in the absorption spectrum of Fig.2.With the exception of D9, all transitions are dominated by one pair of canonical MOs and most of the time, an excitation of an electron with β spin is involved.

Table S5 :
Hyperfine couplings for FMNH • in MHz obtained from DFT calculations with ORCA.
a In the DFT calculations, a methyl-group replaced the side-chain of FMNH • .Average of three protons is given here.

Table S6 :
Fitting parameters for the three identified individual components of W98-N1 in trehalose (Figure3, top).

Table S7 :
Transitions, excitation energies in nm and eV, oscillator strengths as well as the MO pair with the highest contribution and its weight for the two lowest bright transitions of FMN calculated with three different functionals with and without PCM.
*The weight for these restricted calculations was determined as twice the squared coefficient.TableS8: Transitions, excitation energies in nm and eV, oscillator strengths as well as the MO pair with the highest contribution and its weight for the two lowest bright transitions of FMNH • calculated with three different functionals with and without PCM.*The weight for these unrestricted calculations was determined as the square of the coefficient.

Table S9 :
Transitions, excitation energies in eV and oscillator strength from vertical excitation calculations of FMN and FMNH • .Furthermore, columns 6 and 7 list the shift in excitation energies in eV and cm -1 , respectively, and column 8 contains the ratio of oscillator strengths.These latter quantities were used to approximate the absorption band shapes of FMNH • as described in the text.