domain: spi phys

text:
P Develter

J Bosse

O Rabaste

P Forster

J.-P Ovarlez

OFF-GRID RADAR TARGET DETECTION WITH THE NORMALIZED MATCHED FILTER: A MONOPULSE-BASED DETECTION SCHEME

Keywords: Radar, Detection, Off-grid, Monopulse, Normalized Matched Filter

In this paper, we tackle the problem of off-grid radar target detection based on the Normalized Matched Filter. State-ofthe-art solutions to this problem include the use of the Generalized Likelihood Ratio test (GLRT), whose implementation can be costly, subspace detectors, or oversampling. In this paper, we introduce a new solution for improving detection of an off-grid target. It is inspired by monopulse angle estimation methods. Using simulations, we show that our solution is comparable to the GLRT under Gaussian noise hypothesis with a known covariance matrix in terms of detection probability. As such, its detection performance appears to be often better than those of detectors in the same computational cost range, and significantly better in some cases.

INTRODUCTION

The goal of radar systems is to detect the presence of targets with unknown parameters in unknown environment. Classically, in presence of unknown parameters, the commonly used detection strategy is the Generalized Likelihood Ratio test (GLRT) that replaces the unknown parameters by their Maximum Likelihood estimators (MLE) in the detection test. Unfortunately, analytical MLE solutions are not available for some target parameters of interest (Doppler shift, distance, and direction for example).

Therefore, for ease of implementation, most detection strategies assume that target parameters lie over a discrete set, called the grid. However, target parameters have no reason to fall exactly on the grid, since they are distributed over a continuous range. This mismatch between the tested parameters and the real target parameters deteriorates the response of most state-of-the-art tests. For example, in homogeneous Gaussian environment, it is well known that the Matched Filter (MF) test can approximately suffer from a maximum of 3dB loss for common grid sampling strategies (e.g. at the resolution cell). This tends to deteriorate the detection probability. The off-grid impact has also been shown to be particularly dramatic for other detection schemes like the Normalized Matched Filter (NMF) test. In some cases, the detection probability may vanish to 0 even for high Signal to Noise ratio (SNR) [START_REF] Rabaste | Off-grid target detection with Normalized Matched Subspace Filter[END_REF], especially for common low probability of false alarm (P F A ).

To overcome this problem, the most obvious solution is to approximate the GLRT on a refined parameter grid, but this can be costly in terms of computations. Other works have addressed this issue in adaptive context with a steering vector mismatch (bounded angle mismatch) [START_REF] Besson | Detection of a signal in linear subspace with bounded mismatch[END_REF], but they are not yet suited for low P F A radar contexts [START_REF] Bosse | Adaptive subspace detectors for off-grid mismatched targets[END_REF]. The authors in [START_REF] Bandiera | Advanced Radar Detection Schemes Under Mismatched Signal Models[END_REF] proposed a two-stage detector to reduce the loss in performance. Those solutions do not cure the asymptotic SNR loss under grid mismatch [START_REF] Rabaste | Geometrical design of radar detectors in moderately impulsive noise[END_REF]. Some authors have proposed to model the mismatch through relevant subspaces [START_REF] Bosse | Subspace rejection for matching pursuit in the presence of unresolved targets[END_REF] using subspace detection framework.

In this paper, we propose a new method that solves the off-grid problem. It enables to achieve a detection probability of 1 at high SNR, even for arbitrary low P F A . Moreover, this is achieved at a low computational cost.

Section 2 presents the signal model and the off-grid detection problem. We present our method in Section 3. Finally, its performance is evaluated in Section 4 through simulations.

Notations: Matrices are in bold and capital, vectors in bold. For any matrix A or vector, A T is the transpose of A and A H is the Hermitian transpose of A. I is the N × N identity matrix and CN (µ, Γ) is the circular complex Normal distribution of mean µ and covariance matrix Γ.

THE OFF-GRID RADAR DETECTION PROBLEM

In radar detection, the main problem consists in detecting a complex signal s ∈ C N corrupted by an additive noise n (clutter, thermal noise, etc.). This problem can be stated as the following binary hypothesis test:

H 0 : r = n , H 1 : r = α s(θ) + n , ( 1
)
where r is the complex N -vector of the received signal, α is an unknown complex target amplitude and s(θ) stands for a generally known steering vector characterized by unknown target parameters θ (time-delay, Doppler or angle). In the sequel, we will assume n is a zero-mean complex circular Gaussian noise vector with known covariance matrix Γ but with unknown variance σ 2 i.e. n ∼ CN (0, σ 2 Γ). This context is known as a partially homogeneous Gaussian environment. Without loss of generality, we will here assume θ to be the scalar Doppler shift of the target and we here investigate only the normalized Doppler steering vector s(θ):

s(θ) = 1 √ N 1, e 2iπθ , . . . , e 2iπ(N -1)θ T . (2)
This model of steering vector is often encountered in radar Range-Doppler detection schemes where the problem consists in estimating a complex sinusoid embedded in noise after range Matched Filter processing.

For unknown parameters {λ} i∈[0,1] depending on each hypothesis {H i } i∈[0,1] (either parameters of interest and/or nuisance parameters), the usual procedure to derive the best strategy relies on the Generalized Likelihood Ratio (GLR) statistic, namely the ratio Λ(r) between the Probability Density Function (PDF) f H1 (.) of the data under H 1 and the PDF f H0 (.) under H 0 where the unknown parameters are replaced by their MLE estimate:

Λ(r) = max λ1 f H1 (r) max λ0 f H0 (r) H1 ≷ H0 η. (3)
When λ 1 = {α, σ} and λ 0 = {σ} with θ = θ 0 known, the corresponding GLRT is known as the NMF (Normalized Matched Filter) [START_REF] Scharf | Signal detection in Gaussian noise of unknown level: an invariance application[END_REF][START_REF] Scharf | Matched subspace detectors[END_REF]:

t Γ (r, θ 0 ) = s(θ 0 ) H Γ -1 r 2 s(θ 0 ) H Γ -1 s(θ 0 ) r H Γ -1 r H1 ≷ H0 η. ( 4
)
This test is also widely used for adaptive radar in non-Gaussian contexts [START_REF] Conte | Asymptotically optimum radar detection in compound-Gaussian clutter[END_REF][START_REF] Pascal | On a SIRV-CFAR detector with radar experimentations in impulsive noise[END_REF] for example when the noise is distributed according to a Complex Elliptically Symmetric (CES) distribution [START_REF] Ollila | Complex elliptically symmetric distributions: Survey, new results and applications[END_REF]. When θ is unknown, what is done in practice is to run a variety of tests. The set of the parameters Θ used for testing is called the grid. For a parameter θ 0 on the grid, we will define the cell of width ∆ associated with this parameter as

ν θ0 = [θ 0 -∆/2, θ 0 + ∆/2] . (5)
The grid step size ∆ is classically taken such that s(θ 0 ) and s(θ 0 + ∆) are orthogonal. In our case, ∆ = 1 N i.e. the grid samples are separated by the Doppler resolution.

Each test is run with the assumption that the target parameters are equal to those under test. If a target is detected for any of those tests, it will be considered as detected. However, target parameters θ are never exactly equal to the parameters under test, as target parameters are continuous.

If the point θ 0 where the NMF is tested is different from the parameter θ of the target, the target is said to be off-grid. This induces a mismatch (θ = θ 0 ) between the real target steering vector s(θ) and the steering vector s(θ 0 ) under test. Unfortunately, it was shown in [START_REF] Rabaste | Geometrical design of radar detectors in moderately impulsive noise[END_REF] that the NMF detector is very sensitive to steering vector mismatch, potentially leading to a dramatic deterioration of the detection performance: in particular for a mismatch larger than the detection threshold, it was shown that the asymptotic detection probability tends to 0 at high SNR: this phenomenon occurs [START_REF] Rabaste | Off-grid target detection with Normalized Matched Subspace Filter[END_REF] for P F A as high as 10 -3 . Indeed, the NMF value can be interpreted as a squared cosine between Γ -1/2 s(θ 0 ) and Γ -1/2 r [START_REF] Rabaste | Geometrical design of radar detectors in moderately impulsive noise[END_REF]. As soon as the mismatch causes this angle to lie outside the detection cone defined by the detection threshold η in (4), no detection occurs even without any noise. This can be seen in Figure 1, which displays the NMF response without any noise as a function of the mismatch: this response falls below the detection thresholds at the edge of the cell. This pathological behavior motivates the search for robust detection schemes.

The most natural solution is to consider the GLRT with unknown θ ∈ ν θ0 :

GLRT (r, θ 0 ) = max θ∈ν θ 0 t Γ (r, θ) H1 ≷ H0 η. (6)
Unfortunately, a closed-form expression of this test is unknown, it has to be approximated using possibly computationally-heavy methods.

PROPOSED MONOPULSE-INSPIRED SCHEME

In this section, we introduce a new method for coping with the mismatch. We took inspiration from monopulse methods [START_REF] Mosca | Angle estimation in amplitude comparison monopulse systems[END_REF], and consider the following function:

h Γ,θ0 (r) = t Γ r, θ 0 - ∆ 2 -t Γ r, θ 0 + ∆ 2 t Γ r, θ 0 -∆ 2 + t Γ r, θ 0 + ∆ 2 . ( 7
)
-0.5/N 0 0.5/N -1 0 1 Fig. 2. Candidate g(.) functions for N=10. Γ(ρ) refers to the covariance matrix model in [START_REF] Pascal | On a SIRV-CFAR detector with radar experimentations in impulsive noise[END_REF] The principle is the following: without noise, knowing two test points of the NMF, namely θ 0 + ∆ 2 and θ 0 -∆ 2 , in the main lobe (here, the resolution cell) is enough to provide an estimate of θ, as the distribution of energy between those points is directly linked to the mismatch:

δ = θ -θ 0 . (8)
The quantity [START_REF] Scharf | Signal detection in Gaussian noise of unknown level: an invariance application[END_REF] known as the monopulse ratio can be seen as an approximation of the MLE [START_REF] Mosca | Angle estimation in amplitude comparison monopulse systems[END_REF]. The link between δ and h Γ,θ0 (r) is made thanks to the noiseless g Γ,θ0 function defined as follows:

g Γ,θ0 (δ) = h Γ,θ0 (s(θ 0 + δ)) (9)
Our goal is to find an estimate θ = δ + θ 0 of θ, to plug it in the NMF in order to approximate the GLRT in [START_REF] Bosse | Subspace rejection for matching pursuit in the presence of unresolved targets[END_REF]. For that purpose, δ is obtained by computing δ = g -1 Γ,θ0 (h I,θ0 (r)). Of course, this only makes sense if g Γ,θ0 is invertible. As can be seen in Figure 2, this is not always the case, depending on Γ and θ 0 . For the particular case Γ = I, the functions g Γ,θ0 are invertible. This is why we will use these functions, even in colored noise. Moreover, they do not depend on θ 0 and will be simply denoted by:

g(δ) = g I,θ0 (δ) = sin (πN (δ + ∆)) sin (π(δ + ∆)) 2 - sin(πN (δ -∆)) sin(π(δ -∆)) 2 sin(πN (δ + ∆)) sin(π(δ + ∆)) 2 + sin(πN (δ -∆)) sin(π(δ -∆)) 2 .
The function g takes its values between -1 (at the right edge of the cell) and 1 (at the left edge of the cell).

To summarize, our proposed method is as follows: for every θ 0 on the grid:

1. compute t I r, θ 0 -∆ 2 and t I r, θ 0 + ∆ 2 ; 2. compute δ = g -1 (h I,θ0 (r));

run the final tests t

Γ r, δ + θ 0 H1 ≷ H0 η g .
Finding η g analytically is much more involved than for the NMF. This is why η g was computed resorting to Monte Carlo methods.

Let us describe some properties of this approach. Firstly, when the SNR tends to infinity, r is equivalent to αs(θ) and our procedure yields the true parameter value i.e. θ = θ. This ensures that the probability of detection tends to 1. Secondly, when Γ = I, θ is an approximate MLE [START_REF] Mosca | Angle estimation in amplitude comparison monopulse systems[END_REF] and our test is an approximate GLRT. Thirdly, simulations show that our procedure is still close to the GLRT even when Γ = I.

Finally, let us evaluate the computational load of this scheme. In practice, the method has to be applied in each of the N resolution cells. In total, t Γ needs to be computed 2N times. Consequently, the overall computational load is equivalent to that of approximating GLRT using 2 points per cell, neglecting the cost of inverting g, which is minimal since g can be tabulated offline. It turns out that our approach outperforms existing methods with equivalent computational cost.

NUMERICAL RESULTS

In this section, the performance of our detection scheme is illustrated using Monte Carlo simulations. In each simulation, target parameter θ is drawn at random, uniformly in a given cell. For a given cell under test, we compared the performance of different detectors as a function of SNR. The detectors we evaluated are the DPSS NSMF with subspaces of dimension 2 introduced in [1], our scheme under the name "Proposed" in the figures, an approximation of the GLRT done computing 50 tests per cell, the classical and mismatched NMF under the name "NMF" and a crude approximation of the GLRT exploiting the maximum of two tests per cell under the name "Oversampling x2". Performance for known θ is also provided as "Oracle". Oracle and the GLRT are given as benchmarks. Other detectors ("DPSS NSMF","Oversampling x2") are in the same computational range as our proposed method. Thresholds are computed for each detector, using 20 P -1

F A
Monte Carlo simulations. For each SNR, 20000 Monte Carlo simulations are run, considering steering vectors of length N = 10 and P F A = 10 -6 . Figure 3 first compares the performance of our method with the other detection schemes under additive white noise (Γ = I). Note that in this case, all the cells are equivalent in terms of detection probability. It can be seen that our detector is very close to the GLRT even though its computational cost is lower. As such, it does better than the detectors it is compared to, at a similar cost.

Our proposed detection scheme was also tested against colored Gaussian noise. Its covariance matrix was generated according to the following well-known model:

Γ(ρ) = T 1 ρ . . . ρ N -1 , (10)
where T (.) is the Toeplitz operator. We here tested all the schemes against colored noise of covariance matrice Γ(0.9).

It should be noted that when Γ = I, tests behave differently for each resolution cell. In Figure 4, the target is located in the cell centered around θ 0 = 0/N , and in Figure 5, θ 0 = 5/N . The relationship between |α| 2 and the SNR in dB is defined as:

SNR = 10 log 10 |α| 2 σ 2 . ( 11
)
Note that for the oracle detector, the detection probability depends only on the non-centrality parameter |α| 2 σ 2 s(θ) H Γ -1 s(θ) . This non-centrality parameter characterizes the ratio between the target power and the noise power in the cell under test. It partly explains why the performance depends on the choice of the cell under test.

In cell ν 0 , the shape of the whitened steering vectors variety makes it so that both DPSS NSMF and oversampling by a factor of two do not approach a detection rate of 1 as SNR becomes very high. However our scheme performs only a bit worse than GLRT, and as expected its detection rate increases towards 1 when the SNR is high. In cell ν 5/N , all detectors perform much better than in cell ν 0/N and than in white noise, which was to be expected because of the noncentrality parameter. In this case, the shape of the whitened steering vectors variety also makes it possible for the detectors to detect targets asymptotically. As a result, the probability of detection of DPSS NSMF and oversampling by a factor of two tends toward 1 as SNR increases. In this context, our scheme does approximately as well as the DPSS NSMF detector asymptotically, which makes it slightly worse than GLRT, as it was before.

CONCLUSION

This paper is motivated by detector performance degradation in the case of off-grid targets. The proposed solution is based on monopulse technique and can be considered as an approximate GLRT for off-grid targets in Gaussian noise. It also overcomes the problem of the off-grid NMF not reaching a probability of detection equal to 1 when SNR tends to infinity. It outperforms existing detectors of the same computational cost order and provides detection performance close to the true GLRT, whatever the noise covariance matrix. Future works will investigate the derivation of the P F Athreshold relationships, and the adaptive case as well as non-Gaussian additive noise environments.

8 Fig. 1 .

 81 Fig. 1. Comparison of the NMF response with various thresholds η = 1 -P 1/(N -1) F A when Γ = I, N = 10.

Fig. 3 .

 3 Fig. 3. P D of the detectors in white Gaussian noise, for a P F A of 10 -6 , N = 10.

Fig. 4 .

 4 Fig.[START_REF] Bandiera | Advanced Radar Detection Schemes Under Mismatched Signal Models[END_REF]. P D versus SNR with ρ = 0.9 at cell θ 0 = 0 for a P F A of 10 -6 , N = 10.

Fig. 5 .

 5 Fig.5. P D versus SNR with ρ = 0.9 at cell θ 0 = 5 for a P F A of 10 -6 , N = 10.


Omar Sadek

Laura Abad Galán

Frédéric Gendron

Bruno Baguenard

Stephan Guy

Amina Bensalah

Boris Le Guennic

Olivier Maury

David M Perrin

Emmanuel Gras

Amina Bensalah-Ledoux

Chiral Benzothiazole Monofluoroborate Featuring Chiroptical and Oxygen-Sensitizing Properties: Synthesis and Photophysical Studies

Keywords: chiral boron, CPL, photosensitizer, benzothiazole, monofluoroborate

published or not. The documents may come

L'archive ouverte

INTRODUCTION

Organoboronates now feature prominently in the development of fluorescent probes, Positron Emission Tomography (PET) imaging agents, sensors, and chiroptical materials. [1][2][3][START_REF] Akgun | Boronic Acids as Bioorthogonal Probes for Site-Selective Labeling of Proteins[END_REF][START_REF] Munch | Fluorine-18-Labeled Fluorescent Dyes for Dual-Mode Molecular Imaging[END_REF] A long-term application of these constructs will be their use in personalized medicine that in turn necessitates the tandem advance of multimodality probes and theranostic compositions as key components to unlock the full potential of precision treatments. [START_REF] Lorenzoni | Nuclear Medicine Theranostics: Between Atoms and Patients[END_REF][START_REF] Bertrand | Metal-based BODIPY derivatives as multimodal tools for life sciences[END_REF] Multimodal probes that enable both fluorescence and PET imaging advantageously expand the possibility of assessing biological events at a cellular and organismal level.

Indeed fluorescence imaging finds applications in fluorescent-guided surgery to evaluate tumour margins, whilst the ability to label the identical molecule to be labelled with [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] Ffluoride allows spatio-temporal evaluation of pharmacodynamic uptake and clearance by PET. [8][START_REF] Louie | Multimodality imaging probes: design and challenges[END_REF][START_REF] Ranyuk | 68Ga/DOTA-and 64Cu/NOTA-Phthalocyanine Conjugates as Fluorescent/PET Bimodal Imaging Probes[END_REF] An early example of such combination has been achieved by [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] F-labeled BODIPY derivatives. [START_REF] Li | Rapid aqueous [18F]-labeling of a bodipy dye for positron emission tomography/fluorescence dual modality imaging[END_REF][START_REF] Hendricks | Synthesis of [ 18F]BODIPY: Bifunctional reporter for hybrid optical/positron emission tomography imaging[END_REF] The fascinating role that boron plays in BODIPY-type fluorophores including facile applications in [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] F-radiolabelling suggests that boron based heterocycles may be of considerable interest in an expanded role for sensors, photosensitizers and latent [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] F-radioprosthetic groups.

Furthermore, the diagnostic value of BODIPY probes can be further enhanced with a therapeutic component through their potential for sensitizing 3 O2 to 1 O2 thereby allowing photodynamic therapy (PDT). [START_REF] Wang | Elucidation of the Intersystem Crossing Mechanism in a Helical BODIPY for Low-Dose Photodynamic Therapy[END_REF][START_REF] Zhou | A bioorthogonally activatable photosensitiser for site-specific photodynamic therapy[END_REF][START_REF] Nguyen | Molecular Design of Highly Efficient Heavy-Atom-Free Triplet BODIPY Derivatives for Photodynamic Therapy and Bioimaging[END_REF] Notwithstanding established extensive applications, well-known limitations of BODIPY fluorophores include very narrow Stokes shifts, which lead to inner filter effects as well as Raman and Rayleigh scattering. Thus, larger Stokes shifts would be highly desirable to enable proper and uncompromised imaging with higher signal-to-noise ratios. Such has been recently achieved by breaking the symmetry of the electronic structures of fluorophores. [START_REF] Ren | A General Method To Increase Stokes Shift by Introducing Alternating Vibronic Structures[END_REF] This induces a strong internal conversion through vibronic contributions to the HOMO and the LUMO.

Since desymmetrization is strongly associated with and readily achievable by the introduction of chirality, the generation of a novel chiral borate would envelope new molecular architectures for expanding multi-modal applications. In the context of a fluoroborate probe, the desymmetrization of a central boron atom with four different substituents represents an entirely unexplored means of achieving such chirality for which there are but scant examples. [START_REF] Noda | Synthesis of Chemically and Configurationally Stable Monofluoro Acylboronates: Effect of Ligand Structure on their Formation, Properties, and Reactivities[END_REF][START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF][START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF][START_REF] Haefele | Boron Asymmetry in a BODIPY Derivative[END_REF] Notably, the desymmetrization of a central boron atom would also establish a new approach to the design and development of circularly polarized luminescence from simple organic molecules by expanding the structural diversity. [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence from Simple Organic Molecules[END_REF][START_REF] Longhi | Circularly Polarized Luminescence: A Review of Experimental and Theoretical Aspects[END_REF] Our on-going interest on applications of fluoroborates for applications in (radio)chemistry, [START_REF] Perrio | 18F]-Fluoride capture and release: azeotropic drying free nucleophilic aromatic radiofluorination assisted by a phosphonium borane[END_REF][START_REF] El Dine | Expanding the Balz-Schiemann Reaction: Organotrifluoroborates Serve as Competent Sources of Fluoride Ion for Fluoro-Dediazoniation[END_REF][START_REF] Sadek | Unsymmetrical diaryliodonium phenyltrifluoroborate salts: Synthesis, structure and fluorination[END_REF] as well as our report on straightforward approaches to 2-aryl substituted benzothiazole fluorophores, [START_REF] Bonin | Highly practical boronic acid surrogates for the Suzuki-Miyaura cross-coupling[END_REF][START_REF] Sadek | Straightforward convergent access to 2-arylated polysubstituted benzothiazoles[END_REF] led us to unveil a new benzothiazole-based fluoroborate probe 1 (Figure 1) where the addition of a single fluorine atom to create the ate-salt will engender stereogenicity at the boron atom in a unique 6,7fused ring system with a tridentate borate, opening new routes for the design of probes featuring novel chiroptical properties. Furthermore, as the 2-arylbenzothiazole scaffold is itself known for its photosensitizing properties, [START_REF] Hu | Synthesis, and biological evaluation of 2-(4aminophenyl)benzothiazole derivatives as photosensitizing agents[END_REF][START_REF] Senadi | Design, synthesis and antimetastatic evaluation of 1-benzothiazolylphenylbenzotriazoles for photodynamic therapy in oral cancer cells[END_REF][START_REF] Chen | Apoptosis Induced by 2-Aryl Benzothiazoles-Mediated Photodynamic Therapy in Melanomas via Mitochondrial Dysfunction[END_REF] we expected that a benzothiazole based tridentate ligand for boron would induce a strong differentiation of the nature of the donor and acceptor moieties of the fluorophore, potentially promoting Stokes shift enlargement. Finally, tetrahedral coordination at B critically induces non-negligible torsion in the polyaromatic ligand, known to favour spin-orbit coupling, which enables 1 O2 generation. [START_REF] Schmidt | Intersystem Crossing Processes in Nonplanar Aromatic Heterocyclic Molecules[END_REF][START_REF] Nagarajan | Enhanced intersystem crossing in core-twisted aromatics[END_REF][START_REF] Galan | Theoretical and experimental investigation on the intersystem crossing kinetics in benzothioxanthene imide luminophores, and their dependence on substituent effects[END_REF] Eyeing the potential for these unique chiroptical properties, here we report our first results on the synthesis of 1, the potential for exchanging its fluoride substituent and its enantiomeric resolution by chiral chromatography, as well as the photophysical and chiroptical properties of the stereoisomers which have been investigated and fully rationalized by theoretical calculations.

RESULTS AND DISCUSSION

Synthesis of Racemic Benzothiazole Monofluoroborate Complex 1.

In pursuit of a stable and isolable chiral borate, the following design principles were considered necessary structural features of the unsymmetrical ligand and complex: (i) the ligand must contain coordinating heteroatoms for boron chelation on a relatively rigid scaffold to enforce stability and disfavour racemization by substituent exchange at boron and (ii) the complex should exhibit sufficient steric congestion about the boron center to facilitate chiral resolution of enantiomers. To this end, the benzothiazole heterocycle was found to be a suitable scaffold given its unsymmetrical nature and facile synthesis. Additionally, the ability to functionalize the heterocycle at the C2 and C4 positions would allow the introduction of chelating motifs to produce a tridentate ligand for boron.

Starting from 2-bromoaniline 2, the corresponding thiourea 3 was synthesized, which was then oxidatively cyclized with Br2 to give 2-amino-4-bromobenzothiazole 4 (Scheme 1). Iodination under Sandmeyer conditions, using catalytic CuI, provided access to 4-bromo-2-iodobenzothiazole 5. [START_REF] Sadek | Straightforward convergent access to 2-arylated polysubstituted benzothiazoles[END_REF] Ligand 6 was then obtained via the one-pot double Suzuki-Miyaura cross-coupling of 5 with 2-hydroxyphenylboronic acid. Finally, complex 1 was obtained by reacting 6 with BF3×OEt2 in the presence of DIPEA as a base. All products were fully characterized by multinuclear NMR spectroscopy, IR spectroscopy and HRMS spectrometry (see SI). Scheme 1. Synthesis of complex 1 and fluoride abstraction from 1 a, BzCl, NH4SCN, acetone, reflux, 1 h, 75%; b, Br2, CHCl3, reflux 1.5 h, 93%; c, (i) p-TsOH•H2O, MeCN, room temperature, (ii) t-BuONO, -5 °C, 30 min, (iii) KI, cat. CuI, H2O, 0 °C then room temperature, 18 h, 90%; d, 2-hydroxyphenylboronic acid, Pd(PPh3)4, Na2CO3, DMF/H2O, microwave, 120 °C, 1 h, 55%; e, DIPEA, BF3×OEt2, CH2Cl2, room temperature, 2 h, 88%; f, TMS-OTf, CDCl3, room temperature, 10 min. Formation of fluoroborate complex 1 was established by [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F-NMR spectroscopy where a signal centered at d -132.09 ppm with a 1:1:1:1 splitting pattern was observed ( 1 JF-B = 34.5 Hz); consistent with the nuclear spin of a boron atom (S = 3/2) coupling to a fluorine atom. The presence of only one fluorine atom (S = 1/2) bound to boron was confirmed by the observation of a doublet with the same 1 JB-F coupling constant centered at d 1.9 ppm in the 11 B-NMR spectrum. This has been further confirmed in IR by the disappearance of OH bands, in 1

Structure of Monofluoroborate Complex 1.

Single crystals, suitable for X-ray crystallographic analysis, were grown by slow vapor diffusion of cyclohexane into saturated CHCl3 solutions of 6 and 1, which crystallised in the monoclinic C2/c and P21/c space groups, respectively (Figure 2). Selected structural parameters for 1 are listed in Table S1 and for 6 in Table S2). To the best of our knowledge, 1 is the first mono-fluoroborate benzothiazole complex that exemplifies a stereogenic boron atom and is a new addition to rare examples of boron-chelated seven-membered ring. [START_REF] Singh | O-chelated chroman-BF2 complexes: Structural variants of BODIPY[END_REF][START_REF] Wu | Syntheses of highly fluorescent GFPchromophore analogues[END_REF][START_REF] Murale | Facile "one pot" route to the novel benzazulene-type dye class: Asymmetric, derivatizable, 5-7-6 fused ring puckered half BODIPY design[END_REF][START_REF] Chen | Boron-phenylpyrrin dyes: Facile synthesis, structure, and pHsensitive properties[END_REF] Interestingly, 1 forms a crystalline racemate in which the two enantiomers are present in equal quantities in the asymmetric unit with inverted configurations at the boron center (Figure 2). The molecule with R or S configuration at boron is designated 1R or 1S, respectively in Table S1. In 1, the boron atom is internally coordinated by the nitrogen atom of the benzothiazole ring, and the oxygen atoms (O1 and O1') of both phenols at positions C2 and C4 of the benzothiazole core, forming six-and seven-membered rings, respectively. The final coordination site, completing the tetrahedral geometry at boron, is occupied by a fluorine atom. For 1R, the B-N, B-F, B-O1 and B-O1' bond lengths are 1.586(5), 1.389(4), 1.434(3) and 1.427(4) Å, respectively; similar bond lengths are found in 1S except for the B-O1 bond which is slightly elongated to 1.450(4) Å. The boron centers in both molecules are highly tetrahedral, as observed from the reported bond angles and calculated Tetrahedral Characters (THC), according to Höpfl's equation, [START_REF] Höpfl | The tetrahedral character of the boron atom newly defined -A useful tool to evaluate the N → B bond[END_REF] of 88 and 89% for 1R and 1S, respectively.

Complex 1 is highly planar across the benzothiazole core and the phenol ring at C2, the angle between these two planes is 3.3°, and this planarity is supported by a small N-C2-C2'-C1' torsion of 2.3(4)° in 1R. However, 1S displays less planarity with an angle between the benzothiazole and phenol planes of 6.1° and increased N-C2-C2'-C1' torsion of -5.1(5)°. In both enantiomers, the phenol ring at C4 is significantly twisted away from the benzothiazole core, with angles between the planes of these two ring systems at 21.4° and 20.7° for 1R and 1S, respectively. Despite the presence of an intramolecular hydrogen-bond between the proton of O1 and N in the benzothiazole ring in ligand 6, the system is significantly less planar with an angle between the planes of both ring systems of 11.2° and a N-C2-C2'-C1' torsion of 9.8(2)° highlighting the structural rigidity and planarity induced by B-F complexation.

Fluorine exchange studies of 1

In line with prospective applications in radiolabelling with [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] F for PET probe synthesis, the ability to exchange a fluoride anion from complex 1 was investigated. Significant developments have been reported in the synthesis and [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F-18 F isotope exchange (IEX) of BODIPY dyes for the generation of bi-modal imaging agents. [START_REF] Li | Rapid aqueous [18F]-labeling of a bodipy dye for positron emission tomography/fluorescence dual modality imaging[END_REF][START_REF] Hendricks | Synthesis of [ 18F]BODIPY: Bifunctional reporter for hybrid optical/positron emission tomography imaging[END_REF][START_REF] Liu | Lewis acid-assisted isotopic 18F-19F exchange in BODIPY dyes: Facile generation of positron emission tomography/fluorescence dual modality agents for tumor imaging[END_REF][START_REF] Keliher | Efficient acid-catalyzed 18F/19F fluoride exchange of BODIPY dyes[END_REF] Such IEX reactions are inherently thermoneutral which can compromise both radiochemical yields or molar activity values or both. By contrast, one particularly attractive strategy involves preactivation of the BODIPY core with TMS-OTf, which removes a fluorine atom to generate a good leaving group for subsequent radiofluorination. This would be the simplest methodology to test fluoride abstraction and would give a potentially stable intermediate upon which radiofluorination conditions could be investigated.

Treatment of 1 with TMS-OTf in CDCl3 resulted in quantitative fluoride anion abstraction to provide 7, as observed by 1 H-, [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F-and 11 B-NMR spectroscopy (Figure S1). The B-F signal in the [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F NMR spectrum, centered at -132.07 ppm, completely disappears and a new peak attributed to TMS-F, centered at -157.77 ppm ( 3 JF-H = 7.4 Hz) is observed. In the 11 B-NMR spectrum, the doublet centered at 1.9 ppm ( 1 JB-F = 34.4 Hz) evolves into a broad singlet centered at 2.2 ppm, confirming fluoride abstraction (loss of B-F coupling) while maintaining a quaternary boron center. Complete conversion of 1 was also substantiated by 1 H-NMR spectroscopy, where all aromatic proton signals are shifted downfield with respect to 1 and the free ligand 6. As single crystals suitable for X-ray crystallographic analysis could be eventually obtained upon standing in solution under inert atmosphere, the structure of 7 could be confirmed in the solid state. Compound 7 crystallised in the triclinic P-1 space group (Figure S20). Interestingly exchanging the fluoride for a triflate on boron exhibited minimum impact on the B-N, B-O1 and B-O1' bond lengths which are measured in 7 at 1.559(1), 1.422(1) and 1.410(1) Å respectively. The B-OTf bond is expectedly significantly longer in 7 (1.572(1) Å) compared the B-F bond in 1, which together with the lower THC of 80% are predicting a higher reactivity at boron. Angles between the aromatic ring appear to be significantly more affected as the one between the benzothiazole core and the phenol at C2 is now 12.2°, while the one with the phenol ring at C4 reaches 26.5°.

As the structural data were indicative of a high reactivity at boron, we first attempted the fluorination of 7 to revert to 1 by slow addition of TBAF (1M in THF) in CDCl3. Although trace amount of 1 were observed by [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F NMR, the obtained spectrum mainly showed decomplexation of boron and formation of BF4 -which was further confirmed by [START_REF] Li | Rapid aqueous [18F]-labeling of a bodipy dye for positron emission tomography/fluorescence dual modality imaging[END_REF] B NMR spectroscopy. To mimic higher dilution that could prevent such degradation, we envisioned a reaction at the solid-liquid interface by adding CsF to a solution of 7 in CDCl3. Unfortunately, no reactivity was observed even after prolonged mixing. Finally it should also be pointed out that upon exposure to air moisture, 7 was shown to progressively degrade, thus illustrating its high reactivity.

Although this result is indicative that 7 would probably not be an appropriate precursor for radiofluorination, it is also indicative of the ability to exchange fluoride on boron thus potentiating in situ isotope exchange as viable approach for future radiolabelling of 1 through the in situ formation of an analog of 7.

Chiral Resolution, and Configurational Stability.

To determine the stereochemical relationship of these molecules, and since they do not crystallise as a conglomerate (i.e. no spontaneous resolution), their resolution was attempted by chiral HPLC, as this has been recently reported for azobenzene boron complexes. [START_REF] Gon | A Highly Efficient Near-Infrared-Emissive Copolymer with a N=N Double-Bond pi-Conjugated System Based on a Fused Azobenzene-Boron Complex[END_REF] Using an analytical Chi-ralPak IA column (5x250 mm, 5 µm) and eluting with MeOH (100%), the enantiomers could be separated by ~4 minutes in elution sequence in a 1:1 ratio (see Figure S2). Resolution was then effected on a preparative scale (ChiralPak IA 20x250 mm, 5 µm) allowing the isolation of 39.8 and 40.9 mg of enantiopure fractions 1A and 1B, respectively. As expected, NMR spectra of both enantiomers are identical (see Figure S3).

The stability of the enantiomers, towards racemization, was also investigated. Repeated analytical HPLC injections of each enantiomer over several days (stored under ambient conditions: room temperature, exposed to light and air) gave only single peaks (see Figure S2). The enantiomers were also found to be stable under more forcing conditions, after 3 hours at 50 °C in CHCl3 no degradation was observed by NMR spectroscopic analysis and no racemization detected by chiral HPLC; this highlights the stability of the enantiomers towards racemization via inversion. Additionally, no racemization was observed when the enantiomers were stored in MeOH at ambient conditions over several days; although trace hydrolysis to the free ligand was detected. Notably, complex 1 also displayed impressive stability (over 289 hours) in the presence of water, as determined by NMR spectroscopic studies in an aqueous medium (see Figure S4). The configurational stability has also been assessed in the presence of PBS buffer by repeated recording of CD spectra of a solution of 1 in a 1:6 mixture MeCN:PBS. No evolution of the CD spectrum and the UV absorbance indicate maintenance of structural integrity.

Optical and chiroptical Properties.

As Circularly Polarized Luminescence (CPL) currently represents a topic of high interest due to potent applications in numerous fields, [START_REF] Ma | Circularly Polarized Luminescence Switching in Small Organic Molecules[END_REF][START_REF] Maeda | Synthesis and Chiroptical Properties of Chiral Carbazole-Based BODIPYs[END_REF][START_REF] Doistau | Beyond Chiral Organic (p-Block) Chromophores for Circularly Polarized Luminescence: The Success of d-Block and f-Block Chiral Complexes[END_REF][START_REF] Arrico | Quantifying the overall efficiency of circularly polarized emitters[END_REF] the photophysical properties of 1 were investigated and their spectra and data are shown in Figures 34and Table 1 (and Figure S5-S13). Complex 1 maintains the same absorption profile as the parent ligand 6, with two main transitions centered at ~300 and ~350 nm that can be associated to π-π* type transitions which are typically solvent-independent (Table 1 and Figures S5, S6 and S7). Complex 1, however, shows a bathochromic shift of ~20 nm in absorption maximum (λabs) (Figure 3 and Table 1). As observed in the solid state, B-F complexation induces rigidity across the entire molecular scaffold, extending the π-conjugation responsible for the observed bathochromic shift. [START_REF] Doistau | Beyond Chiral Organic (p-Block) Chromophores for Circularly Polarized Luminescence: The Success of d-Block and f-Block Chiral Complexes[END_REF][START_REF] Zhao | Excited state intramolecular proton transfer (ESIPT): From principal photophysics to the development of new chromophores and applications in fluorescent molecular probes and luminescent materials[END_REF] Upon excitation, ligand 6 is essentially non-emissive (ΦF < 0.01). This behaviour may be explained by an Excited-State Intramolecular Proton Transfer (ESIPT) [START_REF] Zhao | Excited state intramolecular proton transfer (ESIPT): From principal photophysics to the development of new chromophores and applications in fluorescent molecular probes and luminescent materials[END_REF][START_REF] Kwak | Photostable BF2-chelated fluorophores based on 2-(2'-hydroxyphenyl)benzoxazole and 2-(2'-hydroxyphenyl)benzothiazole[END_REF] resulting in non-radiative energy loss due to structural rearrangements in the excited state, accounting for the large Stokes shift ΔSS (10,630 cm -1 ) and the low quantum yield (Table 1). Since this mechanism is blocked by borate formation, a nice green emission at 530 nm can be easily observed in the case of 1 (see Figure S8), and a greater quantum yield of 0.11 could be determined (Table 1 and Figures S9 andS10). Importantly, 1 also presents a significant ΔSS of 8,911 cm -1 in contrast to previously reported BF2 dyes. [START_REF] Liu | Benzothiazole-enamide-based BF2 complexes: luminophores exhibiting aggregation-induced emission, tunable emission and highly efficient solid-state emission[END_REF] Its emission properties certainly resemble those of highly conjugated systems or systems with significant Donor-π-Acceptor architectures. [START_REF] Li | Efficient luminescence from easily prepared fluorine-boron core complexes based on benzothiazole and benzoxazole[END_REF][START_REF] Santra | Dramatic substituent effects on the photoluminescence of boron complexes of 2-(benzothiazol-2-yl)phenols[END_REF][START_REF] Xie | Fluorescent coumarin derivatives with large stokes shift, dual emission and solid state luminescent properties: An experimental and theoretical study[END_REF] The emission of 1 was also measured at low temperature in organic glass (77 K, MeOH-EtOH v/v 1:4, Figure S12, see Figure S11 for comparison with 6). After applying a 50 µs delay the short-lived fluorescence emission at 545 nm (MeOH at RT) disappears and is replaced by a long-lived well-structured phosphorescence emission at 486 nm that can be assigned to the emission from the lowest triplet state (T1) with an energy of 2.55 eV (20,576 cm -1 ). Given the described criteria for photosensitizer dyes, namely that the T1 state is long-lived and of appropriate energy (≥0.98 eV), [START_REF] Wang | A novel BODIPY-based photosensitizer with pH-active singlet oxygen generation for photodynamic therapy in lysosomes[END_REF][START_REF] Alberto | Photophysical origin of the reduced photodynamic therapy activity of temocene compared to Foscan®: Insights from theory[END_REF][START_REF] Quartarolo | Structures and electronic absorption spectra of a recently synthesised class of photodynamic therapy agents[END_REF] we postulated that 1 may function as a photosensitizer and convert 3 O2 to 1 O2. We therefore studied the ability of 1 to sensitize singlet oxygen by directly observing the phosphorescent emission of 1 O2 at 1268 nm (Figure 3). [START_REF] Khan | Direct spectroscopic observation of singlet oxygen emission at 1268 nm excited by sensitizing dyes of biological interest in liquid solution[END_REF][START_REF] Andersen | Absorption spectrum of singlet oxygen (a1Δg → b1Σg+) in D2O: Enabling the test of a model for the effect of solvent on oxygen's radiative transitions[END_REF] Indeed, complex 1 was found to be an efficient photosensitizer, in the absence of heavy atoms, with a phosphorescence quantum yield of oxygen (ΦΔ) of 0.30 by direct comparison with phenalenone as a reference, in CH2Cl2 (Figure S13).

The enantiomeric nature of 1A and 1B was unequivocally confirmed by circular dichroism (CD) spectroscopy as the spectra of 1A and 1B were mirror images (Figure 4a) while 1, as a racemic mixture, did not interact with circularly polarized light. 1A and 1B also display the emission of opposite circularly polarized luminescence (CPL), where the CPL emission maximum perfectly matches the fluorescence emission band (Figure 4b). The maximal glum value is estimated to be 0.2•10 -3 in the classical range for chiral boron containing dyes. [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF][START_REF] Maeda | Synthesis and Chiroptical Properties of Chiral Carbazole-Based BODIPYs[END_REF]

Theoretical Calculations.

Density functional theory (DFT), time-dependent DFT (TDDFT) and wave-function theory (WFT) were employed to further understand and rationalize the photophysical and photosensitizing properties of complex 1 (see computational details). Firstly, the diabatic (vertical) and adiabatic (relaxed) energies of the lowest excited states of complex 1s were calculated (see Table S3); a schematic representation of the Jablonski diagram based on these calculations is represented in Figure S14. In both cases, the lowest excited state corresponds to a triplet spin state lying above the ground state S0 by 2.7 and 2.0 eV using the diabatic and adiabatic energies, respectively. The ordering of the next excited states strongly depends on whether structural relaxations are performed or not. The vertical excitations, using the structure of the ground state S0 for the calculations, locate the excited triplet spin states T2 and T3 lower in energy than the first excited singlet spin state S1 (see ΔEvertical in Table S3). On the other hand, S1 is found lower in energy than T2 and T3 after structural relaxations of the excited states (see ΔErelax in Table S3).

The main calculated absorption and CD properties of complex 1S, obtained with the hybrid functional PBE0, are given in Table 2 (for full data see Table S4). Additional data obtained with the hybrid B3LYP functional and its range-separated version CAM-B3LYP are provided in the SI (Tables S5 and S6). The lowest transitions to S1 and S2 are calculated at 367 and 350 nm, respectively, in excellent agreement with the first absorption band measured experimentally at 360 nm. These transitions correspond to excitations from the highest occupied molecular orbital (HOMO) and the HOMO-1 into the lowest unoccupied molecular orbital (LUMO) of complex 1. A second set of two transitions is then calculated at ca. 310 nm, again in excellent agreement with the experimental data; these transitions correspond to excitations from the HOMO-2 and HOMO-3 into the LUMO, respectively. The natural transition orbitals (NTOS) associated with these transitions are shown in Figure 5. They principally correspond to π-π* type transitions with orbitals mostly delocalized over the entire system. However, the transition calculated at 367 nm is an exception (Figure 5, left). The HOMO orbital electron density is concentrated on the benzothiazole core as well as the phenol ring at position C4, whereas in the LUMO, there is a significant rearrangement of electron density from the C4 to C2 phenol ring. This considerable redistribution of electron density may be a plausible explanation for the large Stokes shift, while also being a factor in the quantum yield observed for 1. [START_REF] Santra | Dramatic substituent effects on the photoluminescence of boron complexes of 2-(benzothiazol-2-yl)phenols[END_REF] [a] Only contributions larger than 5% are given. The chiroptical properties associated to the lowest excitations of complex 1 are also given in Table 2, while the corresponding calculated CD spectrum is shown in Figure 6. A Cotton effect is calculated for the first absorption band at ca. 360 nm, which exhibits positive and negative bands in CD. The rotatory strength of the former excitation is calculated twice larger in absolute magnitude than of the latter. The second largest CD band is calculated at 281 nm; it corresponds to an excitation from the HOMO into the LUMO+1 and gives rise to a strong negative rotatory strength. The energy of this calculated transition is probably underestimated and could correspond to the negative band measured experimentally at ca. 240 nm (see Figure 4a). As visible in Figures S15 andS16, the energies and the magnitude of the calculated R are strongly functional dependent. However, the sign of the calculated rotatory strengths was confirmed with the help of multi-reference CASPT2 calculations (see Table S4). Calculations of emission and CPL properties of 1S were performed on the relaxed structure of the S1 state, and these results are given in Table 3 and the corresponding calculated CPL spectrum is shown in Figure S17. The calculated transition (542 nm with B3LYP) formally corresponds to a relaxation from the LUMO to the HOMO of the corresponding S0 state (Figure 7) and is in excellent agreement with emission observed experimentally at 530 nm. The rotatory strength associated to the S0¬S1 emission is calculated positive with the different functional tested as well as with the CASSCF/CASPT2 calculations.

Table 2. Energy (ΔE in eV and (nm)), oscillator strength (f), rotatory strength (R in cgs), electric dipole (D in cgs), absorption dissymmetry factor (gabs), and assignment (in per-cent) of the lowest absorption transitions calculated in 1S at

Combining calculated CD and CPL properties gave a clean chiroptical fingerprint of compound 1S. Comparison with the experimental spectra of the two enantiopure fractions

ACCEPTED MANUSCRIPT

1A,B (Figure 4a) permits the unambiguous determination of their absolute configuration. 1A correspond to 1S, and consequently its mirror isomer 1B to 1R.

CONCLUSION

In summary, we have defined a new molecular scaffold comprising a stereogenic fluoroborate for generating chiral photosensitizers based on a novel chromophore. The structure of 1 allows a significant increase of the Stokes shift compared to regular boron derived fluorophores, as well as light harvesting and intersystem crossing to efficiently populate its triplet state, along with the potential for generation of reactive singlet oxygen species. This compound also features a fluoride atom that can be selectively activated for displacement by reaction with TMS-OTf, leading us to anticipate that while IEX was not attempted here, radiofluorination of 1 by IEX is an alternative means for introducing radioactive [START_REF] Sánchez-Carnerero | Circularly Polarized Luminescence by Visible-Light Absorption in a Chiral O-BODIPY Dye: Unprecedented Design of CPL Organic Molecules from Achiral Chromophores[END_REF] F-fluoride for future use in PET imaging. At the same time, the potential for a unique structure to potentially act as an imaging probe in two modes, fluorescence for cell-based cytology to whole body PET, combined with the added therapeutic potential by PDT makes this approach unique for addressing developments of innovative tools for health sciences. Investigations towards these goals including enhanced photophysical properties and in vivo imaging are currently underway in our groups. Other applications in chirality transfer to and from a stereogenic borate for use in sensing and catalysis along with chiroptical applications in solid-state materials and molecular medicine are readily anticipated by these results and will be pursued in due course.

EXPERIMENTAL SECTION

General information.

Solvents and Reagents: All chemicals were purchased from commercial sources and used as received unless otherwise noted. All solvents used were commercial grade and used as received with no drying unless otherwise noted; dry CH2Cl2 was obtained from a PureSolv solvent purification system. All reactions were performed in oven-dried glassware under argon atmosphere unless otherwise stated. All chemicals were purchased from commercial sources and used as received unless otherwise stated. Deuterated solvents for NMR spectroscopic analysis were purchased from Euriso-top. Analysis: NMR experiments were performed in deuterated solvents. 1 H NMR, [START_REF] Wang | Elucidation of the Intersystem Crossing Mechanism in a Helical BODIPY for Low-Dose Photodynamic Therapy[END_REF] C NMR, [START_REF] Li | Rapid aqueous [18F]-labeling of a bodipy dye for positron emission tomography/fluorescence dual modality imaging[END_REF] B NMR and [START_REF] Aupic | Highly diastereoselective preparation of chiral NHC-boranes stereogenic at the boron atom[END_REF] F spectra were recorded on 300 Avance (300 MHz), 400 Avance (400 MHz) and 400 AvanceIII (400 MHz) Bruker spectrometers. All spectra were recorded at ambient temperature (298 K). Chemical shifts (δ) are reported in parts per million (ppm) relative to the residual protium in the solvents ( 1 H) or the solvent carbon ( 13 C) as internal standards. Multiplicity of signals is indicated using the following abbreviations: s (singlet), br (broad), d (doublet), dd (doublet of doublet), ddd (doublet of doublet of doublet), dt (doublet of triplets), t (triplet), td (triplet of doublet), q (quartet), qB (1:1:1:1 set of peaks arising from coupling to 11 B with S=3/2, midpoint of signal reported) and m (multiplet). Reactions were monitored using Merck Silica gel 60 F254 or Aluminium Oxide (Basic) 60 F254 glass backed plates. TLC plates were visualized by UV fluorescence (λ= 254, 365 nm) and one of the following stains: KMNO4 or HBQ. Flash column chromatography was performed using VWR Chemicals Silica gel 60 -200 µm, Acros Aluminium Oxide (Basic) Brockmann I 50-200 µm or on an automated Interchim puriFlash system using pre-packed Interchim 30 µm Silica gel cartridges. IR spectra were recorded on a PerkinElmer Spectrum One or Frontier FT-IR spectrometer with frequencies expressed in cm-1. Circular Dichroism spectra were recorded on a Jasco J-815 CD Spectropolarimeter using a 10 mm Quartz cuvette, with D.I.T = 0.5 sec, Scanning Speed = 100 nm/min, Band width = 1.00 nm at 25 °C. High-resolution mass spectra (HRMS) were recorded using either electrospray ionization (ESI) or desorption chemical ionization (DCI) using a Waters GCT Premier or Sciex QTRAP 4500 AB or Thermo Fisher Scientific DSQ II spectrometers. X-ray crystallography was performed on single crystal diffractometers: Agilent Gemini, Bruker Nonius and Bruker Kappa Apex II.

2-bromophenylthiourea (3)

A two-necked 250 mL round-bottom flask was charged with a stir bar, condenser, NH4SCN (10.9250 g, 0.13 mol) and acetone (50 mL). Benzoyl chloride (13.93 mL, 0.12 mol) was added dropwise via syringe to the rapidly stirring reaction mixture. The mixture was heated at reflux, using a heating block, for 15 minutes, and then cooled back down to room temperature. In an addition funnel, 2-bromoaniline (22.63 mL, 0.1 mol) was dissolved in acetone (25 mL), this solution was added dropwise to the vigorously stirring reaction mixture over 15 minutes. The reaction mixture was then heated at reflux, using a heating block, for 1 hour. The crude mixture was then dropped onto excess water and vigorously stirred. A yellow precipitate formed and was collected by filtration and washed with water until washes were colourless. The precipitate was then washed with cold MeOH/H2O solution (1:1). In a 1L Erlenmyer flask, 10% aq. NaOH solution (400 mL) was prepared and heated to 80 °C using a heating block. The washed precipitate was then added to this base solution for hydrolysis. The precipitate dissolved into the base solution producing a clear yellow solution, this was stirred at 80 °C for 15 minutes. The solution was then acidified to pH 2 using concentrated HCl (37%, 12 M), producing a white precipitate. The solution was then basified to pH 9 using a 25% aq. NH4OH solution. The white precipitate was collected and washed with water until washes were neutral; product was then dried under high vacuum (17.3748

2-amino-4-bromobenzothiazole (4)

A 50 mL two-necked round-bottom flask was charged with a stir bar, 2-bromophenylthiourea (2.3204 g, 10 mmol) and CHCl3 (10 mL). Bromine (0.51 mL, 10 mmol) was dissolved in CHCl3 (5 mL) in an addition funnel and affixed to the main neck of the roundbottom flask, the second neck was connected to a base trap to neutralize HBr fumes developed during the course of the reaction. The flask was cooled to 0 °C in an ice-bath and the bromine solution was added dropwise to the vigorously stirring reaction mixture (note: often the sides needed to be scraped down as the bromine solution would coagulate on the bottom and sides of the flask). The addition funnel was then replaced with a condenser and the reaction mixture heated at reflux, using a heating block, for 1.5 hours until complete conversion of starting material was determined by TLC (with heating HBr gas evolution became consistently rapid). During the course of the reaction a fine yellow precipitate evolved in a clear red/brown solution. After cooling to room temperature, solvent was removed under reduced pressure. The remaining residue was dissolved in EtOAc (100 mL) and washed with saturated aq. NaHCO3 (2 x 100 mL), 5% aq. Na2S2O3 (2 x 50 mL) and finally brine (2 x 50 mL). The organic phase was dried over anhydrous MgSO4 the filtered and concentrated under reduced pressure and further dried under high vacuum overnight to furnish the product as a yellow powder (2.1296 g, 93%). IR νmax/cm

4-bromo-2-iodobenzothiazole (5)

A 500 mL round-bottom flask was charged with a stir bar, 2amino-4-bromobenzothiazole (9.85 g, 42 mmol), p-TsOH•H2O (24.9 g, 129 mmol) and MeCN (172 mL). The heterogenous reaction mixture was stirred and cooled in an ice-brine bath to 0 °C, at which point t-BuONO (15.3 mL, 129 mmol) was added dropwise, over 10 min, via an addition funnel; after the addition was complete the reaction mixture was stirred at 0 °C for 30 minutes. An additional funnel was then charged with a water (43 mL) solution of KI (21.4 g, 129 mmol) and CuI (819 mg, 4.3 mmol). The KI solution was added dropwise to the vigorously stirred reaction mixture at 0 °C over 20 minutes; the reaction mixture was then allowed to warm to room temperature overnight. The crude reaction mixture was concentrated under reduced pressure to ~70 mL and then dropped on saturated aq. NaHCO3 (150 mL) and the aqueous phase extracted with EtOAc (4 x 150 mL), the combined organic phases were then washed with a 5% aqueous Na2S2O3 solution (4 x 150 mL). The organic phase was dried over anhydrous MgSO4, filtered, and concentrated under reduced pressure to furnish the product as a brown powder (13.1607 g, 90%). IR νmax/cm -1 (neat film): 3089, 3064, 2931, 2851, 1442, 1391, 1203, 952, 842, 764, 732. 1 H NMR (400 MHz, DMSO-d6) δ 8.12 (dd, J = 8.1, 1.0 Hz, 1H), 7.72 (dd, J = 7.8, 1.0 Hz, 1H), 7.37 (t, J = 7.9 Hz, 1H). [START_REF] Wang | Elucidation of the Intersystem Crossing Mechanism in a Helical BODIPY for Low-Dose Photodynamic Therapy[END_REF]

2,4-di(2-hydroxyphenyl)benzothiazole (6)

A 35 mL microwave vial was charged with a stir bar, 2-iodo-4bromobenzothiazole (368.5 mg, 1.1 mmol), 2-hydroxyphenylboronic acid (383 mg, 2.8 mmol), Pd(PPh3)4 (132 mg, 10 mol%), Na2CO3 (1.07 g, 10 mmol), DMF (9 mL) and water (3 mL). The reaction mixture was degassed (freeze-pump-thaw x 3) and then purged with Ar. The vial was loaded into a microwave reactor and programmed to be heated at 120 °C for 1 hour, after which the crude was dropped onto water (50 mL) and the aqueous phase was extracted with EtOAc (3 x 25 mL). The combined organic phases were dried over anhydrous MgSO4, filtered and concentrated onto Celite. The crude residue was purified by Silica gel flash column chromatography using cyclohexane/EtOAc (4:2 to 1:1). Desired fractions were collected and concentrated to furnish the desired product as a tan foam which was further dried under vacuum overnight (189.5 mg, 55%). Single crystals, suitable for X-ray crystallographic analysis, were grown by slow vapor diffusion of cyclohexane into a saturated CHCl3 solution of 6. IR νmax/cm -1 (neat film): 3377, 2926, 2855, 1613, 1583, 1489, 1470, 1450, 1350, 977, 743, 716. 1 H NMR (400 MHz, Chloroform-d) δ 11.97 (br s, 1H, -OH), 7.95 (dd, J = 7.8, 1.4 Hz, 1H), 7.69 (dd, J = 7.9, 1.6 Hz, 1H), 7.58 (dd, J = 7.5, 1.4 Hz, 1H), 7.53 (t, J = 7.6 Hz, 1H), 7.43 (dd, J = 7.5, 1.7 Hz, 1H), 7.37 (ddd, J = 8.7, 7.3, 1.6 Hz, 2H), 7.14 -7.07 (m, 2H, H16, H18), 7.04 (dd, J = 8.4, 1.1 Hz, 1H), 6.95 (ddd, J = 8.2, 7.3, 1.2 Hz, 1H), 5.53 (br s, 1H, -OH). [START_REF] Wang | Elucidation of the Intersystem Crossing Mechanism in a Helical BODIPY for Low-Dose Photodynamic Therapy[END_REF]

Complex 1

A 10 mL Wheaton vial was charged with a stir bar, 2,4-di(2-hydroxyphenyl)benzothiazole (33.8 mg, 0.1 mmol), dry CH2Cl2 (2 mL) and DIPEA (53 µL, 0.3 mmol). The mixture was allowed to stir at room temperature for 10 minutes at which point BF3•OEt2 (100 µL, 4.8 mmol) was added. The clear brown reaction mixture was allowed to stir at room temperature for 2 hours, at which point complete consumption of starting material was determined by TLC (basic Alumina, cyclohexane/CH2Cl2 1:1). The mixture was then dropped onto excess pentane, causing precipitation of a white solid. The precipitate was collected by filtration, washed with pentane and finally dissolved into CHCl3; the filtrate was collected and concentrated onto Celite and purified by basic Alumina flash column chromatography using cyclohexane/CH2Cl2 (1:1) as the eluent. Fractions were collected and concentrated to furnish the

Figure 1 .

 1 Figure 1. Structure of the target stereogenic borate 1 shown in racemic form, with selected atom numbering.

  H NMR by a downfield shift of most signals, especially the ones for protons ortho to the hydroxyl substituents related to the inductive electron withdrawal

  BF complex formation, and by the molecular formula corroborated by HR-MS.

Figure 2 .

 2 Figure 2. X-ray crystal structure of 1 with thermal ellipsoids at 50% probability: asymmetric unit (left) with 1R and 1S; inplane (top right) and top-face (bottom right) views of 1R. Boron in pink, carbon in grey, nitrogen in blue, oxygen in red, fluorine in green and sulfur in yellow; H atoms omitted for clarity.

  Measured using Coumarin -153 as a reference (ΦF = 0.45 in MeOH). [b] Measured at the 0-phonon transition. [c] Measured using Phenalenone as a reference (ΦΔ = 0.95 in CH2Cl2).

Figure 3 .

 3 Figure 3. Normalized absorption for 6 (black trace) and 1 (red trace), emission of 1 (blue trace) and phosphorescence of singlet oxygen (green trace) in a CH2Cl2 solution.

Figure 4 .

 4 Figure 4. a) CD spectra and b) CPL spectra of racemic 1 (grey trace), 1A (purple trace) and 1B (green trace) in CH2Cl2 at 25 °C.

Figure 5 .

 5 Figure 5. Selected occupied (top row) and vacant (bottom row) natural transition orbitals for the lowest excitations. PBE0/TZ2P results. Iso-surface values = ± 0.03 au.

Figure 6 .

 6 Figure 6. Calculated CD spectrum of 1S, PBE0/TZ2P results. A Gaussian broadening was used with a σ value of 0.13 eV.

Figure 7 .

 7 Figure 7. Selected occupied (left) and vacant NTOS for the lowest fluorescence transition. PBE0/TZ2P results. Iso-surface values = ± 0.03 au. Overlap (right) of the optimized structure of S0 (orange) and S1 (blue).

  C{ 1 H} NMR (101 MHz, Chloroform-d) δ 169.9 (Cq), 157.9 (Cq), 153.0 (Cq), 150.0 (Cq), 133.5 (Cq), 133.3 (CH), 131.6 (Cq), 131.3 (CH), 130.2 (CH), 128.6 (CH), 128.4 (CH), 126.3 (CH), 125.4 (Cq), 121.4 (CH), 121.1 (CH), 119.8 (CH), 118.1 (CH), 116.9 (CH), 116.8 (Cq). HRMS (ESI) m/z: [M+H]+ Calcd for C19H14NO2S 320.0745; Found 320.0753.

Table 1 . Photophysical properties of ligand 6 and com- plex 1 in CH2Cl2 solutions.

 1

the PBE0/TZ2P level.

	ΔE	f	R	D	gabs	Nature [a]
			(×	(× 10 -	(×
			10 -	40 )	10 3 )
			40 )
	3.38	0.40	-	31558	-	HOMO®LUMO
	0	4	22.	0	0.27	(84%)
	(367 )		1		9	HOMO-1®LUMO (14%)
	3.54					HOMO-1®LUMO
	0	0.41	57.	30970	0.74	(84%)
	(350	5	6	6	3	HOMO®LUMO
	)					(14%)
	4.01 4 (309 )	0.01 9	-6.1 13127	-1.86 5	HOMO-2®LUMO (93%)
	4.03 4 (307 )	0.37 9	-7.2	24223 4	-0.11 8	HOMO-3®LUMO (92%)
	4.40 6 (281 )	0.52 7	-67. 7	31542 2	-0.85 8	HOMO®LUMO+ 1 (93%)

Table 3 . Energy (ΔE in eV and nm), oscillator strength (f), rotatory strength (R in cgs), electric dipole (D in cgs), emission dissymmetry factor (gems), and assign- ment (in per-cent) of the lowest fluorescence transition of 1s.

 3

		ΔE	f	R	D	Gems	Na-
				×10 -	×10 -40	×10 3	ture [a]
				40
	B3LYP	2.28 8 (542 )	0.13 9	11.7	16012 2	0.29 1	HO¬ LU (99%)
	PBE0	2.51 7 (492 )	0.19 1	15.5	20002 3	0.31 1	HO¬ LU (99%)
							HO¬
	CAM B3LYP	3.08 5 (402 )	0.45 4	45.2	38820 1	0.46 6	LU (79%) HO-1¬ LU
							(16%)
	CAS	2.83
	(10,10 )	1 (438	0.15 4	6.4	14321 5	0.17 0	-
	SCF	)
	CAS	2.26
	(10,10 )	3 (548	0.08 9	7.7	10353 3	0.30 0	-
	PT2	)
		2.29
	Expt.	6 (540	-	+	-	-	-
		)

[a] Only contributions larger than 5% are given.

  C{ 1 H} NMR (101 MHz, DMSO-d6) δ 152.0 (Cq), 139.8 (Cq), 129.7 (CH), 126.9 (CH), 121.1 (CH), 114.6 (Cq), 112.8 (Cq). HRMS (ESI) m/z: [M79Br+H]+ Calcd for C7H4NS79BrI 339.8293; Found 339.8298, [M81Br+H]+ Calcd C7H4NS81BrI 341.8272; Found 341.8279.

ACKNOWLEDGMENT O.S. acknowledges support from Université Toulouse III and the French-Canadian Research Fund (FCRF). B.B., S.G., A.B.L., B.L.G., O.M. and L.A.G., O.S. and E.G. acknowledge support from Agence Nationale de la Recherche (ANR-18-CE07-0016/ ANR-19-CE29-0012-02). F.G. and B.L.G. acknowledge support from the European Research Council (ERC-CoG MULTIPROSMM, Grant agreement 7255184). F.G. thanks the Région Bretagne for its support (SAD 18006-LnCPLSMM). F.G. and B.L.G. thank the French GENCI/IDRIS-CINES centers for high-performance computing resources (allocations A0020800649 and A0040800649).

Complex 7

In a glovebox, a J-Young NMR tube was charged with 1 (41.7 mg, 0.12 mmol) and CDCl3 (1.2 mL). After all solids were completely dissolved, TMS-OTf (1.0 eq., 21.6 μL, 0.12 mmol) was added to the NMR tube and the mixture vigorously shaken. NMR spectra collected after 10 minutes showed complete conversion of 1 to 7. After approximately 6 hours at room temperature, single crystals, suitable for X-ray crystallographic analysis, spontaneously deposited in the NMR tube from the CDCl3 solution. In a glovebox, the reaction mixture was transferred to a 20 mL Schlenk flask, and all volatiles removed under reduced pressure. The residue was washed with pentane (3 x 3 mL) and dried under vacuum overnight to provide the product as a light yellow/green powder (36.3 mg, 63%). 1 H NMR (500 MHz, CD2Cl2) δ 8.09 (d, J = 7.9 Hz, 1H), 8.00 (d, J = 7.9 Hz, 1H), 7.83 (ddd, J = 7.9, 6.5, 1.8 Hz, 2H), 7.74 (t, J = 7.9 Hz, 1H), 7.72 (td, J = 8.7, 8.0, 1.7 Hz, 1H), 7.49 -7.44 (m, 1H), 7.33 (d, J = 8.1 Hz, 1H), 7.30 -7.24 (m, 2H), 7.21 (t, J = 7.6 Hz, 1H). [START_REF] Wang | Elucidation of the Intersystem Crossing Mechanism in a Helical BODIPY for Low-Dose Photodynamic Therapy[END_REF]

ASSOCIATED CONTENT

The supporting Information (SI) is available free of charge at http://pubs.acs.org. Stability assays, NMR spectra, X-ray structures for compound 1, 6 and 7, photophysical and theoretical studies.

AUTHOR INFORMATION Corresponding Authors

Emmanuel Gras -LCC, CNRS UPS 8241, Université de Toulouse, UPS, INPT, 205 route de Narbonne, 31077, Toulouse, Cedex 4, France; E-mail: emmanuel.gras@univ-tlse3.fr Boris Le Guennic -Univ Rennes, CNRS, Institut des Sciences Chimiques de Rennes (ISCR) -UMR 6226, F-35000 Rennes, France; E-mail: boris.leguennic@univ-rennes1.fr Olivier Maury -Université Lyon, ENS de Lyon, CNRS UMR 5182, Laboratoire de Chimie, F-69342 Lyon, France; E-mail: olivier.maury@ens-lyon.fr Present Address †Emmanuel Gras -Laboratoire Hétérochimie Fondamentale et Appliquée (LHFA), Université Paul Sabatier -CNRS UMR 5069, 118 Route de Narbonne, 31062 Toulouse, Cedex 09, France.

AUTHOR CONTRIBUTIONS

O.S. performed all the experimental work and spectroscopic analyses. L.A.G. carried out all fluorescence studies. B.B., S.G. and A.B.L performed the EDC and CPL investigations. O.M. supervised the photophysical studies. F.G. and B.L.G. performed all computational work and theoretical calculations. All authors analyzed the data and contributed to manuscript preparation. E.G. conceived and supervised the project. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

NOTES

The authors declare no competing financial interest. Dedicated to the memory of Professor Victor A. Snieckus