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Paper | Regular issue | Vol. 83, No. 2, 2011, pp. 311-322
Received, 6th November, 2010, Accepted, 20th December, 2010, Published online, 14th January, 2011.
DOI: 10.3987/COM-10-12099
Investigations into the Nucleophilic meso-Substitution of F-BODIPYs and Improvements to the Synthesis of 4,4-Difluoro-4-bora-3a,4a-diaza-s-indacene

Sarah M. Crawford and Alison Thompson*

Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J3, Canada

Abstract
A series of three F-BODIPYs, with varying levels of steric crowding about the meso-position were selected to investigate nucleophilic meso-substitution of F-BODIPYs. The synthesis of one of these F-BODIPYs, 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (totally unsubstituted dipyrrin skeleton), was optimized to give higher yields over routine literature procedures. This modified procedure involves oxidation of a dipyrromethane using p-chloranil, instead of DDQ, to give a dipyrrin which is then trapped in situ as its BF2 complex. Nucleophilic meso-alkylation of the series of F-BOIDPYs with n-butyllithium gave meso-butyl F-BODIPYs in moderate to good yields. This work represents a new, synthetically viable method for the synthesis of meso-alkylated F-BODIPYs. Extension of the nucleophilic substitution methodology to meso-arylation was possible. However, the reaction was unselective: substitution at boron, to give the boron-diaryl C-BOIDPYs, occurred preferentially to nucleophilic meso-substitution and thus a mixture of products was obtained.

INTRODUCTION
Molecules containing the 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (F-BODIPY) framework have wide applications as dyes, fluorescent probes in biological systems, and materials for incorporation into electroluminescent devices.1,2 Both symmetrical and unsymmetrical F-BODIPYs are routinely synthesized in high yields from the isolated dipyrrins free-bases or HX salts or by trapping the dipyrrin in situ.3 However, dipyrrin free-bases and salts are historically difficult to manipulate and purify. Furthermore, there are only a few methods available to synthesize meso-substituted dipyrrins.
To produce
meso-substituted dipyrrins (Figure 1), one can condense two equivalents of an α-unsubstituted pyrrole with a carboxylic acid,4 an acid chloride5 or an orthoformate6 (method 1) or oxidize a 5-unsubstituted dipyrromethane to the corresponding meso-unsubstituted dipyrrin (method 2).7 The first method is limited to the synthesis of symmetrical dipyrrins, while the second method is currently limited to the synthesis of dipyrrins with meso-aryl substituents and it requires the synthesis of the dipyrromethane starting material. Dipyrrins with meso-alkyl substituents can be synthesized from alkyl acid chlorides (method 1); however, the meso-alkyl dipyrrins are generally unstable and are thus trapped in situ using boron trifluoride diethyletherate and then isolated as their corresponding F-BODIPYs, with overall yields often below 20%.8-11

As shown in Figure 1, another potential strategy to meso-substituted dipyrrins involves substitution of meso-unsubstituted dipyrrins. However, examples of such direct meso-substitution of dipyrrins or dipyrrinato complexes are rare in the literature. meso-Cyano dipyrrins can be directly generated from meso-unsubstituted dipyrrins through cyanide anion attack at the meso-position to give the corresponding dipyrromethane, which can then be oxidized back to the dipyrrin.12 Oligopyrrolic bile pigments,13,14 containing one or more dipyrrin units, are reported to undergo meso-substitution in the presence of ethanethiole. A prodigiosin analogue,15 which contains a dipyrrin unit, was also reported to undergo photo-induced substitution with sulfur-based nucleophiles to give meso-substituted derivatives.
Direct
meso-modification of F-BODIPYs has recently received interest and attempts at modification have utilized a meso-thioalkyl F-BODIPY as starting material.16 The meso-thioalkyl substituent was shown to undergo nucleophilic substitution with amines,16,17 and it was also coupled with aryl boronic acids, via the Liebeskind-Srögl cross-coupling reaction,18 to generate other meso-substituted F-BODIPYs. Although this approach represents a great improvement in the synthesis of meso-aryl F-BODIPYs, it is limited to the generation of symmetrical derivatives as the meso-thioalkyl F-BODIPY is generated by the reaction of thiophosgene with two equivalents of a substituted pyrrole to give the corresponding dipyrrolthione, which is then alkylated and trapped as its BF2 complex.16
meso-Unsubstituted porphyrins and their metal complexes are susceptible to nucleophilic substitution at the meso-position, and the resulting intermediate is oxidized in situ to give meso-aryl and meso-alkyl substituted porphyrins.19,20 Aryl and alkyl lithium reagents, with varying levels of functionalization, are the nucleophiles employed in these reactions. Interestingly, a small amount of a meso-butyl substituted BODIPY was isolated from the reaction of a meso-unsubstituted BODIPY with 2 equivalents of a perfluorinated aryl lithium reagent (prepared from reacting the perfluorinated bromobenzene with n-butyl lithium).21 Based on this knowledge, we aimed to develop a methodology for the generation of meso-substituted F-BODIPYs via nucleophilic substitution at the meso-position of meso-unsubstituted F-BODIPYs.

RESULTS AND DISCUSSION
An ideal synthetic route for the synthesis of a meso-substituted F-BODIPY would be to begin with a chemically robust meso-unsubstituted F-BODIPY, which would undergo nucleophilic substitution at the meso-position. Three F-BODIPYs (Figure 2), containing examples with increasing steric crowding flanking the meso-position, were selected as test compounds to investigate a methodology for the nucleophilic meso-modification of meso-unsubstituted F-BOIDPYs to give the corresponding meso-substituted F-BOIDPYs.

F-BODIPYs 2 and 3 were synthesized from the corresponding dipyrrins using traditional methods.22 The synthesis of F-BODIPY 1 has only very recently been reported.23-25 One synthesis involves a four-step procedure from pyrrole, in 35 % overall yield.16,23,26 The other two methods are one-pot reactions and involve trapping the unstable dipyrrin intermediate: both have reported yields under 10 %.24,25 In order for this one-pot method for the preparation of 1 to be synthetically viable as a starting point for preparing derivatized F-BODIPYs, the yields needed to be increased.
The one-pot procedure involving the oxidation of an unsubstituted dipyrrin was selected for optimization.
25 The dipyrrin starting material (4) was synthesized using a literature method.27 A series of trials were conducted in order to optimize the reaction conditions, the oxidant used in the dipyrrin formation reaction, and the base used in the F-BODIPY formation reaction. The results of these trials are outlined in Scheme 1.

The bases used in the F-BODIPY formation were explored first (Trial 1 through Trial 3), using DDQ as an oxidant to generate the dipyrrin. When triethylamine was used as a base, none of the desired unsubstituted F-BODIPY (1) was formed; however, when DIPEA or DBU were used, 1 was isolated in very low yield (Trials 2 and 3) in our hands, even though the literature reports indicate yields between 8 and 10% when using DIPEA.24,25 DIPEA was thus selected as the base to use in further trials as it reproducibly gave the best yield (e.g. Trial 2). After the base for the F-BODIPY formation was selected, the oxidant for the dipyrrin formation was investigated. The isolated yield of the F-BODIPY 1 increased substantially when the oxidant was modified from DDQ to the milder p-chloranil (Trials 4-6). Using these modified conditions, the F-BODIPY 1 was generated in an average yield of 21% on a 100 mg scale.
With
F-BODIPYs 1, 2 and 3 in hand, investigations proceeded regarding nucleophilic meso-substitution. Solutions of each compound were treated with n-butyllithium at -78 °C. The reaction mixture was slowly warmed to room temperature and then treated with DDQ. The meso-butyl substituted F-BODIPYs 5, 6,28 and 728 were isolated in moderate yields as shown in Scheme 2.

This transformation represents a new method for the synthesis of alkyl substituted F-BODIPYs in better yields than the existing published methods.8-11 In the only previous example of the synthesis of a meso-butylated BODIPY from the meso-unsubstituted analogue, the authors speculated that a perfluorinated aryl lithium reagent (prepared from reacting the perfluorinated bromobenzene with n-butyl lithium) deprotonated the meso-position of the BODIPY, followed by reaction of the resultant monoanionic species with the residual n-butylbromide.21 We postulate,28 based on color changes during the course of the reaction, that the alkylation addition occurs by the nucleophilic attack of the n-butyl anion at the meso-position to give a charged dipyrromethane-type intermediate, as shown in Figure 3.

The decrease in yield of the meso-butyl F-BODIPYs with decreasing substitution about the F-BODIPY is likely due to a decrease in the stability of boron-containing dipyrromethane-type intermediate with decreasing substitution, analogous to that of the corresponding dipyrrin series.29 Isolated yields of the meso-butylated F-BODIPYs 5, 6 and 7 increased with increasing substitution from 26%, for the least substituted, to 61%, for the most substituted. Nevertheless, this strategy provides a reasonable and reliable route to meso-butyl substituted F-BODIPYs.
We also investigated the
meso-arylation of the F-BODIPYs 1, 2 and 3. We have previously reported that when the F-BODIPY 3 is treated phenyllithium the meso-phenyl product was not produced; however, the B-diphenyl C-BODIPY 8 was isolated in 22% yield.28 Interestingly, when the reaction with 10 eq phenyllithium was conducted at room temperature, in the absence of DDQ, a mixture of the C-BODIPY 8 and the C-BODIPY 9, with the desired meso-phenyl substituent, were generated as shown in Scheme 3. Presumably the substitution at boron is accompanied/followed by nucleophilic attack and then elimination at the meso-position.

Integration of the corresponding peaks in the 1H NMR spectrum, from the reaction carried out at room temperature, showed BODIPY 8 and BODIPY 9 to be isolated in a 0.2:1.0 ratio. The absence of F-BODIPY material in the reaction mixture indicates that nucleophilic attack at the boron centre appears to occur preferentially to nucleophilic attack at the meso-position in the case of the aryllithium reagent. This reactivity has been exploited to synthesize C-BODIPYs from meso-substituted F-BODIPYs although the products are generally isolated in yields below 50%.30 The absence of DDQ in this reaction also indicates that this transformation may be occurring through an alternate mechanism than the analogous meso-alkylation. Color observations are not useful in this case because the phenyllithium reagent itself is a red color and obscures any loss of color due to the dipyrrinato construct.
When
F-BODIPY 1 and F-BODIPY 2 were treated with phenyllithium, mixtures of meso-unsubstituted C-BODIPYs and meso-phenyl C-BODIPYs were isolated in yields of 10% and 6%, respectively (Scheme 4).

The reaction of the F-BODIPY 1 with phenyllithium resulted in two products, which could not be fully characterized. The mass spectrum (ESI+) the mixture indicated the formation of a mixture of C-BODIPY 10 and C-BODIPY 11, as shown in Scheme 4. A comparison of the relative integrations of the pyrrolic hydrogen peaks in the proton NMR spectrum of the product indicated that C-BODIPY 10 and C-BODIPY 11 were present in a 1 to 0.6 ratio. The reaction of F-BODIPY 2 with phenyllithium gave the C-BODIPY 12 and the C-BODIPY 13 in a 1 to 0.7 ratio. Under the same conditions, the meso-arylated C-BODIPY 9 could not be isolated. This indicates that steric factors play a role in meso-arylation, with low temperature meso-arylation being favored when the meso-position is not blocked by nearby substituents; however, B-arylation is favored over meso-arylation in all cases when using phenyllithium.
To conclude, as the interest in and possible applications of BODIPYs grows, methods for the direct modification of
F-BODIPYs will be needed. In order to investigate the meso-modification of F-BODIPYs we optimized a reported synthesis24,25 of the totally unsubstituted F-BODIPY such that 1 can now be routinely isolated in 20-30% yield. We have also developed a synthetically viable, alternative method for the production of meso-butylated F-BODIPYs by exploiting the nucleophilic attack of n-butyllithium at the meso-position of F-BODIPYs. Expansion of this methodology to other alkyllithium reagents is currently under investigation. meso-Arylation, using the same method, was not successful as nucleophilic attack at the boron centre was more favorable to nucleophilic attack at the meso-position and mixtures of products were isolated.

EXPERIMENTAL
All 1H NMR (500 MHz), 13C NMR (125 MHz), and 11B NMR (160 MHz) spectra were recorded using a Bruker Avance AV-500 spectrometer.31 Chemical shifts are expressed in parts per million (ppm) using the solvent signal [CDCl3 (1H 7.26 ppm; 13C 71.16 ppm)] as an internal reference for 1H and 13C and BF3•OEt2 as an external reference for 11B. Splitting patterns are indicated as follows: br, broad; s, singlet; d, doublet; t, triplet; q, quartet; m, multiplet. All coupling constants (J) are reported in Hertz (Hz). Mass spectra were obtained using ion trap time-of-flight (ESI) instruments. Column chromatography was performed using 230-400 mesh ultra pure silica or 150 mesh Brockmann III activated, basic aluminum oxide, as indicated. Spectral data for compounds 1,23-25 2,3,22,28,31 3,22,28 4,27 6,28 7, 28 and 828 have been previously reported in the literature.

4-Bora-3a,4a-diaza-s-indacene (1)

Following a modified literature procedure,25 a suspension of 2,3,5,6-tetrachloro-p-benzoquinone (174 mg, 0.71 mmol) in DCM (7.5mL) under a nitrogen atmosphere was added drop-wise to a stirred solution of di(1H-pyrrol-2-yl)methane27 (100 mg, 0.68 mmol) in DCM (7.5 mL) at -80 ˚C under nitrogen. Once the addition was complete, the solution was stirred at -80 ˚C for 1 h. Diisopropylethylamine (0.71 mL, 4.08 mmol) was added drop-wise to the reaction mixture followed by BF3•OEt2 (0.68 mL, 6.12 mmol) and the reaction mixture was stirred for 3 h while warming to -30 oC. The reaction mixture was filtered through celite and the solvent was removed in vacuo. The crude solid was purified over silica gel eluting with 50% DCM in hexanes. The combined fractions were concentrated in vacuo and then purified over silica gel eluting with 15% ethyl acetate in hexanes and the combined fractions were then concentrated in vacuo to give 1 as a red solid (30 mg, 23%). δH (500 MHz, CDCl3) 7.90 (s, 2H), 7.42 (s, 1H), 7.16 (d, J = 4.0, 2H), 6.55 (d, J = 4.5, 2H); δC (125 MHz, CDCl3) 145.2, 135.0, 131.5 (q, J = 2), 131.4, 118.9 (q, J = 2); δB (160 MHz, CDCl3) 0.15 (t, J = 30); m/z ESI+ found 215.0564 [M+Na]+ calculated for C9H7BF2N2Na 215.0568. 13C NMR data matches that previously reported.23-25

8-Butyl-4-bora-3a,4a-diaza-s-indacene (5)

n-Butyllithium (1.9 mL of a 1.6 M solution in hexanes, 3.1 mmol) was slowly added under a nitrogen atmosphere to a round-bottom flask containing a solution of 1 (60 mg, 0.31 mmol) in THF (10 mL) at -78 ˚C. The solution was stirred while slowly warming to -30 ˚C. At -30 ˚C, methanol (2 mL) was added drop-wise followed by a 0.1 M aqueous solution of HCl (2 mL) and the mixture was stirred for 10 min. The mixture was removed from the cooling bath and 2,3-dichloro-5,6-dicyano-p-benzoquinone (541 mg, 2.4 mmol) was added and the reaction mixture was stirred for 3 h at room temperature. The reaction mixture was diluted with DCM (75 mL) and water (150 mL). The layers were separated and the organic layer was washed with water (3 x 150 mL). The organic layer was dried over anhydrous Na2SO4 and the solvent was removed in vacuo. The crude solid was dissolved in DCM and the solution was filtered through a pad of silica eluting with DCM. Purification over silica gel eluting with 50% DCM in hexanes gave 5 as an orange solid (20 mg, 26%). δH (500 MHz, CDCl3) 7.85 (s, 2H), 7.27-7.28 (m, 2H), 6.53-6.54 (m, 2H), 2.95-2.92 (m, 2H), 1.81-1.75 (m, 2H), 1.47 (sextet, J = 7.5, 2H), 0.97 (t, J = 7.5, 3H); δC (125 MHz, CDCl3) 151.4, 143.4, 135.3, 127.9, 118.1, 36.1, 31.3, 23.3, 13.9; δB (160 MHz, CDCl3) 0.02 (t, J = 30); m/z ESI+ found 271.1178 [M+Na]+ calculated for C13H15BF2N2Na 271.1194.

4,4-Diphenyl-1,3,5,7-tetramethyl-2,6-diethyl-8-H-4-bora-3a,4a-diaza-s-indacene (8) and 4,4- diphenyl-1,3,5,7-tetramethyl-2,6-diethyl-8-phenyl-4-bora-3a,4a-diaza-s-indacene (9)

Phenyllithium (4.6 mL of a 1.8 M solution in di-n-butyl ether, 8.2 mmol) was slowly added under a nitrogen atmosphere to a round-bottom flask containing a solution of 3 (250 mg, 0.82 mmol) in diethyl ether (15 mL) at 25 ˚C. The solution was allowed to stir at room temperature for 18 h. Methanol (5 mL) was added drop-wise and the reaction mixture was concentrated in vacuo to give an orange oil. The crude oil was purified over silica gel eluting with 4% EtOAc in hexanes to give a mixture of 8 and 9 as an orange solid (28 mg 8, 7%, and 142 mg 9, 29%). δH (500 MHz, CDCl3) 7.49-7.47 (m, 3H, 9), 7.42-7.40 (m, 4H, 9), 7.36-7.34 (m, 2H, 9), 7.30-7.16 (m, 8.5H, 8 and 9), 7.13 (s, 0.20H, 8), 2.33 (q, J = 7.0, 0.84H, 8), 2.22 (m, J = 7, 5H, 8 and 9), 1.77-1.76 (m, 6.7H, 8 and 9), 1.31 (s, 6H, 9), 0.99 (t, J = 7, 1.3H, 8), 0.90 (t, J = 7, 6H, 9); δC (125 MHz, CDCl3) 154.0, 153.1, 140.8, 137.1, 135.4, 134.1, 133.9, 133.8, 132.9, 131.6, 130.9, 129.0, 128.9, 128.5, 127.28, 127.26, 125.7, 125.6, 119.5, 19.5, 17.7, 17.5, 14.9, 14.7, 14.5, 12.1, 9.5; δB (160 MHz, CDCl3) -0.34 (broad s); m/z ESI+ [M+Na]+ 443.3, 519.3. Although this mixture could not be separated, assignments are based on those of a pure sample of the C-BODIPY 8.28

4,4-Diphenyl-8H-4-bora-3a,4a-diaza-s-indacene (10) and 4,4-diphenyl-8-phenyl-4-bora-3a,4a- diaza-s-indacene (11)

Phenyllithium (0.65 mL of a 1.8 M solution in di-n-butyl ether, 1.2 mmol) was slowly added under a nitrogen atmosphere to a round-bottom flask containing a solution of 1 (56 mg, 0.29 mmol) in THF (11 mL) at -45 ˚C. The solution was stirred for 30 min and then the cooling bath was removed and the mixture was stirred at room temperature for 1 h. A 0.1 M aqueous solution of HCl (4 mL) was added drop-wise and the reaction mixture was stirred for 5 min. 2,3-Dichloro-5,6-dicyano-p-benzoquinone (658 mg, 10 mmol) was added and the reaction mixture was stirred for 1 h at room temperature. The reaction mixture was filtered through a pad of Brockman III neutral alumina, dried over Na2SO4, and concentrated in vacuo to give a brown oil. The crude oil was filtered through silica gel eluting with 15% EtOAc in hexanes and the combined fractions were concentrated in vacuo to give an orange solid. Purification over silica using a gradient of 1% EtOAc in hexanes to 3% EtOAc in hexanes, and concentration in vacuo gave a mixture of 10 (3.4 mg, 4 %) and 11 (2.1 mg, 2%) as an orange solid. δH (500 MHz, CDCl3) 7.55-7.54 (m, 1H), 7.52-7.51 (m, 0.5H), 7.50-7.49 (m, 0.5H), 7.40-7.39 (m, 0.5H), 7.31 (d, J = 4, 0.50H), 7.25-7.17 (m, 4H), 7.13-7.11 (m, 2H), 7.07-7.01 (m, 6H), 6.91-6.87 (m, 2H), 6.59 (d, J = 4.5, 0.5H), 6.53 (d of d, J = 2.0, 4.0, 1H), 6.40 (d of d, J = 1.5, 4.0, 0.5H); δC (125 MHz, CDCl3) 145.9, 144.5, 136.9, 135.0, 132.8, 132.4, 131.4, 130.6, 129.8, 129.3, 129.2, 128.4, 128.1, 127.6, 127.2, 127.1, 126.4, 126.0, 125.3, 121.2, 117.92, 117.86; δB (160 MHz, CDCl3) 0.80 (broad s); m/z ESI+ found 331.1375 [M+Na]+ calculated for C21H17BN2Na 331.1382 (10) and found 407.1675 [M+Na]+ calculated for C27H21BN2Na 407.1695 (11).

4,4-Diphenyl-1,3-dimethyl-2-ethyl-8H-4-bora-3a,4a-diaza-s-indacene (12) and 4,4-diphenyl-1,3- dimethyl-2-ethyl-8-phenyl-4-bora-3a,4a-diaza-s-indacene (13)

Phenyllithium (2.2 mL of a 1.8 M solution in di-n-butyl ether, 4.0 mmol) was slowly added under a nitrogen atmosphere to a round-bottom flask containing a solution of 2 (100 mg, 0.40 mmol) in THF (15 mL) at -45 ˚C. The solution was stirred for 30 min and then the cooling bath was removed and the mixture was stirred at room temperature for 1 h. A 0.1 M aqueous solution of HCl (5 mL) was added drop-wise and the reaction mixture was stirred for 5 min. 2,3-Dichloro-5,6-dicyano-p-benzoquinone (908 mg, 10 mmol) was added and the reaction mixture was stirred for 1 h at room temperature. The reaction mixture was filtered through a pad of Brockmann III neutral alumina, dried over Na2SO4, and concentrated in vacuo to give a brown oil. The crude oil was purified over silica gel eluting with 2% EtOAc in hexanes to give a mixture of 12 and 13 as a bright orange solid. The mixture was purified over silica gel eluting with a gradient of hexanes to 2% EtOAc in hexanes. Concentration in vacuo gave a mixture of 12 and 13 as a bright orange solid (14 mg 12, 10% and 10 mg 13, 6%). The crude mixture of 12 and 13 was again purified over silica eluting with a gradient of hexanes to 2% EtOAc in hexanes. Concentration of the pure fractions in vacuo gave 12 as an orange solid and 13 as an orange solid.

4,4-Diphenyl-1,3-dimethyl-2-ethyl-8 H-4-bora-3a,4a-diaza-s-indacene (12)

δH (500 MHz, CDCl3) 7.29 (s, 1H), 7.23-7.14 (m, 11H), 6.89 (d of d, J = 1.0, 4.0, 1H), 6.31 (d of d, J = 1.0, 4.0, 1H), 2.41 (q, J = 7.5, 2H), 2.26 (s, 3H), 1.84 (s, 3H), 1.06 (t, J = 7.5, 3H); δC (125 MHz, CDCl3) 139.6, 138.0, 136.1, 134.2, 133.3, 132.0, 127.4, 126.0, 124.3, 123.6, 114.9, 105.6, 17.7, 15.0, 14.7, 9.6 (1 C missing); δB (160 MHz, CDCl3) 0.19 (broad s); m/z ESI+ found 387.1985 [M+Na]+ calculated for C25H25BN2Na 387.2003.

4,4-Diphenyl-1,3-dimethyl-2-ethyl-8-phenyl-4-bora-3a,4a-diaza-s-indacene (13)

δH (500 MHz, CDCl3) 7.48-7.46 (m, 3H), 7.39-7.37 (m, 2H), 7.28-7.23 (m, 8H, overlaps with CHCl3 solvent signal), 7.21-7.17 (m, 3H), 6.36 (d of d, J = 1.0, 4.0, 1H), 6.24 (d of d, J = 1.0, 4.0, 1H), 2.34 (q, J = 7.5, 2H), 1.85 (s, 3H), 1.50 (s, 3H), 1.00 (t, J = 7.5, 3H); δC (125 MHz, CDCl3) 160.3, 142.4, 139.2, 139.0, 135.6, 135.4, 134.2, 133.5, 133.3, 129.2, 128.9, 128.3, 127.4, 125.9, 124.1, 114.6, 17.6, 15.3, 14.7, 12.7 (1 C missing); δB (160 MHz, CDCl3) - 0.09 (broad s); m/z ESI+ found 463.2288 [M+Na]+ calculated for C31H29BN2Na 463.2316.

ACKNOWLEDGEMENTS
This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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