I tried with two equivalent iodomethane in presence of caesium carbonate or potassium carbonate in DMF but the yield are disappointing and the principal product was the mono-methylated derivative.
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Multi-functionalization of gallic acid towards improved synthesis of α- and β-DDBFull TextBy Alam, Ashraful et al From Tetrahedron, 61(7), 1909-1918; 2005
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I remember making the 'tri-methylated' derivative of this with sodium hydride iodomethane. Getting only the 'disubstitued' derivative will be tedious but not impossible. When I ran the column I remember getting an appreciable amount of the 'dimethylated' derivative (which I kept and converted to my intended product later). Perhaps changing the equivalents of base here and adding the CH3I at different times afterwards might offer you another alternative with a better yield. Although it is a rather brutal 'heavy handed approach' keep in mind it's not the most elegant of reactions to begin with.
I also noticed your sci-finder reference says 'one step'?? Did I read that correctly?? You will have to add 2/2.5 eq. of the K2CO3 then add your CH3I in a second step. I don't see why this doesn't work to begin with. The prevalence of the 'mono-methylated' product makes me wonder how this was run.
I also know that you can buy it rather cheaply. If your yields continue to be under par and you are burning through materials due to yield or method this also maybe worth the $$$ here in the beginning.
I would try completely methylating and then trying to demethylate the least hindered methoxy with boron trichloride. This may also demethylate the the ester which could be remethylated with diazomethane.
I am sorry to say but most of the procedures presented here are quite lengthy and will give so many side products;
Except for the hydrogens on the hydroxy groups the whole (3,4,5-trihydroxy-benzoate) is planar.
Heres my opinion;
1) Use dil NaOH at low temperature ( below 5 C) and add in 1,4-dibromo-butane.
2)Let this overnight. I would create a diether linkage between the sp3 hybridized oxygen on the carboxylate portion and the oxygen of the hydroxyl groups which lies on its plane.
3) use any "less harsh" methylation agenf like iodomethane.
4) this would methylate the 4,5-postions
5)remove the diether using any "less harsh" agent for example use --- MeMgBr, CuBr, PBu3 at O degrees celcius.
This would give u ( 3-hydroxy-4,5-dimethoxy-benzoic acid. I HOPE THATS WHAT U WANT!
Try protection of 1,2 diol which you will get in the book Greene's protective group in organic synthesis and it may protect any of the two adjacent hydroxy groups. then protect the third hydroxy group with any protecting group which require different deprotection conditions ten the protected diol and I hope you can get the desired molecule. See above mentioned book its really helpful