Methods for conversion of methane to useful hydrocarbons, catalysts for use therein, and regeneration of the catalysts

A method for regenerating a catalyst composition that has been derived from at least (i) AlHnX1mRp, where Al is aluminum, H is hydrogen, each X1 is a halogen and can be the same as, or different from, any other X1, each R is a C1 to C4 alkyl and can be the same as, or different from, any other R, each of n and m is independently 0, 1, or 2, and p is 1 or 2, all such that (n+m+p)=3, and (ii) MvHqX2r, where Mv is a metal of valence v, H is hydrogen, each X2 is a halogen and can be the same as, or different from, any other X2, and each of q and r is 0 or any integer through and including v, all such that (q+r)=v, the method comprising applying voltage across the catalyst composition.