Theoretical transition frequencies beyond 0.1 ppb accuracy in H2+, HD+, and antiprotonic helium

We present improved theoretical calculations of transition frequencies for the fundamental transitions (L = 0, nu = 1) -> (L ' = 0, nu ' = 0) in the hydrogen molecular ions H-2(+) and HD+ with a relative uncertainty 4 x 10(-11) and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty 10(-10). To do that, the one-loop self-energy correction of order alpha(Z alpha) 6 is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin- independent corrections of order m alpha(7). The leading order corrections of alpha(2) ln(3)(Z alpha)(-2)(Z alpha)(6) are also considered that allows one to estimate a magnitude of yet uncalculated contributions.