be a valuable approximation to QCD [@Brodsky:2014yha]. The efforts to improve light-front holography can be roughly cast into two categories: one is on the holographic QCD side (see [@Brodsky:2014yha] and the references therein); the other is on the light-front Hamiltonian side (see [@Hiller:2016itl] for a recent review).

The present work falls into the second category. We generalize the light-front holographic QCD of Brodsky and de Téramond to incorporate quark masses and quarkonium spin structure by extending the “soft-wall” light-front Hamiltonian. Our model introduces a phenomenological effective Hamiltonian. Key elements include a confining potential in the longitudinal direction and an effective one-gluon exchange interaction derived from light-front QCD [@Li:2015zda; @Li:2016wwu]. It was long pointed out by Lepage and Brodsky [@Lepage:1980fj] that the dominant ultraviolet (UV) physics can be analyzed through one-gluon exchange. Here, we combine the one-gluon exchange physics at short distance and the holographic QCD at long distance. The present work improves our previous calculation [@Li:2015zda] by including the evolution of the strong coupling as a function of invariant 4-momentum transfer. Incorporating the running coupling not only implements important QCD physics, but also improves the UV asymptotics of the kernel. In particular, a previous non-covariant UV counterterm is now removed 