and the hyperfine structure is readily improved as we present in this work.

The motivation of the present work is multi-fold. As stated, we supplement the light-front holographic QCD interaction with one-gluon exchange, rather than patching the holographic wave functions with, e.g., spin structures (see, e.g., Ref. [[@Chen:2016dlk] and the references therein)]{}. The spectroscopy and the wave functions are obtained as a natural output. More importantly, we solve the problem using the basis function method [@Vary:2009gt]. Effectively, we are applying BLFQ to a phenomenological interaction that emulates features of QCD. Indeed, this work is a direct extension of the BLFQ approach to positronium in QED [@Wiecki:2014ola]. Finally, we acknowledge the similarities between our work and the relativistic bound-state models in QCD (e.g., Refs. [@Sommerer:1994bk; @Spence:1995bm; @Spence:1999db; @Maris:1999nt; @Leitao:2016bqq]), especially the light-front QCD bound-state models [@Pauli:1996ne; @Brisudova:1995hv; @Brisudova:1996vw; @Glazek:2003ky; @Glazek:2006cu; @Choi:2015ywa].

We organize this paper as follows. In Sect. \[sec:ingredients\], we introduce the theoretical model, including the longitudinal confinement and a running strong coupling. The formulation and the methods are detailed in Sect. \[sect:formalism\]. Sect. \[sect:numerical\_results\] summarizes and analyzes the numerical results, including the spectroscopy, decay constants and radii. Sect. \[sect:lfwfs\] presents LFWFs and light-cone distributions computed from them. We summarize 