We calculate the adiabatic Potential Energy Surfaces (PESs) and the Non-Adiabatic Coupling Terms (NACTs) for the three lowest singlet states of H 3 + in hyperspherical coordinates as functions of hyperangles (θ and φ) for a grid of fixed values of hyperradius (1.5 ≤ ρ ≤ 20 bohrs) using the MRCI level of methodology employing ab initio quantum chemistry package (MOLPRO). The NACT between the ground and the first excited state translates along the seams on the θ - φ space, i.e., there are six Conical Intersections (CIs) at each θ (60° ≤ θ ≤ 90°) within the domain, θ ≤ φ ≤ 2π. While transforming the adiabatic PESs to the diabatic ones, such surfaces show up six crossings along those seams. Our beyond Born-Oppenheimer approach could incorporate the effect of NACTs accurately and construct single-valued, continuous, smooth, and symmetric diabatic PESs. Since the location of CIs and the spatial amplitudes of NACTs are most prominent around ρ = 10 bohrs, generally only those results are depicted. © 2014 AIP Publishing.