Large-scale calculations of accurate energy levels for the system HCO+/HOC+ in its electronic ground state are reported. The rovibrational levels are calculated for total angular momentum J = 0, 1, and 2 by means of the discrete variable representation of the angular coordinate in conjunction with a distributed Gaussian basis for the radial degrees of freedom. A new analytical potential energy surface is used which is based on high level ab initio calculations [CCSD(T)/cc-pVQZ]. The rovibrational energy spectra of HCO+ and HOC+, as well as of the isotopomers DCO+ and DOC+, are analyzed in detail up to the ground state adiabatic isomerization barrier at 28 798 cm(-1). Spectroscopic parameters calculated for low lying vibrational states show distinct differences between HCO+ and HOC+. A total number of 6042 bound states up to the first classical dissociation limit (H+ + CO) at 51 621 cm(-1) and a density at the threshold of 0.52/cm(-1) are estimated for J = 0. Semiclassical phase space integration yields nearly identical results for the numbers and densities of bound states for the given surface. An empirical model employing Morse oscillators, an explicit treatment of the hindered rotation, and stretch-bend coupling is used to simulate the quantum mechanical data.