Born-Oppenheimer vibrational-rotational dissociation energies eigenvalues for the hydrogen molecular ion

These are the vibrational-rotational energies for the ground electronic state of the hydrogen molecular ion calculated using the Born-Oppenheimer potential without corrections. The 423 energies E(v,N), where v is the vibrational quantum number and N is the rotational quantum number are expressed in energy units (inverse cm) relative to the dissociation limit of -0.5 atomic units appropriate to the present treatment. The proton mass is taken to be 1836.1527 in units of the electron mass. Adiabatic, relativistic, and radiative corrections lead to better energies (see discussion below), but the present values using only the Born-Oppenheimer potential are evidently not readily available in the literature. There is an earlier calculation using only the Born-Oppenheimer potential by Beckel, Hansen, and Peek [J. Chem. Phys. 53 (1970), 3681; doi: 10.1063/1.1674549], and their Table II lists 20 values for (v,0) up to and including (19,0); they used a proton mass of 1836.096. As a check, their calculations and the present calculations (performed using their proton mass value) were compared for the energy differences E(19,0)-E(18,0) ,...,E(13,0)-E(12,0) and E(5,0)-E(4,0), ..., E(1,0)-E(0,0). The resulting values agreed to at least 7 significant figures. Ishikawa, Nakashima, and Nakatsuji, Chem. Phys. 401 (2012), 62,<br>( doi:10.1016/j.chemphys.2011.09.013 ), in their Table 3,<br>give the transition energies for (00)-(10),<br>(10-20), (20-30), determined using three approaches,<br>extended Rydberg (ER), extended Morse (EM-HH), and extended<br>Morse-Dunham(EM-D),<br>from their free complement (FC) method calculations.<br>These can be compared to the present results and<br>the discrepancy is large for (20)-(30). all energy values in cm-1<br>transition-&gt;A=(00)-(10), B=(10)-(20), C=(20)-(30) <br>method, transition (A, B, C), notes ----------------------------------<br>ER, 2190.43, 2058.37, 1921.02, (from Ishikawa et al.)<br>EM-HH, 2191.19, 2061.88, 1932.01, (from Ishikawa et al.)<br>EM-D, 2191.17, 2061.46, 1930.94, (from Ishikawa et al.)<br>present, 2192.02, 2064.69, 1941.58, see figshare table<br>other, 2192.05, 2064.72, 1941.61, (from Beckel et al.) More precise eigenvalues can be found in the literature using adiabatic and nonadiabatic methods and with further correction terms. R.E. Moss [Molec. Phys. 80 (1993), 1541, doi:10.1080/00268979300103211] calculated non-adiabatic dissociation energies for the bound levels, considered quasi-bound states, and gave further relativistic and radiative corrections. The reported non-adiabatic calculation also yielded 423 bound levels. The potential corrected in the adiabatic approximation was used by Hunter, Yau, and Pritchard [Atomic &amp; Nuclear Data Tables 14 (1974), 11] to calculate the vibrational-rotational energies, where again 423 levels were found.