Potential energy curves and analytical potential energy functions of the metastable states of B₂²⁺

The multi-reference configuration interaction method and aug-cc-pvqz (AVQZ) have been used to calculate potential energy curves (PECs) of the singlet and triplet states of the \prod _\rm u and \prod _\rm g symmetry of B_2^ + + . All of the four states (^1\prod_\rm u, ^ 1\!\prod _\rm g, ^ 3\!\prod _\rm u and ^3\!\prod _\rm g) are found to be metastable states, though the potential well of ^3\!\prod _\rm u symmetry is very shallow. Based on the PECs, the analytical potential energy functions (APEFs) of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the Schr\"odinger equation of nuclear motion.