Ab initio investigation of potential energy curves of He₂, He₂⁺, and extrapolation by the machine learning method

Diatomic molecules He-2(+), He-2 are common compositions in plasmas using the helium as the working gas, and play key roles in quenching O-2 and N-2. However, the potential energy curve (PEC) of the first state He-2 (a(3)Sigma(+)(u)) obtained at the CASSCF level of theory is not accuracy and data of higher excited states of He-2(+) are lacking. Here, we calculated PECs of four excited states of He-2 and nine lowest electronic states of He-2(+) by employing CASSCF+MRCI/Aug-cc-pV5Z and CCSD(T)/Aug-cc-pV5Z level of theory with sample internuclear distance interval of 0.005 angstrom. PECs were extrapolated to the complete basis sets. There are double local maxima in PECs of three excited states He-2(+) (B-2 Sigma(+)(u)), He-2(+) (C-2 Pi(u)), He-2(+) (D-2 Pi(g)). The machine learning method based on the Gaussian process was used to interpolate and extrapolate the PECs, and then vibrational wave functions are solved numerically. This ab initio investigation provided rotational-vibrational constants and new data for experimental research in the future.