Implementation of explicitly correlated complex Gaussian functions in calculations of molecular rovibrational J=1 states without Born-Oppenheimer approximation

In our previous work (Bubin et al., 2016) it was established that complex explicitly-correlated one-center all-particle Gaussian functions (CECGs) provide an effective basis set for very accurate non-relativistic molecular non-Born-Oppenheimer (non-BO) calculations for vibrational ground and excited states corresponding to the rotational ground state. In this work we advance the molecular CECGs approach further by implementing and testing the algorithms for calculating the vibrational states corresponding to the first rotational excited state (the J=1 state). The test concerns all bound J=1 rovibrational states of the HD⁺ ion.