Accurate potential energy curves for HeH⁺ isotopologues

New accurate ground-state potential energy curves (PEC) for the ⁴HeH⁺, ⁴HeD⁺, ³HeH⁺, and ³HeD⁺ isotopologues are calculated with 600 explicitly correlated Gaussian (ECG) functions with shifted centers in the range between R = 0.35 a₀ and 145 a₀. The calculations include the adiabatic corrections (AC). The absolute accuracy of all Born-Oppenheimer (BO) PEC points is better than 0.0018 cm⁻¹ and it is better than 0.0005 cm⁻¹ for the ACs. With respect to the very recent BO PEC calculations performed by Pachucki with 20 000 generalized Heitler-London explicitly correlated functions [K. Pachucki, Phys. Rev. A 85, 042511 (2012)] https://doi.org/10.1103/PhysRevA.85.042511, the present energy calculated at R = 1.46 a₀ (a point near the BO equilibrium distance) lies above by only 0.0012 cm⁻¹. Using Pachucki's BO energy at the equilibrium distance of R = 1.463 283 a₀, and the adiabatic corrections calculated in this work for the ⁴HeH⁺, ⁴HeD⁺, ³HeH⁺, and ³HeD⁺ isotopologues, the following values are obtained for their PEC depths: 16 448.99893 cm⁻¹, 16 456.86246 cm⁻¹, 16 451.50635 cm⁻¹, and 16 459.36988 cm⁻¹, respectively. We also calculate the rovibrational (rovib) frequencies for the four isotopologues using the BO PEC of Pachucki augmented with the present ACs. The improvements over the BO+AC PEC of Bishop and Cheung (BC) [J. Mol. Spectrosc. 75, 462 (1979)] https://doi.org/10.1016/0022-2852(79)90090-0 are 1.522 cm⁻¹ at R = 4.5 a₀ and 0.322 cm⁻¹ at R = ∞. To partially account for the nonadiabatic effects in the rovib calculations an effective reduced-mass approach is used. With that, the present ⁴HeH⁺ rovibrational transitions are considerably improved over the BC transitions as compared with the experimental values. Now the rovibrational transitions near the dissociation limit are as well reproduced by the present calculations as the lower transitions. For example, for the ⁴HeD⁺ transitions corresponding to the ν = 13-9 hot bands the results are off from the experimental values by less than 0.023 cm⁻¹. This confirms high accuracy of the present PECs at larger internuclear separations.