Asymmetrical linear structures including three-electron hemibonds or other interactions in the (ABA)-type triatomic cations: Ne3+, (He-Ne-He)+, (Ar-Ne-Ar)+, (Ar-O-Ar)+, (He-O-He)+, and (Ar-He-Ar)+

By the counterpoise geometry optimization at the level of CCSD(T)aug-cc-pVDZ, the asymmetrical linear structures with all the real frequencies were obtained for the triatomic cations of (ABA)+ type: Ne3+, (He-Ne-He)+, (Ar-Ne-Ar)+, (Ar-He-Ar)+, (He-O-He)+, and (Ar-O-Ar)+. The validity of this optimization method is confirmed by comparing with the method of the potential-energy surface for the calculations of Ne3+ and (He-Ne-He)+. Using the molecular-orbital theory, it is found that the interaction within the triatomic cations is dominated by the contribution from the first two atoms while the contribution from the third atom is small. This result is justified as a direct consequence of forming an asymmetrical linear structure. Specifically, four types of interaction within the triatomic cations are identified: three-electron sigma-type hemibond, three-electron pi-type hemibond, two-electron sigma bond, and the attraction between cation and atoms. For Ne3+, (He-Ne-He)+, and (He-O-He)+ clusters, it is shown that the electron correlation effect supports the asymmetry.