A search for configuration space with well-defined topological (Berry) phases corresponding to Jahn-Teller (JT) conical intersection (CI) and Renner-Teller (RT) parabolic intersection (PI) in the linear tetra-atomic molecular system on introduction of bending demonstrates the interesting aspect that these potential intersections may appear in the molecular plane as well as out of the molecular plane. While understanding this aspect is important for following the class of phenomena led by potential intersections, till date, studies on molecular systems, including pairs such as (C2H2 +, HCNH) and (N2H2 +, HBNH+), have not been able to clarify the issue. The present article includes calculation of nonadiabatic coupling terms involving four low-lying states of slightly bent HCNO+, a motivated choice of tetra-atomic with all four different atoms, to study this aspect associated with JT-CI and RT-PI in a slightly bent linear system. The plane of appearance of these effects has been advocated to be related to the electronic configuration of the concerned states of the molecular system. © 2020 Wiley Periodicals, Inc.