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Search for configuration space with welldefined 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, reveal the interesting aspect that these potential intersections may appear in 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 like (C2H2plus , HCNH) as well as (N2H2plus , HBNHplus ), have not been able to clarify the issue. The present paper embodies calculation of non-adiabatic coupling terms (NACTs) involving four low lying states of slightly bent HCNOplus , a motivated choice of tetra-atomic with all four different atoms, to study this aspect associated with JTCI and RTPI in slightly bent linear system. The plane of appearance of these effects, has been advocated to be related to electronic configuration of the concerned states of the molecular system.

The present study is devoted to the possibility that tri-atomic molecules were formed during or shortly after the Big Bang. For this purpose we consider the ordinary $H_3^{+}$ and $H_3$ and the primitive tri-atomic molecular system, $H_3^{++}$, which, as is shown, behaves differently. The study is carried out by comparing the topological features of these systems as they are reflected through their non-adiabatic coupling terms. Although the $H_3^{++}$ is not known to exist as a molecule, we found that it behaves as such at intermediate distances. However this illusion breaks down as its asymptotic region is reached. Our study indicates that whereas $H_3^{+}$ and $H_3$ dissociate smoothly, the $H_3^{++}$, does not seem to do so. Nevertheless, the fact that $H_3^{++}$ is capable of living as a molecule on borrowed time enables it to catch an electron and form a molecule via the reaction $H_3^{++} + e \to H_3^{+}$ that may dissociate properly: $H_3^{+} \to H^{+} + H_2$ or $H + H_2^+$. Thus, the two unique features acquired by $H_3^{++}$ namely, that it is the most primitive system formed by three protons and one electron and topologically, still remain for an instant a molecule, may make it the sole candidate for becoming the \bold{cornerstone} for creating the molecules.

A process, carried out in a stepwise manner, becomes quasi-static when the number of intermediate steps tends to infinity. Usually, the net entropy production approaches zero under this limiting condition. Hence, such cases are termed reversible. A favorite example is the introduction of an infinite number of intermediate-temperature reservoirs in between the source and the sink for a non-isothermal heat transfer process. We analyze the situation and conclude that such quasi-static processes are not reversible. Indeed, no non-isothermal heat transfer process can ever be made reversible due to an extraneous work term., Comment: 11 pages