B. Mukherjee, D. Mukhopadhyay, A. Adhikari, and M. Baer. (2018). Topological study of the H3++ molecular system: H3++ as a cornerstone for building molecules during the Big Bang. Molecular Physics. DOI:https://doi.org/10.1080/00268976.2018.1442940.
When the article was first published online Figures 1(b–d) and 2(b–d) in Table 2 and Figures 2(b–d) in Table 3 were wrongly plotted due to incorrect analysis. As a result, the graphical abstract, and the corresponding discussions in pages 6 and 8 in Section 3.1 and the analysis section available at page 10 will also need modification.
In page 6 under Section 3.1, starting from the first line of the left column to the fourth line of the right column, the text:
Whereas the NACTs in Table 1 are seen to be smooth and friendly, the NACTs in Table 2 are, unexpectedly, rather spiky. Moreover, whereas the contours in Table 1 are seen to surround only one single ci formed by the two upper states – thus a (2,3) ci – the contours in Table 2 surround four cis – two (1,2) cis and two (2,3) cis. It could very well be that the two phenomena are interrelated and because they are derived for what seems to be the asymptotic region namely, at r = 10.0 a.u. (RD3h = 8.66 a.u.) and r = 12.0 a.u. (RD3h = 10.39 a.u.) of the H3++ molecular system.
is replaced by
Whereas the NACTs in Table 1 are seen to be smooth and friendly, the NACTs in Table 2 are spiky. The more characteristic feature encountered here is that within the considered circular region it is seen that, the NACTs form one single ci – a (2,3) ci – which is produced by the two upper (excited) states.
In page 8 under Section 3.1, starting from the last line of the left column to the tenth line of the right column, the text:
As is noticed, the two studies presented in Table 3 yield, for significantly different conditions as presented in Tables 1 and 2, similar quantizations due to the equilateral D3hcis at r = 8.0 a.u. and 10.0 a.u., respectively. In other words, the results in the first row of Table 3 are presented with the aim of supporting the corresponding results of Table 1 where the encountered NACTs are formed by a single ci whereas the results in the second row of Table 3 are presented to support the corresponding results in Table 2 where the encountered NACTs are formed by four coalesced cis.
is replaced by
As is noticed, the two studies presented in Table 3 yield, for significantly different situations as presented in Tables 1 and 2, similar quantizations due to the equilateral D3h cis at r = 8.0 a.u. and 10.0 a.u., respectively. In other words, the results presented in Table 3 support the corresponding results in Tables 1 and 2 that indeed the encountered NACTs form, in the corresponding configuration space (CS), one single ci.
In the analysis section, in page 10 under Section 4, the third, fourth and fifth paragraphs in the left column:
The H3++ does not seem to behave like that at all. As before, we follow the D3h NACTs along the same axis but a much more complicated situation is encountered which can be summarized as follows: (i) In contrast to the two previous cases the corresponding D3h NACTs are significantly affected while moving from the internal region towards the asymptotic one (see Table 1); (ii) once the asymptotic region is reached, we find, instead of NACTs formed by one D3h ci, NACTs formed by four cis – two (1,2) cis and two (2,3) cis – which coalesce at the corresponding D3h point (see Table 2). Moreover, each pair is seen to form spiky NACTs to the level of the Dirac-δ function.
In this respect, it is important to mention that four coalesce cis were already revealed by us while studying the H3 system several years ago [26]. Still, this happened only at the close, intimate region (∼ 1 a.u.) and, as far as the NACTs are concerned, they were hardly spiky, certainly not to the level seen here.
Thus, summarizing the findings regarding the H3++ molecular system, the following can be said: although along the intermediate CS, the behavior of this system as reflected via the contour-dependent NACTs is bearable, we encounter essentially an unbearable conduct at its asymptotic region, most likely, due to the coalescing process.
have been replaced by the following two paragraphs:
The H3++ does not seem to behave like that at all. While watching the NACTs produced at CSs surrounding different D3h points, the following is revealed: (i) The D3h NACTs are significantly affected while moving from the internal region towards the asymptotic one (cf. results in Table 1 and Table 2); (ii) once the asymptotic region is reached we find, that the smoothly behaving NACTs formed in the internal regions are replaced by spiky NACTs to the level of becoming Dirac-δ functions.
Thus, summarizing the findings regarding the H3++ molecular system, the following can be said: although along the intermediate regions of CS the behavior of this system as reflected via the contour-dependent NACTs is bearable, we encounter essentially a non-molecular conduct at its asymptotic region
The authors apologize for these errors.