##### NCNCS the perfect molecule which exhibits quasi-linear behaviour and quantum monodromy

###### Tilden Lecture Intro

My memory is that we were trying to produce NCBS by pyrolysis of S(CN)2 over crystalline boron at high temperature and Mike King discovered that S(CN)2 isomerised to NCNCS. This was a very nice discovery as this molecule is probably the most beautiful example of a quasi-linear system. Barry Landsberg did a really superb job of analysis and found it was a truly beautiful example in that the rotational spectrum in the lowest vibrational state was that of an asymmetric top but as the bending vibrational quantum increased to about v=3 the molecule was flexing through the linear configuration (it had a sombrero hat potential – see below) and for these levels the rotational structure was much more like that of a linear molecule. In the case of linear molecule the l (k) = 1 lines form an l-doublet and lie between the l=0 and l=2 lines whereas for an asymmetric top these latter lines lie between the k (l) = 1 (see my book!). Basically the structure was averaging over a linear configuration for v= 3.

Mike King who discovered the isomerisation and Barry Landsberg who worked out what was happening (both older and wiser?)

###### Quantum Monodromy in the Rotational Spectrum of NCNCS

Later on Brenda and Manfred Winnewisser and their colleagues went on to carry out an amazingly elegant and exhaustive study to show that the molecule had even more beautiful tricks up its sleeve in that as the vibrational quantum number increases even more the rotational structure reverts back to an asymmetric top pattern at v=6. It is in fact a beautiful example of quantum monodromy – see spectrum below

https://kb.osu.edu/dspace/bitstream/handle/1811/30600/abstract.gif?sequence=42

Note that in this spectrum the high frequency end is to the right… The opposite way round from the original Sussex spectrum published.

###### Brenda and Manfred note:

The B for K=0 and v = 3 is an absolute minimum because the molecule can just, barely, scrape over the top of the barrier, so it slows down and spends a lot of time there. Ergo it has its maximum time average extension and moment of inertia for end-over-end rotation, and its minimum B value. The wave function confirming this is shown in a plot in our 2010 paper. It was the stunning simplicity of the graphical representation of that (quantum-mechanically) obvious fact that blew us way when we plotted our first monodromy plot of B-values.

In this diagram we see that for v=0 the wave unction has one maximum at ca 37 degrees and at v=3 the maximum is around the linear configuration as it slows down at the potential maximum. As v increases it spends less an less time a 0 degrees and more time spread over a range of bent configurations as indicated at v=6

7) PCCP-Winnewisser_et_al 2010

PCCP-2014-16-17373-Perspective-authorreprints NCNCS pp3-20

PCCP-2014-16-17373-Perspective-authorreprints NCNCS pp 21-37

https://kb.osu.edu/dspace/handle/1811/30600