Line broadening inverse

At -40 °C the spectrum corresponds to an intermediate rate of interconversion. The outer lines and four of the six components of the central line retain the same spin assignment upon ring inversion and remain fixed and narrow, while the remaining lines broaden and disappear. 

The composite filter 7(g)) may either be the true inverse filter, truncated for oo large if necessary, or any of the variations described in Section IV. In their original work, Rendina and Larson chose 7(g)) = (co)/t(co), where //(co) is a Gaussian line-broadening function that limits the ultimate resolution obtainable but yields a manageable 7(g)). For their studies Rendina and Larson used Ns = 4. 

It is noteworthy that the width of an absorption line is inversely proportional to the lifetime of the excited state (Heisenberg s uncertainty principle). Hence, for gases, the lifetime is long and the absorption lines are sharp. However, the lifetime is short for compounds in the condensed phase and band broadening occurs. Except for very simple molecules, no instrument allows the observation of individual lines. 

The stereochemistry of the trioxanes (40), (41), and (42) was determined using variable temperature NMR experiments. The presence of characteristic line broadening effects in the spectrum of the cis isomers (41) and (42), due to ring inversion, distinguished them from the rigid trans isomer (40) <88JOC4986>. 

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