In a conformational analysis, I have found that by varying the dihedral angle C-C=N-N (See attached picture) of a thiosemicarbazone derivative a conformer b is obtained which is more unstable than the conformer a by only 3.8 kCal/mol. Should the conformer b be analyzed? Can I talk about conformational analysis by varying a dihedral angle that involves a double bond?
It's more geometrical than confrmational, as you has E/Z system here, so you should mention that the E is more stable than Z, usually Z more stable in solvents.
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It is completely reasonable to investigate conformational isomerism by rotating about a (nominal) double bond. Double bonds do not have to be "flat" because competing factors may force them out if plane.
Some useful related discussion may be found here:
Article 2-Phenylpyridine: To Twist or Not To Twist?
As pointed out by Radwan, yu are not deailing with conformation but with geometrical isomers that can be separated and have different spectra. Conformational analysis is about rotation about single bonds, giving rotamers / conformers that -in general- cannot be separated.
Each isomer a and b have a multiple conformers corresponding to rotation about R-O, O-C, C-C, N-N, C-N... single bonds. Examining the relative energy of conformers (and related conformer composition) is the aim of conformational analysis.
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