Symmetry and rearrangement

Unexpected rearrangements

• Recent spectroscopic analysis of reaction crude confirms that meso substitution reactions tend to include spontaneous side reactions where the group migrates to the adjacent beta carbon or generates stereocenters.

​

Hypothesis

• Enthalpy difference between meso and beta bonds may favor the rearrangement

​

• Many possible contributions:
1. Vibrational entropy
2. Increased entropy of rotation
3. Increased tautomeric states for inner protons
4. Generation of new stereocenters

Methodology

1. Structure is pre-optimized using MMFF94 in Avogadro 2.0
2. Further structure optimization and frequency calculations are performed in the Gaussian 16 engine using DFT (B3LYP functional, 6-31G(d) basis set) on WebMO computational cluster.
1. Upon confirming that the calculation converged at the lowest energy solution, the enthalpy, ground state structure, number of vibrational modes, symmetry coefficient and point group etc. can be used to make conclusions regarding enthalpy and entropy changes of the isomers.

Partition function description of rotational entropy

Point groups and symmetry operations

Symmetry of common porphyrin motifs

Entropy contribution to proton tautomerism

• Rigorous calculation of entropy increase due to creation of new chemical environments in the porphyrin ring current is beyond the scope of this presentation due to prominent tunneling effect and the large computational cost.
• S=Rln(W), where W is the number of ways to produce one state.
• Define the state as any porphyrin compound with 2 protic and 2 aprotic nitrogens.
• The relative position of protons and differing chemical environments will be counted as a different way to generate the same state.
• More chemical environments, more entropy.

A3B: W=4

• 2 types of nitrogen: AA, BA
• Protons can either be together or apart

​

A4: W=2

The protons are either opposite or next to each other

A3H meso, B beta: W=6 (probably wrong)

Each nitrogen is unique, and the protons are either close to each other or at opposite ends.

Computed thermodynamic values

Citations

1.Cramer, C. J. Essentials of Computational Chemistry: Theories and Models; J. Wiley: West Sussex, England, 2002.

2.Vallance, C. Symmetry Classification of Molecules: Point Groups. Chemistry LibreTexts, 2020. https://chem.libretexts.org (accessed 2026-07-17).

3.Houde, M. Geometrical Symmetry. Physics 9624/Astronomy 9701 Lecture Notes, University of Western Ontario. https://physics.uwo.ca/~mhoude2/courses/astro610/Geometrical_symmetry.pdf (accessed 2026-07-17).

4.Yin, Y.-B. DFT Study on Deprotonation and Protonation of Porphyrins: How Many Protons Can the Porphyrin Core Take Up? Comput. Theor. Chem. 2016, *1090*, 23–33. DOI: 10.1016/j.comptc.2016.01.022.

5.Shelnutt, J. A.; Song, X.-Z.; Ma, J.-G.; Jia, S.-L.; Jentzen, W.; Medforth, C. J. Nonplanar Porphyrins and Their Significance in Proteins. Chem. Soc. Rev. 1998, *27*, 31–41. DOI: 10.1039/a827031z.

(6.)Barkigia, K. M.; Berber, M. D.; Fajer, J.; Medforth, C. J.; Renner, M. W.; Smith, K. M. Nonplanar Porphyrins. X-ray Structures of (2,3,7,8,12,13,17,18-Octaethyl-5,10,15,20-tetraphenylporphinato)nickel(II) and Its Radical Cation. J. Am. Chem. Soc. 1994, *116*, 6593–6598. 

7. Medforth, C. J.; Senge, M. O.; Smith, K. M.; Sparks, L. D.; Shelnutt, J. A. Nonplanar Distortions of Porphyrins. J. Chem. Soc., Perkin Trans. 2 1992, 1079–1084. DOI: 10.1039/P29920001079.

�