Density Functional Theory Study on the Isomerism in Porphyrins: Structural, Tautomerism and Atropisomerism

Density functional theory (DFT) and time-dependent DFT (TD-DFT) methods were systematically assessed for their ability to describe multiple forms of isomerism in porphyrin systems, including structural isomerism, N-H tautomerism, and atropisomerism, as well as their impact on electronic and optical properties. The structural isomers porphine (anti-H₂P) and porphycene (anti-H₂Pc) were examined using eight exchange-correlation functionals spanning Jacob's ladder, revealing that nonlocal hybrid and range-separated functionals provide the most accurate geometries and stability trends. Relative stability analyses, supported by conceptual DFT descriptors, consistently identify anti-H₂P as the hardest and least polarizable isomer. Calculated N-H tautomerization barriers for anti-H₂P agree well with experimental NMR data, particularly with the ωB97XD functional, while anti-H₂Pc exhibits a low-barrier anti-syn₁ pathway consistent with rapid proton dynamics and a second, energetically inaccessible syn₂ pathway. The challenging equilibrium among atropisomers of 5,10,15,20-tetra(ortho-hydroxyphenyl)porphyrin is shown to involve energy differences below 1.0 kcal/mol, with dispersion-corrected and range-separated hybrid functionals best reproducing experimental trends in solution. TD-DFT calculations of substituted porphyrins demonstrate that ωB97XD offers, again, the most balanced description of Soret and Q bands, enabling clear structure-property relationships between substitution patterns, oscillator strengths, and singlet oxygen generation. Overall, this work establishes reliable DFT protocols for describing complex isomerism and photophysical behavior in porphyrin-based organic systems, guidance for the rational design of functional porphyrinoids.