Theoretical study of triplet state properties of free-base porphin

This paper presents results and analysis of various properties of the triplet state of free-base porphin (FBP) as calculated by density-functional theory. The radiative lifetime of phosphorescence lines and microwave signals in optical detection of magnetic resonance (ODMR) spectra are obtained using the B3LYP hybrid density-functional and the quadratic response method. The zero-field splitting (ZFS) in the lowest triplet state, a³ B _2u, of FBP is calculated as an expectation value of spin-spin coupling operator using the self-consistent field wavefunction. The second-order contribution to ZFS from the spin-orbit coupling operator is found to be almost negligible. The interpretation of the ODMR spectrum is completed by computing the hyperfine tensors of the ¹⁴N, ¹³C and hydrogen atoms in the lowest triplet state. The most intense phosphorescence emission corresponds to the T^z-spin-sublevel of the a³ B _2u state, where the z-axis lies in the N-H direction of the FBP molecule in a qualitative agreement with ODMR data. The results indicate that the observed decay of the lowest triplet state of FBP molecule is determined by non-radiative deactivation. The calculated radiative rate constant for the T^z-spin-sublevel k_z = 2.65 × 10^-3 s ^-1 is in agreement with the value k_z ≃ 2 × 10^-3 s^-1, estimated by van Dorp et al. [W. van Dorp, W. Schoemaker, M. Soma, J. van der Waals, Mol. Phys. 30 (1975) 1701] from kinetic analysis of microwave-induced fluorescent signals. The correct prediction of the spin quantization axis of the most active spin sublevel and of its radiative lifetime in the lowest triplet state of the FBP molecule is taken as a proof of capability of the quadratic response time-dependent density-functional theory.