Spin Hamiltonian Simulations and Quantum Chemical Estimation of Magnetic Parameters in Radical Systems

Electron spin resonance (ESR) spectroscopy provides fundamental insights into unpaired electrons in atoms and molecules through magnetic parameters. Key quantities such as the g-factor, hyperfine coupling constants, and zero-field splitting (observed when the spin quantum number S ≥ 1) are determined via spectral simulations based on the diagonalization of the spin Hamiltonian. Although analytical solutions for the eigenvalues and eigenstates exist in limited cases, most simulations have been performed phenomenologically, employing parameters not rigorously derived from quantum mechanics [1-3].

In this study, we present spin Hamiltonian simulations for one-center spin-1/2 and spin-3/2 systems under static and vibrational magnetic fields to validate their theoretical foundations from a quantum mechanical perspective. Furthermore, we explore the estimation of magnetic parameters using high-accuracy quantum chemical calculations implemented on quantum computers. The proposed approach offers a pathway toward elucidating spin dynamics in multicentric radicals, including bi- and triradicals coupled through exchange interactions [4,5].

[1] T. Yamane, et al., Phys. Chem. Chem. Phys. 19, 24769 (2017).

[2] T. Yamane, et al., Dalton Trans. 47, 16429 (2018).

[3] T. Yamane, et al., Appl. Magn. Reson. published online. https://doi.org/10.1007/s00723-025-01794-9 (2025).

[4] K. Ayabe, et al., Mol. Phys. 111, 2767 (2013).

[5] K. Sato, et al., J. Phys. Chem. A 123, 7507 (2019).