Misra, Sushil K., and Hamid Reza Salahi. “Relaxation in Pulsed EPR: Thermal Fluctuation of Spin-Hamiltonian Parameters of an Electron-Nuclear Spin-Coupled System in a Malonic Acid Single Crystal in a Strong Harmonic-Oscillator Restoring Potential.” Applied Magnetic Resonance 52, no. 3 (March 1, 2021): 247–61.
https://doi.org/10.1007/s00723-020-01308-9.
Random fluctuations in the $$\tilde{g}$$and $$\tilde{A}$$matrices of a spin system due to thermal motion of a molecule are specifically considered to calculate the relaxation matrix for the four-level electron-nuclear spin-coupled system ($$S = 1/2$$; $$I = 1/2$$) in a malonic acid crystal, using the formalism outlined by Lee et al. (J Chem Phys 98:3665–3689, 1993). The correlation time, τc, and the value of the parameter λ, characterizing the harmonic-oscillator restoring potential of the small-amplitude fluctuation of the director of the malonic-acid molecule due to thermal motion are estimated from the knowledge of the experimental values of (τc, λ). The four electronic, $$T_{2e} ,$$and the two nuclear, $$T_{{2{\text{n}}}}$$, spin relaxation times are calculated to be functions of (τc, λ) governing the fluctuations. The values of (τc, λ), evaluated with these expressions, when fitted to the experimental values of $$T_{2e}$$and $$T_{2n}$$, assuming the molecule to be in the ground state (n = 0) in the harmonic-oscillator potential, a rather narrow region of (τc, λ) values about τc = 0.081 μs and $$\lambda = 4.4$$is found. These values are then used to calculate the time-dependent echo-ELDOR signal by the relevant Liouville von-Neumann (LVN) equation. The resulting Fourier transform is found to be in excellent agreement with the experimental data. The (τc, λ) values for the excited states described by $$n = 1,2$$have also been calculated, although these states are unlikely to be populated at room temperature.