Simulation of slow-motion CW EPR spectrum using stochastic Liouville equation for an electron spin coupled to two nuclei with arbitrary spins: Matrix elements of the Liouville superoperator

An algorithm is developed that extends the well known nitroxide slow-motional continuous wave electron paramagnetic resonance (EPR) simulation technique developed originally by Meirovitch et al. [E. Meirovitch, D. Inger, E. Inger, G. Moro, J.H. Freed, J. Chem. Phys. 77 (1982) 3915-3938], and implemented by Schneider and Freed [D.J. Schneider, J.H. Freed, Calculating slow motional magnetic resonance spectra: a user's guide, in: Biological Magnetic Resonance, vol. 6, Plenum Publishing Corporation, 1989]. This paper deals with the more general case of coupling of one electron spin to two nuclear spins. A complete listing of the matrix elements of the Liouville superoperator for this extension has been included. This advance has been successfully tested by reproducing the observed spectral lineshapes of a solution of the novel radical Mes∗(CH3)P-PMes∗ [Mes∗ = 2,4,6 (tBu)3C2H2] in tetrahydrofuran (THF), in which the radical is undergoing slow tumbling, with the coupling of one electron spin to two physically and magnetically inequivalent phosphorus (31P) nuclei.