# ESR Lineshape for Exchanging Anisotropic Spin Systems

## Abstract

The ESR lineshape of one electron spin coupled by anisotropic hyperfine interaction to a number of nuclei is calculated when at least two different configurations of the molecule interchange according to a given reaction scheme. The spectrum calculation includes also the anisotropic electron- zeeman and the nuclear quadrupole interaction. The lineshape, which simulates a nonsaturated CW experiment, is calculated numerically by a direct method and includes the nonsecular terms of the electron spin. The density matrix theory, combined with Liouville formalism, is used allowing both for an accurate treatment of spin dynamics as well as detailed description of the reorganization of the system during exchange [1]. The exchange is treated phenomenologically by a sudden-jump, markov model in which the steady-state populations are calculated prior to the lineshape and are used for the lineshape calculation. For a given overall molecular orientation each configuration (site) is characterized by a set of three strength constants and three Euler angles per interaction [2]. This basic system is used to simulate a single crystal case or is appropriately averaged to simulate a powder sample. The above theory is compared with two experiments.

SYSTEM (1): We model the rotation of the CH_{2} group around the C-C bond in the radical CH_{2}COO^{-}. Zn(acetate)_{2} crystals were grown from a water solution and were irradiated by X-rays. The spectra were produced with an X band ESR spectrometer for a couple of orientation of the crystal.

SYSTEM (11): A three-site model was incorporated to model the ring dynamics of C_{4}H_{9}N^{+}. The cations were isolated by irradiation in inert halogenide matrix by standard methods [3] at low temperature. The ring was studied lately in a quantum chemical calculation [3].

## References

- [1]Nonperturbative ESR Lineshapes of an Isotropic Three-Site System and Comparison with Experimental CH3-COOD and CD3-COOD Spectra. U. Nord, N.P. Benetis, N.A. Salih and A. Lund Manuscript.Google Scholar
- [2]The Use and Transformations of Second-Order Tensors in Magnetic Resonance. N.P. Benetis and A. Lund Manuscript.Google Scholar
- [3]An ESR Theoretical Ab Initio UHF/CI Investigation of the Structure and Dynamics of the Pyrrolidine Radical Cation of a Neutral Pyrrolidine Radical M. Shiotani, L. Sjöqvist, A. Lund, S. Lunell, L. Eriksson and M.B. Huang SubmittedGoogle Scholar