Fourier transform electron spin echo envelope modulation of a S=1/2, I=5/2 spin system: An exact analysis and a second order perturbation approach

Abstract

Electron spin echo envelope modulation (ESEEM) induced by 27Al nuclei can be used to characterize the interactions of paramagnetic transition metal cations with the framework of various aluminosilicates. The quantitative analysis of such systems is complex due to the 27Al nuclear quadrupole interaction which is often large and unknown. In order to obtain a better understanding of the various spectral features of the 27Al modulation, the ESEEM of a S= (1)/(2) I= (5)/(2) spin system in orientationally disordered systems was investigated in the frequency domain. The relative contributions of the various electron-nuclear double resonance (ENDOR) frequencies to the Fourier transform (FT) ESEEM spectrum were studied as a function of the size of the nuclear quadrupole coupling constant and of the relative orientation of the nuclear quadrupole tensor with respect to the g-tensor. The parameters range investigated is that expected from Cu2+ interacting with framework Al in zeolites. Two approaches were employed in the calculations, exact diagonalization of the nuclear Hamiltonian and a second order perturbation treatment of the quadrupole interaction. It is found that the second order perturbation approach applies up to e2qQ/h<7 MHz. The conditions under which the FT-ESEEM spectrum is dominated by the ‖ (1)/(2) 〉−‖− (1)/(2) 〉 ENDOR transitions were explored as well. This occurs when e2qQ/h is relatively large and it strongly depends on the orientation of the quadrupole tensor. When the FT-ESEEM can be described only by the ‖ (1)/(2) 〉−‖− (1)/(2) 〉 ENDOR transitions, the simulations are significantly simplified since these can be calculated using the analytical expressions obtained by perturbation theory also for a quadrupole coupling constant as large as 10 MHz.