The NMR Chemical Shift for 4d$^n$ Systems(Ⅲ). Calculation of the NMR Shift for a 4d$^1$ System in a Strong Crystal Field Enviroment of Tetragonal Symmetry

The NMR Chemical Shift for 4d$^n$ Systems(Ⅲ). Calculation of the NMR Shift for a 4d$^1$ System in a Strong Crystal Field Enviroment of Tetragonal Symmetry

The NMR shift arising from the electron angular momentum and electron spin dipolar-nuclear spin angular momentum interactions has been investigated for a $4d^1$system in a strong crystal field environment of tetragonal symmetry. A general formula for NMR shift is used to compute the NMR shifts along the (100), (010), (001), (110) and (111) axes. We find that from the computed results, the NMR shift along the (100) and (010) axes is consistent with each other in a strong crystal field environment of tetragonal symmetry, but the NMR shift along the (001) axis is about triply greater in magnitude than those along the (100) and (010) axes and is opposite in sign to those along (100) and (010) axes. In this work, we express the expansion coefficients $a_1^{(i)}$ and $b_1^{(i)}$ of $A_i$ and $B_i$ in terms of $g_m^{(i)}$ and $h_m^{(i)}$ and two matrices $c_{lm}$ and $d_{lm}$ of radial dependence. The NMR shift is also separated into the contributions of multipolar terms. We find that $1/R^3$ term contributes dominantly to the NMR shift along the (100), (010), (001) and (110) axes while along the (111) axis $1/R^5$ term dominantly contributes. However, the contribtions of the other terms may not be negligible.