Second-order effect of spin-orbit coupling on the angular dependence of the zero-field splitting in CH2

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The theoretical zero-field splitting of a molecule is the sum of two contributions: (1) the first-order perturbation terms of the spin-spin coupling and (2) the second-order perturbation terms of the spin-orbit coupling. We have calculated contribution (2) for the methylene radical as a function of the H–C–H bond angle. We found that the magnitude of contribution (2) is about 0.07 cm−1 at the experimental bond angle 135°. For this bond angle the value of contribution (1), as calculated by Harrison is about 0.71 cm−1 and the sum of the two contributions is 0.78 cm−1 which compares satisfactorily with the experimental value 0.93± 0.30 cm−1. Even though the total value of contribution (2) is only 10% of the total effect it varies much more strongly with the bond angle than contribution (1). For example, the values for contribution (2) vary by as much as 0.14 cm−1 as a function of the bond angle whereas the values of contribution (1), as calculated by Harrison, vary only by an amount of 0.05 cm−1. We conclude therefore that the angular dependence of the zfs is mainly due to the second-order effect of the spin-orbit coupling.