Zero-Point Corrections for Isotropic Coupling Constants for Cyclohexadienyl Radical, C6H7 and C6H6Mu: Beyond the Bond Length Change Approximation

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Abstract
Zero-point vibrational level averaging for electron spin resonance (ESR) and muon spin resonance (µSR) hyperfine coupling constants (HFCCs) are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of H by D on 13C-NMR chemical shifts is used. DFT methods are used to compute the change in energy and HFCCs when the geometry is changed from the equilibrium values for the stretch and both bend degrees of freedom. This variation is then averaged over the probability distribution for each degree of freedom. The method is tested using data for the methylene group of C6H7, cyclohexadienyl radical and its Mu analog. Good agreement is found for the difference between the HFCCs for Mu and H of CHMu and that for H of CHMu and CH2 of the parent radical methylene group. All three of these HFCCs are the same in the absence of the zero point average, a one-parameter fit of the static HFCC, a(0), can be computed. That value, 45.2 Gauss, is compared to the results of several fixed geometry electronic structure computations. The HFCC values for the ortho, meta and para H atoms are then discussed.

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