Department of Chemistry, Syracuse University, Syracuse, NY 13244-4100, USA.
Molecules. 2013 Apr 25;18(5):4906-16. doi: 10.3390/molecules18054906.
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.
零点位振动能级平均化方法用于电子自旋共振（ESR）和μ子自旋共振（µSR）超精细耦合常数（HFCCs）的计算，研究对象为环己二烯基自由基的 H 和 Mu 同位素。该方法先前用于计算由 D 取代 H 对 ¹³C-NMR 化学位移的影响，所采用的局域模式近似法。使用 DFT 方法来计算当几何形状发生变化时，能量和 HFCCs 的变化，自由度包括伸缩和两个弯曲。然后，通过对每个自由度的概率分布进行平均，得到最终结果。该方法通过对 C₆H₇的亚甲基、环己二烯基自由基及其 Mu 类似物的数据进行测试。Mu 和 H 的 CHMu 的 HFCC 之间的差异，以及 Mu 和 H 的 CHMu 和母体自由基亚甲基的 CH₂之间的 HFCC 差异，都得到了很好的验证。在没有零点平均的情况下，所有这三个 HFCC 都是相同的，可以计算静态 HFCC，a(0)，的一个参数拟合值。该值为 45.2 高斯，与几个固定几何电子结构计算的结果进行了比较。然后讨论了 HFCC 值对邻位、间位和对位 H 原子的影响。
