EPR and ENDOR Studies of Deuteron Hyperfine and Quadrupole Coupling in •CD(COOD)2: Experimental and Theoretical Estimates of Electric Field Gradients from an α-Carbon

Abstract

In single crystals of malonic acid grown from heavy water, the methylene protons have been partially exchanged with deuterons. Upon X irradiation at room temperature, the •CD(COOD)2 radical is formed in an amount comparable to the •CH(COOD)2 radical species. In the present work, EPR and ENDOR analyses of the α-deuteron hyperfine coupling (hfc) and nuclear quadrupolar coupling (nqc) tensors at room temperature have been performed. The hyperfine coupling tensor is, when scaled with the differences in the nuclear g-factor, almost identical to the α-proton coupling of the •CH(COOH)2 radical at room temperature. The quadrupolar coupling tensor was found to be virtually coaxial with the hyperfine coupling tensor. The quadrupolar coupling constant is 149.8 ± 1 kHz, and the asymmetry factor η = 0.092 ± 0.020. It is known that, at room temperature, the malonic acid radical exhibits thermal motion between two potential energy minima separated by about ±12°. Assuming that the observed hfc and nqc tensors are the result of thermal averaging between these two conformations of the radical, a simple two-site jump model was used to estimate the rigid-limit tensors. The most significant result obtained was for the nqc tensor, for which the calculations resulted in a quadrupolar coupling constant of 160 kHz and an asymmetry factor η = 0.026. These values are fairly close to the nqc parameters for the methylene deuterons in malonic acid at low temperature. The quadrupolar coupling tensor has been theoretically modeled using Slater orbitals and formal electronic populations, as well as electron populations obtained from RHF/CI INDO-type calculations. The simple model to compute the electric field gradient at the α-deuteron caused by the charge distribution at the sp2-hybridized α-carbon was found to be as successful as more advanced methods. Furthermore, density functional theoretical (DFT) calculations for both the malonic acid radical and the native malonic acid molecule have been performed. Field gradients calculated by the DFT method significantly overestimate the quadrupolar tensors for both the α-deuteron of the radical and the methylene deuterons of the malonic acid molecule. Calculations using electron populations from the RHF/CI INDO calculations show that contributions to the quadrupolar coupling tensor from electrons and nuclei beyond the nearest-neighbor atom of the deuteron are significant.