A quantum mechanical theory of the effects of a uniform electric field on electron-spin-resonance hyperfine couplings is presented. The electric-field effects are described in terms of perturbation coefficients which can be used to probe the local symmetry as well as the strength of the electric field at paramagnetic sites in a solid. Results are presented for the first-order perturbation coefficients describing the Bloembergen effect (linear electric-field effect on hyperfine coupling tensor) for the O atom and the OH radical. [S0031-9007(97)03633-8] PACS numbers: 31.30.Gs, 31.15.Md, 32.10.Fn, 33.15.Kr In 1961 Bloembergen [1] predicted that a paramagnetic site lacking inversion symmetry will experience linear shift in its electron spin resonance (ESR) spectrum by a uniform external electric field. Using secondorder perturbation theory, Bloembergen [2] also showed that the magnetic hyperfine interactions, either isotropic or anisotropic, can be linear functions of the applied external field. Bloembergen's predictions were soon verified through independent experiments by Kushida and Saiki [3], by Ludwig and Woodbury [4], and by Pershan and Bloembergen [5]. Since these early experiments, the Bloembergen effect or the linear-electric-field effect (LEFE) on hyperfine interaction has been observed in a number of crystalline materials [6,7]. The Bloembergen effect provides detailed information on local symmetry [6] and can be also used to determine the strength of electric field at paramagnetic centers in solids.While attention to date has been focused on the LEFE, there are also reports in the literature of nonlinear electric field effects (NLEFE) on the hyperfine coupling (HFC) of paramagnetic systems [8,9]. The NLEFE are considered to be especially important for issues related to the atomic clock [10].Theoretical treatments of the electric field effects on the ESR HFC have been limited to phenomenological description [2,11,12] or ad hoc quantum mechanical approximations [13]. In view of the importance and broad range of applications of the electric field effects on ESR hyperfine interaction, we present in this Letter a general quantum mechanical theory of the effects of a uniform electric field on HFC within the framework of the coupled perturbation approach [14]. By treating the external electric field as a perturbation, analytical expressions are derived to calculate the corrections to HFC in terms of the matrix elements of the hyperfine interaction operator ͑S ? I͒ and electricfield-perturbed spin density matrix ͓͑r͑E͔͒. The spin density matrix formulation allows a self-consistent determination of the perturbation coefficients from the ground state wave function. Test results from ab initio calculations are presented for the first-order coefficients describing the Bloembergen effect for the O atom and the OH radical.The Hamiltonian operator describing the hyperfine interaction between the magnetic moments associated with the electron spin S and nuclear spin I in a system containing N magnetic nuclei is given b...