Charge exchange is one of the most important atomic processes in plasmas. Charge exchange and crossings of corresponding energy levels that enhance charge exchange are strongly connected with problems of energy losses and of diagnostics in high temperature plasmas. Charge exchange was also proposed as an effective mechanism for population inversion in the soft X-ray and vacuum ultraviolet ranges. One of the most fundamental theoretical domains for studying charge exchange is the problem of electron terms in the field of two stationary Coulomb centers (TCC) of charges Z and Z′ separated by a distance R. It presents an intriguing atomic physics: the terms can have crossings and quasi crossings. These intrinsic features of the TCC problem also manifest in different areas of physics, such as plasma spectroscopy: a quasi crossing of the TCC terms, by enhancing charge exchange, can result in an unusual structure (a dip) in the spectral line profile emitted by a Z-ion from a plasma consisting of both Z- and Z′-ions, as was shown theoretically and experimentally. Before the year 2000, the paradigm was that the preceding sophisticated features of the TCC problem and its flourishing applications were inherently quantum phenomena. In 2000, a purely classical description of the crossings of energy terms was presented. In the present paper we study the effect of an electric field (along the internuclear axis) on circular Rydberg states of the TCC system. We provide analytical results for strong fields, as well as numerical results for moderate fields. We show that the electric field has several effects. First, it leads to the appearance of an extra energy term: the fourth classical energy term — in addition to the three classical energy terms at zero field. Second, but more importantly, the electric field creates additional crossings of these energy terms. We show that some of these crossings significantly enhance charge exchange, while other crossings enhance the ionization of the Rydberg quasi molecule.