Molecular quantum-dot cellular automata (QCA) is a promising paradigm for realizing molecular electronics. In molecular QCA, binary information is encoded in the distribution of intramolecular charge, and Coulomb interactions between neighboring molecules combine to create long-range correlations in charge distribution that can be exploited for signal transfer and computation. Appropriate mixed-valence species are promising candidates for single-molecule device operation. A complication arises because many mixed-valence compounds are ions and the associated counterions can potentially disrupt the correct flow of information through the circuit. We suggest a self-doping mechanism which incorporates the counterion covalently into the structure of a neutral molecular cell, thus producing a zwitterionic mixed-valence complex. The counterion is located at the geometrical center of the QCA molecule and bound to the working dots via covalent bonds, thus avoiding counterion effects that bias the system toward one binary information state or the other. We investigate the feasibility of using multiply charged anion (MCA) boron clusters, specifically closo-borate dianion, as building blocks. A first principle calculation shows that neutral, bistable, and switchable QCA molecules are possible. The self-doping mechanism is confirmed by molecular orbital analysis, which shows that MCA counterions can be stabilized by the electrostatic interaction between negatively charged counterions and positively charged working dots.