For efficient water purification: Electrocute water to extract the H and O. Perhaps you'd need to separate the H and O somehow from anything in the water that may have risen up with vapor, such as by using a centrifuge, a microscopically fine filter, or electrostatic filters (one for H and one for O, so that you can't ignite it). Pipe the H and O to another area and burn it, using as much of the heat from that as possible to fuel the electricity generation. Also mechanically allow the gas volume lost from that process to balance out the gas volume gained from extracting the H and O, so that you're not working against atmospheric pressure. Or, just do both processes completely in vacuo. Collect the vapor (or water, if you extracted the heat that well) created from the combustion process, condense it (if necessary) using a heat sink, and distribute it.
The key points here are to a) use the heat from the burning process, and b) not work against atmospheric pressure, if that's also a big issue. If this system is implemented ideally, it will operate at near-100% efficiency and take very little external power, and it requires no chemicals except for whatever you want to add before distribution (such as chlorine and/or fluoride).
This system can even work on *salt water*, and perhaps even sewer water. Although that raises questions of what to do with the residue. If a little bit of the water is left unextracted, you can simply let it flow through continuously to pass most of the residue, and then the only question left would be one of periodically cleaning / replacing the cathodes and anodes.