We present a linear-scaling method based on self-consistent charge non-orthogonal tight-binding. Linear scaling is achieved using a many-body expansion, which is adjusted dynamically to the instantaneous molecular configuration of a liquid. The method is capable of simulating liquids over large length and time scales, and also handles reactions correctly. Benchmarking on typical carbonate electrolytes used in Li-ion batteries displays excellent agreement with results from full tight-binding calculations. The decomposition slightly breaks the Hellmann-Feynman theorem, which is demonstrated by application to water. However, an additional correction also enables dynamical simulation in this case.
