Effect of electron energy on ice rules

The ice rules determine the structure of the proton system of ice and play a fundamental role in ice physics. Usually, the ice rules are viewed as a result of minimizing the Coulomb interaction energy between protons. In this work, we studied the influence of electronic energy on the formation of ice rules. It is shown that the energy of electrons does not break the ice rules but strongly affects the creation energies of ice rules violations and the mechanism of their movement, leading to stronger quantum tunneling of protons along bonds. We also discussed the possibility of a quantum state of ice, which is a superposition of different proton configurations that satisfy the ice rules.