A huge amount of water at supercritical conditions exists in Earth's interior, where its dielectric properties play a critical role in determining how it stores and transports materials. However, it is very challenging to obtain the static dielectric constant of water, E-0, in a wide pressure-temperature (P-T) range as found in deep Earth either experimentally or by first-principles simulations. Here, we introduce a neural network dipole model, which, combined with molecular dynamics, can be used to compute P-T dependent dielectric properties of water as accurately as first-principles methods but much more efficiently. We found that E-0 may vary by one order of magnitude in Earth's upper mantle, suggesting that the solvation properties of water change dramatically at different depths. Although E-0 and the molecular dipole moment increase with an increase in pressure along an isotherm, the dipolar angular correlation has its maximum at 5 GPa-7 GPa, which may indicate that hydrogen bonds become weaker at high pressure. We also calculated the frequency-dependent dielectric constant of water in the microwave range, which, to the best of our knowledge, has not been calculated from first principles, and found that temperature affects the dielectric absorption more than pressure. Our results are of great use in many areas, e.g., modeling water-rock interactions in geochemistry. The computational approach introduced here can be readily applied to other molecular fluids.
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