Thermodynamic functions of harmonic Coulomb crystals

Phonon frequency moments and thermodynamic functions (electrostatic and vibrational parts of the free energy, internal energy, and heat capacity) are calculated for bcc and fcc Coulomb crystals in the harmonic approximation with a fractional accuracy $\lesssim {10}^{-5}.$ Temperature dependence of thermodynamic functions is fitted by analytical formulas with an accuracy of a few parts in ${10}^5.$ The static-lattice (Madelung) part of the free energy is calculated with an accuracy of $\sim {10}^{-12}.$ The Madelung constant and frequency moments of hcp crystals are also computed.