High order multipole three-body forces and their contribution to the elastic constants and zero point energy of the rare gas crystals

High order multipole three-body forces are shown to contribute significant amounts to the theoretical values of the elastic constants of the rare gas crystals. Their effect is to make the quantity delta =(C 44 -C 12 )/C 12 slightly more negative than the value obtained using dipole interactions only. Their effect on the harmonic zero point energy is small but of the same order as the two-body anharmonic zero point energy.