Results of detailed calculations of the anharmonic and the quantum corrections to the equation of state and to Gr¿neisen's parameter &ggr; are given for pressures P from zero to 2B0 (where B0 is the bulk modulus at P=0 and T=0) and for temperatures T from zero to (0.6)T&egr; (where T&egr;=&egr;/k, &egr; is the depth of the potential well and k is Boltzmann's constant). Interionic potentials of the form A/r+ϕR with ϕR proportional to r-12, r-8, and e-αr were used. It was found, for example, that at T?(T-italic)=&egr; the anharmonic corrections to P for the potentials in the order just given were approximately 7, 6, and 4% at P?(B-italic)=0, while they were approximately 1, 1, and 1/2% at Quantum corrections to P were found to depend very weakly on P and to be about 1% or less for (0.2)B0<P<2B0 for temperatures above the zero-pressure Debye temperature. Anharmonic corrections decreased the values of &ggr; and of P, while quantum corrections decreased the value of &ggr; but increased the value of P.