Recent experimental work has shown that the pressure dependence of the thermal expansion coefficient can be expressed as: (&agr;/&agr;0)=(&rgr;/&rgr;0)-ΔT where ΔT, the Anderson-Gruneisen parameter, is assumed to be independent of pressure, and for the materials studied has a value that lies between 4 and 6. Calculation of ΔT from seismic data, however, appears to suggest a contradictory value of between 2 and 3 for mantle-forming phases. Using an atomistic model based on our previously successful many-body interatomic potential set (THB1), we have performed calculations to obtain values of ΔT for four major mantle-forming minerals. Our model results are in excellent agreement with experimental data, yielding values of between 4 and 6 for forsterite and MgO, and values in the same range for MgSiO3-perovskite and &ggr;-Mg2SiO4. Moreover, the calculations confirm that ΔT is indeed constant with pressure up to the core-mantle boundary. The apparent conflict between the values of ΔT predicted from seismic data and those obtained from experiment, and now from theory, is discussed. ¿ American Geophysical Union 1990