The thermoelectric effect of magnesium silicide is studied by using it thermodynamical method in the presence of an electric field. The thermoelectric potential is evaluated from the partial derivative of free energy with respect to charge in which the free energy is calculated at the B3LYP/6-31G(d,p) level of density functional theory. This free energy is also utilized to determine the average dipole moment from which the polarizability, alpha; molar polarization, Psi; and dielectric constant can be computed. The present calculation for the dielectric constant (similar to 24-20) is in very good agreement with the experimental value (20). This accurate dielectric constant can be used to derive the relation of the thermoelectric potential with respect to temperature, from which the thermoelectric power or the Seebeck coefficients are calculated. The present result shows good agreement with experiment measurement for the Seebeck coefficients. In comparison, that calculation from the energy band structure theory is far off from the experimental values.