  The Mihalas-Hummer-Dappen (MHD) equation of state is a part of the Opacity
Project (OP), where it mainly provides ionization equilibria and level
populations of a large number of astrophysically relevant species. Its basic
concept is the idea of perturbed atomic and ionic states. The MHD equation of
state was originally restricted to the plasma of stellar envelopes, that is, to
relatively moderate densities, which should not exceed rho < 10**-2 g/cm**3.
However, helioseismological analysis has demonstrated that this restriction is
much too conservative. The principal feature of the original Hummer & Mihalas
(1988) paper was a simplified form of the Holtsmark microfield for randomly
distributed ions. An improved MHD equation of state (Q-MHD) is introduced. It
is based on a more realistic microfield distribution (Hooper 1966, 1968) that
includes plasma correlations. Comparison with an alternative post-Holtsmark
formalism (APEX) is made, and good agreement is shown. There is a clear
signature of the choice of the microfield distribution in the adiabatic index
gamma_1, which makes it accessible to present-day helioseismological analysis.
But since these thermodynamic effects of the microfield distribution are quite
small, it also follows that the approximations chosen in the original MHD
equation of state were reasonable. A particular feature of the original MHD
papers was an explicit list of the adopted free energy and its first- and
second-order analytical derivatives. The corresponding Q-MHD quantities are
given in the Appendix.
