  "Quasi-harmonic" (QH) theory should not be considered a low-order theory of
anharmonic effects in crystals, but should be recognized as an important effect
separate from "true" anharmonicity. The original and widely used meaning of QH
theory is to put T=0 volume-dependent harmonic phonon energies omega_Q(V) into
the non-interacting phonon free energy. This paper uses that meaning, but
extends it to include the use of T=0 V-dependent single-particle electron
energies epsilon_K(V). It is demonstrated that the "bare" quasiparticle (QP)
energies omega_Q(V) and epsilon_K(V) correctly give the first-order term in the
V-dependence of the Helmholtz free energy F(V,T). Therefore, they give the
leading order result for thermal expansion alpha(T) and for the
temperature-dependence of the bulk modulus B(T)-B_0. However, neglected
interactions which shift and broaden omega_Q with T, also shift the free
energy. In metals, the low T electron-phonon mass enhancement of states near
the Fermi level causes a shift in free energy that is similar in size to the
electronic QH term. Before T reaches the Debye temperature, the mass
renormalization essentially disappears, and remaining electron-phonon shifts of
free energy contribute only higher-order terms to thermal expansion. Similarly,
anharmonic phonon-phonon interactions shift the free energy, but contribute to
thermal expansion only in higher order. Explicit next order formulas are given
for thermal expansion, which relate "true" anharmonic and similar free energy
corrections to quasiparticle self-energy shifts. The text below, except for
Sec. IX, was already published in Modern Physics Letters B, Vol. 34, No. 2
(2020) 2050025. Since then an important error was discovered. The error is
corrected in Sec. IX, and will be published as an erratum in Modern Physics
Letters B.
