  The widely used thermal Hartree-Fock (HF) theory is generalized to include
the effect of electron correlation while maintaining its
quasi-independent-particle framework. An electron-correlated internal energy
(or grand potential) is defined by the second-order finite-temperature
many-body perturbation theory (MBPT), which then dictates the corresponding
thermal orbital (quasi-particle) energies in such a way that all thermodynamic
relations are obeyed. The associated density matrix is of the one-electron
type, whose diagonal elements take the form of the Fermi-Dirac distribution
functions, when the grand potential is minimized. The formulas for the entropy
and chemical potential are unchanged from those of Fermi-Dirac or thermal HF
theory. The theory thus postulates a finite-temperature extension of the
second-order Dyson self-energy of one-particle many-body Green's function
theory and can be viewed as a second-order, diagonal, frequency-independent,
thermal inverse Dyson equation. At low temperature, the theory approaches
finite-temperature MBPT of the same order, but it outperforms the latter at
intermediate temperature by including additional electron-correlation effects
through orbital energies. A physical meaning of these thermal orbital energies
(including that of thermal HF orbital energies, which has been elusive) is
proposed.
