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An accurate expression for the exchange‐correlation free energy  f   xc   of homogeneous electron fluids at finite temperatures is presented on the basis of Singwi–Tosi–Land–Sjölander ( STLS ) approximation. In addition to the derivation for the paramagnetic state, that for the ferromagnetic state is carried out afresh in which a correction in the strong Coulomb coupling regime is incorporated into the construction of the analytic expression as a function of the coupling constant and Fermi degeneracy. The fitting formula for  f   xc   is then extended over any degree of spin polarization with the aid of available interpolation scheme. The proposed equation of state, called the  iSTLS  formula, shows reasonable agreement with the existing quantum Monte Carlo evaluations at finite temperatures in the paramagnetic state, thus giving a consensus for the thermodynamic functions between many‐body theories and computer simulations. On the other hand, the current status for the agreement between various evaluations of  f   xc   is relatively unsatisfactory in the ferromagnetic state, suggesting the necessity for further investigations.

Improved equation of state for finite‐temperature spin‐polarized electron liquids on the basis of Singwi–Tosi–Land–Sjölander approximation