Heavy rare earths (HREs), namely Ho3+, Er3+, Tm3+, Yb3+ and Lu3+, are rarer and more exceptional than light rare earths, due to the stronger extraction capacity for 100 000 extractions. Therefore, their incomplete stripping and high acidity of stripping become problems for HRE separation by organophosphoric extractants. However, the theories of extractant structure performance relationship and molecular design method of novel HRE extractants are still not perfect. Beyond the coordination chemistry of the HRE-extracted complex, the extractant dimer dissociation, acid ionization, and complexation behaviors can be crucial to HRE extraction and reactivity of ionic species for understanding and further improving the extraction performance. To address the above issues, three primary fundamental processes, including extractant dimer dissociation, acid ionization, and HRE complexation, were identified and investigated systematically. The intrinsic extraction performances of HRE cations with four acidic organophosphoric extractants (P507, P204, P227 and Cyanex 272) were studied by using relativistic energy-consistent 4f core pseudopotentials, combined with density functional theory and a solvation model. Four acidic organophosphoric extractants have been qualified quantitatively from microscopic structures to chemical properties. It has been found that the Gibbs free energy changes of the overall extraction process (sequence: P204 > P227 > P507 > Cyanex 272) and their differences as a function of HREs (sequence: Ho/Er > Er/Tm > Tm/Yb > Yb/Lu) are in good agreement with the experimental maximum extraction capacities and separation factors. These results could provide an important approach to evaluate HRE extractants by the comprehensive consideration of dimer dissociation, acid ionization, and complexation processes. This paper also demonstrates the importance of the P O bond, the P C bond, isomer substituent, and solvation effects on the structure performance relationship that can be used to guide molecular designs of HRE extraction in future.