A comparative study of correlation and relativistic effects on atomic ionization energy

• Our work represents a comparative study of relativistic and correlation effects on ionization energies in heavy atoms, revealing several important conclusions: • First, relativistic effects show consistent behavior across the periodic table: they increase ionization energies for lighter elements in this series (Au–Pb), and decrease them for heavier elements (Bi–Rn). This pattern holds regardless of whether correlation is included. • Second, correlation effects show more complex behavior. They can change sign when relativity is included, indicating that these effects are not independent. • Third, and most importantly, relativistic and correlation effects are not additive. The combined effect of both corrections does not equal the sum of their individual contributions. For specific cases (Z = 81 and 82), the additive approach, treating correlation as an additive correction to the relativistic HF, yields superior results with far less computational effort compared to the combined effects strategy. • These findings underscore the importance of treating relativistic and correlation effects on equal footing in computational studies of heavy-element systems, in line with earlier studies [1] that these contributions are not independent; our work however provides a systematic quantitative demonstration of this non-additivity across a series of heavy atoms. • Future work should extend this analysis to other properties beyond ionization energy and to other classes of heavy-element systems to determine the generality of these conclusions. This study investigates the interplay between relativistic effects and electron correlation effects on the first ionization energies of heavy atoms (Au through Rn, Z = 79–86). We perform two complementary analyses: (1) comparing relativistic corrections computed at both the Hartree-Fock (HF) and coupled cluster CCSD(T) levels to assess how correlation influences the magnitude of relativistic corrections, and (2) comparing correlation corrections computed within both non-relativistic and relativistic frameworks to determine how relativity influences the magnitude of correlation corrections. Our results reveal a striking non-linear relationship between these two effects. Specifically, the combined effect of relativity and correlation on ionization energy does not equal the sum of their individual contributions. This non-additivity indicates that relativistic and correlation effects are not independent; they interact in complex ways that depend on the atomic system. We find that for some atoms, the two effects enhance each other, while for others they partially cancel. Moreover, the order in which one may add “separate” effects also counts, in that adding “pure” relativistic effects to the remaining outcome (including correlation) would give a different result than when adding “pure” correlation effects to the remaining outcome (including relativity). These findings demonstrate that relativistic and correlation effects are inherently non-additive, reflecting the non-linearity of the quantum many-body problem. Accurate computational predictions of ionization energies in heavy-element systems thus require simultaneous treatment of both effects rather than treating them as independent contributions