This highlights presents examples of scientific contributions arising from relativistic quantum chemistry. They are widely applied in the daily lives. It also briefly introduces several scientific investigations and research teams in the field of relativistic quantum chemistry, based on the author’s interpretation.

In this study, we develop an analytical energy gradient for picture-change-corrected density functional theory within the spin-free infinite-order two-component Hamiltonian. The proposed method is implemented based on the local unitary transformation (LUT) scheme that is one of the linear-scaling techniques for relativistic transformation. Numerical assessments for diatomic molecules confirm the validity of the LUT approximation. Performing geometry optimization for diatomic molecules and transition-metal complexes using the developed analytical energy gradient, the relativistic effects of one- and two-electron operators and density operator are investigated. The results suggest that effects for the one-electron operator are significant, while those of two-electron and density operators are negligible.

Quantum electrodynamics effects are high-order relativistic effects that cannot be captured within the framework of the no-pair four-component relativistic Hamiltonian. In this review, we summarize the theoretical framework of the effective QED potential, a methodology for including QED effects in the four-component Hamiltonian. We also demonstrate that including QED effects improves agreement between theoretical and experimental spectroscopic constants for a heavy molecular system.