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This article is a response to a comment made by Professor Liu regarding a previously published paper. The response addresses questions raised by Professor Liu and focuses on three key aspects of the validity of the paper. It explains the use of different contractions in the construction of the QED Hamiltonians and clarifies the commutation relations used in the calculations. The article also highlights that the formulation of the molecular orbital method described in the paper is independent of the ordering of the operators and can derive expressions for various perturbation theories. The response concludes by stating that alternative criteria for the QED Hamiltonians are not ruled out and could be explored in future research. [Extracted from the article]

The generalized Foldy–Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two‐component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two‐component methods. New two‐component methods were also systematically derived based on the GFW transformation. These various two‐component methods were applied to hydrogen‐like and helium‐like ions. Numerical errors in energy were evaluated and classified into four types: the one‐electron Hamiltonian approximation, the two‐electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi‐electron systems were discussed based on this classification. [ABSTRACT FROM AUTHOR]

Inclusion of a heteroatom to the phosphole ring is a promising strategy to intrinsically modulate the optical properties of phosphole derivatives. We report on a series of 2-aryl-3H-1,3-benzazaphosphole oxides that were efficiently prepared via sequential C-P cross-coupling, dehydrative [3+2] cycloaddition, and ring-oxidation reactions. The inclusion of one nitrogen atom into the benzophosphole framework caused red shifting of the absorption and emission maxima, reflecting the greater stabilization of the LUMO level. 2-(2-Hydroxyphenyl)benzazaphosphole oxide underwent excited state intramolecular proton transfer and emitted a weak fluorescence from the excited state of the N-H tautomer., (© 2024 Wiley-VCH GmbH.)