RESUMO
Born-Huang expansion is the cornerstone for studying potential energy surfaces and non-adiabatic couplings (NACs) in molecular systems. However, the traditional approach is insufficient to describe the molecular system, which strongly interacts with quantum light. Inspired by the work by Schäfer et al., we develop the generalized Born-Huang expansion theory within a macroscopic quantum electrodynamics (QED) framework. The theory we present allows us to describe electromagnetic vacuum fluctuations in dielectric media and incorporate the effects of dressed photons (or polaritons) into NACs. With the help of the generalized Born-Huang expansion, we clearly classify electronic nuclear NACs, polaritonic nuclear NACs, and polaritonic electronic NACs. Furthermore, to demonstrate the advantage of the macroscopic QED framework, we estimate polaritonic electronic NACs without any free parameter, such as the effective mode volume, and demonstrate the distance dependence of the polaritonic electronic NACs in a silver planar system. In addition, we take a hydrogen atom in free space as an example and derive spontaneous emission rates from photonic electronic NACs (polaritonic electronic NACs are reduced to photonic electronic NACs). We believe that this work not only provides an avenue for the theoretical exploration of NACs in a nucleus-electron-polariton coupled system but also offers a more comprehensive understanding for molecules coupled with quantum light.
RESUMO
To explore non-adiabatic effects caused by electromagnetic (EM) vacuum fluctuations in molecules, we develop a general theory of internal conversion (IC) in the framework of quantum electrodynamics and propose a new mechanism, "quantum electrodynamic internal conversion" (QED-IC). The theory allows us to compute the rates of the conventional IC and QED-IC processes at the first-principles level. Our simulations manifest that, under experimentally feasible weak light-matter coupling conditions, EM vacuum fluctuations can significantly affect IC rates by an order of magnitude. Moreover, our theory elucidates three key factors in the QED-IC mechanism: the effective mode volume, coupling-weighted normal mode alignment, and molecular rigidity. The theory successfully captures the nucleus-photon interaction in the factor "coupling-weighted normal mode alignment". In addition, we find that molecular rigidity plays a totally different role in conventional IC versus QED-IC rates. Our study provides applicable design principles for exploiting QED effects on IC processes.
RESUMO
The extraction equilibrium of indium(III) from a nitric acid solution using di(2-ethylhexyl) phosphoric acid (D2EHPA) as an acidic extractant of organophosphorus compounds dissolved in kerosene was studied. By graphical and numerical analysis, the compositions of indium-D2EHPA complexes in organic phase and stoichiometry of the extraction reaction were examined. Nitric acid solutions with various indium concentrations at 25 °C were used to obtain the equilibrium constant of InR3 in the organic phase. The experimental results showed that the extraction distribution ratios of indium(III) between the organic phase and the aqueous solution increased when either the pH value of the aqueous solution and/or the concentration of the organic phase extractant increased. Finally, the recovery efficiency of indium(III) in nitric acid was measured.
