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reaction is important in understanding the production mechanisms of anionic molecules in interstellar environments. Herein, the rate coefficients for the H − + C 2 H 2 → H 2 + C 2 H − reaction were calculated using ring-polymer molecular dynamics (RPMD), classical molecular dynamics (MD), and quasi-classical trajectory (QCT) approaches on a newly developed ab initio potential energy surface (PES) in full dimensions. PES was constructed by fitting a large number of ab initio energy points and their gradients using the permutationally invariant polynomial basis set method. There was no barrier in the reaction coordinates, which was a collinear-dominated reaction, and the reaction proceeded exothermically. It is found that the fitted PES provides the appropriate thermal rate coefficients based on all RPMD, classical MD, and QCT simulations at higher temperatures. The evaluation of the rate coefficients at lower temperatures should be conducted carefully because the fitting of the PES associated with the long-range interaction should be further improved. The spatial distribution of the nucleus allows a more effective attraction between the reactants.

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Accurate prediction of blood toxin concentration during and after dialysis will greatly contribute to the determination of dialysis treatment conditions. Conventional models, namely single-compartment model and two-compartment model, have advantages and disadvantages in terms of accuracy and practical application. In this study, we attempted to derive the mathematical model that predicts blood toxin concentrations during and after dialysis, which has both accuracy and practicality. To propose the accurate model, a new two-compartment model was mathematically derived by adapting volume-averaging theory to the mass transfer around peripheral tissues. Subsequently, to propose a practical model for predicting the blood toxin concentration during dialysis, an analytical solution expressed as algebraic expression was derived by adopting variable transformation. Furthermore, the other analytical solution that predicts rebound phenomena after dialysis was also derived through similar steps. The comparisons with the clinical data revealed that the proposed analytical solutions can reproduce the behavior of the measured blood urea concentration during and after dialysis. The analytical solutions proposed as algebraic expressions will allow a doctor to estimate the blood toxin concentration of a patient during and after dialysis. The proposed analytical solutions may be useful to consider the treatment conditions for dialysis, including the rebound phenomenon.

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