双视角下偶极泊松模型中的离子溶剂化
Ion Solvation in Dipolar Poisson models in a dual view
AI总结：
本研究针对偶极泊松模型中的离子溶剂化问题，通过勒让德变换推导得到两类模型的凸对偶泛函，并证明Dipolar-Poisson-Langevin泛函可推广Marcus理论的谐极化泛函至非线性区，且可通过SPC/E水的分子动力学模拟定量参数化。
摘要：
我们在偶极-泊松（Dipolar-Poisson）模型的连续介质理论框架内研究离子溶剂化这一经典问题。该方法将离子视为点偶极子海中的点电荷。标准Dipolar-Poisson模型与保持偶极密度固定的Dipolar-Poisson-Langevin模型，均为标量静电势$\phi$的非凸泛函。应用A.C. Maggs提出的勒让德变换方法[A.C. Maggs, Europhys. Lett. 98, 16012 (2012)]，我们推导了这些模型的对偶泛函，它们由介电位移与极化场的凸矢量场泛函给出。我们证明Dipolar-Poisson-Langevin泛函将Marcus电子转移速率理论中使用的谐极化泛函推广到了非线性区域，并且可以通过针对SPC/E水的分子动力学模拟进行定量参数化。
英文摘要：
We study the classic problem of ion solvation within the continuum theory of Dipolar-Poisson models. In this approach an ion is treated as a point charge within a sea of point dipoles. Both the standard Dipolar-Poisson model as well as the Dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential $ϕ$. Applying the Legendre transform approach introduced by A.C. Maggs [A.C. Maggs, Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement and the polarization field. We show that the Dipolar-Poisson-Langevin functional generalizes the harmonic polarization functional used in the theory of Marcus for electron transfer rate to nonlinear regimes and can be quantitatively parametrized by molecular dynamics simulations for SPC/E-water.
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