非平衡溶剂化的连续介质模型和超快过程溶剂效应

Continuum Medium Model of Non-equilibrium Solvation and Solvent Effect for Ultra-fast Process

在连续介质理论基础上,根据Jackson的能量积分公式导出非平衡态静电自由能和溶剂化能的正确表达式.引入“弹簧能”概念,对平衡态和非平衡态的静电能构成给出了合理解释,即此能量由溶质自由电荷和溶剂极化电荷的自能、两者之间的相互作用能和极化电荷的“弹簧能”构成.对目前几种代表性的非平衡溶剂化理论进行了论证和比较,指出其中存在的基本理论问题.根据新的非平衡溶剂化能建立了电子转移反应溶剂重组能的双球模型、光谱移动的单球孔穴点偶极模型,多级展开方法和非平衡溶剂效应的数值解方法.在Poisson方程求解中引入类导体屏蔽模型,建立了任意孔穴极化电荷数值解方法并应用到C loss-M ill-er电子转移体系,得到与实验值吻合的溶剂重组能,解决了传统非平衡溶剂化理论高估溶剂重组能的问题.

In the 1950s of the 20th century, the non-equilibrium solvation theory for ultra-fast processes such as electron transfer and light absorption/emission was paid particular attention to. A number of scientists made efforts to study this area and various models, which give reasonable qualitative descriptions for solvent reorganization energy in electron transfer and spectral shift in solution, were developed within the framework of continuous medium theory. However, in a series of publications by the authors （ see for example J. Comput. Chem. 2004, 25： 500; J. Comput. Chem. 2004, 25： 835; J. Comput. Chem. 2005, 26： 399; Chinese Sci. Bull. 2003, 48 ： 965 ; J. Mole. Struct. -Theochem 2005, 715 ： 157 ）, it was clarified that the expression of the nonequilibrium electrostatic free energy, which is at the dominant position of non-equilibrium solvation and serves as the basis of various models, was incorrectly formulated. In this work, the authors argue that reversible charging work integration δW =∫vФδρdV was inappropriately applied to an irreversible path linking the equilibrium state and the non-equilibrium one in the past. Because the step from the equilibrium state to the non-equilibrium one is factually thermodynamically irreversible, the conventional expression for non-equilibrium free energy, G2^non（M） = （1/2）∫v（ρ2Ф2^non ＋ ρ2Ф1^non-ρ2Ф1^non） dV that was deduced in different ways, is unreasonable. Here the authors derive the non-equilibrium free energy to a quite different form of G2^non= = （1/2）∫vρ2Ф2^non dV according to Jackson integral formula, dG = （1/2）∫v（Фδρ ＋ρδФ）dV. Such a difference throws doubts to the models including the famous Marcus two-sphere model for solvent reorganization energy of electron transfer and the Lippert-Mataga equation for spectral shift. By introducing the concept of ＂spring energy＂ arising from medium polarizations, the energy constitution of the non-equilibrium state is highlighted. For a solute-solvent system, the authors separate the total electrostatic energy into different components： the self-energies of solute charge and polarized charge, the interaction energy between them and the ＂spring energy＂ of the solvent polarization. With detailed reasoning and derivation, our formula for non-equilibrium free energy can be reached through different ways. Based on the new expression of non-equilibrium free energy, the generalized form for solvent reorganization energy, λav= （ 1/4 ）∫v△ρ（△φop -△φs）dV, has been attained. A new two-sphere model for solvent reorganization energy is proved to have the form of λav= （1/2）△q^2 （1/εop -1/εs） （ 1/（ 2rD ） ＋ 1/（2rA） -1/d）. Compared with Marcus＇ expression, this new formula estimates the solvent reorganization energy only one half of the latter. This difference provides a pretty explanation for why Marcus＇ theory often overestimated the solvent reorganization energy by a factor about two in the past. With the single-sphere model and point dipole approximation, the authors argue that the total spectral shift should look like △hvtotal= （1/2） Ralow （μ1-μm）^2, and this is also one half of the Lippert-Mataga result. The novel expressions for the spectral shifts for individual absorption and emission have also been given. Finally, a numerical algorism for the solution of Poisson equation is presented and the total non-equilibrium solvation energy is deduced to a quite differ ent and much more compact form as △F2^non =〈ψ2^non｜H^0＋ （1/2）H^n｜ψ2^non〉 - 〈ψ2^gas｜H^0｜ψ2^gas） ＋ （1/2）∑i∑j[q2,fast（i） ＋q1,alow（i） ]Zj（ ｜ri-Rj｜） when compared with the most recently developed expression by other authors. As an application, the numerical algorism incorporated with COSMO was applied to a model system, and the solvent reorganization energy is found in excellent agreement with the experimental fitting, while the conventional theories always estimate twice this quantity.