An overview of continuum models for nonequilibrium solvation: Popular theories and new challenge

Abstract

The effect of solvent on the electron transfer (ET) and spectral shifts has been the focus of experimental and theoretical studies and a key quantity in these studies is the solvent reorganization energy. There are a number of theoretical models toward the evaluation of nonequilibrium solvation free energy that were proposed decades ago and have been applied widely. In the past decade, however, we revisited the original theoretical derivations and identified a serious defect in the popular nonequilibrium solvation models which causes the significant overestimation of solvent reorganization energy and hence predicts a much lowed rate constant for ET in some cases. A rigorous derivation by means of contrained equilibrium principle of thermodynamics was subsequently conducted for the study of nonequilibrium solvation. In this review, the author outlined the intimate interplays among the representative models and analyzed what the possible problem could be. The key idea presented in our recent papers was highlighted. The constrained equilibrium principle in classical thermodynamics and its application to the nonequilibrium solvation were detailed, and a few argumentative examples in literature were taken for the validation of our theory.

Higher activation barriers can lift exothermic rate restrictions in electron transfer and enable faster reactions

“…A vibrational frequency hν v = 1500 cm –1 is often used to represent aromatic donors and acceptors 11 , although the coupling to very high-frequency modes (e.g., hν v = 3000 cm –1 C–H vibration) increases FCWD at very high driving forces 34 . The dielectric continuum approximation is frequently used to calculate λ s , but it is increasingly clear that it overestimates λ s 35 , probably by a factor of two 36 – 38 . The calculations in Supplementary Note 7 suggest λ s = 6 ± 3 kcal mol –1 in our solvents.…”

Dielectric continuum methods for quantum chemistry

“…The solvent parameter ε ∞ also makes an appearance in Marcus' theory of electron transfer, 572–577 in which the “outer‐sphere” reorganization energy is given by This formula is derived from what is essentially a nonequilibrium formulation of the Born ion model [Equation ()], combined with a Coulomb interaction between charges centered in a donor sphere (radius R D centered at r D ) and an acceptor sphere (radius R A centered at r A ). The electron transfer is assumed to occur instantaneously—before the orientational motion of the solvent molecules can respond—hence the change in involves ε ∞ in addition to ε s .…”

“…The phenomenology introduced above can be generalized to a rigorous description of electrostatics, 579,580 affording a continuum theory of nonequilibrium solvation 539,576,578–582 . Several variants have been formulated for use with PCMs, 221,583–587 as well as for continuum solvation based on Poisson's equation 44,588 .…”

A comparison of methods for theoretical photochemistry: Applications, successes and challenges

“…In continuum solvent models this is generally achieved by separating the solvent response into a dynamic component, which is relaxed alongside the new solute electron density, and an inertial component, which is kept frozen in equilibrium with the initial state of the molecule. 302 Li 303 provides a comprehensive overview of continuum models for nonequilibrium solvation. Generally, however, studies explicitly dealing with nonequilibrium versus equilibrium solvation effects do so with respect to comparing state-specific and linear-response formalisms for excited state calculations.…”