Diabatic free energy curves and coordination fluctuations for the aqueous Ag+∕Ag2+ redox couple: A biased Born-Oppenheimer molecular dynamics investigation

Abstract

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction Ag(+)-->Ag(2+)+e(-) in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of Ag(+). Diabatic free energy curves of reduced (R) and oxidized (O) states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of Ag(+) and Ag(2+) are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of Ag(+) and find different values for the reorganization free energy of R (1.4 eV) and O (0.9 eV). The computed reorganization free energy of Ag(2+) is in good agreement with the experimental estimate of 0.9-1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for Ag(+) is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation.

Water at an electrochemical interface—a simulation study

“…Following Sprik and co-workers [7,8], and making use of the special properties of the mean vertical gap for oxidation (∆E = δE Ru 2+ →Ru 3+ = −δE Ru 3+ →Ru 2+ ) as a reaction coordinate [6,9], we may evaluate the free energies of the Ru 2+ and Ru 3+ ions along this reaction coordinate from the probability distributions…”

“…Blumberger, Sprik and co-workers [7,8] have demonstrated how the Marcus curves can be calculated for a homogeneous electron transfer reaction within an ab initio molecular dynamics scheme. Following Warshel [9] they emphasize the advantages for computation of choosing the "vertical energy-gap" as the reaction coordinate.…”

Reorganization Energy for Internal Electron Transfer in Multicopper Oxidases

“…15,20,21,22,27 Alternatively, ΔE et was defined as the reaction coordinate and the free energy for each state was estimated from the probability of each energy (p(ΔE et ), obtained by binning all the calculated ΔE et energy differences): 16,17,18 …”

Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

“…However, unbiased equilibrium simulations give only accurate results close to the free energy minimum of A M and are of limited use for regions of ∆E far away from the minimum. Fortunately, due to the exact linear free energy relation between the free energy gap and the energy gap [1,7,37,38],…”

“…Thus, using information from two distinct regions of ∆E one can construct a reasonably accurate free energy profile without the use of computationally expensive enhanced sampling methods [38,39].…”