Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe²⁺/Fe³⁺ Redox Reaction**

Abstract

Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe 2+ /Fe 3+ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe 2+ /Fe 3+ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe 2+ /Fe 3+ system computed from these simulations are compared with the available experimental data for validation.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

“…Another redox system of considerable interest is Fe 3+ ion in water. ,− Here, we could achieve a speed-up of 31 with the help of the RF-MTACE method; see Table .…”

“…We considered a configuration with a single Fe 3+ ion solvated in 64 water molecules inside a periodic cubic box of 12.414 Å edge length, as in ref . BLYP functional was used in the GGA run, while the B3LYP functional was taken for VV and RF-MTACE - n MTS runs.…”

Evidence of Sharp Transitions between Octahedral and Capped Trigonal Prism States of the Solvation Shell of the Aqueous Fe3+ Ion

“…The ϕ norm 6 criterion used to differentiate between the CTP and OH states is depicted by a dashed gray line in Figure 4, validating the efficacy of the criterion. 46 The use of a uniform background charge gives results that are significantly different from those for which explicit counterions are included, especially for a high concentration. The inset shows a closeup with a different range on the vertical axis.…”

“…At a low [Fe 3+ ]:[H 2 O] ratio of 1:597, the lifetime of the OH state, τ OH , is 1.75 ns. This concentration is typical for simulations based on potential energy functions. , On the contrary, simulations based on electronic structure calculations of the energy and atomic forces, in particular DFT calculations, tend to be performed at a higher concentration, for instance, an [Fe 3+ ]:[H 2 O] ratio of ∼1:61. Strikingly, τ OH is then 2.5 times longer compared to that at the lower concentration.…”

“…Unlike the calculations based on potential energy functions, the simulations in which energy and atomic forces are obtained from density functional theory (DFT), using the PBE , or B3LYP − functional approximations, have not shown deviations from the octahedral form of the solvation shell. − As the computational effort is large, the time interval represented by such simulations has necessarily been short, spanning at most a few tens of picoseconds, and an indication of a change in the structure of the first solvation shell has not been found. , The simulations have, furthermore, been carried out using a uniform negative background charge instead of explicit counterions and for a high Fe 3+ concentration corresponding to an [Fe 3+ ]:[H 2 O] ratio ranging from 1:18 to 1:137. These ion concentrations are much higher than those that have been used in the simulations based on potential energy functions, 1:600 to 1:1085. , …”