A Classical Point Charge Model Study of System Size Dependence of Oxidation and Reorganization Free Energies in Aqueous Solution

Sequential Selective Dissolution of Coinage Metals in Recyclable Ionic Media

Coinage metals Cu, Ag, and Au are essential for modern electronics and their recycling from waste materials is becoming increasingly important to guarantee the security of their supply. Designing new sustainable and selective procedures that would substitute currently used processes is crucial. Here, we describe an unprecedented approach for the sequential dissolution of single metals from Cu, Ag, and Au mixtures using biomass-derived ionic solvents and green oxidants. First, Cu can be selectively dissolved in the presence of Ag and Au with a choline chloride/urea/H2O2 mixture, followed by the dissolution of Ag in lactic acid/H2O2. Finally, the metallic Au, which is not soluble in either solution above, is dissolved in choline chloride/urea/Oxone. Subsequently, the metals were simply and quantitatively recovered from dissolutions, and the solvents were recycled and reused. The applicability of the developed approach was demonstrated by recovering metals from electronic waste substrates such as printed circuit boards, gold fingers, and solar panels. The dissolution reactions and selectivity were explored with different analytical techniques and DFT calculations. We anticipate our approach will pave a new way for the contemporary and sustainable recycling of multi-metal waste substrates.

Comment on "Applicability of perturbed matrix method for charge transfer studies at bio/metallic interfaces: a case of azurin" by O. Kontkanen, D. Biriukov and Z. Futera, Phys. Chem. Chem. Phys., 2023, , 12479

Polarizability is a fundamental property of all molecular systems describing the deformation of the molecular electronic density in response to an applied electric field. The question of whether polarizability of the active site needs to be included in theories of enzymatic activity remains open. Hybrid quantum mechanical/molecular mechanical calculations are hampered by difficulties faced by many quantum-chemistry algorithms to provide sufficiently accurate estimates of the anisotropic second-rank tensor of molecular polarizability. In this Comment, we provide general theoretical arguments for the values of polarizability of the quantum region or a molecule which have to be reproduced by electronic structure calculations.

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

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 Fe²⁺ /Fe³⁺ 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, standard plane-wave based 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 Fe²⁺ /Fe³⁺ 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 Fe²⁺ /Fe³⁺ system computed from these simulations are compared with the available experimental data for validation.

Electrochemical Properties and Local Structure of the TEMPO/TEMPO+ Redox Pair in Ionic Liquids

Redox-active organic species play an important role in catalysis, energy storage, and biotechnology. One of the representatives is the 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radical, used as a mediator in organic synthesis and considered a safe alternative to heavy metals. In order to develop a TEMPO-based system with well-controlled electrochemical and catalytic properties, a reaction medium should be carefully chosen. Being highly conductive, stable, and low flammability fluids, ionic liquids (ILs) seem to be promising solvents with easily adjustable physical and solvation properties. In this work, we give an insight into the local structure of ILs around TEMPO and its oxidized form, TEMPO⁺, underlining striking differences in the solvation of these two species. The analysis is coupled with a study of thermodynamics and kinetics of oxidation in the frame of Marcus theory. Our systematic investigation includes imidazolium, pyrrolydinium, and phosphonium families combined with anions of different size, polarity, and flexibility, opting to provide a clear and comprehensive picture of the impact of the nature of IL ions on the behavior of radical/cation redox pairs. The obtained results will help to explain experimentally observed effects and to rationalize the design of TEMPO/IL systems.

First-principles redox energy estimates under the condition of satisfying the general form of Koopmans’ theorem: An atomistic study of aqueous iron

In this work, we explore the relative accuracy to which a hybrid functional, in the context of density functional theory, may predict redox properties under the constraint of satisfying the general form of Koopmans’ theorem. Taking aqueous iron as our model system within the framework of first-principles molecular dynamics, direct comparison between computed single-particle energies and experimental ionization data is assessed by both (1) tuning the degree of hybrid exchange, to satisfy the general form of Koopmans’ theorem, and (2) ensuring the application of finite-size corrections. These finite-size corrections are benchmarked through classical molecular dynamics calculations, extended to large atomic ensembles, for which good convergence is obtained in the large supercell limit. Our first-principles findings indicate that while precise quantitative agreement with experimental ionization data cannot always be attained for solvated systems, when satisfying the general form of Koopmans’ theorem via hybrid functionals, theoretically robust estimates of single-particle redox energies are most often arrived at by employing a total energy difference approach. That is, when seeking to employ a value of exact exchange that does not satisfy the general form of Koopmans’ theorem, but some other physical metric, the single-particle energy estimate that would most closely align with the general form of Koopmans’ theorem is obtained from a total energy difference approach. In this respect, these findings provide important guidance for the more general comparison of redox energies computed via hybrid functionals with experimental data.

Ewald sum corrections in simulations of ion and dipole solvation and electron transfer

Periodic boundary conditions and Ewald sums used in standard simulation protocols require finite-size corrections when the total charge of the simulated system is nonzero. Corrections for ion solvation were introduced by Hummer, Pratt, and García, [J. Chem. Phys. 107, 9275 (1997)]. The latter approach is extended here to derive finite-size correction for the Stokes-shift and reorganization energy applied to electron-transfer reactions. The same correction term, scaling inversely with the box size, adds to the reorganization energy from the energy-gap variance but is subtracted from the reorganization energy calculated from the Stokes shift. Finite-size corrections thus widen the gap between these two quantities, which were recently found to diverge for protein electron transfer. Corrections to the free energy of dipole solvation and the variance of the electric field scale as m²/L³ with the solute dipole m and the box size L.

Comparison of Penta and Tetra-pyridyl Cobalt-based Catalysts for Water Reduction: H2 Production Cycle, Solvent Response and Reduction Free Energy

Understanding water reduction towards H₂ generation is crucial to overcome today's renewable energy obstacles. Previous studies have shown the superior H₂ production performances of Cobalt based penta-pyridyl (CoaPPy) and tetra-pyridyl (CoaTPy) complexes in solution. We investigate H₂ production cycles of CoaPPy and CoaTPy complexes immersed in water solution by means of Ab-initio Molecular Dynamics and Density Functional Theory. We monitor dynamic properties of the systems, solvent response and structural changes occurring in the catalysts, by simulating all intermediate steps of the H₂ production cycle. Reduction free energies and reorganization energies are calculated. Our results show that, following the first electron injection, H₂ production proceeds with the singlet spin state. Following the first electron insertion, we observe a significant rearrangement of the hydrogen bonding network in the first solvation shell. The cobalt center turns out to be more accessible for the surrounding water molecules in the case of CoaTPy at all the intermediate steps, which explains its higher catalytic performance over CoaPPy. Following the first reduction reaction, a larger gain in reduction free energy is estimated for CoaTPy with respect to CoaPPy, with a difference of 0.14 eV, in line with the experiments. For the second reduction, instead, CoaPPy shows more negative reduction potential, by 0.41 eV.

Ionization energies in solution with the QM:QM approach

We discuss a fragment-based QM:QM scheme as a practical way to access the energetics of vertical electronic processes in the condensed phase. In the QM:QM scheme, we decompose the large molecular system into small fragments, which interact solely electrostatically. The energies of the fragments are calculated in a self-consistent field generated by the other fragments and the total energy of the system is calculated as a sum of the fragment energies. We show on two test cases (cytosine and a sodium cation) that the method allows one to accurately simulate the shift of vertical ionization energies (VIE) while going from the gas phase to the bulk. For both examples, the predicted solvent shifts and peak widths estimated at the DFT level agree well with the experimental observations. We argue that the QM:QM approach is more suitable than either an electrostatic embedding based QM/MM approach, a full quantum description at the DFT level with a generally used functional or a combination of both. We also discuss the potential scope of the applicability for other electronic processes such as Auger decay.

Polaronic structure of excess electrons and holes for a series of bulk iron oxides

With the use of a gap-optimized hybrid functional and large supercells, it is found that while the electron hole polaron generally localises onto a single iron site, the electron polaron localises across two iron sites of the same spin layer.

Microscopic Picture of the Solvent Reorganization During Electron Transfer to Flavin in Water

The redox potential of molecular species is largely modulated by its molecular environment so that a change of the environment will lead to a different redox potential. However, a detailed molecular picture of reorganization of the environment upon reduction is still unclear. To unravel the details of the solvent reorganization during electron transfer, we have performed density functional theory-based molecular dynamics (DFT-MD) and hybrid quantum mechanics/molecular mechanics (QM/MM) simulations of the reduction of lumiflavin. Previously, we have calculated the reduction free energy curves of the redox half reactions of lumiflavin in water as a function of the instantaneous gap energy (ΔE) ( J. Chem. Theory Comput. 2013 , 9 , 3889 - 3899 ). In this work, we focus on finding the changes in the solvent environment that correlate with this ΔE reaction coordinate. Comparing the QM/MM simulations, in which the solvent is modeled with an empirical force field, with the (full) DFT-MD simulations, we find that the response through electronic polarization plays a significant role in the latter case. Also a small charge transfer between flavin and solvent is observed in the full DFT treatment. As a result, we find only in the case of the QM/MM model a strong correlation between ΔE and the (pairwise computed) electrostatic potential (ESP) at the flavin due to the solvent. By analyzing the contribution of the ESP at the flavin per solvent molecule, we cannot only distinguish between the different modes of hydration by solvent molecules that coordinate at the hydrophilic and hydrophobic sides of the flavin molecule but also quantify their contribution to the reorganization free energy by measuring the ESP fluctuations per solvent molecule.

Role of solvent-anion charge transfer in oxidative degradation of battery electrolytes

Electrochemical stability windows of electrolytes largely determine the limitations of operating regimes of lithium-ion batteries, but the degradation mechanisms are difficult to characterize and poorly understood. Using computational quantum chemistry to investigate the oxidative decomposition that govern voltage stability of multi-component organic electrolytes, we find that electrolyte decomposition is a process involving the solvent and the salt anion and requires explicit treatment of their coupling. We find that the ionization potential of the solvent-anion system is often lower than that of the isolated solvent or the anion. This mutual weakening effect is explained by the formation of the anion-solvent charge-transfer complex, which we study for 16 anion-solvent combinations. This understanding of the oxidation mechanism allows the formulation of a simple predictive model that explains experimentally observed trends in the onset voltages of degradation of electrolytes near the cathode. This model opens opportunities for rapid rational design of stable electrolytes for high-energy batteries.

Nature of Monomeric Molybdenum(VI) Cations in Acid Solutions Using Theoretical Calculations and Raman Spectroscopy

The composition and structures of the two protonated species formed from uncharged molybdic acid, MoO₂(OH)₂(OH₂)₂⁰, in strongly acidic solutions have been investigated using a combination of density functional theory calculations, first-principles molecular dynamics simulations, and Raman spectroscopy. The calculations show that both protonated species maintain the original octahedral structure of molybdic acid. Computed p K_a values indicated that the ═O moieties are the proton acceptor sites and, therefore, that MoO(OH)₃(OH₂)₂⁺ and Mo(OH)₄(OH₂)₂²⁺ are the probable protonated forms of Mo(VI) in strong acid solutions, rather than the previously accepted MoO₂(OH)_{2- x}(OH₂)_{2+ x} ^x+ ( x = 1, 2) species. This finding is shown to be broadly consistent with the observed Raman spectra. Structural details of MoO(OH)₃(OH₂)₂⁺ and Mo(OH)₄(OH₂)₂²⁺ are reported.

Acidity Constants of the Hematite-Liquid Water Interface from Ab Initio Molecular Dynamics

The interface between transition metal oxides (TMO) and liquid water plays a crucial role in environmental chemistry, catalysis, and energy science. Yet, the mechanism and energetics of chemical transformations at solvated TMO surfaces is often unclear, largely because of the difficulty to characterize the active surface species experimentally. The hematite (α-Fe₂O₃)-liquid water interface is a case in point. Here we demonstrate that ab initio molecular dynamics is a viable tool for determining the protonation states of complex interfaces. The p K_a values of the oxygen-terminated (001) surface group of hematite, ≡OH, and half-layer terminated (012) surface groups, ≡²OH and ≡¹OH₂, are predicted to be (18.5 ± 0.3), (18.9 ± 0.6), and (10.3 ± 0.5) p K_a units, respectively. These are in good agreement with recent bond-valence theory based estimates, and suggest that the deprotonation of these surfaces require significantly more free energy input than previously thought.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Electronic structure of aqueous solutions: Bridging the gap between theory and experiments

Predicting the electronic properties of aqueous liquids has been a long-standing challenge for quantum mechanical methods. However, it is a crucial step in understanding and predicting the key role played by aqueous solutions and electrolytes in a wide variety of emerging energy and environmental technologies, including battery and photoelectrochemical cell design. We propose an efficient and accurate approach to predict the electronic properties of aqueous solutions, on the basis of the combination of first-principles methods and experimental validation using state-of-the-art spectroscopic measurements. We present results of the photoelectron spectra of a broad range of solvated ions, showing that first-principles molecular dynamics simulations and electronic structure calculations using dielectric hybrid functionals provide a quantitative description of the electronic properties of the solvent and solutes, including excitation energies. The proposed computational framework is general and applicable to other liquids, thereby offering great promise in understanding and engineering solutions and liquid electrolytes for a variety of important energy technologies.

Dehydrogenation Free Energy of Co2+(aq) from Density Functional Theory-Based Molecular Dynamics

Electron and proton transfers are important steps occurring in chemical reactions. The often used approach of calculating the energy differences of those steps using methods based on geometry optimizations neglects the influence of dynamic effects. To further investigate this issue and inspired by research in water oxidation, we calculate in the present study the dehydrogenation free energy of aqueous Co²⁺, which is the free energy change associated with the first step of the water oxidation reaction mechanism of recently investigated model Co(II)-aqua catalysts. We employ a method based on a thermodynamic integration scheme with strong ties to Marcus theory to obtain free energy differences, solvent reorganization free energies, and dynamic structural information on the systems from density functional theory-based molecular dynamics. While this method is computationally orders of magnitude more expensive than a static approach, it potentially allows for predicting the validity of the approximation of neglecting dynamic effects.

Calculation of Electrochemical Energy Levels in Water Using the Random Phase Approximation and a Double Hybrid Functional

Understanding charge transfer at electrochemical interfaces requires consistent treatment of electronic energy levels in solids and in water at the same level of the electronic structure theory. Using density-functional-theory-based molecular dynamics and thermodynamic integration, the free energy levels of six redox couples in water are calculated at the level of the random phase approximation and a double hybrid density functional. The redox levels, together with the water band positions, are aligned against a computational standard hydrogen electrode, allowing for critical analysis of errors compared to the experiment. It is encouraging that both methods offer a good description of the electronic structures of the solutes and water, showing promise for a full treatment of electrochemical interfaces.

Explicit solvent simulations of the aqueous oxidation potential and reorganization energy for neutral molecules: gas phase, linear solvent response, and non-linear response contributions

First principles simulations were used to predict aqueous one-electron oxidation potentials (Eox) and associated half-cell reorganization energies (λaq) for aniline, phenol, methoxybenzene, imidazole, and dimethylsulfide. We employed quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations of the oxidized and reduced species in an explicit aqueous solvent, followed by EOM-IP-CCSD computations with effective fragment potentials for diabatic energy gaps of solvated clusters, and finally thermodynamic integration of the non-linear solvent response contribution using classical MD. A priori predicted Eox and λaq values exhibit mean absolute errors of 0.17 V and 0.06 eV, respectively, compared to experiment. We also disaggregate Eox into several well-defined free energy properties, including the gas phase adiabatic free energy of ionization (7.73 to 8.82 eV), the solvent-induced shift in the free energy of ionization due to linear solvent response (-2.01 to -2.73 eV), and the contribution from non-linear solvent response (-0.07 to -0.14 eV). The linear solvent response component is further apportioned into contributions from the solvent-induced shift in vertical ionization energy of the reduced species (ΔVIEaq) and the solvent-induced shift in negative vertical electron affinity of the ionized species (ΔNVEAaq). The simulated ΔVIEaq and ΔNVEAaq are found to contribute the principal sources of uncertainty in computational estimates of Eox and λaq. Trends in the magnitudes of disaggregated solvation properties are found to correlate with trends in structural and electronic features of the solute. Finally, conflicting approaches for evaluating the aqueous reorganization energy are contrasted and discussed, and concluding recommendations are given.

Acidity constants and redox potentials of uranyl ions in hydrothermal solutions

We report a first principles molecular dynamics (FPMD) study of the structures, acidity constants (pK_a) and redox potentials (E⁰) of uranyl (UO₂²⁺) from ambient conditions to 573 K.

Frustrated Solvation Structures Can Enhance Electron Transfer Rates

Polar surfaces can interact strongly with nearby water molecules, leading to the formation of highly ordered interfacial hydration structures. This ordering can lead to frustration in the hydrogen bond network, and, in the presence of solutes, frustrated hydration structures. We study frustration in the hydration of cations when confined between sheets of the water oxidation catalyst manganese dioxide. Frustrated hydration structures are shown to have profound effects on ion-surface electron transfer through the enhancement of energy gap fluctuations beyond those expected from Marcus theory. These fluctuations are accompanied by a concomitant increase in the electron transfer rate in Marcus's normal regime. We demonstrate the generality of this phenomenon-enhancement of energy gap fluctuations due to frustration-by introducing a charge frustrated XY model, likening the hydration structure of confined cations to topological defects. Our findings shed light on recent experiments suggesting that water oxidation rates depend on the cation charge and Mn-oxidation state in these layered transition metal oxide materials.

Redox potentials and acidity constants from density functional theory based molecular dynamics

CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials. Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree-Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1-2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.

Computational electrochemistry: prediction of liquid-phase reduction potentials

This article reviews recent developments and applications in the area of computational electrochemistry. Our focus is on predicting the reduction potentials of electron transfer and other electrochemical reactions and half-reactions in both aqueous and nonaqueous solutions. Topics covered include various computational protocols that combine quantum mechanical electronic structure methods (such as density functional theory) with implicit-solvent models, explicit-solvent protocols that employ Monte Carlo or molecular dynamics simulations (for example, Car-Parrinello molecular dynamics using the grand canonical ensemble formalism), and the Marcus theory of electronic charge transfer. We also review computational approaches based on empirical relationships between molecular and electronic structure and electron transfer reactivity. The scope of the implicit-solvent protocols is emphasized, and the present status of the theory and future directions are outlined.

Charge transfer in model peptides: obtaining Marcus parameters from molecular simulation

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.

Interplay of flavin's redox states and protein dynamics: an insight from QM/MM simulations of dihydronicotinamide riboside quinone oxidoreductase 2

Dihydronicotinamide riboside quinone oxidoreductase 2 is known to catalyze a two-electron reduction of quinone to hydroquinone using its cofactor, flavin adenine dinucleotide. Using quantum mechanical/molecular mechanical simulations, we have computed the reorganization free energies of the electron and proton transfer processes of flavin in the free state as well as when it is bound in the active site of the enzyme. The calculated energetics for electron transfer processes demonstrate that the enzyme active site lowers the reorganization energy for the redox process as compared to the enzyme-free aqueous state. This is most apparent in the two electron reduction step, which eliminates the possibility of flavosemiquinone generation. In addition, essential dynamics study of the simulated motions revealed spectacular changes in the principal components of atomic fluctuations upon reduction of flavin. This alteration of active site dynamics provides an insight into the "ping-pong" kinetics exhibited by the enzyme upon a change in the redox state of the enzyme-bound flavin. A charge perturbation analysis provides further support that the observed change in dynamics is correlated with the change in energetics due to the altered electrostatic interactions between the flavin ring and the active site residues. This study shows that the effect of electrostatic preorganization goes beyond the chemical catalysis as it strongly impacts the postcatalytic intrinsic protein dynamics.

Redox potentials and pKa for benzoquinone from density functional theory based molecular dynamics

The density functional theory based molecular dynamics (DFTMD) method for the computation of redox free energies presented in previous publications and the more recent modification for computation of acidity constants are reviewed. The method uses a half reaction scheme based on reversible insertion/removal of electrons and protons. The proton insertion is assisted by restraining potentials acting as chaperones. The procedure for relating the calculated deprotonation free energies to Brønsted acidities (pK(a)) and the oxidation free energies to electrode potentials with respect to the normal hydrogen electrode is discussed in some detail. The method is validated in an application to the reduction of aqueous 1,4-benzoquinone. The conversion of hydroquinone to quinone can take place via a number of alternative pathways consisting of combinations of acid dissociations, oxidations, or dehydrogenations. The free energy changes of all elementary steps (ten in total) are computed. The accuracy of the calculations is assessed by comparing the energies of different pathways for the same reaction (Hess's law) and by comparison to experiment. This two-sided test enables us to separate the errors related with the restrictions on length and time scales accessible to DFTMD from the errors introduced by the DFT approximation. It is found that the DFT approximation is the main source of error for oxidation free energies.

Acidity constants from DFT-based molecular dynamics simulations

In this contribution we review our recently developed method for the calculation of acidity constants from density functional theory based molecular dynamics simulations. The method is based on a half reaction scheme in which protons are formally transferred from solution to the gas phase. The corresponding deprotonation free energies are computed from the vertical energy gaps for insertion or removal of protons. Combined to full proton transfer reactions, the deprotonation energies can be used to estimate relative acidity constants and also the Brønsted pK(a) when the deprotonation free energy of a hydronium ion is used as a reference. We verified the method by investigating a series of organic and inorganic acids and bases spanning a wide range of pK(a) values (20 units). The thermochemical corrections for the biasing potentials assisting and directing the insertion are discussed in some detail.

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids "on-the-fly" QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

The electron attachment energy of the aqueous hydroxyl radical predicted from the detachment energy of the aqueous hydroxide anion

Combining photoemission and electrochemical data from the literature we argue that the difference between the vertical and adiabatic ionization energy of the aqueous hydroxide anion is 2.9 eV. We then use density functional theory based molecular dynamics to show that the solvent response to ionization is nonlinear. Adding this to the experimental data we predict a 4.1 eV difference between the energy for vertical attachment of an electron to the aqueous hydroxyl radical and the corresponding adiabatic electron affinity. This places the state accepting the electron only 2.2 eV below vacuum or 7.7 eV above the edge of the valence band of water.