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Author(s): Waiz Karim [1, 2, 3]; Clelia Spreafico [4]; Armin Kleibert [5]; Jens Gobrecht [2]; Joost VandeVondele [4]; Yasin Ekinci (corresponding author) [2]; Jeroen A. van Bokhoven (corresponding author) [1, [...]

In this paper, real-time time-dependent density functional theory (RT-TDDFT) calculations of realistically sized nanodevices are presented. These microcanonical simulations rely on a closed boundary approach based on recent advances in the software package CP2K. The obtained results are compared to those derived from the open-boundary Non-equilibrium Green's Function (NEGF) formalism. A good agreement between the "current vs. voltage" characteristics produced by both methods is demonstrated for three representative device structures, a carbon nanotube field-effect transistor, a GeSe selector for crossbar arrays, and a conductive bridging random-access memory cell. Different approaches to extract the electrostatic contribution from the RT-TDDFT Hamiltonian and to incorporate the result into the NEGF calculations are presented. [ABSTRACT FROM AUTHOR]

A combination of density functional theory (DFT) and classical molecular dynamics is used to quantitatively estimate the key redox properties of two variants of rubredoxin, a small and comparatively simple iron-sulfur protein. The results have confirmed that in the case of rubredoxin the redox potential modulation is obtained by the short-range contribution, while the reorganization free energy is dominated by long-range effects.

Massively parallel algorithms are presented in this paper to reduce the computational burden associated with quantum transport simulations from first-principles. The power of modern hybrid computer architectures is harvested in order to determine the open boundary conditions that connect the simulation domain with its environment and to solve the resulting Schrödinger equation. While the former operation takes the form of an eigenvalue problem that is solved by a contour integration technique on the available central processing units (CPUs), the latter can be cast into a linear system of equations that is simultaneously processed by SplitSolve, a two-step algorithm, on general-purpose graphics processing units (GPUs). A significant decrease of the computational time by up to two orders of magnitude is obtained as compared to standard solution methods. [ABSTRACT FROM AUTHOR]

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated. [ABSTRACT FROM AUTHOR]

The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene. [ABSTRACT FROM AUTHOR]

Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaricisothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance. [ABSTRACT FROM AUTHOR]

The ultrafast dynamics of the cationic hole formed in bulk liquid water following ionization is investigated by ab initio molecular dynamics simulations and an experimentally accessible signature is suggested that might be tracked by femtosecond pump-probe spectroscopy. This is one of the fastest fundamental processes occurring in radiation-induced chemistry in aqueous systems and biological tissue. However, unlike the excess electron formed in the same process, the nature and time evolution of the cationic hole has been hitherto little studied. Simulations show that an initially partially delocalized cationic hole localizes within ∼30 fs after which proton transfer to a neighboring water molecule proceeds practically immediately, leading to the formation of the OH radical and the hydronium cation in a reaction which can be formally written as H2O+ + H2O → OH + H3O+. The exact amount of initial spin delocalization is, however, somewhat method dependent, being realistically described by approximate density functional theory methods corrected for the self-interaction error. Localization, and then the evolving separation of spin and charge, changes the electronic structure of the radical center. This is manifested in the spectrum of electronic excitations which is calculated for the ensemble of ab initio molecular dynamics trajectories using a quantum mechanics/molecular mechanics (QM/MM) formalism applying the equation of motion coupled-clusters method to the radical core. A clear spectroscopic signature is predicted by the theoretical model: as the hole transforms into a hydroxyl radical, a transient electronic absorption in the visible shifts to the blue, growing toward the near ultraviolet. Experimental evidence for this primary radiation-induced process is sought using femtosecond photoionization of liquid water excited with two photons at 11 eV. Transient absorption measurements carried out with ∼40 fs time resolution and broadband spectral probing across the near-UV and visible are presented and direct comparisons with the theoretical simulations are made. Within the sensitivity and time resolution of the current measurement, a matching spectral signature is not detected. This result is used to place an upper limit on the absorption strength and/or lifetime of the localized H2O+(aq) species. [ABSTRACT FROM AUTHOR]

We compare three different methods for direct energy minimization in electronic structure calculations where the gradient of the energy functional with respect to the molecular orbitals is available. These methods make use of the preconditioned gradient to increase robustness. An orbital transformation is used to ensure that the orthogonality constraint on the orbitals remains satisfied when using standard minimization methods. In addition, we propose an adaptive scheme for estimating the curvature of the energy functional to increase the performance of a line search free quasi-Newton method. We show that the performance of all methods is similar when robustness of the methods is ensured. [ABSTRACT FROM AUTHOR]

Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree–Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions. [ABSTRACT FROM AUTHOR]

The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained energy functional to an approximate unconstrained functional, which is correct to some order in a neighborhood of an orthogonal but approximate solution. A conjugate gradient scheme can then be used to find the ground state orbitals from the minimization of a sequence of transformed unconstrained electronic energy functionals. The technique provides an efficient, robust, and numerically stable approach to direct total energy minimization in first principles electronic structure theory based on tight-binding, Hartree–Fock, or density functional theory. For sparse problems, where both the orbitals and the effective single-particle Hamiltonians have sparse matrix representations, the effort scales linearly with the number of basis functions N in each iteration. For problems where only the overlap and Hamiltonian matrices are sparse the computational cost scales as O(M2N), where M is the number of occupied orbitals. We report a single point density functional energy calculation of a DNA decamer hydrated with 4003 water molecules under periodic boundary conditions. The DNA fragment containing a cis-syn thymine dimer is composed of 634 atoms and the whole system contains a total of 12 661 atoms and 103 333 spherical Gaussian basis functions. [ABSTRACT FROM AUTHOR]

We present a library of Gaussian basis sets that has been specifically optimized to perform accurate molecular calculations based on density functional theory. It targets a wide range of chemical environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition number of the overlap matrix for a set of molecules with respect to the exponents and contraction coefficients of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles molecular dynamics simulations and is well suited for linear scaling calculations. [ABSTRACT FROM AUTHOR]

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the temperature range of 280–380 K. We find a pronounced influence of temperature on the pair correlation functions and on the diffusion constant including nonergodic behavior on the time scale of the simulation in the lower temperature range (which includes ambient temperature). These observations were taken into account in a consistent comparison of a series of density functionals (BLYP, PBE, TPSS, OLYP, HCTH120, HCTH407). All simulations were carried out using an ab initio molecular dynamics approach in which wave functions are represented using Gaussians and the density is expanded in an auxiliary basis of plane waves. Whereas the first three functionals show similar behavior, it is found that the latter three functionals yield more diffusive dynamics and less structure.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An efficient method for optimizing single-determinant wave functions of medium and large systems is presented. It is based on a minimization of the energy functional using a new set of variables to perform orbital transformations. With this method convergence of the wave function is guaranteed. Preconditioners with different computational cost and efficiency have been constructed. Depending on the preconditioner, the method needs a number of iterations that is very similar to the established diagonalization-DIIS approach, in cases where the latter converges well. Diagonalization of the Kohn-Sham matrix can be avoided and the sparsity of the overlap and Kohn-Sham matrix can be exploited. If sparsity is taken into account, the method scales as O(MN[SUP2]), where M is the total number of basis functions and N is the number of occupied orbitals. The relative performance of the method is optimal for large systems that are described with high quality basis sets, and for which the density matrices are not yet sparse. We present a benchmark calculation on a DNA crystal containing 2312 base pairs, solvent and counter ions (2388 atoms), using a TZV(2d,2p) basis (38 688 basis functions) and conclude that the electronic structure of systems of this size can now be studied routinely. [ABSTRACT FROM AUTHOR]

We present a fully Hamiltonian and computationally efficient scheme to include the electrostatic effects due to the classical environment in a Car–Parrinello mixed quantum Mechanics/molecular mechanics (QM/MM) method. The polarization due to the MM atoms close to the quantum system is described by a Coulombic potential modified at short range. We show that the functional form of this potential has to be chosen carefully in order to obtain the correct interaction properties and to prevent an unphysical escape of the electronic density to the MM atoms (the so-called spill-out effect). The interaction between the QM system and the more distant MM atoms is modeled by a Hamiltonian term explicitly coupling the multipole moments of the quantum charge distribution with the classical point charges. Our approach remedies some of the well known deficiencies of current electrostatic coupling schemes in QM/MM methods, allowing molecular dynamics simulations of mixed systems within a fully consistent and energy conserving approach. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We derive an expression that enables the accurate estimation of equilibrium properties using non-Hamiltonian dynamics. The major advantage of our scheme is that a time average over a single non-Hamiltonian trajectory can be employed instead of an ensemble average. Hence, it can directly be used in standard molecular dynamics simulations. The connection between non-Hamiltonian dynamics and equilibrium properties is established by assigning to the individual frames of the trajectory a weight that is based on the fluctuations of the phase space compression factor. Additionally, a simple scheme that takes into account only fluctuation of a given maximum duration is introduced to reduce the statistical error. By systematically extending the duration of the allowed fluctuations, increasingly accurate results can be obtained. Non-Hamiltonian dynamics schemes that are capable to enhance sampling efficiency are applied to two model systems in order to demonstrate the practical performance of our approach for the calculation of equilibrium free energy differences and probability density profiles. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Photoemission and electrochemical data are used for showing the difference between the vertical and adiabatic ionization energy of aqueous hydroxide anion to be 2.9 eV. The solvent response to ionization is nonlinear and the studies have predicted 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.

The first-principles molecular dynamics simulations are employed to demonstrate the significance of the number of acid molecules and the strength of the base for double-ion formation in [([H.sub.2]S[O.sub.4]).sub.m].base.[([H.sub.2]O).sub.6] clusters. The presence of two sulfuric acid molecules in the clusters is shown to be sufficient to form a double ion.

Molecular dynamics based density functional theory (DFT) is used for studying the chromophore, p-coumaric acid (pCA), in different isomerization and protonation states in bulk solution. The presence of the chromophore has influenced the charge and polarization of the water molecules around it.

The analytic dependence of the dynamical electrostatic potential derived (D-RESP) charges on the coordinates of the system, on the position of the atoms and on the electronic density, is illustrated. The interaction potentials helps in improving the computational efficiency of the electrostatic coupling between the quantum mechanics (QM) and the molecular mechanics (MM) subsystems and also defines the QM/MM analogue of the exclusion schemes.

The structure of the hydrated electron is a matter of debate as it evades direct experimental observation owing to the short life time and low concentrations of the species. Herein, the first molecular dynamics simulation of the bulk hydrated electron based on correlated wave‐function theory provides conclusive evidence in favor of a persistent tetrahedral cavity made up by four water molecules, and against the existence of stable non‐cavity structures. Such a cavity is formed within less than a picosecond after the addition of an excess electron to neat liquid water, with less regular cavities appearing as intermediates. The cavities are bound together by weak H−H bonds, the number of which correlates well with the number of coordinated water molecules, each type of cavity leaving a distinct spectroscopic signature. Simulations predict regions of negative spin density and a gyration radius that are both in agreement with experimental data. [ABSTRACT FROM AUTHOR]

The method, which makes direct use of the intrinsic chemical information encoded in the electronic structure, and is therefore able to lower selectivity chemically relevant activation energies even in systems where many competing low-energy pathways for conformational transitions or diffusive motions are present is presented. The simple method presented works surprisingly well in the case of orbital-driven chemical reactions that are dominated by the HOMO and LUMO orbitals for which impressive acceleration factors of several orders of magnitude, often more than five, can be achieved in a straightforward manner.

Dynamic density functional calculations are performed on the three isomeric title compounds. The finite temperature properties are dominated by the facile dissociation of the phosphine ligands, an effect that can be related to the presence of three- and four-center trans effects.

The pivotal importance of TiO2 as a technological material involves most applications in an aqueous environment, but the single-crystal TiO2/bulk-water interfaces are almost completely unexplored, since up to date solid/liquid interfaces are more difficult to access than surfaces in ultrahigh vacuum (UHV). Only a few techniques (as scanning probe microscopy) offer the opportunity to explore these systems under realistic conditions. The rutile TiO2(110) surface immersed in high-purity water is studied by in situ scanning tunneling microscopy. The large-scale surface morphology as obtained after preparation under UHV conditions remains unchanged upon prolonged exposure to bulk water. Moreover, in contrast to UHV, atomically resolved images show a twofold periodicity along the [001] direction, indicative of an ordered structure resulting from the hydration layer. This is consistent with density-functional theory based molecular dynamics simulations where neighboring interfacial molecules of the first water layer in contact with the bulk liquid form dimers. By contrast, this dimerization is not observed for a single adsorbed water monolayer, i.e., in the absence of bulk water. [ABSTRACT FROM AUTHOR]

The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid density functional theory (DFT) and the random phase approximation (RPA). Consistent with experiment, charge trapping and polaron formation is observed in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is observed also with standard hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amount of Hartree–Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with experimental data, is observed, and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calculations serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree–Fock exchange), as a suitable method to study the rich chemistry and physics of TiO2. [ABSTRACT FROM AUTHOR]

The high overpotential in water oxidation on anodes is a limiting factor for the large-scale application of photoelectrochemical cells. To overcome this limitation, it is essential to understand the four proton-coupled electron transfer (PCET) steps in the reaction mechanism and their implications to the overpotential. Herein, a simple scheme to compute the energies of the PCET steps in water oxidation on the aqueous TiO2 surface using a hybrid density functional is described. An energy level diagram for fully decoupled electron- and proton-transfer reactions in which both electronic and protonic levels are placed on the same potential scale is also described. The level diagram helps to visualize the electronic and protonic components of the overpotential, and points out what are needed to improve. For TiO2, it is found that its catalytic activity is due to aligning the protonic energy levels in the PCET steps, while improving the activity requires also aligning the electronic levels. [ABSTRACT FROM AUTHOR]

The high overpotential in water oxidation on anodes is a limiting factor for the large‐scale application of photoelectrochemical cells. To overcome this limitation, it is essential to understand the four proton‐coupled electron transfer (PCET) steps in the reaction mechanism and their implications to the overpotential. Herein, a simple scheme to compute the energies of the PCET steps in water oxidation on the aqueous TiO2 surface using a hybrid density functional is described. An energy level diagram for fully decoupled electron‐ and proton‐transfer reactions in which both electronic and protonic levels are placed on the same potential scale is also described. The level diagram helps to visualize the electronic and protonic components of the overpotential, and points out what are needed to improve. For TiO2, it is found that its catalytic activity is due to aligning the protonic energy levels in the PCET steps, while improving the activity requires also aligning the electronic levels. [ABSTRACT FROM AUTHOR]

cp2 k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2 k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website. [ABSTRACT FROM AUTHOR]

The article discusses a study which investigated self-trapping of holes in titania which have utilized advanced density functional theory (DFT) methods. The study made the link to oxidation catalysis using oxidative dehydrogenation (ODH) of a terminal water at the aqueous rutile titania interface as an example. It indicated that the net activation of ODH by the titania surface is attributable to an increase of the acidity of an adsorbed water molecule.

We present a hybrid QM/MM Car-Parrinello molecular dynamics study of the copper-loaded C-terminal domain of the mouse prion protein. By means of a statistical analysis of copper coordination in known protein structures, we localized the protein regions with the highest propensity for copper ion binding. The identified candidate structures were subsequently refined via QM/MM simulations. Their EPR characteristics were computed to make contact with the experimental data and to probe the sensitivity to structural and chemical changes. Overall best agreement with the experimental EPR data (Van Doorslaer et al., J Phys Chem B 2001; 105: 1631-1639) and the information currently available in the literature is observed for a binding site involving H187. Moreover, a reinterpretation of the experimental proton hyperfine couplings was possible in the light of the present computational findings. Proteins 2008. © 2007 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]

Examines mechanism for the cis-trans isomerization in triple bonded ditungsten complexes. Dissociation of phosphine ligands; Formation of two intramolecular hydrogen-bonds between chlorides and amino ligands; Use of antibody initio molecular dynamic simulation for the characterization of the dynamic properties in isomeric form.

We present a method for calculating multidimensional free energy surfaces within the limited time scale of a first-principles molecular dynamics scheme. The sampling efficiency is enhanced using selected terms of a classical force field as a bias potential. This simple procedure yields a very substantial increase in sampling accuracy while retaining the high quality of the underlying ab initio potential surface and can thus be used for a parameter free calculation of free energy surfaces. The success of the method is demonstrated by the applications to two gas phase molecules, ethane and peroxynitrous acid, as test case systems. A statistical analysis of the results shows that the entire free energy landscape is well converged within a 40 ps simulation at 500 K, even for a system with barriers as high as 15 kcal/mol. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]