Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering.

Dimeric complexes composed of d8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir2 (dimen)4]2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population─often termed the ground state hole─with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d8-d8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

Doping-Induced Enhancement of Hydrogen Evolution at MoS2 Electrodes.

Rate theory and DFT calculations of hydrogen evolution reaction (HER) on MoS2 with Co, Ni and Pt impurities show the significance of dihydrogen (H2*) complex where both hydrogen atoms are interacting with the surface. Stabilization of such a complex affects the competing Volmer-Heyrovsky (direct H2 release) and Volmer-Tafel (H2* intermediate) pathways. The resulting evolution proceeds with a very small overpotential for all dopants ( η ${\eta }$ =0.1 to 0.2 V) at 25 % edge substitution, significantly reduced from the already low η ${\eta }$ =0.27 V for the undoped edge. At full edge substitution, Co-MoS2 remains highly active ( η ${\eta }$ =0.18 V) while Ni- and Pt-MoS2 are deactivated ( η ${\eta }$ =0.4 to 0.5 V) due to unfavorable interaction with H2*. Instead of the single S-vacancy, the site of intrinsic activity in the basal plane was found to be the undercoordinated central Mo-atom in threefold S-vacancy configurations, enabling hydrogen evolution with η ${\eta }$ =0.52 V via a H2* intermediate. The impurity atoms interact favorably with the intrinsic sulfur vacancies on the basal plane, stabilizing but simultaneously deactivating the triple vacancy configuration. The calculated shifts in overpotential are consistent with reported measurements, and the dependence on doping level may explain variations in experimental observations.

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Is the doped MoS2 basal plane an efficient hydrogen evolution catalyst? Calculations of voltage-dependent activation energy.

Transition metal dichalcogenides are cheap and earth-abundant candidates for the replacement of precious metals as catalyst materials. Experimental measurements of the hydrogen evolution reaction (HER), for example, have demonstrated significant electrocatalytic activity of MoS2 but there is large variation depending on the preparation method. In order to gain information about the mechanism and active sites for the HER, we have carried out calculations of the reaction and activation energy for HER at the transition metal doped basal plane of MoS2 under electrochemical conditions, i.e. including applied electrode potential and solvent effects. The calculations are based on identifying the relevant saddle points on the energy surface obtained from density functional theory within the generalized gradient approximation, and the information on energetics is used to construct voltage-dependent volcano plots. Doping with 3d-metal atoms as well as Pt is found to enhance hydrogen adsorption onto the basal plane by introducing electronic states within the band gap, and in some cases (Co, Ni, Cu, Pt) significant local symmetry breaking. The Volmer-Heyrovsky mechanism is found to be most likely and the associated energetics show considerable dopant and voltage-dependence. While the binding free energy of hydrogen can be tuned to be seemingly favorable for HER, the calculated activation energy turns out to be significant, at least 0.7 eV at a voltage of -0.5 V vs. SHE, indicating low catalytic activity of the doped basal plane. This suggests that other sites are responsible for the experimental activity, possibly edges or basal plane defects.

Sulfur-deficient edges as active sites for hydrogen evolution on MoS2.

A grand-canonical approach is employed to calculate the voltage-dependent activation energy and estimate the kinetics of the hydrogen evolution reaction (HER) on intrinsic sites of MoS2, including edges of varying S-coverage as well as S-vacancies on the basal plane. Certain edge configurations are found to be vastly more active than others, namely S-deficient edges on the Mo-termination where, in the fully S-depleted case, HER can proceed with activation energy below 0.5 eV at an electrode potential of 0 V vs. SHE. There is a clear distinction between the performance of Mo-rich and S-rich adsorption sites, as HER at the latter sites is characterized by large (generally above 1.5 eV) Heyrovsky and Tafel energy barriers despite near-thermoneutral hydrogen adsorption energy. Thus, exposing Mo-atoms on the edges to which hydrogen can directly bind is crucial for efficient hydrogen evolution. While S-vacancies on the basal plane do expose Mo-rich sites, the energy barriers are still significant due to high coordination of the Mo atoms. Kinetic modelling based on the voltage-dependent reaction energetics gives a theoretical overpotential of 0.25 V and 1.09 V for the Mo-edge with no S atoms and the weakly sulfur-deficient (2% S-vacancies) basal plane, respectively, with Volmer-Heyrovsky being the dominant pathway. These values coincide well with reported experimentally measured values of the overpotential for the edges and basal plane. For the partly Mo-exposed edges, the calculated overpotential is 0.6-0.7 V while edges with only S-sites give overpotential exceeding that of the basal plane. These results show that the overpotential systematically decreases with increased sulfur-deficiency and reduced Mo-coordination. The fundamental difference between Mo- and S-rich sites suggests that catalyst design of transition metal dichalcogenides should be focused on facilitating and modifying the metal sites, rather than activating the chalcogen sites.

A general-purpose machine learning Pt interatomic potential for an accurate description of bulk, surfaces, and nanoparticles.

A Gaussian approximation machine learning interatomic potential for platinum is presented. It has been trained on density-functional theory (DFT) data computed for bulk, surfaces, and nanostructured platinum, in particular nanoparticles. Across the range of tested properties, which include bulk elasticity, surface energetics, and nanoparticle stability, this potential shows excellent transferability and agreement with DFT, providing state-of-the-art accuracy at a low computational cost. We showcase the possibilities for modeling of Pt systems enabled by this potential with two examples: the pressure-temperature phase diagram of Pt calculated using nested sampling and a study of the spontaneous crystallization of a large Pt nanoparticle based on classical dynamics simulations over several nanoseconds.

Orbital-optimized density functional calculations of molecular Rydberg excited states with real space grid representation and self-interaction correction.

Density functional calculations of Rydberg excited states up to high energy are carried out for several molecules using an approach where the orbitals are variationally optimized by converging on saddle points on the electronic energy surface within a real space grid representation. Remarkably good agreement with experimental estimates of the excitation energy is obtained using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE) when Perdew-Zunger self-interaction correction is applied in combination with complex-valued orbitals. Even without the correction, the PBE functional gives quite good results despite the fact that corresponding Rydberg virtual orbitals have positive energy in the ground state calculation. Results obtained using the Tao, Perdew, Staroverov, and Scuseria (TPSS) and r2SCAN meta-GGA functionals are also presented, but they do not provide a systematic improvement over the results from the uncorrected PBE functional. The grid representation combined with the projector augmented-wave approach gives a simpler and better representation of diffuse Rydberg orbitals than a linear combination of atomic orbitals with commonly used basis sets, the latter leading to an overestimation of the excitation energy due to confinement of the excited states.

Simulations of the Oxidation and Degradation of Platinum Electrocatalysts.

Improved understanding of the fundamental processes leading to degradation of platinum nanoparticle electrocatalysts is essential to the continued advancement of their catalytic activity and stability. To this end, the oxidation of platinum nanoparticles is simulated using a ReaxFF reactive force field within a grand-canonical Monte Carlo scheme. 2-4 nm cuboctahedral particles serve as model systems, for which electrochemical potential-dependent phase diagrams are constructed from the thermodynamically most stable oxide structures, including solvation and thermochemical contributions. Calculations in this study suggest that surface oxide structures should become thermodynamically stable at voltages around 0.80-0.85 V versus standard hydrogen electrode, which corresponds to typical fuel cell operating conditions. The potential presence of a surface oxide during catalysis is usually not accounted for in theoretical studies of Pt electrocatalysts. Beyond 1.1 V, fragmentation of the catalyst particles into [Pt6 O8 ]4- clusters is observed. Density functional theory calculations confirm that [Pt6 O8 ]4- is indeed stable and hydrophilic. These results suggest that the formation of [Pt6 O8 ]4- may play an important role in platinum catalyst degradation as well as the electromotoric transport of Pt2+/4+ ions in fuel cells.

Variational calculations of excited states via direct optimization of the orbitals in DFT.

A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the energy as a function of the electronic degrees of freedom, thereby avoiding convergence to a minimum and corresponding variational collapse to the ground electronic state. The method is based on an exponential transformation of the molecular orbitals, making it possible to use efficient quasi-Newton optimization approaches. Direct convergence on a target nth-order saddle point is guided by an appropriate preconditioner for the optimization as well as the maximum overlap method. Results of benchmark calculations of 52 excited states of molecules indicate that the method is more robust than a standard self-consistent field (SCF) approach especially when degenerate or quasi-degenerate orbitals are involved. The method can overcome challenges arising from rearrangement of closely spaced orbitals in a charge-transfer excitation of the nitrobenzene molecule, a case where the SCF fails to converge. The formulation of the method is general and can be applied to non-unitary invariant functionals, such as self-interaction corrected functionals.

On the interplay of solvent and conformational effects in simulated excited-state dynamics of a copper phenanthroline photosensitizer.

Copper(i) bis-phenanthroline complexes represent Earth-abundant alternatives to ruthenium-based sensitizers for solar energy conversion and photocatalysis. Improved understanding of the solvent-mediated excited-state structural dynamics can help optimize their photoconversion efficiency. Through direct dynamics simulations in acetonitrile and excited-state minimum energy path calculations in vacuum, we uncover the mechanism of the photoinduced flattening motion of the prototypical system [Cu(dmphen)2]+ (dmphen = 2,9-dimethyl-1,10-phenanthroline). We find that the ligand distortion is a two-step process in acetonitrile. The fast component (∼110 fs) is due to spontaneous pseudo Jahn-Teller instability and is largely solvent independent, while the slow component (∼1.2 ps) arises from the mutual interplay between solvent molecules closely approaching the metal center and rotation of the methyl substituents. These results shed new light on the influence of a donor solvent such as acetonitrile and methyl substituents on the flattening dynamics of [Cu(dmphen)2]+.

Density functional theory calculations and thermodynamic analysis of bridgmanite surface structure.

Bridgmanite, a high temperature and pressure form of MgSiO3, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of the chemical potential of oxygen and magnesium. The vibrational contribution to the Gibbs free energy is found to be essential for obtaining a stability region of bridgmanite in the phase diagram. The most stable surface termination of bridgmanite varies between three different atomic structures depending on the chemical potential of oxygen and magnesium. The results presented provide a basis for further theoretical studies of the chemical processes on bridgmanite surfaces in the Earth's mantle and slip plane analysis.

Elucidation of temperature-programmed desorption of high-coverage hydrogen on Pt(211), Pt(221), Pt(533) and Pt(553) based on density functional theory calculations.

In this work we compute high-coverage hydrogen adsorption energies and geometries on the stepped platinum surfaces Pt(211) and Pt(533) which contain a (100)-step type and the Pt(221) and Pt(553) surface with a (111) step edge. We discuss these results in relation to ultra-high-vacuum temperature programmed desorption (TPD) data to elucidate the origin of the desorption features. Our results indicated that on surfaces with a (100)-step type, two distinct ranges of adsorption energy for the step and terrace are observed, which mirrors the TPD spectra for which we find a clear separation of the desorption peaks. For the (111) step type, the TPD spectra show much less separation of the step and terrace features, which we assign to the low individual adsorption energies for H atoms on this step edge. From our results we obtain a much clearer understanding of the surface-hydrogen bonding at high coverages and the origin of the different TPD features present for the two step types studied.

Duplication, Collapse, and Escape of Magnetic Skyrmions Revealed Using a Systematic Saddle Point Search Method.

Various transitions that a magnetic Skyrmion can undergo are found in calculations using a method for climbing up the energy surface and converging onto first order saddle points. In addition to collapse and escape through a boundary, the method identifies a transition where the Skyrmion divides and forms two Skyrmions. The activation energy for this duplication process can be similar to that of collapse and escape. A tilting of the external magnetic field for a certain time interval is found to induce the duplication process in a dynamical simulation. Such a process could turn out to be an important avenue for the creation of Skyrmions in future magnetic devices.

Efficient evaluation of atom tunneling combined with electronic structure calculations.

Methodology for finding optimal tunneling paths and evaluating tunneling rates for atomic rearrangements is described. First, an optimal JWKB tunneling path for a system with fixed energy is obtained using a line integral extension of the nudged elastic band method. Then, a calculation of the dynamics along the path is used to determine the temperature at which it corresponds to an optimal Feynman path for thermally activated tunneling (instanton) and a harmonic approximation is used to estimate the transition rate. The method is illustrated with calculations for a modified two-dimensional Müller-Brown surface but is efficient enough to be used in combination with electronic structure calculations of the energy and atomic forces in systems containing many atoms. An example is presented where tunneling is the dominant mechanism well above room temperature as an H3BNH3 molecule dissociates to form H2. Also, a solid-state example is presented where density functional theory calculations of H atom tunneling in a Ta crystal give close agreement with experimental measurements on hydrogen diffusion over a wide range in temperature.

Coherence in nonradiative transitions: internal conversion in Rydberg-excited N-methyl and N-ethyl morpholine.

The survival of coherent wavepacket motion during internal conversions is observed in relatively large molecules, N-methyl morpholine and N-ethyl morpholine, where standard models imply fast decoherence in a statistical limit. Optical excitation in the region of 194 to 230 nm excites the molecule to 3s or 3p Rydberg states, launching a wavepacket motion in the umbrella mode of the tertiary amine chromophore. In the short wavelength range, <214 nm, the molecules are excited to the 3p Rydberg state, which decays by internal conversion on a time scale of about 100 fs to the lower-lying 3s Rydberg state. Time-resolved photoionization photoelectron experiments reveal that the coherent wavepacket motion survives the internal conversion with oscillations continuing in the 3s state for several 650 fs periods before the phase lock is lost due to dephasing into the dense bath of vibrational modes of the molecule.

Ultrafast X-ray absorption study of longitudinal-transverse phonon coupling in electrolyte aqueous solution.

Ultrafast X-ray absorption spectroscopy is applied to study the conversion of longitudinal to transverse phonons in aqueous solution. Permanganate solutes serve as X-ray probe molecules that permit the measurement of the conversion of 13.5 GHz, longitudinal phonons to 27 GHz, transverse phonons that propagate with high-frequency sound speed. The experimental results, combined with QM/MM MD simulations, show that the hydrogen bond network around the charged solutes has a glass-like stiffness that persists for at least tens of picoseconds.

Nudged elastic band calculations accelerated with Gaussian process regression.

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional Müller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.

Faraday efficiency and mechanism of electrochemical surface reactions: CO2 reduction and H2 formation on Pt(111).

An atomic scale model of the electrical double layer is used to calculate the mechanism and rate of electrochemical reduction of CO2 as well as H2 formation at a Pt(111) electrode. The water layer contains solvated protons and the electrode has excess electrons at the surface. Density functional theory within the generalized gradient approximation is used to describe the electronic structure while the mechanism and activation energy of the various elementary reactions is obtained by calculating minimum energy paths using the nudged elastic band method. The applied electrical potential is deduced from the calculated work function. The optimal reaction mechanism for CO2 reduction to either methane or methanol is found and the estimated rate compared with that of the competing reaction, H2 formation. When the free energy of only the intermediates and reactants is taken into account, not the activation energy, Pt(111) would seem to be a good electrocatalyst for CO2 reduction, significantly better than Cu(111). This, however, contradicts experimental findings. Detailed calculations reported here show that the activation energy for CO2 reduction is high for both Heyrovsky and Tafel mechanisms on Pt(111) in the relevant range of applied potential. The rate-limiting step of the Heyrovsky mechanism, *COOH + H+ + e- → *CO + H2O, is estimated to have an activation energy of 0.95 eV at -0.9 V vs. standard hydrogen electrode. Under the same conditions, the activation energy for H2 formation is estimated to be only 0.5 eV. This explains why attempts to reduce CO2 using platinum electrodes have produced only H2. A comparison is made with analogous results for Cu(111) [J. Hussain et al., Procedia Comput. Sci., 2015, 51, 1865] where a reaction mechanism with low activation energy for CO2 electroreduction to methane was identified. The difference between the two electrocatalysts is discussed.

Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states.

Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn4 group. The results are in excellent agreement with previously reported experimental measurements on this system.

Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier.

The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch between the initial and final state energy wells while the polymer beads undergo diffusive motion back and forth over the barrier. We present an efficient method for evaluating the correction factor by constructing a sequence of hyperplanes starting at the transition state and calculating the probability that the system advances from one hyperplane to another towards the product. This is analogous to what is done in forward flux sampling except that there the hyperplane sequence starts at the initial state. The method is applied to the escape of polymers with up to 64 beads from a potential well. For high temperature, the results are compared with direct Langevin dynamics simulations as well as forward flux sampling and excellent agreement between the three rate estimates is found. The use of a sequence of hyperplanes in the evaluation of the recrossing correction speeds up the calculation by an order of magnitude as compared with the traditional approach. As the temperature is lowered, the direct Langevin dynamics simulations as well as the forward flux simulations become computationally too demanding, while the harmonic transition state theory estimate corrected for recrossings can be calculated without significant increase in the computational effort.