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.

Single-Atom Substituents in Copper Surfaces May Adsorb Multiple CO Molecules.

Copper is a good CO2 electroreduction catalyst as products beyond CO form, but efficiency and selectivity is low. Experiments have shown that an admixture of other elements can help, and computational screening studies have pointed out various promising candidates based on the adsorption of a single CO molecule as a descriptor. Our calculations of CO adsorption on surfaces where a first row transition metal atom replaces a Cu atom show that multiple CO molecules, not just one, bind to the substitutional atom. For Fe, Co, and Ni atoms, a decrease in binding energy is found, but the reverse trend, namely, increasing bond strength, is found for V, Cr, and Mn and the first three CO molecules. Magnetic moment, charge, and position of the substitutional atom are also strongly affected by the CO adsorption in most cases. Magnetic moment is stepwise reduced to zero, and the outward displacement of the substitutional atom increased.

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.

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

The structure of the solvation shell of the aqueous Fe3+ ion has been a subject of controversy due to discrepancies between experiments and different levels of theory. We address this issue by performing simulations for a wide range of ion concentrations, using various potential energy functions, supplemented by density functional theory calculations of selected configurations. The solvation shell undergoes abrupt transitions between two states: a hexacoordinated octahedral (OH) state and a capped trigonal prism (CTP) state with 7-fold coordination. The lifetime of these states is dependent on concentration. In dilute FeCl3 solutions, the lifetimes of both are similar (≈1 ns). However, the lifetime of the OH state increases with ion concentration, while that of the CTP state decreases slightly. When a uniform negative background charge is used instead of explicit counterions, the lifetime of the OH state is greatly overestimated. These findings underscore the need for further experimental measurements and higher-level simulations.

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.

Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface.

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.

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.

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.

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following.

Calculations of excited electronic states are carried out by finding saddle points on the surface describing the variation of the energy of the system as a function of the electronic degrees of freedom. This approach has several advantages over commonly used methods especially in the context of density functional calculations, as collapse to the ground state is avoided, and yet, the orbitals are variationally optimized for the excited state. Such a state-specific optimization makes it possible to describe excitations with large charge transfer, where calculations based on ground state orbitals, such as linear response time-dependent density functional theory, can be problematic. A generalized mode following method is presented where an nth-order saddle point is found by inverting the components of the gradient in the direction of the eigenvectors of the n lowest eigenvalues of the electronic Hessian matrix. This approach has the distinct advantage of following a chosen excited state by its saddle point order through molecular configurations where the symmetry of the single determinant wave function is broken, thereby making it possible to calculate potential energy curves even at avoided crossings, as demonstrated here in calculations of the ethylene and dihydrogen molecules. Results of calculations are, furthermore, presented for charge transfer excitations in nitrobenzene and N-phenylpyrrole, corresponding to fourth- and sixth-order saddle points, respectively, where an approximate initial estimate of the saddle point order could be found by energy minimization with excited electron and hole orbitals frozen. Finally, calculations of a diplatinum-silver complex are presented, illustrating the applicability of the method to larger molecules.

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.

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.

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials.

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H2O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

Polarizable Force Field for Acetonitrile Based on the Single-Center Multipole Expansion.

A polarizable potential function describing the interaction between acetonitrile molecules is introduced. The molecules are described as rigid and linear, with three mass sites corresponding to the CH3 group (methyl, Me), the central carbon atom (C), and the nitrogen atom (N). The electrostatic interaction is represented using a single-center multipole expansion as has been done previously for H2O [Wikfeldt et al., Phys. Chem. Chem. Phys. 15, 16542 (2013)], by including multipole moments from dipole up to and including hexadecapole, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model is free of point charges. The non-electrostatic part is described in a pair-wise fashion by a Born-Mayer repulsion and damped dispersion attraction. The potential function is parameterized to fit the interaction energy of small (CH3CN)n, n = 2-6, clusters calculated using the PBE0 hybrid functional with an additional atomic many-body dispersion contribution. The parameterized potential function is found to compare well with results of the electronic structure calculations of dissociation curves for different dimer orientations and cohesive properties (the equilibrium volume, cohesive energy, and the bulk modulus) of the α-phase of acetonitrile crystal. The average value of the molecular dipole moment obtained in the α-phase is 5.53 D, corresponding to ca. 40% increase as compared to the dipole moment of an isolated acetonitrile molecule, 3.92 D. The calculated densities of solid and liquid acetonitrile turn out to be 8-10% higher than experimental values. This appears to be caused by an overestimate of the atomic many-body dispersion interaction in the density functional calculations used as input in the parametrization of the potential function.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion.

A potential function is presented for describing a system of flexible H2O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H2O)n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Reassignment of magic numbers for icosahedral Au clusters: 310, 564, 928 and 1426.

Icosahedral Au clusters with three and four shells of atoms are found to deviate significantly from the commonly assumed Mackay structures. By introducing additional atoms in the surface shell and creating a vacancy in the center of the cluster, the calculated energy per atom can be lowered significantly, according to several different descriptions of the interatomic interaction. Analogous icosahedral structures with five and six shells of atoms are generated using the same structural motifs and are similarly found to be more stable than Mackay icosahedra. The lowest energy per atom obtained here is for clusters containing 310, 564, 928 and 1426 atoms, as compared with the commonly assumed magic numbers of 309, 561, 923 and 1415. Some of the vertices in the optimized clusters have a hexagonal ring of atoms, rather than a pentagon, with the vertex atom missing. An inner shell atom in some cases moves outwards by more than an Ångström into the surface shell at such a vertex site. This feature, as well as the wide distribution of nearest-neighbor distances in the surface layer, can strongly influence the properties of icosahedral clusters, for example catalytic activity. The structural optimization is initially carried out using the GOUST method with atomic forces estimated with the EMT empirical potential function, but the atomic coordinates are then refined by minimization using electron density functional theory (DFT) or Gaussian approximation potential (GAP). A single energy barrier is found to separate the Mackay icosahedron from a lower energy structure where a string of atoms moves outwards in a concerted manner from the center so as to create a central vacancy while placing an additional atom in the surface shell.

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting.

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Observation of Electric-Field-Induced Liberation of Guest Molecules from Clathrate Hydrate.

Clathrate hydrates can store a high density of guest molecules in cages. However, as a gas-storage material, the controllable release of guests therefrom is still challenging. Here we report on the utilization of an electric field as a control agent. Attenuated total reflectance surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS) is used to investigate the release of tetrahydrofuran (THF) from the clathrate in the electrochemical double layer (EDL). When voltage is applied, the ATR-SEIRA signal from encaged THF rapidly decreases, and the water characteristic O-H absorption peak exhibits an appreciable blue-shift. Our measurements indicate a transformation of the hydrate lattice to a less H-bonded configuration at the electrode surface. In combination with previous experimental results on the orientation of water molecules in the EDL, we propose that the strong electric field in the EDL aligns the water molecules of the clathrate and distorts the hydrate lattice structure enough to release the trapped guest molecules.

Assessment of the Accuracy of Density Functionals for Calculating Oxygen Reduction Reaction on Nitrogen-Doped Graphene.

Experimental studies of the oxygen reduction reaction (ORR) at nitrogen-doped graphene electrodes have reported a remarkably low overpotential, on the order of 0.5 V, similar to Pt-based electrodes. Theoretical calculations using density functional theory have lent support to this claim. However, other measurements have indicated that transition metal impurities are actually responsible for the ORR activity, thereby raising questions about the reliability of both the experiments and the calculations. To assess the accuracy of the theoretical calculations, various generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are employed here and calibrated against high-level wave-function-based coupled-cluster calculations (CCSD(T)) of the overpotential as well as self-interaction corrected density functional calculations and published quantum Monte Carlo calculations of O adatom binding to graphene. The PBE0 and HSE06 hybrid functionals are found to give more accurate results than the GGA and meta-GGA functionals, as would be expected, and for a low dopant concentration, 3.1%, the overpotential is calculated to be 1.0 V. The GGA and meta-GGA functionals give a lower estimate by as much as 0.4 V. When the dopant concentration is doubled, the overpotential calculated with hybrid functionals decreases, while it increases in GGA functional calculations. The opposite trends result from different potential-determining steps, the *OOH species being of central importance in the hybrid functional calculations, while the reduction of *O determines the overpotential obtained in GGA and meta-GGA calculations. The results presented here are mainly based on calculations of periodic representations of the system, but a comparison is also made with molecular flake models that are found to give erratic results due to finite size effects and geometric distortions during energy minimization. The presence of the electrolyte has not been taken into account explicitly in the calculations presented here but is estimated to be important for definitive calculations of the overpotential.

Elastic Collision Based Dynamic Partitioning Scheme for Hybrid Simulations.

In hybrid simulations, such as the QM/MM approach, the system is partitioned into regions that are treated at different levels of theory. The key question then becomes how to evaluate the interactions between particles on opposite sides of the boundary. One approach is to place the boundary in such a way that particles near the boundary on both sides are of the same type, thus simplifying the evaluation of the interactions. If mobile particles are present, such as solvent molecules, and particles are allowed to cross the boundary, the conservation of energy and atomic forces is problematic unless the computational effort is increased significantly. By preventing particles from crossing the boundary but allowing the boundary to be flexible, an accurate estimate of average thermodynamic properties is obtained in principle as illustrated by the flexible inner region ensemble separator (FIRES) method [C. Rowley and B. Roux, J. Chem. Theory Comput. 2012, 8, 3526]. In FIRES, a harmonic restraint is applied to particles near the boundary. Therefore, it can occur that particle cross the boundary to some extent resulting in anomalies in the particle density. Here, a constraint approach is presented where particles instantaneously scatter from the boundary. This scattering-adapted FIRES (SAFIRES) implementation makes use of a variable-time-step propagation algorithm where the time step is scaled automatically to identify the moment a collision should occur. If the length of the time step is kept constant, this propagator reduces to a regular Langevin dynamics algorithm, and to the velocity Verlet algorithm for conservative dynamics if the friction coefficient is set to zero. Correct average ensemble statistics are obtained as demonstrated in simulations where, for testing purposes, the particles in the two regions are treated at the same level of theory, namely, a homogeneous Lennard-Jones (LJ) liquid and liquid water based on the TIP4P potential function. In order to illustrate this approach in solid-liquid interface simulations, a LJ liquid in contact with the surface of a crystal is also simulated. The simulations using SAFIRES are shown to reproduce the unconstrained reference simulations without significant deviations in the particle density and the dynamics are shown to conserve energy when coupling to the heat bath is turned off.

Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following.

The climbing image nudged elastic band method (CI-NEB) is used to identify reaction coordinates and to find saddle points representing transition states of reactions. It can make efficient use of parallel computing as the calculations of the discretization points, the so-called images, can be carried out simultaneously. In typical implementations, the images are distributed evenly along the path by connecting adjacent images with equally stiff springs. However, for systems with a high degree of flexibility, this can lead to poor resolution near the saddle point. By making the spring constants increase with energy, the resolution near the saddle point is improved. To assess the performance of this energy-weighted CI-NEB method, calculations are carried out for a benchmark set of 121 molecular reactions. The performance of the method is analyzed with respect to the input parameters. Energy-weighted springs are found to greatly improve performance and result in successful location of the saddle points in less than a thousand energy and force evaluations on average (about a hundred per image) using the same set of parameter values for all of the reactions. Even better performance is obtained by stopping the calculation before full convergence and complete the saddle point search using an eigenvector following method starting from the location of the climbing image. This combination of methods, referred to as NEB-TS, turns out to be robust and highly efficient as it reduces the average number of energy and force evaluations down to a third, to 305. An efficient and flexible implementation of these methods has been made available in the ORCA software.