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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. [ABSTRACT FROM AUTHOR]

The structure and properties of self-trapped excitons (STE), were investigated using density functional theory (DFT) and wave function-based [UHF, UMP2, CAS-SCF, and CCSD(T)] electronic structure methods. The DFT results were compared to those obtained using the different wave function-based electronic structure methods that treat the electron correlation and exchange with varying degrees of accuracy. The calculations were carried out on cluster configurations extracted from supercell DFT calculations of the STE in α-quartz. Two luminescent STEs were found, as well as a nonradiative state at a crossing of the singlet and triplet surfaces. One of the luminescent STEs is the same as that previously found by Fisher, Hayes, and Stoneham [J. Phys.: Condens. Matter 2, 6707 (1990)]. It was furthermore determined that the PW91 functional underestimates the energy of the triplet state, and that this error is greater with greater delocalization of the excess spin density of the state. [ABSTRACT FROM AUTHOR]

Experimental diffraction peaks and resonance splittings are analyzed with a close coupling scattering calculation to give a consistent He–graphite interaction potential. The interaction is modeled as a sum of effective He–C pair interactions. Previous, more approximate, estimates of bound state matrix elements of the potential were 30% larger than present estimates. The corrugation of the equipotential surface is estimated to be a little smaller than previous ‘‘hard wall’’ estimates. The results are compared with recent ab initio potentials. [ABSTRACT FROM AUTHOR]

Transitions between magnetic states of one and two ring kagome spin ice elements consisting of 6 and 11 prolate magnetic islands are calculated and the lifetime of the ground states evaluated using harmonic transition state theory and the stationary state approximation. The calculated values are in close agreement with experimental lifetime measurements made by Farhan and co-workers (Farhan et al 2013 Nat. Phys. 9 375) when values of the parameters in the Hamiltonian are chosen to be best estimates for a single island, obtained from measurements and micromagnetic modeling. The effective pre-exponential factor in the Arrhenius rate law for the elementary steps turns out to be quite small, on the order of 109 s-1, three orders of magnitude smaller than has been assumed in previous analysis of the experimental data, while the effective activation energy is correspondingly lower than the previous estimate. The application of an external magnetic field is found to strongly affect the energy landscape of the system. Even a field of 4 mTcan eliminate states that correspond to ground states in the absence of a field. The theoretical approach presented here and the close agreement found with experimental data demonstrates that the properties of spin ice systems can be calculated using the tools of rate theory and a Hamiltonian parametrized only from the properties of a single island. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Calculations of skyrmions in antiferromagnets (AFMs) are presented, and their properties compared with skyrmions in corresponding ferromagnets (FMs). The rates of skyrmion collapse and escape through the boundary of a track, as well as the binding to and collapse at a non-magnetic impurity, are calculated as a function of an applied magnetic field. The activation energy for skyrmion annihilation is the same in AFMs and corresponding FMs in the absence of an applied magnetic field. The pre-exponential factor in the Arrhenius rate law is, however, different because skyrmion dynamics is different in the two systems. An applied magnetic field has opposite effects on skyrmions in the two types of materials. In AFMs, the rate of collapse of skyrmions as well as the rate of escape through the edge of a magnetic strip decreases slightly with increasing field, while these rates increase strongly for a skyrmion in the corresponding FMs when the field is directed antiparallel to the magnetization in the center of the skyrmion. A non-magnetic impurity is less likely to trap a skyrmion in AFMs, especially in the presence of a magnetic field. This, together with the established fact that a spin polarized current moves skyrmions in AFMs in the direction of the current, while in FMs skyrmions move at an angle to the current, demonstrates that skyrmions in AFMs have several advantageous properties over skyrmions in FMs for memory and spintronic devices. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Computer simulations of surface processes can reveal unexpected insight regarding atomic-scale structure and transitions. Here, the strengths and weaknesses of some commonly used approaches are reviewed as well as promising avenues for improvements. The electronic degrees of freedom are usually described by gradient- dependent functionals within Kohn-Sham density functional theory. Although this level of theory has been remarkably successful in numerous studies, several important problems require a more accurate theoretical description. It is important to develop new tools to make it possible to study, for example, localized defect states and band gaps in large and complex systems. Preliminary results presented here show that orbital density-dependent functionals provide a promising avenue, but they require the development of new numerical methods and substantial changes to codes designed for Kohn-Sham density functional theory. The nuclear degrees of freedom can, in most cases, be described by the classical equations of motion; however, they still pose a significant challenge, because the time scale of interesting transitions, which typically involve substantial free energy barriers, is much longer than the time scale of vibrations-often 10 orders of magnitude. Therefore, simulation of diffusion, structural annealing, and chemical reactions cannot be achieved with direct simulation of the classical dynamics. Alternative approaches are needed. One such approach is transition state theory as implemented in the adaptive kinetic Monte Carlo algorithm, which, thus far, has relied on the harmonic approximation but could be extended and made applicable to systems with rougher energy landscape and transitions through quantum mechanical tunneling. [ABSTRACT FROM AUTHOR]

Abstract: Long-timescale simulations of hydrogen atom diffusion in aluminum at low concentration were carried out to study the effect grain boundaries can have on the diffusion mechanism and diffusion rate. Three different grain boundaries were studied: twist, tilt and general, twist+tilt, grain boundaries. The adaptive kinetic Monte Carlo method was used to simulate the system over time intervals spanning tens of microseconds. A potential function of the effective medium form was parametrized to density functional theory calculations and used to describe the atomic interactions. The twist boundary turns out to block diffusion across the boundary – only a few high-energy sites are found in the boundary layer. However, diffusion parallel to the boundary is slightly enhanced because of the reduced configuration space. The twist and twist+tilt grain boundaries have strong binding sites within the boundary layer, up to 0.1 and 0.3eV stronger, respectively, than binding sites in the crystal. In the latter case, the H atom spends more than 99% of the time in the grain boundary layer and diffusion parallel to the grain boundary occurs only when the H atom re-enters a crystal grain. Because of the trapping, the diffusion is reduced by more than an order of magnitude compared with the crystal. [Copyright &y& Elsevier]

Abstract: Triplet electron–hole excitations were introduced into amorphous silica to study self-trapping (localization) and damage formation using density functional theory. Multiple self-trapped exciton (STE) states are found that can be differentiated based on the luminescence energy, the localization and distribution of the excess spin density of the triplet state, and relevant structural data, including the presence or absence of broken bonds. The trapping is shown to be affected by the relaxation response of the silica network, and by comparing results of quartz and amorphous silica systems the effects of the inherent disordered structures on exciton self-trapping are revealed. A key result is that the process of exciton trapping can lead directly to the formation of point defects, without thermal activation. The proposed mechanism includes a non-radiative decay from the excited to the ground state followed by structure relaxation to a defect configuration in the ground state. [Copyright &y& Elsevier]

An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first derivative of the energy and can, therefore, easily be applied in plane wave based density-functional theory calculations. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al(100) surface, and dissociative adsorption of CH[sub 4] on an Ir(111) surface. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The rate of escape of polymers from a two-dimensionally confining potential well has been evaluated using self-avoiding as well as ideal chain representations of varying length, up to 80 beads. Long timescale Langevin trajectories were calculated using the path integral hyperdynamics method to evaluate the escape rate. A minimum is found in the rate for self-avoiding polymers of intermediate length while the escape rate decreases monotonically with polymer length for ideal polymers. The increase in the rate for long, self-avoiding polymers is ascribed to crowding in the potential well which reduces the free energy escape barrier. An effective potential curve obtained using the centroid as an independent variable was evaluated by thermodynamic averaging and Kramers rate theory then applied to estimate the escape rate. While the qualitative features are well reproduced by this approach, it significantly overestimates the rate, especially for the longer polymers. The reason for this is illustrated by constructing a two-dimensional effective energy surface using the radius of gyration as well as the centroid as controlled variables. This shows that the description of a transition state dividing surface using only the centroid fails to confine the system to the region corresponding to the free energy barrier and this problem becomes more pronounced the longer the polymer is. A proper definition of a transition state for polymer escape needs to take into account the shape as well as the location of the polymer. [ABSTRACT FROM AUTHOR]

Self-consistent calculations using the Perdew-Zunger self-interaction correction (PZ-SIC) to local density and gradient dependent energy functionals are presented for the binding energy and equilibrium geometry of small molecules as well as energy barriers of reactions. The effect of the correction is to reduce binding energy and bond lengths and increase activation energy barriers when bond breaking is involved. The accuracy of the corrected functionals varies strongly, the correction to the binding energy being too weak for the local density approximation but too strong for the gradient dependent functionals considered. For the Perdew, Burke, and Ernzerhof (PBE) functional, a scaling of the PZ-SIC by one half gives improved results on average for both binding energy and bond lengths. The PZ-SIC does not necessarily give more accurate total energy, but it can result in a better cancellation of errors. An essential aspect of these calculations is the use of complex orbitals. A restriction to real orbitals leads to less accurate results as was recently shown for atoms [S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A 84, 050501 (2011)]. The molecular geometry of radicals can be strongly affected by PZ-SIC. An incorrect, non-linear structure of the C2H radical predicted by PBE is corrected by PZ-SIC. The CH3 radical is correctly predicted to be planar when complex orbitals are used, while it is non-planar when the PZ-SIC calculation is restricted to real orbitals. [ABSTRACT FROM AUTHOR]

The results of theoretical calculations of associative desorption of CH4 and H2 from the Ni(111) surface are presented. Both minimum-energy paths and classical dynamics trajectories were generated using density-functional theory to estimate the energy and atomic forces. In particular, the recombination of a subsurface H atom with adsorbed CH3 (methyl) or H at the surface was studied. The calculations do not show any evidence for enhanced CH4 formation as the H atom emerges from the subsurface site. In fact, there is no minimum-energy path for such a concerted process on the energy surface. Dynamical trajectories started at the transition state for the H-atom hop from subsurface to surface site also did not lead to direct formation of a methane molecule but rather led to the formation of a thermally excited H atom and CH3 group bound to the surface. The formation (as well as rupture) of the H–H and C–H bonds only occurs on the exposed side of a surface Ni atom. The transition states are quite similar for the two molecules, except that in the case of the C–H bond, the underlying Ni atom rises out of the surface plane by 0.25 Å. Classical dynamics trajectories started at the transition state for desorption of CH4 show that 15% of the barrier energy, 0.8 eV, is taken up by Ni atom vibrations, while about 60% goes into translation and 20% into vibration of a desorbing CH4 molecule. The most important vibrational modes, accounting for 90% of the vibrational energy, are the four high-frequency CH4 stretches. By time reversibility of the classical trajectories, this means that translational energy is most effective for dissociative adsorption at low-energy characteristic of thermal excitations but energy in stretching modes is also important. Quantum-mechanical tunneling in CH4 dissociative adsorption and associative desorption is estimated to be important below 200 K and is, therefore, not expected to play an important role under typical conditions. An unexpected mechanism for the rotation of the adsorbed methyl group was discovered and illustrated a strong three-center C–H–Ni contribution to the methyl-surface bonding. [ABSTRACT FROM AUTHOR]

We simulate the compression of a two-component Lennard-Jones liquid at a variety of constant temperatures using a molecular dynamics algorithm in an isobaric–isothermal ensemble. The viscosity of the liquid increases with pressure, undergoing a broadened transition into a structurally arrested, amorphous state. This transition, like the more familiar one induced by cooling, is correlated with a significant increase in icosahedral ordering. In fact, the structure of the final state, as measured by an analysis of the bonding, is essentially the same in the glassy, frozen state whether produced by squeezing or by cooling under pressure. We have computed an effective hard-sphere packing fraction at the transition, defining the transition pressure or temperature by a cutoff in the diffusion constant, analogous to the traditional laboratory definition of the glass transition by an arbitrary, low cutoff in viscosity. The packing fraction at this transition point is not constant, but is consistently higher for runs compressed at higher temperature. We show that this is because the transition point defined by a constant cutoff in the diffusion constant is not the same as the point of structural arrest, at which further changes in pressure induce no further structural changes, but that the two alternate descriptions may be reconciled by using a thermally activated cutoff for the diffusion constant. This enables estimation of the characteristic activation energy for diffusion at the point of structural arrest. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A theoretical basis is presented for reversible work evaluation of transition rates within the framework of transition state theory. The method involves computing statistical averages of forces without having to evaluate transition state partition functions or densities, and therefore eliminates the need for a harmonic reference system. The method can be applied to systems of high dimensionality which is particularly important in calculations on quantum systems, where each quantum particle may be represented by several images in a Feynman path integral chain. The relationship between this method and the fixed centroid method of Gillan and centroid density theories is established. The various methods are compared on a model quantum system consisting of an Eckart barrier coupled to a harmonic oscillator. [ABSTRACT FROM AUTHOR]

The mechanism and activation energy for the annihilation of a magnetic skyrmion is studied by finding the minimum energy path for the transition in a system described by a Heisenberg-type Hamiltonian extended to include dipole-dipole, Dzyaloshinskii-Moriya, and anisotropy interactions so as to represent a Co monolayer on a Pt(111) surface. The annihilation mechanism involves isotropic shrinking of the skyrmion and slow increase of the energy until the transition state is reached after which the energy drops abruptly as the ferromagnetic final state forms. The maximum energy along the minimum energy path, which gives an estimate of the activation energy within the harmonic approximation of transition state theory, is found to be in excellent agreement with direct Langevin dynamics simulations at relatively high temperature carried out by Rohart et al. [Phys. Rev. B 93, 214412 (2016)]. The dipole-dipole interaction, the computationally most demanding term in the Hamiltonian, is found to be important but its effect on the stability of the skyrmion and shape of the transition path can be mimicked accurately by reducing the anisotropy constant in the Hamiltonian. [ABSTRACT FROM AUTHOR]

The effect of solvation on the free energy of reaction intermediates adsorbed on electrocatalyst surfaces can significantly change the thermochemical overpotential, but accurate calculations of this are challenging. Here, we present computational estimates of the solvation energy for reaction intermediates in oxygen reduction reaction (ORR) on a B-doped graphene (BG) model system where the overpotential is found to reduce by up to 0.6 V due to solvation. BG is experimentally reported to be an active ORR catalyst but recent computational estimates using state-of-the-art hybrid density functionals in the absence of solvation effects have indicated low activity. To test whether the inclusion of explicit solvation can bring the calculated activity estimates closer to the experimental reports, up to 4 layers of water molecules are included in the simulations reported here. The calculations are based on classical molecular dynamics and local minimization of energy using atomic forces evaluated from electron density functional theory. Data sets are obtained from regular and coarse-grained dynamics, as well as local minimization of structures resampled from dynamics simulations. The results differ greatly depending on the method used and the solvation energy estimates are deemed untrustworthy. It is concluded that a significantly larger number of water molecules is required to obtain converged results for the solvation energy. As the present system includes up to 139 atoms, it already strains the limits of computational feasibility, so this points to the need for a hybrid simulation approach where efficient simulations of much larger number of solvent molecules is carried out using a lower level of theory while retaining the higher level of theory for the reacting molecules as well as their near neighbors and the catalyst. The results reported here provide a word of caution to the computational catalysis community: activity predictions can be inaccurate if too few solvent molecules are included in the calculations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Calculations of stable and metastable magnetic states as well as minimum energy paths for transitions between states are carried out using a noncollinear extension of the multiple-impurity Alexander-Anderson model and a magnetic force theorem which is derived and used to evaluate the total energy gradient with respect to orientation of magnetic moments—an important tool for efficient navigation on the energy surface. By using this force theorem, the search for stable and metastable magnetic states as well as minimum energy paths revealing the mechanism and activation energy of transitions can be carried out efficiently. For Fe monolayer on W( 110) surface, the model gives magnetic moment as well as exchange coupling between nearest and next-nearest neighbors that are in good agreement with previous density functional theory calculations. When applied to nanoscale Fe islands on this surface, the magnetic moment is predicted to be 10% larger for atoms at the island rim, explaining in part an experimentally observed trend in the energy barrier for magnetization reversal in small islands. Surprisingly, the magnetic moment of the atoms does not change much along the minimum energy path for the transitions, which for islands containing more than 15 atom rows along either [001] or [1̄10] directions involves the formation of a thin, temporary domain wall. A noncollinear magnetic state is identified in a 7 × 7 atomic row Fe island where the magnetic moments are arranged in an antivortex configuration with the central ones pointing out of the (110) plane. This illustrates how the model can describe complicated exchange interactions even though it contains only a few parameters. The minimum energy path between this antivortex state and the collinear ground state is also calculated and the thermal stability of the antivortex state estimated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The effect of hydrogen adsorption on the magnetic properties of an Fe3 cluster immersed in a Cu(111) surface has been calculated using density functional theory and the results used to parametrize an Alexander-Anderson model which takes into account the interaction of d electrons with itinerant electrons. A number of adatom configurations containing one to seven H atoms were analyzed. The sequential addition of hydrogen atoms is found to monotonically reduce the total magnetic moment of the cluster with the effect being strongest when the H atoms sit at low-coordinated sites. Decomposition of the charge density indicates a transfer of 0.3 electrons to each of the H atoms from both the Fe atoms and from the copper substrate, irrespective of adsorption site and coverage. The magnetic moment of only the nearest neighbor Fe atoms is reduced, mainly due to increased population of minority spin d states. This can be modeled by increased indirect coupling of d states via the conduction s band in the Alexander-Anderson model. [ABSTRACT FROM AUTHOR]

Theoretical calculations of thermal spin transitions in nanoscale clusters on a surface are presented. The mechanisms for magnetization reversal are identified and the activation energy and pre-exponential factor for the rate are evaluated using a recently developed harmonic transition state theory and a Heisenberg-type Hamiltonian. A maximum is found in the pre-exponential factor as a function of cluster size corresponding to a crossover from a uniform rotation mechanism to temporary domain wall formation. As the islands grow, the energy barrier increases up to a limit where the domain wall is fully established. For larger islands, the minimum energy path becomes flat resulting in a significant recrossing correction to the transition state theory estimate of the rate. The parameters of the Hamiltonian are chosen to mimic Fe clusters on a W(l 10) surface, a system that has previously been studied extensively in the laboratory and the calculated results are found to be in close agreement with the reported measurements. [ABSTRACT FROM AUTHOR]

Abstract: Two forms of the methanol electro-oxidation intermediate with stoichiometry C:H:O, COH (hydroxymethylidyne) and HCO (formyl), on Pt (111) with and without coadsorbed water were studied using density functional theory calculations. The structure, adsorption energy and stability with respect to dissociation were calculated. Both HCx2013;OH were stable on clean Pt (111) and with a single coadsorbed water molecule, while only the HCO configuration was stable in the presence of a whole water layer. The vibrational modes of HCidge site showed no mode around 1700cm−1 characteristic of C making it hard to distinguish it from C–OH. [Copyright &y& Elsevier]

A rate theory for thermally activated transitions in spin systems is presented. It is based on a transition-state approximation derived from Landau-Lifshitz equations of motion and quadratic expansion of the energy surface at minima and first order saddle points. While the flux out of the initíal state vanishes at first order saddle points, the integrated flux over the hyperplanar transition state is nonzero and gives a rate estimate in good agreement with direct dynamical simulations of test systems over a range in damping constant. The preexponential factor obtained for transitions in model systems representing nanoclusters with 3 to 139 transition metal adatoms is on the order of 1011 to 1013 s-1, similar to that of atomic rearrangements. [ABSTRACT FROM AUTHOR]

Abstract: Surface diffusion of water monomer, dimer, and trimer on the (111) terrace, (221) and (322) stepped, and (763) and (854) kinked surfaces of platinum was studied by density functional theory using the PW91 approximation to the energy functional. Monomer diffusion on the terrace is facile, with an activation barrier of 0.20eV, while dimer and trimer diffusions are restricted due to their high activation barriers of 0.43 and 0.48eV, respectively. During monomer diffusion on the terrace the O–Pt distance increases by 0.54Å, about 23% of the initial distance of 2.34Å. The calculated rate of monomer diffusion hops is in good agreement with the onset temperature of diffusion measurements of Daschbach et al., J. Chem. Phys., 120 (2004) 1516. Alternative monomer diffusion pathways, in which the molecule rolls or flips, were also found. These pathways have diffusion barriers of 0.22eV. During dimer diffusion on the terrace, the donor molecule rises 0.4Å at the saddle point, while the acceptor rises by only 0.03Å. Monomer diffusion up to steps and kinks, with activation barriers of 0.11–0.13eV, facilitate chain formation on top of step edges. The energy landscape of monomer diffusion from terrace to step to kink sites is downhill with a maximum activation barrier of 0.26eV. A model for water adsorption is presented in which monomer diffusion leads to concurrent formation of terrace clusters and population of steps/kinks, the latter consistent with the STM measurements of Morgenstern et al., Phys. Rev. Lett., 77 (1996) 703. [Copyright &y& Elsevier]

The problem of sampling low lying, first-order saddle points on a high dimensional surface is discussed and a method presented for improving the sampling efficiency. The discussion is in the context of an energy surface for a system of atoms and thermally activated transitions ill solids treated within the harmonic approximation to transition state theory. Given a local minimum as all initial state and a small, initial displacement, the minimum-mode following method is used to climb up to a saddle point. The goal is to sample as many of the low lying saddle points as possible when such climbs are repeated from different initial displacements. Various choices for the distribution of initial displacements are discussed and a comparison made between (1) displacements along eigenmodes at the minimum, (2) purely random displacements with a maximum cutoff, and (3) Gaussian distribution of displacements. The last choice is found to give best overall results in two test problems studied, a heptamer island on a surface and a grain boundary in a metal. A method referred to as "skipping-path method" is presented to reduce redundant calculations when a climb heads towards a saddle point that has already been identified. The method is found to reduce the computational effort of finding new saddle points to as little as a third, especially when a thorough sampling is performed. [ABSTRACT FROM AUTHOR]

Abstract: Adsorption and rotation of water monomer, dimer, and trimer on the (111) terrace, (221) and (322) stepped, and (763) and (854) kinked surfaces of platinum were studied by density functional theory calculations using the PW91 approximation to the energy functional. On the (111) terrace, water monomer and the donor molecule of the dimer and trimer adsorb at atop sites. The per-molecule adsorption energies of the monomer, dimer, and trimer are 0.30, 0.45, and 0.48eV, respectively. Rotation of monomers, dimers, and trimers on the terrace is facile with energy barriers of 0.02eV or less. Adsorption on steps and kinks is stronger than on the terrace, as evidenced by monomer adsorption energies of 0.46 to 0.55eV. On the (221) stepped surface the zigzag extended configuration is most stable with a per-molecule adsorption energy of 0.57eV. On the (322) stepped surface the dimer, two configurations of the trimer, and the zigzag configuration have similar adsorption energies of 0.55±0.02eV. Hydrogen bonding is strongest in the dimer and trimer adsorbed on the terrace, with respective energies of 0.30 and 0.27eV, and accounts for their increased adsorption energies relative to the monomer. Hydrogen bonding is weak to moderate for adsorption at steps, with energies of 0.04 to 0.15eV, as the much stronger water–metal interactions inhibit adsorption geometries favorable to hydrogen bonding. Correlations of hydrogen bond angles and energies with hydrogen bond lengths are presented. On the basis of these DFT/PW91 results, a model for water cluster formation on the Pt(111) surface can be formulated where kink sites nucleate chains along the top of step edges, consistent with the experimental findings of Morgenstern et al., Phys. Rev. Lett., 77 (1996) 703. [Copyright &y& Elsevier]

Abstract: The deposition and ripening of Pd atoms on the MgO(100) surface are modeled using kinetic Monte Carlo simulations. The density of Pd islands is obtained by simulating the deposition of 0.1ML in 3min. Two sets of kinetic parameters are tested and compared with experiment over a 200–800K temperature range. One model is based upon parameters obtained by fitting rate equations to experimental data and assuming the Pd monomer is the only diffusing species. The other is based upon transition rates obtained from density functional theory calculations which show that small Pd clusters are also mobile. In both models, oxygen vacancy defects on the MgO surface provide strong traps for Pd monomers and serve as nucleation sites for islands. Kinetic Monte Carlo simulations show that both models reproduce the experimentally observed island density versus temperature, despite large differences in the energetics and different diffusion mechanisms. The low temperature Pd island formation at defects is attributed to fast monomer diffusion to defects in the rate-equation-based model, whereas in the DFT-based model, small clusters form already on terraces and diffuse to defects. In the DFT-based model, the strong dimer and trimer binding energies at charged oxygen vacancy defects prevent island ripening below the experimentally observed onset temperature of 600K. [Copyright &y& Elsevier]

Abstract: An algorithm is presented for carrying out decomposition of electronic charge density into atomic contributions. As suggested by Bader [R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990], space is divided up into atomic regions where the dividing surfaces are at a minimum in the charge density, i.e. the gradient of the charge density is zero along the surface normal. Instead of explicitly finding and representing the dividing surfaces, which is a challenging task, our algorithm assigns each point on a regular (x, y, z) grid to one of the regions by following a steepest ascent path on the grid. The computational work required to analyze a given charge density grid is approximately 50 arithmetic operations per grid point. The work scales linearly with the number of grid points and is essentially independent of the number of atoms in the system. The algorithm is robust and insensitive to the topology of molecular bonding. In addition to two test problems involving a water molecule and NaCl crystal, the algorithm has been used to estimate the electrical activity of a cluster of boron atoms in a silicon crystal. The highly stable three-atom boron cluster, B3I is found to have a charge of −1.5e, which suggests approximately 50% reduction in electrical activity as compared with three substitutional boron atoms. [Copyright &y& Elsevier]

The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

We report results of long timescale adaptive kinetic Monte Carlo simulations aimed at identifying possible molecular reordering processes on both proton-disordered and ordered (Fletcher) basal plane (0001) surfaces of hexagonal ice. The simulations are based on a force field for flexible molecules and span a time interval of up to 50 \xs at a temperature of 100 K, which represents a lower bound to the temperature range of earth's atmosphere. Additional calculations using both density functional theory and an ab initio based polarizable potential function are performed to test and refine the force field predictions. Several distinct processes are found to occur readily even at this low temperature, including concerted reorientation (flipping) of neighboring surface molecules, which changes the pattern of dangling H-atoms, and the formation of interstitial defects by the downwards motion of upper-bilayer molecules. On the proton-disordered surface, one major surface roughening process is observed that significantly disrupts the crystalline structure. Despite much longer simulation time, such roughening processes are not observed on the highly ordered Fletcher surface which is energetically more stable because of smaller repulsive interaction between neighboring dangling H-atoms. However, a more localized process takes place on the Fletcher surface involving a surface molecule transiently leaving its lattice site. The flipping process provides a facile pathway of increasing proton-order and stabilizing the surface, supporting a predominantly Fletcher-like ordering of low-temperature ice surfaces. Our simulations also show that eventual proton-disordered patches on the surface may induce significant local reconstructions. Further, a subset of the molecules on the Fletcher surface are susceptible to forming interstitial defects which might provide active sites for various chemical reactions in the atmosphere. [ABSTRACT FROM AUTHOR]

Theoretical calculations of Rydberg excited states of molecular clusters consisting of N,Ndimethylisopropylamine molecules using a Perdew-Zunger self-interaction corrected energy functional are presented and compared with results of resonant multiphoton ionization measurements. The binding energy of the Rydberg electron in the monomer is calculated to be 2.79 eV and 2.27 eV in the 3s and 3p state, respectively, which compares well with measured values of 2.88 eV and 2.21 eV. Three different stable configurations of the dimer in the ground state were found using an energy functional that includes van der Waals interaction. The lowest ground state energy conformation has the two N-atoms widely separated, by 6.2 Â, while the Rydberg state energy is lowest for a configuration where the N-atoms of the two molecules come close together, separated by 3.7 Â. This conformational change is found to lower the Rydberg electron binding energy by 0.2 eV. The self-interaction corrected functional gives a highly localized hole on one of the two molecules, unlike results obtained using the PBE functional or the hybrid B3LYP functional which give a delocalized hole. For the trimer, the self-interaction corrected calculation gives a Rydberg electron binding energy lowered further by 0.13 eV as compared with the dimer. The calculated results compare well with trends observed in experimental measurements. The reduction of the Rydberg electron binding energy with cluster size can be ascribed to an effective delocalization of the positive charge of the hole by the induced and permanent dipole moments of the neighboring molecules. A further decrease observed to occur on a time scale of tens of ps can be ascribed to a structural rearrangement of the clusters in the Rydberg state where molecules rotate to orient their dipoles in response to the formation of the localized hole. [ABSTRACT FROM AUTHOR]

A method is presented for generating a good initial guess of a transition path between given initial and final states of a system without evaluation of the energy. An objective function surface is constructed using an interpolation of pairwise distances at each discretization point along the path and the nudged elastic band method then used to find an optimal path on this image dependent pair potential (IDPP) surface. This provides an initial path for the more computationally intensive calculations of a minimum energy path on an energy surface obtained, for example, by ab initio or density functional theory. The optimal path on the IDPP surface is significantly closer to a minimum energy path than a linear interpolation of the Cartesian coordinates and, therefore, reduces the number of iterations needed to reach convergence and averts divergence in the electronic structure calculations when atoms are brought too close to each other in the initial path. The method is illustrated with three examples: (1) rotation of a methyl group in an ethane molecule, (2) an exchange of atoms in an island on a crystal surface, and (3) an exchange of two Si-atoms in amorphous silicon. In all three cases, the computational effort in finding the minimum energy path with DFT was reduced by a factor ranging from 50% to an order of magnitude by using an IDPP path as the initial path. The time required for parallel computations was reduced even more because of load imbalance when linear interpolation of Cartesian coordinates was used. [ABSTRACT FROM AUTHOR]

A method is presented for calculating the wave function and energy of Rydberg excited states of molecules. A good estimate of the Rydberg state orbital is obtained using ground state density functional theory including Perdew-Zunger self-interaction correction and an optimized effective potential. The total energy of the excited molecule is obtained using the Delta Self-Consistent Field method where an electron is removed from the highest occupied orbital and placed in the Rydberg orbital. Results are presented for the first few Rydberg states of NH3, H2O, H2CO, C2H4, and N(CH3)3. The mean absolute error in the energy of the 33 molecular Rydberg states presented here is 0.18 eV. The orbitals are represented on a real space grid, avoiding the dependence on diffuse atomic basis sets. As in standard density functional theory calculations, the computational effort scales as NM2 where N is the number of orbitals and M is the number of grid points included in the calculation. Due to the slow scaling of the computational effort with system size and the high level of parallelism in the real space grid approach, the method presented here makes it possible to estimate Rydberg electron binding energy in large molecules. [ABSTRACT FROM AUTHOR]

Magnetic skyrmions are nano-scale magnetic states that could be used in various spintronics devices. A central issue is the mechanism and rate of various possible annihilation processes and the lifetime of metastable skyrmions. While most studies have focused on classical over-the-barrier mechanism for annihilation, it is also possible that quantum mechanical tunneling through the energy barrier takes place. Calculations of the lifetime of magnetic skyrmions in a two-dimensional lattice are presented and the rate of tunneling compared with the classical annihilation rate. A remarkably strong variation in the onset temperature for tunneling and the lifetime of the skyrmion is found as a function of the values of parameters in the extended Heisenberg Hamiltonian, i.e. the out-of-plane anisotropy, Dzyaloshinskii–Moriya interaction and applied magnetic field. Materials parameters and conditions are identified where the onset of tunneling could be observed on a laboratory time scale. In particular, it is predicted that skyrmion tunneling could be observed in the PdFe/Ir(111) system when an external magnetic field on the order of 6T is applied. [ABSTRACT FROM AUTHOR]

A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH[sub 4] dissociative adsorption on Ir(111) and H[sub 2] on Si(100) using plane wave based density functional theory are presented. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We have studied the electric field near water clusters and in ice Ih using first principles calculations. We employed Mo\ller-Plesset perturbation theory (MP2) for the calculations of the clusters up to and including the hexamer, and density functional theory (DFT) with a gradient dependent functional [Perdew-Wang (PW91)] for ice Ih as well as the clusters. The electric field obtained from the first principles calculations was used to test the predictions of an induction model based on single center multipole moments and polarizabilities of an isolated water molecule. We found that the fields obtained from the induction model agree well with the first principles results when the multipole expansion is carried out up to and including the hexadecapole moment, and when polarizable dipole and quadrupole moments are included. This implies that accurate empirical water interaction potential functions transferable to various environments such as water clusters and ice surfaces could be based on a single center multipole expansion carried out up to the hexadecapole. Since point charges are not included, the computationally intensive Ewald summations can be avoided. Molecular multipole moments were also extracted from the first principles charge density using zero flux dividing surfaces as proposed by Bader. Although the values of the various molecular multipoles obtained with this method are quite different from the ones resulting from the induction model, the rate of convergence of the electric field is, nevertheless, quite similar. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract A global optimization procedure is used to predict the structure and electronic properties of the b = c [001] edge dislocation in rutile TiO 2. Over 1000 different atomic configurations have been generated using both semi-empirical and density functional theory estimates of the energy of the system to identify the most stable structure. Both stoichiometric and oxygen deficient dislocation core structures are predicted to be stable depending on the oxygen chemical potential. The latter is associated with Ti3+ species in the dislocation core. The dislocation is predicted to act as a trap for electrons but not for holes suggesting they are not strong recombination centers. The predicted structures and properties are found to be consistent with experimental results obtained using scanning transmission electron microscopy and electron energy loss spectroscopy on samples produced using the bicrystal approach. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Abstract The stability of magnetic skyrmions against thermal fluctuations and external perturbations is investigated within the framework of harmonic transition state theory for magnetic degrees of freedom. The influence of confined geometry and atomic scale non-magnetic defects on the skyrmion lifetime is estimated. It is shown that a skyrmion on a track has lower activation energy for annihilation and higher energy for nucleation if the size of the skyrmion is comparable with the width of the track. Two mechanisms of skyrmion annihilation are considered: inside the track and escape through the boundary. For both mechanisms, the dependence of activation energy on the track width is calculated. Non-magnetic defects are found to localize skyrmions in their neighborhood and strongly decrease the activation energy for creation and annihilation. This is in agreement with experimental measurements that have found nucleation of skyrmions in presence of spin-polarized current preferably occurring near structural defects. [ABSTRACT FROM AUTHOR]

[Display omitted] When CO 2 is encapsulated in clathrate hydrate, where the concentration is nearly-two orders of magnitude greater than in saturated aqueous solution, the rate of the CO 2 reduction reaction (CO 2 RR) increases, and the corresponding Faradaic efficiency becomes up to three times higher than that of the competing hydrogen evolution reaction (HER) at applied potential of −0.5 to −0.7 vs RHE. The energy efficiency of the CO 2 RR is correspondingly increased. The enhanced CO 2 RR in clathrate is ascribed to non-equilibrium release of the CO 2 due to the electric field near the electrode, analogous to what has been observed recently for tetrahydrofuran [Li et al. J. Phys. Chem. Letters 125, 13802 (2021)]. This raises the chemical potential of CO 2 beyond that of saturated aqueous solution, thereby reversing the relative rates of the CO 2 RR and the HER. The experimental demonstration of this release mechanism for the application of CO 2 up-conversion illustrates how the electric field can not only influence electrochemical reactions at the surface but also the reactant supply from clathrate hydrates to the surface. Experimental focus rests on the low applied-potential regime, where the consequences of the reactant release mechanism are well-observable unobscured by mass-transport effects. [ABSTRACT FROM AUTHOR]

The temperature dependence of the response of a magnetic system to an applied field can be understood qualitatively by considering variations in the energy surface characterizing the system and estimated quantitatively with rate theory. In the system analysed here, Fe/Sm-Co spring magnet, the width of the hysteresis loop is reduced to a half when temperature is raised from 25 K to 300 K. This narrowing can be explained and reproduced quantitatively without invoking temperature dependence of model parameters as has typically been done in previous data analysis. The applied magnetic field lowers the energy barrier for reorientation of the magnetization but thermal activation brings the system over the barrier. A 2-dimensional representation of the energy surface is developed and used to gain insight into the transition mechanism and to demonstrate how the applied field alters the transition path. Our results show the importance of explicitly including the effect of thermal activation when interpreting experiments involving the manipulation of magnetic systems at finite temperature. [ABSTRACT FROM AUTHOR]

Wehave explored the ultrafast molecular structural dynamics associatedwith charge transfer in N,N,N′,N′-tetramethylethylenediamineusing Rydberg fingerprint spectroscopy in conjunction with self-interactioncorrected density functional theory. Excitation at 239 nm preparesthe molecule in the Franck–Condon region of the 3s state withthe charge localized on one of the two amine groups. As seen fromthe time-dependent Rydberg electron binding energies, the pathwayof the rapidly ensuing dynamics leads through several structurallydistinct conformers with various degrees of charge localization beforereaching the fully charge-delocalized structure on a picosecond timescale. At several steps along the reaction path, the transient structuresare identified through a comparison of the spectroscopically observedbinding energies with computed values. The molecular structure isseen to evolve dynamically from an initially folded conformer to thestretched form that supports charge delocalization before an equilibriumsets in with forward and backward time constants of 1.19 (0.14) and2.61 (0.31) ps, respectively. A coherent wavepacket motion in thecharge-localized state with a period of 270 (17) fs and damping of430 (260) fs is observed and tentatively assigned to the nitrogenumbrella motion. The damping time constant indicates the rate of theenergy flow into other vibrations that are not activated by the opticalexcitation. [ABSTRACT FROM AUTHOR]