Harmonic Transition State Theory Research Articles

Harmonic transition state theory applied to vacancy diffusion pre-exponential factors in a concentrated solid-solution alloy

Harmonic transition state theory applied to vacancy diffusion pre-exponential factors in a concentrated solid-solution alloy

Understanding muon diffusion in perovskite oxides below room temperature based on harmonic transition state theory

Understanding muon diffusion in perovskite oxides below room temperature based on harmonic transition state theory

Estimating Free Energy Barriers for Heterogeneous Catalytic Reactions with Machine Learning Potentials and Umbrella Integration.

Predicting the rate constants of elementary reaction steps is key for the computational modeling of catalytic processes. Within transition state theory (TST), this requires an accurate estimation of the corresponding free energy barriers. While sophisticated methods for estimating free energy differences exist, these typically require extensive (biased) molecular dynamics simulations that are computationally prohibitive with the first-principles electronic structure methods that are typically used in catalysis research. In this contribution, we show that machine-learning (ML) interatomic potentials can be trained in an automated iterative workflow to perform such free energy calculations at a much reduced computational cost as compared to a direct density functional theory (DFT) based evaluation. For the decomposition of CHO on Rh(111), we find that thermal effects are substantial and lead to a decrease in the free energy barrier, which can be vanishingly small, depending on the DFT functional used. This is in stark contrast to previously reported estimates based on a harmonic TST approximation, which predicted an increase in the barrier at elevated temperatures. Since CHO is the reactant of the putative rate limiting reaction step in syngas conversion on Rh(111) and essential for the selectivity toward oxygenates containing multiple carbon atoms (C2+ oxygenates), our results call into question the reported mechanism established by microkinetic models.

Heliknoton in a film of cubic chiral magnet

Cubic chiral magnets exhibit a remarkable diversity of two-dimensional topological magnetic textures, including skyrmions. However, the experimental confirmation of topological states localized in all three spatial dimensions remains challenging. In this paper, we investigate a three-dimensional topological state called a heliknoton, which is a hopfion embedded into a helix or conic background. We explore the range of parameters at which the heliknoton can be stabilized under realistic conditions using micromagnetic modeling, harmonic transition state theory, and stochastic spin dynamics simulations. We present theoretical Lorentz TEM images of the heliknoton, which can be used for experimental comparison. Additionally, we discuss the stability of the heliknoton at finite temperatures and the mechanism of its collapse. Our study offers a pathway for future experimental investigations of three-dimensional topological solitons in magnetic crystals.

Enhanced Sampling for Free Energy Profiles with Post-Transition-State Bifurcations

We present a strategy to explore the free energy landscapes of chemical reactions with post-transition-state bifurcations using an enhanced sampling method based on well-tempered metadynamics. Obviating the need for computationally expensive density functional theory-level ab initio molecular dynamics simulations, we obtain accurate energetics by utilizing a free energy perturbation scheme and deep learning estimator for the single-point energies of substrate configurations. Using a pair of easily interpretable collective variables, we present a quantitative free energy surface that is compatible with harmonic transition state theory calculations and in which the bifurcations are clearly visible. We demonstrate our approach with the example of the SpnF-catalyzed Diels-Alder reaction, a cycloaddition reaction in which post-transition-state bifurcation leads to the [4+2] as well as the [6+4] cycloadduct. We obtain the free energy landscapes for different stereochemical reaction pathways and characterize the mechanistic continuum between relevant reaction channels without explicitly searching for the pertinent transition state structures.

A defect formation mechanism induced by structural reconstruction of a well-known silicon grain boundary.

Diamond-structured grain boundaries (GBs) are important because they have notable effects on the performances of many functional devices. Previous studies have suggested that the most stable structures of some silicon GBs can be obtained by structural reconstruction from some meta-stable GBs explored at 0 K by atomic simulation. While GB reconstruction is possible to enable these meta-stable GBs to exist at elevated temperatures, reports on such behaviors are rare. This work unveiled a non-reported GB reconstruction from two degenerate ground-states of a well-known silicon GB which can be distinguished by an orientational feature of their unit structures. The reconstructing structures were verified stable by density-functional-theory (DFT) simulation. By thermodynamical and kinetical discussion, we have shown that the structural variation of this well-known GB at elevated temperatures is more likely to be dominated by this reconstruction mechanism rather than by transforming to other metastates. Such a reconstruction mechanism allows the whole GB system to be treated as an Ising model with a second-ordered phase transition. By applying harmonic transition state theory, we predicted the possible concentration of the defects induced by reconstruction at elevated temperatures and discussed their effects on the band structure of the GB by DFT simulation. An explanation was made on the cause of the difference between the phase transition behavior of this silicon GB and that of a reported copper GB. Our research made new insights into understanding the behavior of reconstructing interfaces in covalent-bonded crystalline materials.

Identification of the Kirkendall effect as a mechanism responsible for thermal decomposition of the InGaN/GaN MQWs system

A drop in the efficiency of light-emitting diodes based on InGaN/GaN QWs known as the ‘green gap’ has been studied intensively over the past dozen years. Several factors were revealed to contribute to its origin, such as random fluctuations in the indium concentration or the diffusion of point defects during the growth of QWs. The aim of this paper is to demonstrate that the Kirkendall effect can be the mechanism responsible for the thermal decomposition of InGaN/GaN MQWs structures, contributing to the green gap problem. By applying density functional theory, harmonic approximation, and harmonic transition state theory, we calculated the heights of the migration energy barriers of In and Ga atoms diffusing in alloys (), the vibrational frequencies of alloys in the presence of migrating point defects, the temperature dependencies of the defect migration energy barriers and diffusion coefficients of Ga and In atoms migrating in alloys. We demonstrated the presence of unbalanced diffusion rates of In and Ga atoms at the interfaces and finally explained the experimentally observed mechanism of void formation at the interfaces by means of the Kirkendall effect.

First principles DFT analysis on the diffusion kinetics of hydrogen isotopes through bcc iron (Fe): Role of temperature and surface coverage

The diffusion of interstitial H, D, and T in Fe metal at different temperature are evaluated using ab-initio density functional theory and transition state theory. The thermal expansion coefficient, Helmholtz free energy of activation, jump factor of diffusion was determined by use of activation energy and phonon calculations. The calculated diffusion coefficient was well described by a constant activation energy, (D = D0exp (-Ea)/kT)) with Ea = 0.016, 0.041, and 0.050 eV and D0 = 1.042 × 10−7, 0.736 × 10−7 and 0.572x10−7 m2.s−1for H, D, and T, respectively using harmonic transition state theory (hTST) with temperature correction. The calculated permeability and solubility also followed the Arrhenius relation.The earlier experimentally reported higher diffusivity of H atom at lower temperatures than that at higher temperature (200–600 K) was well explained by Wigner + hTST model with temperature correction and semi-classical transition state theory (SC-TST). The present computed results followed the similar trend of experimental findings. Further, the ideal fracture energy was evaluated using the Born-Haber thermodynamic cycle for varied coverage of H, D and T to account for decohesion-based embrittlement. The lighter H atom was seen to cause more decohesion-based embrittlement compared to D and T due to reduced cohesion. Additionally, the effect of temperature on ideal fracture energy was evaluated for H, D and T in Fe. The decohesion-based embrittlement was increased with increase in the temperature for H, D and T up to certain temperature (for H lower than 500 K, for D around 500 K and for T above 500 K) but with further increase in the temperature, the ideal fracture energy was reduced due to decrease in the adsorption energy and increase in the solution enthalpy of H isotopes. Further, the path and kinetics of dissociation and reassociation of H2 molecule were established on Fe (100) surface at 0.5 and 2.0 ML coverage. At lower concentration (0.5 ML), dissociation of H2 molecule on Fe (100) surface was favored, whereas at high concentration (2.0 ML), reassociation of H2 molecule was favored.

Theoretical study of metal-free catalytic for catalyzing CO-oxidation with a synergistic effect on P and N co-doped graphene

P and N co-doped graphene (PNxCy-G with x = 1, 2, 3 and y = 0, 1, 2) is designed to enhance graphene reactivity with a synergistic effect of the P and N atoms for the CO oxidation reaction, focusing on the influence of the N dopant concentration on graphene. The calculated results indicate that increasing two or three coordinated N to P can facilitate charge transfer from the surface onto O2 molecules. However, the adsorbed O2 molecule breaks apart on PN3-G surface, affecting CO oxidation performance. Furthermore, PN2C1-G exhibits excellent catalytic activity towards the oxidation of CO via the ER mechanism, which catalyzes CO oxidation with the rate-determining step of only 0.26 eV for the first and 0.25 eV for the second oxidation at 0 K. Additionally, the catalytic oxidation of PN2C1-G via Eley–Rideal mechanism prefers to occur at room temperature (298.15 K), with a rate-determining step of 0.77 eV. The reaction rates at 298.15 K is calculated to be 5.36 × 1016 mol s–1. The rate constants are obtained according to harmonic transition state theory, which could be supportive for catalytic oxidation of CO on the experiment.

First-Principles Study on the Impact of Stress on Depassivation of Defects at a-SiO2/Si Interfaces

The amorphous silicon dioxide-silicon (a-SiO2/Si) interface is an important part of silicon devices. It is difficult to avoid interface defects during the device production process. The passivated interface defects will undergo a depassivation reaction with the protons in the silicon dioxide generated by irradiation and convert to positively charged dangling bonds, thereby affecting device performance. In engineering practice, there is a final passivation layer on top of a-SiO2, and it is inevitable to introduce stress on the a-SiO2/Si interface. Therefore, studying the depassivation reaction mechanism of a-SiO2/Si interface defects under stress is of great significance to understand the performance degeneration in real devices. By using molecular dynamics and first-principles calculations, Pb defects at a-SiO2/Si (111) interface and Pb1 defects at a-SiO2/Si (100) interface are selected in this work to investigate the effect of stress on their depassivations. Biaxial strains are applied to the models, energy curves of the depassivation reactions under stress are calculated using the CI-NEB (Climbing Image Nudged Elastic Band) method, and transition states are identified. According to the Harmonic Transition State Theory (HTST), the reaction rate constants of the depassivation reactions of Pb and Pb1 defects at a certain temperature can be obtained. Finally, the relative concentration curves during depassivation reactions of PbH and Pb1H under stress and room temperature are obtained. Detailed data and figure analyses are presented to demonstrate differences between the two typical interface defects when depassivating under stress. Appropriate degrees of interface stress are proved to extend the depassivation time of defects, therefore prolonging the service life of devices.

Thermal generation of droplet soliton in chiral magnet

Controlled creation of localized magnetic textures beyond conventional $\ensuremath{\pi}$-skyrmions is an important problem in the field of magnetism. Here, by means of spin dynamics simulations, Monte Carlo simulations, and harmonic transition state theory we demonstrate that an elementary chiral magnetic soliton with zero topological charge---the chiral droplet---can be created by thermal fluctuations in the presence of the tilted magnetic field. The proposed protocol relies on an unusual kinetics combining the effects of the entropic stabilization and low-energy barrier for the nucleation of a topologically trivial state. Following this protocol by varying temperature and the tilt of the external magnetic field, one can selectively generate chiral droplets or $\ensuremath{\pi}$-skyrmions in a single system. The coexistence of two distinct magnetic solitons establishes a basis for a rich magnetization dynamics and opens up the possibility for the construction of more complex magnetic textures such as skyrmion bags and skyrmions with chiral kinks.

Understanding the role of anharmonic phonons in diffusion of bcc metals

Diffusion in the high-temperature bcc phase of IIIB-IVB metals such as Zr, Ti, and their alloys is observed to be orders of magnitude higher than bcc metals of group VB-VIB, including Cr, Mo, and W. The underlying reason for this higher diffusion is still poorly understood. To explain this observation, we compare the first-principles-calculated parameters of monovacancy-mediated diffusion between bcc Ti, Zr, and dilute Zr- Sn alloys and bcc Cr, Mo, and W. Our results indicate that strongly anharmonic vibrations promote both the vacancy concentration and the diffusive jump rate in bcc IVB metals and can explain their markedly faster diffusion compared to bcc VIB metals. Additionally, we provide an efficient approach to calculate diffusive jump rates according to the transition state theory (TST). The use of standard harmonic TST is impractical in bcc IIIB/IVB metals due to the existence of ill-defined harmonic phonons, and most studies use classical or ab initio molecular dynamics for direct simulation of diffusive jumps. Here, instead, we use a stochastically sampled temperature-dependent phonon analysis within the transition state theory to study diffusive jumps without the need of direct molecular dynamics simulations. We validate our first-principles diffusion coefficient predictions with available experimental measurements and explain the underlying reasons for the promotion of diffusion in bcc IVB metals/alloys compared to bcc VIB metals.

Carbon-induced strengthening of bcc iron at the atomic scale

In steels, the interaction between screw dislocations and carbon solutes has a great influence on the yield strength. Fe-C potentials used in molecular dynamics (MD) simulations yield a poor description of screw dislocation properties---their core structure and Peierls barrier---compared to ab initio calculations. Here we combine two EAM potentials from the literature, which greatly improves dislocation property accuracy in FeC alloys. Using this hybrid potential, MD simulations of dislocation glide in random solid solutions confirm a powerful solute strengthening, caused by complex interaction processes. We analyze these processes in a model geometry, where a row of carbon atoms is inserted in the dislocation core with varying separations. We use a combination of MD simulations, minimum-energy path calculations, and a statistical model based on the harmonic transition state theory to explain the strengthening induced by carbon. We unveil that carbon disrupts the glide process, as unpinning requires the successive nucleation of two kink pairs. When solute separation is below about 100 Burgers vectors, the activation enthalpy of both kink pairs are markedly increased compared to pure iron, resulting in a strong dependence of the unpinning stress on solute spacing. Our simulations also suggest an effect of carbon spacing on the kink-pair activation entropy. This work provides elementary processes and parameters that will be useful for larger-scale models and, in particular, kinetic Monte Carlo simulations.

Lifetime of skyrmions in discrete systems with infinitesimal lattice constant

Topological protection of chiral magnetic structures is investigated by taking a two-dimensional magnetic skyrmion as an example. The skyrmion lifetime is calculated based on harmonic transition state theory for a discrete lattice model using various values of the ratio of the lattice constant and the skyrmion size. Parameters of the system corresponding to exchange, anisotropy and Dzyaloshinskii–Moriya interaction are chosen in such a way as to keep the energy and size of the skyrmion unchanged for small values of the lattice constant, using scaling relations derived from continuous micromagnetic description. The number of magnetic moments included in the calculations reaches more than a million. The results indicate that in the limit of infinitesimal lattice constant, the energy barrier for skyrmion collapse approaches the Belavin–Polyakov lower bound of the energy of a topological soliton in the σ-model, the entropy contribution to the pre-exponential factor in the Arrhenius rate expression for collapse approaches a constant and the skyrmion lifetime can, for large enough number of spins, correspond to thermally stable skyrmion at room temperature even without magnetic dipole–dipole interaction.

Ab initio molecular dynamics of pipe diffusion in fcc Ni beyond transition state theory

Advances in first principles methods provide a means to explore the rate constants of mechanisms that constitute diffusion. We apply these to atom-vacancy exchanges near a partial core of a 12〈11¯0〉 screw dislocation in fcc Ni at finite temperatures. Intrinsic properties of this dynamic approach contrast limitations of transition state theory (TST) and widely used harmonic TST (HTST) approximations, revealing direction-dependent free energy profiles within the zero-temperature period of the dislocation and temperature-dependent correlation effects. The calculated free energy profiles indicate increased dislocation periods at elevated temperatures, similar to temperature-dependent period doubling in semiconductors. In contrast to static HTST, the dynamic approach indicates an intra-cell asymmetry in energy profile that is related to the dynamic geometry rearrangements. This arises from different philosophies underlying the two methodologies. The absolute values of the rate constants, however, are within the same order of magnitude, with the HTST method generally underestimating rates by a factor of 2–5. Combined with a twofold increase in rates due to thermal expansion at high temperatures, this partially explains why previous theoretical works report lower diffusivities for pipe diffusion than experiments.

Density Functional Theory Study of Reaction Equilibria in Signal Amplification by Reversible Exchange.

An in-depth theoretical analysis of key chemical equilibria in Signal Amplification by Reversible Exchange (SABRE) is provided, employing density functional theory calculations to characterize the likely reaction network. For all reactions in the network, the potential energy surface is probed to identify minimum energy pathways. Energy barriers and transition states are calculated, and harmonic transition state theory is applied to calculate exchange rates that approximate experimental values. The reaction network energy surface can be modulated by chemical potentials that account for the dependence on concentration, temperature, and partial pressure of molecular constituents (hydrogen, methanol, pyridine) supplied to the experiment under equilibrium conditions. We show that, under typical experimental conditions, the Gibbs free energies of the two key states involved in pyridine-hydrogen exchange at the common Ir-IMes catalyst system in methanol are essentially the same, i. e., nearly optimal for SABRE. We also show that a methanol-containing intermediate is plausible as a transient species in the process.

First-Principles Calculations of the Diffusivity of Interstitial Helium in Alpha-U Considering Anisotropy, Isotope Effects, and Quantum Effects

The interstitial migration of helium in alpha-U, which is planned to be used as a tritium storage material for nuclear fusion reactors and as a metallic fuel for advanced nuclear reactors, is studied by first-principles calculations. First, all migration paths are identified using the nudged elastic band method, and the migration barrier is determined for each path considering the thermal expansion of the lattice. In addition, the jump attempt frequencies are determined by applying harmonic transition state theory coupled with vibration analysis. Subsequently, the diffusion coefficient is evaluated numerically by kinetic Monte Carlo calculations using the determined migration barriers and jump attempt frequencies for all migration paths. Diffusion in the [010]-direction is found to be the most unlikely until sufficiently high temperature, while [001]-diffusion is the most dominant diffusion direction through the whole temperature range. The isotope effect, which is important because the beta decay of tritium produces helium-3, is not large and approaches the classical limit as the temperature increases. The quantum tunneling crossover temperature is computed to be approximately 100 K for helium-3 and 86 K for helium-4, which ensures the validity of the present calculation results over a wide temperature range. The diffusion coefficients are obtained as D=(9.67×10−4)×exp(−0.202eVkT)cm2/s for helium-3 and D=(8.48×10−4)×exp(−0.201eVkT)cm2/s for helium-4 over a temperature range from 200 to 900 K.

The lifetime of micron scale topological chiral magnetic states with atomic resolution

A new method for the numerical computation of the lifetimes of magnetic states within harmonic transition state theory (HTST) has been developed. In the simplest case, the system is described by a Heisenberg-like Hamiltonian with short-range interaction. Calculations are performed in Cartesian coordinates. Constraints on the values of magnetic moments are taken into account using Lagrange multipliers. The pre-exponential factor in the Arrhenius law in HTST is written in terms of the determinants of the Hessian of energy at the minima and saddle points on the multidimensional energy surface. An algorithm for calculating these determinants without searching for eigenvalues of the Hessian but using recursive relations is proposed. The method allows calculating determinants for systems containing millions of magnetic moments. This makes it possible to calculate the pre-exponential factor and estimate the lifetimes of micron-scale topological structures with atomic resolution, which until now has been impossible using standard approaches. The accuracy of the method is demonstrated by calculating 2D and 3D skyrmionic structures.

Passivation and dissociation of P b-type defects at a-SiO2/Si interface* *Project supported by the Science Challenge Project, China (Grant No. TZ2016003-1-105), the Tianjin Natural Science Foundation, China (Grant No. 20JCZDJC00750), and the Fundamental Research Funds for the Central Universities, Nankai University (Grant Nos. 63211107 and 63201182).

It is well known that in the process of thermal oxidation of silicon, there are P b-type defects at amorphous silicon dioxide/silicon (a-SiO2/Si) interface due to strain. These defects have a very important impact on the performance and reliability of semiconductor devices. In the process of passivation, hydrogen is usually used to inactivate P b-type defects by the reaction P b + H2 → P bH + H. At the same time, P bH centers dissociate according to the chemical reaction P b H → P b +H. Therefore, it is of great significance to study the balance of the passivation and dissociation. In this work, the reaction mechanisms of passivation and dissociation of the P b-type defects are investigated by first-principles calculations. The reaction rates of the passivation and dissociation are calculated by the climbing image-nudged elastic band (CI-NEB) method and harmonic transition state theory (HTST). By coupling the rate equations of the passivation and dissociation reactions, the equilibrium density ratio of the saturated interfacial dangling bonds and interfacial defects (P b, P b0, and P b1) at different temperatures is calculated.

Unveiling alloying effects on the catalytic activities of Cu3Pt and Cu3Pd for nonoxidative dehydrogenation and esterification of ethanol

To investigate the alloying effects of the Cu catalyst, we performed extensive density functional theory (DFT) calculations to study the reaction mechanisms of ethanol dimerization to form ethyl acetate (EA) on Cu(111) and CuM(111) with M = Pt or Pd. Specifically, thirty-three reactions along the minimum energy reaction pathways were studied by calculating the energy barrier and reaction energy. To evaluate catalytic performance and determine the rate-determining step (RDS), we calculated reaction rate constants based on the harmonic transition state theory. The DFT results showed that the most widely recognized Colley mechanism for ethanol dimerization to form EA should be revised by including CH3CHO hydrogenation to form CH3CH2O. While the first dehydrogenation was found to be the RDS on Cu(111) and Cu3Pt(111), CH3CHO hydrogenation was identified to be the RDS on Cu3Pd(111). Furthermore, Cu3Pt(111) is about 3 orders of magnitude faster than Cu(111) and Cu3Pd(111) for ethanol nonoxidative dehydrogenation and esterification. This work also provides a benchmark for further examination of ethanol dimerization over other Cu alloys.