Daniel Sheppard

Optimization methods for finding minimum energy paths.

A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).

A generalized solid-state nudged elastic band method

A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid-solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rock-salt to wurtzite transition in CdSe, we demonstrate that the method is robust for mechanisms dominated either by atomic motion or by unit-cell deformation; notably, the lowest-energy transition mechanism found by our G-SSNEB changes with cell size from a concerted transformation of the cell coordinates in small cells to a nucleation event in large cells. The method is efficient and can be applied to systems in which the force and stress tensor are calculated using density functional theory.

Intrinsic Diffusion of Hydrogen on Rutile TiO2(110)

The combined experimental and theoretical study of intrinsic hydrogen diffusion on bridge-bonded oxygen (BBO) rows of TiO 2(110) is presented. Sequences of isothermal scanning tunneling microscopy images demonstrate a complex behavior of hydrogen formed by water dissociation on BBO vacancies. Different diffusion rates are observed for the two hydrogens in the original geminate OH pair suggesting the presence of a long-lived polaronic state. For the case of separated hydroxyls, both theory and experiment yield comparable temperature-dependent diffusion rates. Density functional theory calculations show that there are two comparable low energy diffusion pathways for hydrogen motion along the BBO from one BBO to its neighbor, one by a direct hop and the other by an intermediate minimum at a terrace O. The values of kinetic parameters (prefactors and diffusion barriers) determined experimentally and theoretically are significantly different and indicate the presence of a more complex diffusion mechanism. We speculate that the hydrogen diffusion proceeds via a two-step mechanism: the initial diffusion of localized charge, followed by the diffusion of hydrogen. Both experiment and theory show the presence of repulsive OH-OH interactions.

Paths to which the nudged elastic band converges.

A recent letter to the editor (Quapp and Bofill, J Comput Chem 2010, 31, 2526) claims that the nudged elastic band (NEB) method can converge toward gradient extremal paths and not to steepest descent paths, as has been assumed. Here, we show that the NEB does in fact converge to steepest descent paths and that the observed tendency for the NEB to approach gradient extremal paths was a consequence of implementation errors. We also note that while the NEB finds steepest descent paths, these are not necessarily minimum energy paths in the sense of being a set of points which are minima in the potential energy surface perpendicular to the path. An example is given where segments of steepest descent paths follow potential energy ridges.

Optimizing transition states via kernel-based machine learning

We present a method for optimizing transition state theory dividing surfaces with support vector machines. The resulting dividing surfaces require no a priori information or intuition about reaction mechanisms. To generate optimal dividing surfaces, we apply a cycle of machine-learning and refinement of the surface by molecular dynamics sampling. We demonstrate that the machine-learned surfaces contain the relevant low-energy saddle points. The mechanisms of reactions may be extracted from the machine-learned surfaces in order to identify unexpected chemically relevant processes. Furthermore, we show that the machine-learned surfaces significantly increase the transmission coefficient for an adatom exchange involving many coupled degrees of freedom on a (100) surface when compared to a distance-based dividing surface.

Kinetic and Thermodynamic Evaluation of the Reversible N-Heterocyclic Carbene−Isothiocyanate Coupling Reaction: Applications in Latent Catalysis

Using stopped flow and other spectroscopic techniques, the thermodynamic parameters of the coupling reaction between 1,3-dimesitylimidazolylidene and phenyl isothiocyanate were determined (H(o) = -96.1 kJ mol(-1) and ΔS(o) = -39.6 J mol(-1) K(-1)). On the basis of these data which indicated that the reaction was reversible (K(eq) = 5.94 × 10(14) M(-1) at 25 °C; k(f) = 252 M(-1) s(-1); k(r) = 4.24 × 10(-13) s(-1)), the adduct formed from the two aforementioned coupling partners was used as a latent catalyst to facilitate the [2 + 2 + 2] cyclotrimerization of phenyl isocyanate and the polymerization of DL-lactide.

Alchemical derivatives of reaction energetics

Based on molecular grand canonical ensemble density functional theory, we present a theoretical description of how reaction barriers and enthalpies change as atoms in the system are subjected to alchemical transformations, from one element into another. The change in the energy barrier for the umbrella inversion of ammonia is calculated along an alchemical path in which the molecule is transformed into water, and the change in the enthalpy of protonation for methane is calculated as the molecule is transformed into a neon atom via ammonia, water, and hydrogen fluoride. Alchemical derivatives are calculated analytically from the electrostatic potential in the unperturbed system, and compared to numerical derivatives calculated with finite difference interpolation of the pseudopotentials for the atoms being transformed. Good agreement is found between the analytical and numerical derivatives. Alchemical derivatives are also shown to be predictive for integer changes in atomic numbers for oxygen binding to a 79 atom palladium nanoparticle, illustrating their potential use in gradient-based optimization algorithms for the rational design of catalysts.

Solubility of several analogues of triphenylphosphine in carbon dioxide

Homogeneous catalysts often have poor solubility in supercritical CO2 (scCO2) because they contain aromatic ligands such as PPh3. The standard approach to this problem, adding fluorinated alkyl groups to the ligands, increases the cost and adds concerns about environmental persistence. Three fluorine-free strategies for increasing the solubility of PPh3-analogs in scCO2 have now been tested and two more soluble ligands identified.

Solid-state dimer method for calculating solid-solid phase transitions

The dimer method is a minimum mode following algorithm for finding saddle points on a potential energy surface of atomic systems. Here, the dimer method is extended to include the cell degrees of freedom for periodic solid-state systems. Using this method, reaction pathways of solid-solid phase transitions can be determined without having to specify the final state structure or reaction mechanism. Example calculations include concerted phase transitions between CdSe polymorphs and a nucleation and growth mechanism for the A15 to BCC transition in Mo.

Z methodology for phase diagram studies: platinum and tantalum as examples

The Z methodology is a novel technique for phase diagram studies. It combines the direct Z method for the computation of melting curves and the inverse Z method for the calculation of solid-solid phase boundaries. In the direct Z method, the solid phases along the melting curve are determined by comparing the solid-liquid equilibrium boundaries of candidate crystal structures. The inverse Z method involves quenching the liquid into the most stable solid phase at various temperatures and pressures to locate a solid-solid boundary. The direct and inverse Z methods in conjunction with the VASP ab initio molecular dynamics package are used to investigate the phase diagrams of tantalum and platinum. We compare our results to the most recent experimental data.