Andreas Heyden

Efficient methods for finding transition states in chemical reactions : Comparison of improved dimer method and partitioned rational function optimization method

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jonnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.

A growing string method for determining transition states: Comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.

Conservative Algorithm for an Adaptive Change of Resolution in Mixed Atomistic/Coarse-Grained Multiscale Simulations.

We derive a Hamiltonian and present a simulation protocol for mixed-resolution systems that allows for a change in resolution of selected groups of atoms during a molecular dynamics simulation. The Hamiltonian uses a low-resolution force field for the part of the system distant from an active site (for efficiency) and an atomistic force field for the active site and its direct environment (for accuracy). A microcanonical simulation protocol conserves energy and angular and linear momentum. The method is also applicable to simulations in other ensembles.

Modeling the noble metal/TiO2 (110) interface with hybrid DFT functionals: A periodic electrostatic embedded cluster model study

The interaction of Au(n) and Pt(n) (n=2,3) clusters with the stoichiometric and partially reduced rutile TiO(2) (110) surfaces has been investigated using periodic slab and periodic electrostatic embedded cluster models. Compared to Au clusters, Pt clusters interact strongly with both stoichiometric and reduced TiO(2) (110) surfaces and are able to enhance the reducibility of the TiO(2) (110) surface, i.e., reduce the oxygen vacancy formation energy. The focus of this study is the effect of Hartree-Fock exchange on the description of the strength of chemical bonds at the interface of Au/Pt clusters and the TiO(2) (110) surface. Hartree-Fock exchange helps describing the changes in the electronic structures due to metal cluster adsorption as well as their effect on the reducibility of the TiO(2) surface. Finally, the performance of periodic embedded cluster models has been assessed by calculating the Pt adsorption and oxygen vacancy formation energies. Cluster models, together with hybrid PBE0 functional, are able to efficiently compute reasonable electronic structures of the reduced TiO(2) surface and predict charge localization at surface oxygen vacancies, in agreement with the experimental data, that significantly affect computed adsorption and reaction energies.

Study of molecular shape and non-ideality effects on mixture adsorption isotherms of small molecules in carbon nanotubes: A grand canonical Monte Carlo simulation study

Abstract The sorption isotherms for binary mixtures of methane, ethane, propane and tetrafluoromethane have been determined in carbon nanotubes using configurational bias Monte Carlo simulation techniques. At high loadings, a curious maximum for equimolar gas-phase mixtures occurs with increasing pressure in the absolute adsorption isotherm of one or both adsorbing species. It was detected that there exist two fundamentally different reasons for this maximum. First, due to a higher packing efficiency, one component is able to displace the other component at high loadings. Here, it must be stressed that the displaced component is not necessarily the larger molecule. Second, non-ideality effects of the bulk gas phase can be made responsible for this maximum. The acceptance probability of a molecule insertion in a grand canonical Monte Carlo step is proportional to the component fugacity. If, owing to non-ideality effects of the gas phase, the fugacity of one component does not increase as steeply with pressure as the other component, a maximum can occur in the absolute adsorption isotherm of this component. These findings were demonstrated for various binary mixtures of CH 4 , CF 4 , C 2 H 6 and C 3 H 8 .

Adaptive-Partitioning QM/MM Dynamics Simulations: 3. Solvent Molecules Entering and Leaving Protein Binding Sites.

The adaptive-partitioning (AP) schemes for combined quantum-mechanical/molecular-mechanical (QM/MM) calculations allow on-the-fly reclassifications of atoms and molecules as QM or MM in dynamics simulations. The permuted-AP (PAP) scheme (J. Phys. Chem. B 2007, 111, 2231) introduces a thin layer of buffer zone between the QM subsystem (also called active zone) and the MM subsystem (also known as the environmental zone) to provide a continuous and smooth transition and expresses the potential energy in a many-body expansion manner. The PAP scheme has been successfully applied to study small molecules solvated in bulk solvent. Here, we propose two modifications to the original PAP scheme to treat solvent molecules entering and leaving protein binding sites. First, the center of the active zone is placed at a pseudoatom in the binding site, whose position is not affected by the movements of ligand or residues in the binding site. Second, the extra forces due to the smoothing functions are deleted. The modified PAP scheme no longer describes a Hamiltonian system, but it satisfies the conservation of momentum. As a proof-of-concept experiment, the modified PAP scheme is applied to the simulations under the canonical ensemble for two binding sites of the Escherichia coli CLC chloride ion transport protein, in particular, the intracellular binding site Sint discovered by crystallography and one putative additional binding site Sadd suggested by molecular modeling. The exchange of water molecules between the binding sites and bulk solvent is monitored. For comparison, simulations are also carried out using the same model system and setup with only one exception: the extra forces due to the smoothing functions are retained. The simulations are benchmarked against conventional QM/MM simulations with large QM subsystems. The results demonstrate that the active zone centered at the pseudo atom is a reasonable and convenient representation of the binding site. Moreover, the transient extra forces are non-negligible and cause the QM water molecules to move out of the active zone. The modified PAP scheme, where the extra forces are excluded, avoids the artifact, providing a realistic description of the exchange of water molecules between the protein binding sites and bulk solvent.

Solving the equations of motion for mixed atomistic and coarse-grained systems

A mixed-resolution molecular dynamics technique is presented that permits simulation of large and complex systems that critically depend on a subtle interplay between energy and entropy and, therefore, require both an accurate energy evaluation and an extensive sampling of a large and complex phase space. The computational approach is based upon the idea that many complex systems can be spatially divided into a relatively small active zone (that requires an accurate energy evaluation but, due to its relatively small size, only a limited sampling of phase space) and a relatively large inactive zone (that requires a less accurate energy description but the sampling of a very large phase space). Mixed-resolution models that use an accurate atomistic model for the active zone and an efficient coarse-grained model (that lumps groups of atoms into pseudo-atoms) for the inactive zone are ideally suited for these systems. One challenge in mixed-resolution simulations is creating a seamless connection between low- and high-resolution zones that exchange groups of atoms. We derive a mixed-resolution Hamiltonian and present a microcanonical simulation protocol that conserves energy and momentum and allows for a change in resolution of selected groups of atoms during a simulation. The method is applicable to simulations in other ensembles and for systems with multiple high-resolution zones. To illustrate the numerical stability of our technique, we present simulation results for a system of mixed-resolution methane molecules.

Solvent effects on the hydrodeoxygenation of propanoic acid over Pd(111) model surfaces

The effects of liquid water, n-octane, and n-butanol on the hydrodeoxygenation of propanoic acid over Pd(111) model surfaces have been studied from first principles. We developed a microkinetic model for the hydrodeoxygenation and studied the reaction mechanism at a temperature of 473 K. Our model predicts that for all reaction media, decarbonylation pathways are favored over decarboxylation pathways. However, in the presence of polar solvents like water, decarboxylation routes become competitive with decarbonylation routes. The activity of the Pd surface varies as a function of the environment as follows: water > n-butanol > octane ≈ gas phase. Finally, a sensitivity analysis of our models suggests that both C–OH and C–H bond cleavages control the overall rate of the catalyst in all environments and are likely to be activity descriptors for the hydrodeoxygenation of organic acids.

Hybrid Quantum Mechanics/Molecular Mechanics Solvation Scheme for Computing Free Energies of Reactions at Metal-Water Interfaces.

We report the development of a quantum mechanics/molecular mechanics free energy perturbation (QM/MM-FEP) method for modeling chemical reactions at metal-water interfaces. This novel solvation scheme combines planewave density function theory (DFT), periodic electrostatic embedded cluster method (PEECM) calculations using Gaussian-type orbitals, and classical molecular dynamics (MD) simulations to obtain a free energy description of a complex metal-water system. We derive a potential of mean force (PMF) of the reaction system within the QM/MM framework. A fixed-size, finite ensemble of MM conformations is used to permit precise evaluation of the PMF of QM coordinates and its gradient defined within this ensemble. Local conformations of adsorbed reaction moieties are optimized using sequential MD-sampling and QM-optimization steps. An approximate reaction coordinate is constructed using a number of interpolated states and the free energy difference between adjacent states is calculated using the QM/MM-FEP method. By avoiding on-the-fly QM calculations and by circumventing the challenges associated with statistical averaging during MD sampling, a computational speedup of multiple orders of magnitude is realized. The method is systematically validated against the results of ab initio QM calculations and demonstrated for C-C cleavage in double-dehydrogenated ethylene glycol on a Pt (111) model surface.

Hydrodeoxygenation of propanoic acid over silica-supported palladium: effect of metal particle size

The effects of metal nanoparticle size on the hydrodeoxygenation (HDO) of propanoic acid (PAc) over Pd/SiO2 catalysts was investigated. Strong electrostatic adsorption (SEA) was used to prepare catalysts with Pd nanoparticles ranging between 1.9 to 12.4 nm. The particle sizes were determined by chemisorption (O2–H2 titration) and scanning transmission electron microscopy (STEM). The HDO was carried out in a continuous gas-phase reactor at 200 °C and 1 atm at differential conversion. The reaction followed decarbonylation and hydrogenation pathways to yield ethane (C2H6) and propionaldehyde (EtCHO), respectively. While the catalytic TOF remained constant between 3.0–12.4 nm, it decreased by a factor of 2–3 with decreasing particle size down to 1.9 nm. The reaction rate is therefore considered to be largely structure-insensitive over the range studied. The selectivity toward EtCHO increased as the particle size increased, indicating hydrogenation is favored on single crystal Pd(111) and Pd(100) planes versus corners and edges. For decarbonylation to produce C2H6, reaction rate orders with respect to PAc (~0.5) and H2 (~0), and the apparent activation energy (~12 kcal per mole), were found to be the same for both 2.0 and 12.4 nm particle sizes. In contrast, the reaction rate order with respect to PAc (~1.0) and H2 (~0.3) was different for hydrogenation to produce EtCHO. These differences are explained by a change in the rate-determining step for the HDO of propanoic acid.