Andreas Pedersen

Improved initial guess for minimum energy path calculations

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.

Magic-number gold nanoclusters with diameters from 1 to 3.5 nm: relative stability and catalytic activity for CO oxidation.

Relative stability of geometric magic-number gold nanoclusters with high point-group symmetry ((Ih), D(5h), O(h)) and size up to 3.5 nm, as well as structures obtained by global optimization using an empirical potential, is investigated using density functional theory (DFT) calculations. Among high-symmetry nanoclusters, our calculations suggest that from Au(147) to Au(923), the stability follows the order Ih > D(5h) > Oh. However, at the largest size of Au(923), the computed cohesive energy differences among high-symmetry I(h), D(5h) and O(h) isomers are less than 4 meV/atom (at PBE level of theory), suggesting the larger high-symmetry clusters are similar in stability. This conclusion supports a recent experimental demonstration of controlling morphologies of high-symmetry Au(923) clusters ( Plant, S. R.; Cao, L.; Palmer, R. E. J. Am. Chem. Soc. 2014, 136, 7559). Moreover, at and beyond the size of Au(549), the face-centered cubic-(FCC)-based structure appears to be slightly more stable than the Ih structure with comparable size, consistent with experimental observations. Also, for the Au clusters with the size below or near Au(561), reconstructed icosahedral and decahedral clusters with lower symmetry are slightly more stable than the corresponding high-symmetry isomers. Catalytic activities of both high-symmetry and reconstructed I(h)-Au(147) and both Ih-Au(309) clusters are examined. CO adsorption on Au(309) exhibits less sensitivity on the edge and vertex sites compared to Au(147), whereas the CO/O2 coadsorption is still energetically favorable on both gold nanoclusters. Computed activation barriers for CO oxidation are typically around 0.2 eV, suggesting that the gold nanoclusters of ∼ 2 nm in size are highly effective catalysts for CO oxidation.

Atomic Scale Plasmonic Switch

The atom sets an ultimate scaling limit to Moores law in the electronics industry. While electronics research already explores atomic scales devices, photonics research still deals with devices at the micrometer scale. Here we demonstrate that photonic scaling, similar to electronics, is only limited by the atom. More precisely, we introduce an electrically controlled plasmonic switch operating at the atomic scale. The switch allows for fast and reproducible switching by means of the relocation of an individual or, at most, a few atoms in a plasmonic cavity. Depending on the location of the atom either of two distinct plasmonic cavity resonance states are supported. Experimental results show reversible digital optical switching with an extinction ratio of 9.2 dB and operation at room temperature up to MHz with femtojoule (fJ) power consumption for a single switch operation. This demonstration of an integrated quantum device allowing to control photons at the atomic level opens intriguing perspectives for a fully integrated and highly scalable chip platform, a platform where optics, electronics, and memory may be controlled at the single-atom level.The atom sets an ultimate scaling limit to Moores law in the electronics industry. And while electronics research already explores atomic scales devices, photonics research still deals with devices at the micrometer scale. Here we demonstrate that photonic scaling-similar to electronics-is only limited by the atom. More precisely, we introduce an electrically controlled single atom plasmonic switch. The switch allows for fast and reproducible switching by means of the relocation of an individual or at most -- a few atoms in a plasmonic cavity. Depending on the location of the atom either of two distinct plasmonic cavity resonance states are supported. Experimental results show reversible digital optical switching with an extinction ration of 10 dB and operation at room temperature with femtojoule (fJ) power consumption for a single switch operation. This demonstration of a CMOS compatible, integrated quantum device allowing to control photons at the single-atom level opens intriguing perspectives for a fully integrated and highly scalable chip platform -- a platform where optics, electronics and memory may be controlled at the single-atom level.

Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies

We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.

Theoretical study of kinks on screw dislocation in silicon

Theoretical calculations of the structure, formation and migration of kinks on a non-dissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic potential functions. The results show that the structure of a single kink is characterized by a narrow core and highly stretched bonds between some of the atoms. The formation energy of a single kink ranges from 0.9 to 1.36 eV, and is of the same order as that for kinks on partial dislocations. However, the kinks migrate almost freely along the line of an undissociated dislocation unlike what is found for partial dislocations. The effect of stress has also been investigated in order to compare with previous silicon deformation experiments which have been carried out at low temperature and high stress. The energy barrier associated with the formation of a stable kink pair becomes as low as 0.65 eV for an applied stress on the order of 1 GPa, indicating that displacements of screw dislocations likely occur via thermally activated formation of kink pairs at room temperature.

EON: software for long time simulations of atomic scale systems

The EON software is designed for simulations of the state-to-state evolution of atomic scale systems over timescales greatly exceeding that of direct classical dynamics. Statesaredefinedascollectionsofatomicconfigurationsfromwhich a minimization of the potential energy gives the same inherent structure. The time evolution is assumed to be governed by rare events, where transitions between states are uncorrelated and infrequent compared with the timescale of atomic vibrations. Several methods for calculating the state-to-state evolution have been implemented in EON, including parallel replica dynamics, hyperdynamics and adaptive kinetic Monte Carlo. Global optimization methods, including simulated annealing, basin hopping and minima hopping are also implemented. The software has a client/server architecture where the computationally intensive evaluations of the interatomic interactions are calculated on the client-side and the state-to-state evolution is managed by the server. The client supports optimization for different computer architectures to maximize computational efficiency. The server is written in Python so that developers have access to the high-level functionality without delving into the computationally intensive components. Communication between the server and clients is abstracted so that calculations can be deployed on a single machine, clusters using a queuing system, large parallel computers using a message passing interface, or within a distributed computing environment. A generic interface to the evaluation of the interatomic interactions is defined so that empirical potentials, such as in LAMMPS, and density functional theory as implemented in VASP and GPAW can be used interchangeably. Examples are given to demonstrate the range of systems that can be modeled, including

Efficient Sampling of Saddle Points with the Minimum-Mode Following Method

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 in solids treated within the harmonic approximation to transition state theory. Given a local minimum as an 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.

Distributed implementation of the adaptive kinetic Monte Carlo method

The program EON2 is a distributed implementation of the adaptive kinetic Monte Carlo method for long time scale simulations of atomistic systems. The method is based on the transition state theory approach within the harmonic approximation and the key step is the identification of relevant saddle points on the potential energy rim surrounding the energy minimum corresponding to a state of the system. The saddle point searches are carried out in a distributed fashion starting with random initial displacements of the atoms in regions where atoms have less than optimal coordination. The main priorities of this implementation have been to (1) make the code transparent, (2) decouple the master and slaves, and (3) have a well defined interface to the energy and force evaluation. The computationally intensive parts are implemented in C++, whereas the less compute intensive server-side software is written in Python. The platform for distributed computing is BOINC. A simulation of the annealing of a twist and tilt grain boundary in a copper crystal is described as an example application.

Long time scale simulation of a grain boundary in copper

A general, twisted and tilted, grain boundary in copper has been simulated using the adaptive kinetic Monte Carlo method to study the atomistic structure of the non-crystalline region and the mechanism of annealing events that occur at low temperature. The simulated time interval spanned 67µs at 135K. Similar final configurations were obtained starting from different initial structures: (i) by bringing the two grains into contact without any intermediate layer, and (ii) by inserting an amorphous region between the grains. The results obtained were analyzed with a radial distribution function and a common neighbor analysis. Annealing events leading to lowering of the energy typically involved concerted displacement of several atoms—even as many as 10 atoms displaced by more than half an Angstrom. Increased local icosahedral ordering is observed in the boundary layer, but local HCP coordination was also observed. In the final low-energy configurations, the thickness of the region separating the crystalline grains corresponds to just one atomic layer, in good agreement with reported experimental observations. The simulated system consists of 1307 atoms and atomic interactions were described using effective medium theory.

Geothermal model calibration using a global minimization algorithm based on finding saddle points and minima of the objective function

The objective function used when determining parameters in models for multiphase flow in porous media can have multiple local minima. The challenge is then to find the global minimum and also to determine the uniqueness of the optimized parameter values. A method for mapping out local minima to search for the global minimum by traversing regions of first order saddle points on the objective function surface is presented. This approach has been implemented with the iTOUGH2 software for estimation of models parameters. The methods applicability is illustrated here with two examples: a test problem mimicking a steady-state Darcy experiment and a simplified model of the Laugarnes geothermal area in Reykjavik, Iceland. A brief comparison with other global optimization techniques, in particular simulated annealing, differential evolution and harmony search algorithms is presented.