Efficient choice of colored noise in the stochastic dynamics of open quantum systems.

The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

Hydrocarbon decomposition kinetics on the Ir(111) surface.

The kinetics of the thermal decomposition of hydrocarbons on the Ir(111) surface is determined using kinetic Monte Carlo (kMC) and rate equations simulations, both based on the density functional theory (DFT) calculated energy barriers of the involved reaction processes. This decomposition process is important for understanding the early stages of epitaxial graphene growth where the deposited hydrocarbon acts as a carbon feedstock for graphene formation. The methodology of the kMC simulations and the rate equation approaches is discussed and a comparison between the results obtained from both approaches is made in the case of the temperature programmed decomposition of ethylene for different initial coverages. The theoretical results are verified against experimental data from in situ X-ray photoelectron spectroscopy (XPS) experiments. Both theoretical approaches give reasonable results; however we find that, as expected, rate equations are less reliable at high coverages. We find that the agreement between experiment and theory can be improved in all cases if slight adjustments are made to the energy barriers in order to account for the intrinsic errors in DFT. Finally we extend our approach to the case where hydrocarbon species are dosed onto the substrate continuously, as in the chemical vapour deposition (CVD) graphene growth method. For ethylene and methane the thermal decomposition mechanism is determined, and it is found that in both cases the formation of C monomers is to be expected, which is limited by the presence of hydrogen atoms.

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths.

We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.

A free energy study of carbon clusters on Ir(111): Precursors to graphene growth.

It is widely accepted that the nucleation of graphene on transition metals is related to the formation of carbon clusters of various sizes and shapes on the surface. Assuming a low concentration of carbon atoms on a crystal surface, we derive a thermodynamic expression for the grand potential of the cluster of N carbon atoms, relative to a single carbon atom on the surface (the cluster work of formation). This is derived taking into account both the energetic and entropic contributions, including structural and rotational components, and is explicitly dependent on the temperature. Then, using ab initio density functional theory, we calculate the work of formation of carbon clusters CN on the Ir(111) surface as a function of temperature considering clusters with up to N = 16 C atoms. We consider five types of clusters (chains, rings, arches, top-hollow, and domes), and find, in agreement with previous zero temperature studies, that at elevated temperatures the structure most favoured depends on N, with chains and arches being the most likely at N<10 and the hexagonal domes becoming the most favourable at all temperatures for N>10. Our calculations reveal the work of formation to have a much more complex character as a function of the cluster size than one would expect from classical nucleation theory: for typical conditions, the work of formation displays not one but two nucleation barriers, at around N = 4-5 and N = 9-11. This suggests, in agreement with existing LEEM data, that five atom carbon clusters, along with C monomers, must play a pivotal role in the nucleation and growth of graphene sheets, whereby the formation of large clusters is achieved from the coalescence of smaller clusters (Smoluchowski ripening). Although the main emphasis of our study is on thermodynamic aspects of nucleation, the pivotal role of kinetics of transitions between different cluster types during the nucleation process is also discussed for a few cases as illustrative examples.

Promoting Atoms into Delocalized Long-Living Magnetically Modified State Using Atomic Force Microscopy.

We report on a low-temperature atomic force microscropy manipulation of Co atoms in ultrahigh vacuum on an oxidized copper surface in which the manipulated atom is kept delocalized above several surface unit cells over macroscopic times. The manipulation employed, in addition to the ubiquitous short-range tip-generated chemical forces, also long-range forces generated via Friedel oscillations of the metal charge density due to Co nanostructures prearranged on the surface by lateral manipulation. We show that our manipulation protocol requires mechanical control of the spin state of the Co atom.

Simulated structure and imaging of NTCDI on Si(1 1 1)-7 × 7 : a combined STM, NC-AFM and DFT study.

The adsorption of naphthalene tetracarboxylic diimide (NTCDI) on Si(1 1 1)-7 × 7 is investigated through a combination of scanning tunnelling microscopy (STM), noncontact atomic force microscopy (NC-AFM) and density functional theory (DFT) calculations. We show that NTCDI adopts multiple planar adsorption geometries on the Si(1 1 1)-7 × 7 surface which can be imaged with intramolecular bond resolution using NC-AFM. DFT calculations reveal adsorption is dominated by covalent bond formation between the molecular oxygen atoms and the surface silicon adatoms. The chemisorption of the molecule is found to induce subtle distortions to the molecular structure, which are observed in NC-AFM images.

Vertical atomic manipulation with dynamic atomic-force microscopy without tip change via a multi-step mechanism.

Manipulation is the most exciting feature of the non-contact atomic force microscopy technique as it allows building nanostructures on surfaces. Usually vertical manipulations are accompanied by an abrupt tip modification leading to a change of contrast. Here we report on low-temperature experiments demonstrating vertical manipulations of 'super'-Cu atoms on the p(2 × 1) Cu(110):O surface, both extractions to and depositions from the tip, when the imaging contrast remains the same. These results are rationalized employing a novel and completely general method that combines density functional theory calculations for obtaining energy barriers as a function of tip height and a Kinetic Monte Carlo algorithm for studying the tip dynamics and extraction of manipulation statistics. The model reveals a novel multi-step manipulation mechanism combining activated jumps of 'super'-Cu atoms to/from the tip with their drag by and diffusion on the tip.

Mapping the force field of a hydrogen-bonded assembly.

Hydrogen bonding underpins the properties of a vast array of systems spanning a wide variety of scientific fields. From the elegance of base pair interactions in DNA to the symmetry of extended supramolecular assemblies, hydrogen bonds play an essential role in directing intermolecular forces. Yet fundamental aspects of the hydrogen bond continue to be vigorously debated. Here we use dynamic force microscopy (DFM) to quantitatively map the tip-sample force field for naphthalene tetracarboxylic diimide molecules hydrogen-bonded in two-dimensional assemblies. A comparison of experimental images and force spectra with their simulated counterparts shows that intermolecular contrast arises from repulsive tip-sample interactions whose interpretation can be aided via an examination of charge density depletion across the molecular system. Interpreting DFM images of hydrogen-bonded systems therefore necessitates detailed consideration of the coupled tip-molecule system: analyses based on intermolecular charge density in the absence of the tip fail to capture the essential physical chemistry underpinning the imaging mechanism.

Optimization algorithm for rate equations with an application to epitaxial graphene.

We describe an algorithm that searches the parameter space of rate theories to optimize the associated rate coefficients based on a fit to experimental (or any other) data. Beginning with an initial set of parameters, which may be estimated, partially calculated, or indeed random, the algorithm follows a path, calculating the error at each point, until a minimum error is reached. We illustrate our method by correcting a previously proposed rate theory for the nucleation and growth of graphene on Ru(0 0 0 1) and Ir(1 1 1) to account for the temperature dependence of the graphene island density. This quantity shows an exponential decrease as the temperature is raised, in contrast to the power law decrease predicted by conventional nucleation theory, which indicates that a qualitatively different mechanism is operative for graphene island formation. Other applications of our method are also discussed.

Critical Importance of van der Waals Stabilization in Strongly Chemically Bonded Surfaces: Cu(110):O.

We provide strong evidence that different reconstructed phases of the oxidized Cu(110) surface are stabilized by the van der Waals (vdW) interactions. These covalently bonded reconstructed surfaces feature templates that are an integral part of the surfaces and are bonded on the bare metal surface by a combination of chemical and physical bonding. The vdW stabilization in this class of systems affects predominantly the intertemplate Cu-O interactions in structures sparsely populated by these templates. The conventional dispersionless density functional theory (DFT) methods fail to model such systems. We find a failure to describe the thermodynamics of the different phases that are formed at different oxygen exposures and spurious minima on the potential energy surface of a diffusing surface adatom. To overcome these issues, we employ a range of different DFT methods that account for the missing vdW correlations. Surprisingly, despite vast conceptual differences in the different formulations of these methods, they yield physically identical results for the Cu(110):O surface phases, provided the massive screening effects in the metal are taken into account. Contrary, the vibrational contribution does not consistently stabilize the experimentally observed surface structures. The van der Waals surface stabilization, so far deemed to play only a minor role in hard-bonded surfaces, is suggested to be a more general key feature for this and other related surfaces.

Complex design of dissipation signals in non-contact atomic force microscopy.

Complex interplay between topography and dissipation signals in Non-Contact Atomic Force Microscopy (NC-AFM) is studied by a combination of state-of-the-art theory and experiment applied to the Si(001) surface prone to instabilities. Considering a wide range of tip-sample separations down to the near-contact regime and several tip models, both stiff and more flexible, a sophisticated architecture of hysteresis loops in the simulated tip force-distance curves is revealed. At small tip-surface distances the dissipation was found to be comprised of two related contributions due to both the surface and tip. These are accompanied by the corresponding surface and tip distortion approach-retraction dynamics. Qualitative conclusions drawn from the theoretical simulations such as large dissipation signals (>1.0 eV) and a step-like dissipation dependent on the tip-surface distance are broadly supported by the experimental observations. In view of the obtained results we also discuss the reproducibility of NC-AFM imaging.

Precise orientation of a single C60 molecule on the tip of a scanning probe microscope.

We show that the precise orientation of a C(60) molecule which terminates the tip of a scanning probe microscope can be determined with atomic precision from submolecular contrast images of the fullerene cage. A comparison of experimental scanning tunneling microscopy data with images simulated using computationally inexpensive Hückel theory provides a robust method of identifying molecular rotation and tilt at the end of the probe microscope tip. Noncontact atomic force microscopy resolves the atoms of the C(60) cage closest to the surface for a range of molecular orientations at tip-sample separations where the molecule-substrate interaction potential is weakly attractive. Measurements of the C(60)-C(60) pair potential acquired using a fullerene-terminated tip are in excellent agreement with theoretical predictions based on a pairwise summation of the van der Waals interactions between C atoms in each cage, i.e., the Girifalco potential [L. Girifalco, J. Phys. Chem. 95, 5370 (1991)].

Ostwald ripening of binary alloy particles.

Classical Lifshitz-Slyozov-Wagner theory is generalized for Ostwald ripening of particles composed of random binary alloy. We show that the steady state ripening process is characterized by self-similar particle size and composition distributions. The shape of particle size distribution depends on whether the process is diffusion controlled (Lifshitz-Slyozov) or reaction controlled (Wagner) and is consistent with the predictions of classical theory for one-component materials. The steady state composition distribution, in contrast, has the same functional form in both extreme cases featuring a universal dependence of the composition upon particle size. We also found that transients in particle's composition can be very quick resulting in a steady state distribution well before it is reached by particles sizes. These transients involve significant changes in particle sizes and open an opportunity for producing metastable particle size distributions of required shape.

Role of van der Waals interaction in forming molecule-metal junctions: flat organic molecules on the Au(111) surface.

The self-assembly of flat organic molecules on metal surfaces is controlled, apart from the kinetic factors, by the interplay between the molecule-molecule and molecule-surface interactions. These are typically calculated using standard density functional theory within the generalized gradient approximation, which significantly underestimates nonlocal correlations, i.e. van der Waals (vdW) contributions, and thus affects interactions between molecules and the metal surface in the junction. In this paper we address this question systematically for the Au(111) surface and a number of popular flat organic molecules which form directional hydrogen bonds with each other. This is done using the recently developed first-principles vdW-DF method which takes into account the nonlocal nature of electron correlation [M. Dion et al., Phys. Rev. Lett. 2004, 92, 246401]. We report here a systematic study of such systems involving completely self-consistent vdW-DF calculations with full geometry relaxation. We find that the hydrogen bonding between the molecules is only insignificantly affected by the vdW contribution, both in the gas phase and on the gold surface. However, the adsorption energies of these molecules on the surface increase dramatically as compared with the ordinary density functional (within the generalized gradient approximation, GGA) calculations, in agreement with available experimental data and previous calculations performed within approximate or semiempirical models, and this is entirely due to the vdW contribution which provides the main binding mechanism. We also stress the importance of self-consistency in calculating the binding energy by the vdW-DF method since the results of non-self-consistent calculations in some cases may be off by up to 20%. Our calculations still support the usually made assumption of the molecule-surface interaction changing little laterally suggesting that single molecules and their small clusters should be quite mobile at room temperature on the surface. These findings support a gas-phase modeling for some flat metal surfaces, such as Au(111), and flat molecules, at least as a first approximation.

Modelling the manipulation of C60 on the Si001 surface performed with NC-AFM.

We present a theoretical model of manipulation of the C(60) molecule on the Si(001) surface with a non-contact atomic force microscope (NC-AFM). The model relies on the lowering of the energy barrier for the C(60) manipulation due to the interaction of the C(60) with an AFM tip and the subsequent thermal movement of the molecule over this barrier. We performed numerical simulations of these energy barriers for a series of tip positions relative to the molecule to show how the barriers change with the tip position. The values of these barriers are then used in kinetic Monte Carlo simulations to estimate the probability of the C(60) movement for different tip positions and temperatures. Virtual atomic force microscope simulations, which include the kinetic Monte Carlo treatment of the C(60) movement, are then performed to describe in real time the process of movement of the C(60) molecule during an NC-AFM scan. Our results demonstrate that manipulation of the C(60) molecule, which is covalently bound to the surface, is possible with NC-AFM, even though there is no continuous tip-molecule contact, which is known to be a necessary requirement for the C(60) manipulation with scanning tunnelling microscopy. We show that the manipulation event can be identified in real NC-AFM experiments as an abrupt change in the distance of the tip closest approach (topography), and as spikes in the frequency shift and dissipation signals.

Partitioning scheme for density functional calculations of extended systems.

We show that, at least for the ground electronic state of systems treated using semilocal density functionals (like in local density or generalized gradient approximations), a calculation of the entire extended nonperiodic system consisting of several well distinguished parts (e.g., a collection of molecules) can be replaced with a finite set of calculations on specifically chosen smaller subsystems that overlap with each other. Every subsystem is terminated with link (or pseudo) atoms (or groups of atoms) to reduce the effect of the termination. However, because of the particular choice of the subsystems, the effect of the link atoms is largely compensated in the final total energy if the subsystems are chosen sufficiently large. In fact, we prove that the proposed method should result in nearly the same total energy, electronic density and atomic forces as a single (considered as a reference) density functional calculation on the entire system. Our method, however, should be much more efficient due to unfavorable scaling of the modern electronic structure methods with the system size. The method is illustrated on examples of serine water, lysine-water and lysine dimer systems. We also discuss possible approximate applications of our method for quantum-classical calculations of extended systems, when, as compared to widely used quantum-mechanical/molecular-mechanical methods, the problem of the quantum cluster boundary can be eliminated to a large degree.

Theoretical modelling of tip effects in the pushing manipulation of C(60) on the Si(001) surface.

We present the results of our theoretical studies on the repulsive (pushing) manipulation of a C(60) molecule on the Si(001) surface with several scanning tunnelling microscopy tips. We show that, for silicon tips, tip-C(60) bonds are formed even with tips that do not initially have dangling bonds, and this tip-C(60) interaction drives the manipulation of the molecule. The details of the atomic structure of the tip and its position relative to the molecule do not have a significant effect on the mechanism and the sequence of adsorption configurations during the pushing manipulation of C(60) along the trough, where the trough itself provides a guiding effect. The pushing manipulation is thus a very robust process that occurs largely independently of the tip structure. On the other hand, the pushing manipulation across an Si-Si dimer row into the neighbouring trough proceeds in a more complex way, with tip deformation and detachment more likely to occur. We demonstrate the role of tip deformation and tip-molecule bond rearrangement in the continuous manipulation of the molecule. Finally, we calculate and analyse the forces acting on the tip during manipulation and identify characteristic patterns.

Theoretical study of melamine superstructures and their interaction with the Au(111) surface.

Using a systematic method, based on considering all possible hydrogen bond connections between two melamine molecules, and ab initio density functional theory (DFT) calculations, we consider the possible planar superstructures that the molecules can form in two dimensions. This is relevant to the assembly of melamine on flat metal surfaces with a small lateral corrugation of the molecule-surface interaction energy. The structures considered include small clusters as well as periodic structures, such as one-dimensional filaments and two-dimensional monolayers. Then, the interaction of melamine structures with the Au(111) surface is considered in detail to elucidate the possible effect of the surface on the formed structures, including the influence of the van der Waals interaction, which is not taken into account in DFT-based methods. The problem of commensurability between the lattices of the gas-phase monolayer and of the substrate is also discussed.

Controlled manipulation of atoms in insulating surfaces with the virtual atomic force microscope.

We predict how single oxygen ions can be manipulated on the MgO (100) surface and demonstrate the possibility of detecting a single-atom event using a noncontact atomic force microscope. The manipulation process is simulated explicitly in real time with a virtual dynamic atomic force microscope including the full response of the instrumentation and demonstrates a strong dependence on temperature. The proposed new atomistic mechanism and protocols for the controlled manipulation of single atoms and vacancies on insulating surfaces may be relevant for anchoring molecules and metal clusters at these surfaces and controlling their electronic properties.

Homopairing possibilities of the DNA base thymine and the RNA base uracil: an ab initio density functional theory study.

All planar homopairings of the DNA base thymine and the RNA base uracil are reported for the first time in this study. Using the idea of binding sites discussed in our previous work (Kelly et al. J. Phys. Chem. B 2005, 109, 11933; J. Phys. Chem. B 2005, 109, 22045) and ab initio density functional theory, we predict and relax 10 thymine and 10 uracil homopairs. The stabilization energies of the homopairs vary from just below zero to -0.82 eV. The results on the pair geometry and energetics are compared with those available in the literature. The collected data on all planar thymine and uracil homopairs can be used to construct the thymine and uracil superstructures seen experimentally on various surfaces.