Simple and efficient way of speeding up transmission calculations with k-point sampling

• Jesper Toft Falkenberg and
• Mads Brandbyge

Beilstein J. Nanotechnol. 2015, 6, 1603–1608, doi:10.3762/bjnano.6.164

• wavefunctions, which tend to be elaborate. In this paper we present a simple and efficient post-processing interpolation scheme which can significantly speed up the convergence with respect to k-points. We illustrate the method by applying it to various graphene-based nano-structures which are prone to bad

• convergence due to its vanishing density of states at the Fermi level. In the remaining parts of the paper we first explain the workings of the interpolation scheme in section Results and Discussion, while we investigate various test cases in section Example cases, and finally discuss limitations to the

• resolution. Often the rough behavior of the transmission is already seen with a limited number of k-points but the convergence of the average is slow since the functions are changing abruptly with energy, e.g., around a band onset or a resonance. The position of the abrupt feature will typically shift in a

Can molecular projected density of states (PDOS) be systematically used in electronic conductance analysis?

• Tonatiuh Rangel,
• Gian-Marco Rignanese and
• Valerio Olevano

Beilstein J. Nanotechnol. 2015, 6, 1247–1259, doi:10.3762/bjnano.6.128

• not affect the conductance profile provided that convergence is reached. What actually changes is rather the PDOS, and hence, the interpretation of the conductance in these terms. Computational details Our calculations are carried out within the DFT-Landauer framework. The exchange-correlation energy

• is approximated using the PBE functional [43]. We use ABINIT [44] for ground state calculations and WanT [45][46] to construct Wannier functions and for conductance calculations. All the results presented here are obtained by well-converged calculations, using the same convergence parameters as in

• several sets of WFs. The one presenting the minimum spread (the most localized) does not necessarily correspond to the real physical situation, and this cannot be known a priori. The calculated conductance does not depend on the chosen basis set, provided the basis is complete and at convergence. On the

Tunable magnetism on the lateral mesoscale by post-processing of Co/Pt heterostructures

• Oleksandr V. Dobrovolskiy,
• Maksym Kompaniiets,
• Roland Sachser,
• Fabrizio Porrati,
• Christian Gspan,
• Harald Plank and
• Michael Huth

Beilstein J. Nanotechnol. 2015, 6, 1082–1090, doi:10.3762/bjnano.6.109

• the step size was 0.8 nm. Nano-diffraction and simulations A convergence angle of 1.0 mrad was used to generate electron nanodiffraction patterns in the STEM mode. These diffraction patterns were recorded energy-filtered on a 16-bit CCD. To collect the nanodiffraction images over the complete layer

Multiscale modeling of lithium ion batteries: thermal aspects

• Arnulf Latz and
• Jochen Zausch

Beilstein J. Nanotechnol. 2015, 6, 987–1007, doi:10.3762/bjnano.6.102

• ]. This method does not constitute an analytical proof that the averaged solution of the microscopic equations does converge in a strict mathematical sense towards the solution of the averaged set of equations. Here, further analytical work or numerical convergence studies will be necessary. If a quantity

• explicit forward Euler discretization based on the same time step and is thus fast to solve. However, due to the time-step limitations for explicit schemes the step size here can automatically decrease based on the given parameters to ensure stable convergence. Despite the fact that on the microscale the

Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases

• Antonello Sindona,
• Michele Pisarra,
• Mario Gravina,
• Cristian Vacacela Gomez,
• Pierfrancesco Riccardi,
• Giovanni Falcone and
• Francesco Plastina

Beilstein J. Nanotechnol. 2015, 6, 755–766, doi:10.3762/bjnano.6.78

• clusters are explicitly taken into account except for the one removed from the reference atom. Convergence for C60 and leads to optimized ground state wave functions made of single Slater determinants of 179 pairs of occupied molecular orbitals (MOs), which are linear combinations of 1135 contracted

Nanometer-resolved mechanical properties around GaN crystal surface steps

• Jörg Buchwald,
• Marina Sarmanova,
• Bernd Rauschenbach and
• Stefan G. Mayr

Beilstein J. Nanotechnol. 2014, 5, 2164–2170, doi:10.3762/bjnano.5.225

• are nearly constant for all step heights except for the closest atom which feels the stress significantly. This behavior reflects the better convergence properties of 1/y2 (Equation 6). From an experimental point of view, it is hardly possible to evaluate the microscopical expressions (Equation 7) for

• presented by Vlassak and Nix [20], who connected the indentation modulus to the Barnett–Lothe tensors for anisotropic materials [21]. For the one-atom indentation, (Figure 3), M behaves similarly to stress fluctuations with better convergence below the step and a similar decrease in the elastic constants on

UHV deposition and characterization of a mononuclear iron(III) β-diketonate complex on Au(111)

• Irene Cimatti,
• Silviya Ninova,
• Valeria Lanzilotto,
• Luigi Malavolti,
• Luca Rigamonti,
• Brunetto Cortigiani,
• Matteo Mannini,
• Elena Magnano,
• Federica Bondino,
• Federico Totti,
• Andrea Cornia and
• Roberta Sessoli

Beilstein J. Nanotechnol. 2014, 5, 2139–2148, doi:10.3762/bjnano.5.223

• together with GTH double-ζ polarized molecularly optimized basis sets for all atomic species. The energy cut-off applied to the plane wave basis sets was set to 400 Ry. Geometry optimizations were performed with the PBEsol functional [49]. In all cases, the convergence criteria were fixed at 1 × 10−6

Quasi-1D physics in metal-organic frameworks: MIL-47(V) from first principles

• Danny E. P. Vanpoucke,
• Jan W. Jaeken,
• Stijn De Baerdemacker,
• Kurt Lejaeghere and
• Veronique Van Speybroeck

Beilstein J. Nanotechnol. 2014, 5, 1738–1748, doi:10.3762/bjnano.5.184

• positions and cell shape. The convergence criterion is set to a difference in energy of less than 1.0 × 10−7 eV between subsequent ionic steps. After full relaxation, the forces on the ions are then found to be below 1.2 meV/Å. The density of states (DOS) was obtained by using a denser k-point grid of 3 × 3

Synthesis, characterization, and growth simulations of Cu–Pt bimetallic nanoclusters

• Subarna Khanal,
• Ana Spitale,
• Nabraj Bhattarai,
• Daniel Bahena,
• J. Jesus Velazquez-Salazar,
• Sergio Mejía-Rosales,
• Marcelo M. Mariscal and
• Miguel José-Yacaman

Beilstein J. Nanotechnol. 2014, 5, 1371–1379, doi:10.3762/bjnano.5.150

• characterized by transmission electron microscope (TEM) and high resolution transmission electron microscopy (HRTEM) by using a JEOL 2010F operated at 200 kV. The STEM images were recorded in a Cs-corrected JEOL JEM-ARM 200F operated at 200 kV. HAADF STEM images were obtained with a convergence angle of 26 mrad

Constant chemical potential approach for quantum chemical calculations in electrocatalysis

• Wolfgang B. Schneider and
• Alexander A. Auer

Beilstein J. Nanotechnol. 2014, 5, 668–676, doi:10.3762/bjnano.5.79

• modification of the density matrix until convergence of the number of electrons (and thus the chemical potential) and the energy is achieved. However, while this scheme is appealing, the crucial point is the convergence of the overall scheme. A robust algorithm is essential in any case, for simple systems like

• absolute potential of the charge neutral O2 with a bond distance of 1.21 Å calculated at the RI-BP86/def2-TZVP level of theory is −5.71 V. For all calculations in this paper the following convergence parameters were applied: The energy was converged up to 10−9 a.u., the maximal density change up to 10−5

• , RMS density change up to 10−6 and the DIIS error up to 10−6 a.u. Furthermore, all calculations have been carried out without level shift for the virtual orbitals. After the convergence of the initial charge state with 16 electrons is achieved, the number electrons is slightly increased. However, in

Effects of the preparation method on the structure and the visible-light photocatalytic activity of Ag₂CrO₄

• Difa Xu,
• Shaowen Cao,
• Jinfeng Zhang,
• Bei Cheng and
• Jiaguo Yu

Beilstein J. Nanotechnol. 2014, 5, 658–666, doi:10.3762/bjnano.5.77

• field (SCF) convergence accuracy to be 1 × 10−6 eV/atom. For the geometric optimization, the convergence criteria were set as follows: 1 × 10−5 eV/atom for total energy, 0.03 eV/Å for maximum force, 0.05 GPa for maximum stress, and 1 × 10−3 Å for maximum displacement. The energy and geometry structure

Analytical development and optimization of a graphene–solution interface capacitance model

• Hediyeh Karimi,
• Rasoul Rahmani,
• Reza Mashayekhi,
• Leyla Ranjbari,
• Amir H. Shirdel,
• Niloofar Haghighian,
• Parisa Movahedi,
• Moein Hadiyan and
• Razali Ismail

Beilstein J. Nanotechnol. 2014, 5, 603–609, doi:10.3762/bjnano.5.71

• the results tabulated, the accuracy of the optimized model is more than 97%, which is in an acceptable range of accuracy. The logarithmic convergence profile of the best fitness value obtained is plotted in Figure 6. The graph indicates that the algorithm converges to the optimized values with an

• acceptable convergence speed after around 1500 iterations. It is apparent that there is a favorable agreement between the optimized proposed model of graphene-based EGFETs device and experimental result. It can be concluded that, the presented model can be applied as a powerful tool to optimize the graphene

• quantum capacitance of EGFETs based single-layer graphene. A flowchart of ACO-based algorithm for optimizing the quantum capacitance model. Comparison between the proposed single-layer graphene quantum capacitance model, the optimized proposed model and the experimental extracted data. The convergence

Single-asperity contact mechanics with positive and negative work of adhesion: Influence of finite-range interactions and a continuum description for the squeeze-out of wetting fluids

• Martin H. Müser

Beilstein J. Nanotechnol. 2014, 5, 419–437, doi:10.3762/bjnano.5.50

• origin behave qualitatively different from the MD or the exponential model. They approach the DMT limit for the contact radius fairly quickly, i.e., roughly with However, convergence to the JKR limit is poor. The latter can be improved by defining the contact line to be located where g′(r) takes its

• including the correct asymptotics in the ac(FN) expression does not necessarily improve the fits in the range from slightly above the pull-off force at negative loads to several times the absolute pull-off force. This is demonstrated in Figure 13. Moreover, convergence to the correct ac(FN) dependence at

• – that the JKR limit is quickly reached as the Tabor coefficient increases. However, convergence to the DMT limit with decreasing is rather slow. It is particularly slow for the normal displacement. E.g., to have a maximum error in ac(FN = 0) and d(FN = 0) that is of order 1% with respect to a desired

Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces

• Adam Sweetman and
• Andrew Stannard

Beilstein J. Nanotechnol. 2014, 5, 386–393, doi:10.3762/bjnano.5.45

• applied [1][6][11][12][13][14] in these types of experiment. We note in passing that even for this simple function it was necessary to constrain the range and starting value of the fit parameters in order to ensure reliable convergence of the curve fitting algorithm (for example the parameter c was

• usually constrained to be between 1 and 3). All parameters were allowed to fully relax within the constraints that allowed for reliable convergence of the curve fitting algorithm, and we note that none of the fit parameter values were limited at the constraint boundaries for any of the fits presented here

Fabrication of carbon nanomembranes by helium ion beam lithography

• Xianghui Zhang,
• Henning Vieker,
• André Beyer and
• Armin Gölzhäuser

Beilstein J. Nanotechnol. 2014, 5, 188–194, doi:10.3762/bjnano.5.20

• a higher resolution and the small convergence angle of the ion beam leads to a larger depth of field. As an imaging tool, this instrument has a high surface sensitivity and is particularly advantageous to distinguish monolayers from the supporting substrate [18][19]. As a tool for nanofabrication

Core level binding energies of functionalized and defective graphene

• Toma Susi,
• Markus Kaukonen,
• Paula Havu,
• Mathias P. Ljungberg,
• Paola Ayala and
• Esko I. Kauppinen

Beilstein J. Nanotechnol. 2014, 5, 121–132, doi:10.3762/bjnano.5.12

• wave method [29] was used with frozen core electrons, and exchange and correlation was estimated by the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation [30]. Periodic boundary conditions were applied with a Monkhorst–Pack [31] k-point mesh up to 5 × 5 × 1 k-points. Convergence checks

• resources was 11 × 11. However, the C 1s energy was fully converged already for a 9 × 9 unit cell (a total of 162 atoms) when employing 3 × 3 × 1 k-points in the calculation. This convergence was checked to be valid also for more extended defects. A vacuum distance of 8 Å in the direction perpendicular to

• the graphene plane was sufficient to ensure convergence in all cases, including the highly non-planar -COOH functional group. All structures were allowed to fully relax so that the maximum forces reached less than 0.01 eV/atom. The all-electron projected density of states of the pristine graphene

The role of oxygen and water on molybdenum nanoclusters for electro catalytic ammonia production

• Jakob G. Howalt and
• Tejs Vegge

Beilstein J. Nanotechnol. 2014, 5, 111–120, doi:10.3762/bjnano.5.11

• is applied, giving a separation of 14 Å between the clusters. When solving the electronic density self-consistently, the convergence criteria have been chosen such that the changes were ≤10−5 eV for the energy and 10−4 electrons per valence electron for the density. In all calculations, a Fermi

Many-body effects in semiconducting single-wall silicon nanotubes

• Wei Wei and
• Timo Jacob

Beilstein J. Nanotechnol. 2014, 5, 19–25, doi:10.3762/bjnano.5.2

• separate periodic images and to avoid spurious interactions. Geometry optimization has been done with an energy convergence criterion of 5.0 × 10−6 eV and a force convergence criterion of 0.01 eV/Å. As already summarized in [47], starting from the LDA wave functions and Coulomb screening, QP energies

Dynamic nanoindentation by instrumented nanoindentation and force microscopy: a comparative review

• Sidney R. Cohen and
• Estelle Kalfon-Cohen

Beilstein J. Nanotechnol. 2013, 4, 815–833, doi:10.3762/bjnano.4.93

Influence of particle size and fluorination ratio of CF_x precursor compounds on the electrochemical performance of C–FeF₂ nanocomposites for reversible lithium storage

• Ben Breitung,
• M. Anji Reddy,
• Venkata Sai Kiran Chakravadhanula,
• Michael Engel,
• Christian Kübel,
• Annie K. Powell,
• Horst Hahn and
• Maximilian Fichtner

Beilstein J. Nanotechnol. 2013, 4, 705–713, doi:10.3762/bjnano.4.80

• mA/g between 1.3 V and 4.3 V (Figure 7). C(FeF2)0.5_300 showed the highest capacity and lowest ICL after a few cycles, which led to a high stability of the capacity for the first 40/30 cycles at 25/40 °C. At 40 °C no convergence to a stable capacity value was observed, instead the capacity faded

Deformation-induced grain growth and twinning in nanocrystalline palladium thin films

• Aaron Kobler,
• Jochen Lohmiller,
• Jonathan Schäfer,
• Michael Kerber,
• Anna Castrup,
• Ankush Kashiwar,
• Patric A. Gruber,
• Karsten Albe,
• Horst Hahn and
• Christian Kübel

Beilstein J. Nanotechnol. 2013, 4, 554–566, doi:10.3762/bjnano.4.64

• lens 6 and extraction voltage 4.5 kV, resulting in a spot size of about 1 nm and a semi convergence angle of 1.4 mrad. An ASTAR system (Nanomegas) was used for ACOM diffraction data acquisition. Data processing consisted of the following steps [23]: Pixel filtering of the orientation maps with a median

Molecular dynamics simulations of mechanical failure in polymorphic arrangements of amyloid fibrils containing structural defects

• Hlengisizwe Ndlovu,
• Alison E. Ashcroft,
• Sheena E. Radford and
• Sarah A. Harris

Beilstein J. Nanotechnol. 2013, 4, 429–440, doi:10.3762/bjnano.4.50

• carbon-α atoms was used to monitor convergence of the MD simulations. This was achieved within 20 and 40 ns for the 8 × 2 and 16 × 2 models, respectively. Steered molecular dynamics simulation The details of the SMD protocol used are identical to those we have described elsewhere [23]; only a summary is

Polynomial force approximations and multifrequency atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

• different types of interpolation polynomials with different convergence properties can also be applied. The polynomial reconstruction based on force quadrature data can be implemented even more efficiently than the reconstruction on spectral data since multiple Fourier transforms to construct the coupling

Influence of the solvent on the stability of bis(terpyridine) structures on graphite

• Daniela Künzel and
• Axel Groß

Beilstein J. Nanotechnol. 2013, 4, 269–277, doi:10.3762/bjnano.4.29

• for atomistic simulation studies) [22], Dreiding [23] and Consistent Valence (CVFF) [24] force fields included in the Forcite module of the Accelrys’ Materials Studio package. The graphite surface is modeled by a five-layer graphite (0001) slab. Convergence criteria are chosen according to the

Hydrogen-plasma-induced magnetocrystalline anisotropy ordering in self-assembled magnetic nanoparticle monolayers

• Alexander Weddemann,
• Judith Meyer,
• Anna Regtmeier,
• Irina Janzen,
• Dieter Akemeier and
• Andreas Hütten

Beilstein J. Nanotechnol. 2013, 4, 164–172, doi:10.3762/bjnano.4.16

• dynamics are not in the scope of this work and the value of the damping parameter may be adjusted to provide a high numerical convergence rate. We chose α = 1 [26]. For the integration with respect to time, a backward differential formula of fifth order is applied. As a model system, we consider a two