Browsing by Subject "APPROXIMATION"

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  • Weller, Stefan; Klenk, Robert; Kelemen, Zsolt; Nyulászi, László; Nieger, Martin; Gudat, Dietrich (2022)
    Ferrocene-1,1 '-dithiol reacts with PCl3 and P(NMe2)(3) to give [3]ferrocenophanes with SPS-ansa-bridges comprising potentially reactive P-Cl and P-N bonds at the central bridge atom. The products were characterized by NMR data and single-crystal XRD studies. The P-chloro-derivative exists both in the solid state and in solution as a mixture of two energetically nearly degenerate conformers with different stereochemical disposition of the ansa-bridge. Activation parameters for the dynamic equilibration between both isomers in solution were determined by dynamic NMR spectroscopy. Computational studies suggest that the isomerization proceeds via a torsional motion of the bridging SPS-unit rather than via configuration inversion at the phosphorus atom.
  • Onninen, Jani; Pankka, Pekka (2021)
    We show that, for each 1 S-3 in the Sobolev class W-1,W-p(S-3, S-3).
  • Greiner, Jonas; Sundholm, Dage (2020)
    A generating function method was used to simulate the vibrationally resolved absorption and emission spectra of perylene, terrylene and quaterrylene. This method operates on the basis of adiabatic excitation energies and electronic ground and excited state vibrational frequencies. These parameters were calculated using density functional theory with the PBE0 functional for perylene and terrylene and with the BH-LYP functional for quaterrylene. The vertical excitation energies of the lower excited states were calculated using functionals with differing amounts of Hartree-Fock exchange. The optimal functional for each molecule was chosen by comparing these energies to literature excitation energies. Using this technique the calculated absorption spectra and the calculated emission spectrum of perylene were found to be in excellent agreement with the literature experimental spectra after introducing a shift and a scaling factor. The most prominent bands of the absorption spectra were assigned to their respective vibronic transitions.
  • Nedic, Mitja (2020)
    In this paper, we study a class of Borel measures on Double-struck capital Rn that arises as the class of representing measures of Herglotz-Nevanlinna functions. In particular, we study product measures within this class where products with the Lebesgue measures play a special role. Hence, we give several characterizations of the n-dimensional Lebesgue measure among all such measures and characterize all product measures that appear in this class of measures. Furthermore, analogous results for the class of positive Borel measures on the unit poly-torus with vanishing mixed Fourier coefficients are also presented, and the relation between the two classes of measures with regard to the obtained results is discussed.
  • Herranen, Joonas; Markkanen, Johannes; Muinonen, Karri (IEEE, 2016)
    URSI International Symposium on Electromagnetic Theory
    We establish a theoretical framework for solving the equations of motion for an arbitrarily shaped, isotropic, and homogeneous dust particle in the presence of radiation pressure. The scattering problem involved is solved by a surface integral equation method, and a rudimentary sketch of the numerical implementation is introduced with preliminary results agreeing with predictions.
  • Mendizabal, Fernando; Mera-Adasme, Raul; Xu, Wen-Hua; Sundholm, Dage (2017)
    Dye-sensitized solar-cell (DSSC) systems have been investigated by calculating light-absorption and electron-injection processes of the LD13 ([5,15-bis(2,6-(1,1-dimethylethyl)-phenyl)-10-4-dimethylaminophenylethynyl-20-4-carboxy phenylethynyl porphyrinato]zinc-(II)) and YD2-o-C8 ([5,15bis( 2,6-dioctoxyphenyl)-10-(bis(4-hexylphenyl)amino-20-4-carboxyphenylethynyl)porphyrinato]zinc-(II)) dyes adsorbed on a TiO2 cluster simulating the semiconductor. The binding energy of the dyes with the TiO2 clusters has been calculated at the density functional theory (DFT) level using the B3LYP and CAM-B3LYP functionals. The electronic excitation energies have been calculated at the time-dependent DFT (TDDFT) level for the dyes in the gas and solvent phase employing the B3LYP, CAM-B3LYP and BHLYP functionals. The calculated excitation energies have been compared to values obtained at the algebraic diagrammatic construction through second order (ADC(2)) level of theory. The TDDFT calculations with the B3LYP in tetrahydrofuran solvent with the dye and dye-TiO2 models yield excitation energies that agree well with the transitions in the experimental absorption spectra. Changes in the free energy for electron injection support the better performance of the dyes on the TiO2 clusters.
  • Leverentz, Hannah R.; Siepmann, J. Ilja; Truhlar, Donald G.; Loukonen, Ville; Vehkamäki, Hanna (2013)
  • Kurten, Theo; Hyttinen, Noora; D'Ambro, Emma Louise; Thornton, Joel; Prisle, Nonne Lyng (2018)
    We have used COSMO-RS (the conductor-like screening model for real solvents), as implemented in the COSMOtherm program, to compute the saturation vapor pressures at 298 K of two photo-oxidation products of isoprene: the dihydroxy dihydroperoxide C5H12O6, and the dihydroperoxy hydroxy aldehyde, C5H10O6. The predicted saturation vapor pressures were significantly higher (by up to a factor of 1000) than recent experimental results, very likely due to the overestimation of the effects of intramolecular hydrogen bonds, which tend to increase saturation vapor pressures by stabilizing molecules in the gas phase relative to the liquid. Modifying the hydrogen bond enthalpy parameter used by COSMOtherm can improve the agreement with experimental results - however the optimal parameter value is likely to be system-specific. Alternatively, vapor pressure predictions can be substantially improved (to within a factor of 5 of the experimental values for the two systems studied here) by selecting only conformers with a minimum number of intramolecular hydrogen bonds. The computed saturation vapor pressures were very sensitive to the details of the conformational sampling approach, with the default scheme implemented in the COSMOconf program proving insufficient for the task, for example by predicting significant differences between enantiomers, which should have identical physical properties. Even after exhaustive conformational sampling, COSMOtherm predicts significant differences in saturation vapor pressures between both structural isomers and diastereomers. For C5H12O6, predicted differences in p(sat) between structural isomers are up to 2 orders of magnitude, and differences between stereoisomers are up to a factor of 20 - though these differences are very likely exaggerated by the overestimation of the effect of intramolecular H-bonds. For C5H10O6, the maximum predicted differences between the three studied structural isomers and their diastereomer pairs are around a factor of 8 and a factor of 2, respectively, when only conformers lacking intramolecular hydrogen bonds are included in the calculations. In future studies of saturation vapor pressures of polyfunctional atmospheric oxidation products using COSMOtherm, we recommend first performing thorough conformational sampling and subsequently selecting conformers with a minimal number of intramolecular H-bonds.
  • Nene, Nuno R.; Mustonen, Ville; Illingworth, Christopher J. R. (2018)
    The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations have commonly been used but the model itself has rarely been tested against time-resolved genomic data. Here, we evaluate the extent to which it can be inferred as the correct model under a likelihood framework. Given genome-wide data from an evolutionary experiment, we validate the Wright-Fisher drift model as the better option for describing evolutionary trajectories in a finite population. This was found by evaluating its performance against a Gaussian model of allele frequency propagation. However, we note a range of circumstances under which standard Wright-Fisher drift cannot be correctly identified. (C) 2017 The Author(s). Published by Elsevier Ltd.
  • Chen, Chi-Chuan; Hyvönen, Jaakko; Schneider, Harald (2020)
    The microsoroid ferns are one of the largest subfamilies of the Polypodiaceae with over 180 species mainly found in the humid forests of tropical Australasia. The phylogenetic relationships are still unclear, especially the delimitation of the genus Microsorum which has been recognized to be non-monophyletic. We analysed the microsoroid ferns using six chloroplast DNA regions (rbcL, rps4+rps4-trnS, trnL+trnL-trnF, atpA, atpB and matK) in order to present a robust hypothesis of their phylogeny. Our results suggest that they comprise up to 17 genera; of them, 12 agree with a previously accepted generic classification. Five tribes are proposed based on the phylogenetic relationships. Most of the species traditionally included in the genus Microsorum are found in six genera belonging to two tribes. In addition to the commonly used DNA markers, the additional atpA and matK are helpful to provide information about the phylogenetic relationships of the microsoroid ferns.
  • Määttä, Jussi; Bazaliy, Viacheslav; Kimari, Jyri; Djurabekova, Flyura; Nordlund, Kai; Roos, Teemu (2021)
    Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and scalable open-source implementation. We derive novel closed form optimization criteria for pruning the models for continuous as well as binary data which arise in a challenging real-world material physics problem. The pruned models are optimized to provide compact and interpretable versions of larger models based on informed assumptions about the data distribution. Visualizations of the pruned models provide insight into the atomic configurations that determine atom-level migration processes in solid matter; these results may inform future research on designing more suitable descriptors for use with machine learning algorithms. (c) 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (
  • Hytonen, Tuomas; Naor, Assaf (2019)
    For every Banach space (Y, parallel to . parallel to(Y)) that admits an equivalent uniformly convex norm we prove that there exists c = c(Y) is an element of(0, infinity) with the following property. Suppose that n is an element of N and that X is an n-dimensional normed space with unit ball B-X. Then for every 1-Lipschitz function f : B-X -> Y and for every epsilon is an element of(0, 1/2] there exists a radius r >= exp (1/epsilon(cn)), a point x is an element of B-X with x + r B-X subset of B-X, and an affine mapping Lambda : X -> Y such that parallel to f (y) - Lambda (y)parallel to(Y)
  • Caron-Huot, Simon; Herranen, Matti (2018)
    The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar N = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.
  • Ducloué, B.; Szymanowski, L.; Wallon, S. (2016)
    We study the production of two forward jets with a large interval of rapidity at hadron colliders, which was proposed by Mueller and Navelet as a possible test of the high energy dynamics of QCD, within a complete next-to-leading logarithm framework. We show that using the Brodsky-Lepage-Mackenzie procedure to fix the renormalization scale leads to a very good description of the recent CMS data at the LHC for the azimuthal correlations of the jets. We show that the inclusion of next-to-leading order corrections to the jet vertex significantly reduces the importance of energy-momentum non-conservation which is inherent to the BFKL approach, for an asymmetric jet configuration. Finally, we argue that the double parton scattering contribution is negligible in the kinematics of actual CMS measurements.
  • Hamedani, A.; Byggmästar, J.; Djurabekova, F.; Alahyarizadeh, G.; Ghaderi, R.; Minuchehr, A.; Nordlund, K. (2020)
    We develop a silicon Gaussian approximation machine learning potential suitable for radiation effects, and use it for the first ab initio simulation of primary damage and evolution of collision cascades. The model reliability is confirmed by good reproduction of experimentally measured threshold displacement energies and sputtering yields. We find that clustering and recrystallization of radiation-induced defects, propagation pattern of cascades, and coordination defects in the heat spike phase show striking differences to the widely used analytical potentials. The results reveal that small defect clusters are predominant and show new defect structures such as a vacancy surrounded by three interstitials. Impact statement Quantum-mechanical level of accuracy in simulation of primary damage was achieved by a silicon machine learning potential. The results show quantitative and qualitative differences from the damage predicted by any previous models.
  • Hirvonen, Juho; Rybicki, Joel; Schmid, Stefan; Suomela, Jukka (2017)
    Let G be a d-regular triangle-free graph with in edges. We present an algorithm which finds a cut in G with at least (1/2 + 0.28125/root d)rn edges in expectation, improving upon Shearer's classic result. In particular, this implies that any d-regular triangle-free graph has a cut of at least this size, and thus, we obtain a new lower bound for the maximum number of edges in a bipartite subgraph of G. Our algorithm is simpler than Shearer's classic algorithm and it can be interpreted as a very efficient randomised distributed (local) algorithm: each node needs to produce only one random bit, and the algorithm runs in one round. The randomised algorithm itself was discovered using computational techniques. We show that for any fixed d, there exists a weighted neighbourhood graph N-d such that there is a one-to-one correspondence between heavy cuts of N-d and randomised local algorithms that find large cuts in any d-regular input graph. This turns out to be a useful tool for analysing the existence of cuts in d-regular graphs: we can compute the optimal cut of N-d to attain a lower bound on the maximum cut size of any d-regular triangle-free graph.
  • Byggmästar, Jesper; Hamedani, Ali; Nordlund, Kai; Djurabekova, Flyura (2019)
    We introduce a machine-learning interatomic potential for tungsten using the Gaussian approximation potential framework. We specifically focus on properties relevant for simulations of radiation-induced collision cascades and the damage they produce, including a realistic repulsive potential for the short-range many-body cascade dynamics and a good description of the liquid phase. Furthermore, the potential accurately reproduces surface properties and the energetics of vacancy and self-interstitial clusters, which have been longstanding deficiencies of existing potentials. The potential enables molecular dynamics simulations of radiation damage in tungsten with unprecedented accuracy.
  • Rauhalahti, M.; Munoz-Castro, A.; Sundholm, D. (2016)
    spherical and cavernous carbocage molecule exhibiting faces with larger ring sizes than regular fullerenes is a suitable species for investigating how molecular magnetic properties depend on the structure of the molecular framework. The studied all-carbon gaudiene (C-72) is a highly symmetrical molecule with three-and four-fold faces formed by twelve membered rings. Here, we attempt to unravel the magnetic response properties of C-72 by performing magnetic shielding and current density calculations with the external magnetic field applied in different directions. The obtained results indicate that the induced current density flows mainly along the chemical bonds that are largely perpendicular to the magnetic field direction. However, the overall current strength for different directions of the magnetic field is nearly isotropic differing by only 10% indicating that C-72 can to some extent be considered to be a spherical aromatic molecule, whose current density and magnetic shielding are ideally completely isotropic. The induced magnetic field is found to exhibit long-range shielding cones in the field direction with a small deshielding region located perpendicularly to the field outside the molecule. The magnetic shielding is isotropic inside the molecular framework of C-72, whereas an orientation-dependent magnetic response appears mainly at the exterior of the molecular cage.
  • Mahmood, Atif; Dimitrova, Maria; Wirz, Lukas N.; Sundholm, Dage (2022)
    The molecular structures of porphyrinoid cages were obtained by constructing small polyhedral graphs whose vertices have degree-4. The initial structures were then fully optimized at the density functional theory (DFT) level using the generalized gradient approximation. Some of polyhedral vertices were replaced with Zn-porphyrin units and their edges were replaced with ethyne or butadiyne bridges or connected by fusing two neighboring Zn-porphyrin units. Molecule 1 is an ethynebridge porphyrinoid nanotube, whose ends are sealed with a Zn-porphyrin. Molecule 2 is the corresponding open porphyrinoid nanotube. Molecule 3 is a clam-like porphyrinoid cage, whose shells consist of fused Zn-porphyrins, and the two halves are connected via butadiyne bridges. Molecule 4 is a cross-belt of fused Zn-porphyrins, and molecule 5 is a cross-belt of Zn-porphyrins connected with butadiyne bridges. The magnetically induced current density of the optimized porphyrinoid cages was calculated for determining the aromatic character, the degree of aromaticity and the current-density pathways. The current-density calculations were performed at the DFT level with the gauge-including magnetically induced currents (GIMIC) method using the B3LYP hybrid functional and def2-SVP basis sets. Calculations of the current densities show that molecule 2 sustains a paratropic ring current around the nanotube, whereas sealing the ends as in molecule 1 leads to an almost nonaromatic nanotube. Fusing porphyrinoids as in molecules 3 and 4 results in complicated current density pathways that differ from the ones usually appearing in porphyrinoids. The aromatic character of molecules 4 and 5 changes upon oxidation. The neutral molecule 4 is antiaromatic, whereas the dication is nonaromatic. Molecule 5 is nonaromatic, and its dication is aromatic.
  • Taubert, Stefan; Sundholm, Dage; Pichierri, Fabio (2010)