238 research outputs found
Ab initio studies of structures and properties of small potassium clusters
We have studied the structure and properties of potassium clusters containing
even number of atoms ranging from 2 to 20 at the ab initio level. The geometry
optimization calculations are performed using all-electron density functional
theory with gradient corrected exchange-correlation functional. Using these
optimized geometries we investigate the evolution of binding energy, ionization
potential, and static polarizability with the increasing size of the clusters.
The polarizabilities are calculated by employing Moller-Plesset perturbation
theory and time dependent density functional theory. The polarizabilities of
dimer and tetramer are also calculated by employing large basis set coupled
cluster theory with single and double excitations and perturbative triple
excitations. The time dependent density functional theory calculations of
polarizabilities are carried out with two different exchange-correlation
potentials: (i) an asymptotically correct model potential and (ii) within the
local density approximation. A systematic comparison with the other available
theoretical and experimental data for various properties of small potassium
clusters mentioned above has been performed. These comparisons reveal that both
the binding energy and the ionization potential obtained with gradient
corrected potential match quite well with the already published data.
Similarly, the polarizabilities obtained with Moller-Plesset perturbation
theory and with model potential are quite close to each other and also close to
experimental data.Comment: 33 pages including 10 figure
Exchange and Correlation Kernels at the Resonance Frequency -- Implications for Excitation Energies in Density-Functional Theory
Specific matrix elements of exchange and correlation kernels in
time-dependent density-functional theory are computed. The knowledge of these
matrix elements not only constraints approximate time-dependent functionals,
but also allows to link different practical approaches to excited states,
either based on density-functional theory, or on many-body perturbation theory,
despite the approximations that have been performed to derive them.Comment: Submitted to Phys. Rev. Lett. (February 4, 1999). Other related
publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm
Linear ensemble-coding in midbrain superior colliculus specifies the saccade kinematics
Recently, we proposed an ensemble-coding scheme of the midbrain superior colliculus (SC) in which, during a saccade, each spike emitted by each recruited SC neuron contributes a fixed minivector to the gaze-control motor output. The size and direction of this ‘spike vector’ depend exclusively on a cell’s location within the SC motor map (Goossens and Van Opstal, in J Neurophysiol 95: 2326–2341, 2006). According to this simple scheme, the planned saccade trajectory results from instantaneous linear summation of all spike vectors across the motor map. In our simulations with this model, the brainstem saccade generator was simplified by a linear feedback system, rendering the total model (which has only three free parameters) essentially linear. Interestingly, when this scheme was applied to actually recorded spike trains from 139 saccade-related SC neurons, measured during thousands of eye movements to single visual targets, straight saccades resulted with the correct velocity profiles and nonlinear kinematic relations (‘main sequence properties– and ‘component stretching’) Hence, we concluded that the kinematic nonlinearity of saccades resides in the spatial-temporal distribution of SC activity, rather than in the brainstem burst generator. The latter is generally assumed in models of the saccadic system. Here we analyze how this behaviour might emerge from this simple scheme. In addition, we will show new experimental evidence in support of the proposed mechanism
Optical response of small silver clusters
The time-dependent local density approximation is applied to the optical
response of the silver clusters, Ag_2, Ag_3, Ag_8 and Ag_9^+. The calculation
includes all the electrons beyond the closed-shell Ag^{+11} ionic core, thus
including for the first time explicitly the filled d-shell in the response. The
excitation energy of the strong surface plasmon near 4 eV agrees well with
experiment. The theoretical transition strength is quenched by a factor of 4
with respect to the pure s-electron sum rule in Ag_8 due to the d-electrons. A
comparable amount of strength lies in complex states below 6 eV excitation. The
total below 6 eV, about 50% of the s sum rule, is consistent with published
experiments.Comment: 13 pages RevTex and 9 Postscript figure
Optimal Control of Saccades by Spatial-Temporal Activity Patterns in the Monkey Superior Colliculus
A major challenge in computational neurobiology is to understand how populations of noisy, broadly-tuned neurons produce accurate goal-directed actions such as saccades. Saccades are high-velocity eye movements that have stereotyped, nonlinear kinematics; their duration increases with amplitude, while peak eye-velocity saturates for large saccades. Recent theories suggest that these characteristics reflect a deliberate strategy that optimizes a speed-accuracy tradeoff in the presence of signal-dependent noise in the neural control signals. Here we argue that the midbrain superior colliculus (SC), a key sensorimotor interface that contains a topographically-organized map of saccade vectors, is in an ideal position to implement such an optimization principle. Most models attribute the nonlinear saccade kinematics to saturation in the brainstem pulse generator downstream from the SC. However, there is little data to support this assumption. We now present new neurophysiological evidence for an alternative scheme, which proposes that these properties reside in the spatial-temporal dynamics of SC activity. As predicted by this scheme, we found a remarkably systematic organization in the burst properties of saccade-related neurons along the rostral-to-caudal (i.e., amplitude-coding) dimension of the SC motor map: peak firing-rates systematically decrease for cells encoding larger saccades, while burst durations and skewness increase, suggesting that this spatial gradient underlies the increase in duration and skewness of the eye velocity profiles with amplitude. We also show that all neurons in the recruited population synchronize their burst profiles, indicating that the burst-timing of each cell is determined by the planned saccade vector in which it participates, rather than by its anatomical location. Together with the observation that saccade-related SC cells indeed show signal-dependent noise, this precisely tuned organization of SC burst activity strongly supports the notion of an optimal motor-control principle embedded in the SC motor map as it fully accounts for the straight trajectories and kinematic nonlinearity of saccades
Real-Space Mesh Techniques in Density Functional Theory
This review discusses progress in efficient solvers which have as their
foundation a representation in real space, either through finite-difference or
finite-element formulations. The relationship of real-space approaches to
linear-scaling electrostatics and electronic structure methods is first
discussed. Then the basic aspects of real-space representations are presented.
Multigrid techniques for solving the discretized problems are covered; these
numerical schemes allow for highly efficient solution of the grid-based
equations. Applications to problems in electrostatics are discussed, in
particular numerical solutions of Poisson and Poisson-Boltzmann equations.
Next, methods for solving self-consistent eigenvalue problems in real space are
presented; these techniques have been extensively applied to solutions of the
Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue
problems arising in semiconductor and polymer physics. Finally, real-space
methods have found recent application in computations of optical response and
excited states in time-dependent density functional theory, and these
computational developments are summarized. Multiscale solvers are competitive
with the most efficient available plane-wave techniques in terms of the number
of self-consistency steps required to reach the ground state, and they require
less work in each self-consistency update on a uniform grid. Besides excellent
efficiencies, the decided advantages of the real-space multiscale approach are
1) the near-locality of each function update, 2) the ability to handle global
eigenfunction constraints and potential updates on coarse levels, and 3) the
ability to incorporate adaptive local mesh refinements without loss of optimal
multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic
Nanooptics of molecular-shunted plasmonic nanojunctions.
Gold nanoparticles are separated above a planar gold film by 1.1 nm thick self-assembled molecular monolayers of different conductivities. Incremental replacement of the nonconductive molecules with a chemically equivalent conductive version differing by only one atom produces a strong 50 nm blue-shift of the coupled plasmon. With modeling this gives a conductance of 0.17G(0) per biphenyl-4,4'-dithiol molecule and a total conductance across the plasmonic junction of 30G(0). Our approach provides a reliable tool quantifying the number of molecules in each plasmonic hotspot, here <200.We acknowledge financial support from EPSRC grant EP/ G060649/1, EP/I012060/1, EP/L027151/1, EP/K028510/1, ERC grant LINASS 320503. F.B. acknowledges support from the Winton Programme for the Physics of Sustainability. C.T. and J.A. acknowledge financial support from Project FIS2013- 41184-P from MINECO, ETORTEK 2014-15 of the Basque Department of Industry and IT756-13 from the Basque consolidated groups.This paper was originally published in Nano Letters under a CC-BY licence (F Benz, C Tserkezis, LO Herrmann, B de Nijs, A Sanders, DO Sigle, L Pukenas, SD Evans, J Aizpurua, JJ Baumberg, Nano Letters 2015, 15, 669−674
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