428 research outputs found
Erratum: âCalculating frequency-dependent hyperpolarizabilities using time-dependent density functional theoryâ [J. Chem. Phys. 109, 10644 (1998)]
An accurate determination of frequency-dependent molecular hyperpolarizabilities is at the same time of possible technological importance and theoretically challenging. For large molecules, HartreeâFock theory was until recently the only available ab initio approach. However, correlation effects are usually very important for this property, which makes it desirable to have a computationally efficient approach in which those effects are (approximately) taken into account. We have recently shown that frequency-dependent hyperpolarizabilities can be efficiently obtained using time-dependent density functional theory. Here, we shall present the necessary theoretical framework and the details of our implementation in the Amsterdam Density Functional program. Special attention will be paid to the use of fit functions for the density and to numerical integration, which are typical of density functional codes. Numerical examples for He, CO, and para-nitroaniline are presented, as evidence for the correctness of the equations and the implementation.<br/
Accurate density functional calculations on frequency-dependent hyperpolarizabilities of small molecules
In this paper we present time-dependent density functional calculations on frequency-dependent first (ÎČ) and second (Îł) hyperpolarizabilities for the set of small molecules,
Improved density functional theory results for frequency-dependent polarizabilities, by the use of an exchange-correlation potential with correct asymptotic behavior.
The exchangeâcorrelation potentials vxc which are currently fashionable in density functional theory (DFT), such as those obtained from the local density approximation (LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic longârange behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequencyâdependent molecular response properties within timeâdependent DFT, which we described in more detail elsewhere, is summarized
Ferromagnetism in Mn doped GaAs due to substitutional-interstitial complexes
While most calculations on the properties of the ferromagnetic semiconductor
GaAs:Mn have focussed on isolated Mn substituting the Ga site (Mn), we
investigate here whether alternate lattice sites are favored and what the
magnetic consequences of this might be. Under As-rich (Ga-poor) conditions
prevalent at growth, we find that the formation energies are lower for
Mn over interstitial Mn (Mn).As the Fermi energy is shifted towards
the valence band maximum via external -doping, the formation energy of
Mn is reduced relative to Mn. Furthermore, under epitaxial growth
conditions, the solubility of both substitutional and interstitial Mn are
strongly enhanced over what is possible under bulk growth conditions. The high
concentration of Mn attained under epitaxial growth of p-type material opens
the possibility of Mn atoms forming small clusters. We consider various types
of clusters, including the Coulomb-stabilized clusters involving two Mn
and one Mn. While isolated Mn are hole killers (donors), and therefore
destroy ferromagnetism,complexes such as Mn-Mn-Mn) are found
to be more stable than complexes involving Mn-Mn-Mn. The
former complexes exhibit partial or total quenching of holes, yet Mn in
these complexes provide a channel for a ferromagnetic arrangement of the spins
on the two Mn within the complex. This suggests that ferromagnetism in
Mn doped GaAs arises both from holes due to isolated Mn as well as from
strongly Coulomb stabilized Mn-Mn-Mn clusters.Comment: 7 figure
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 âspike vectorâ depend exclusively on a cellâs location within the SC motor map (Goossens and Van Opstal, in J Neurophysiol 95: 2326â2341, 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 (âmain sequence propertiesâ and âcomponent stretchingâ) 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
Initial-state dependence in time-dependent density functional theory
Time-dependent density functionals in principle depend on the initial state
of the system, but this is ignored in functional approximations presently in
use. For one electron it is shown there is no initial-state dependence: for any
density, only one initial state produces a well-behaved potential. For two
non-interacting electrons with the same spin in one-dimension, an initial
potential that makes an alternative initial wavefunction evolve with the same
density and current as a ground state is calculated. This potential is
well-behaved and can be made arbitrarily different from the original potential
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
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
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
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