135,814 research outputs found
Reliable estimation of prediction uncertainty for physico-chemical property models
The predictions of parameteric property models and their uncertainties are
sensitive to systematic errors such as inconsistent reference data, parametric
model assumptions, or inadequate computational methods. Here, we discuss the
calibration of property models in the light of bootstrapping, a sampling method
akin to Bayesian inference that can be employed for identifying systematic
errors and for reliable estimation of the prediction uncertainty. We apply
bootstrapping to assess a linear property model linking the 57Fe Moessbauer
isomer shift to the contact electron density at the iron nucleus for a diverse
set of 44 molecular iron compounds. The contact electron density is calculated
with twelve density functionals across Jacob's ladder (PWLDA, BP86, BLYP, PW91,
PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error
diagnostics and reliable, locally resolved uncertainties for isomer-shift
predictions. Pure and hybrid density functionals yield average prediction
uncertainties of 0.06-0.08 mm/s and 0.04-0.05 mm/s, respectively, the latter
being close to the average experimental uncertainty of 0.02 mm/s. Furthermore,
we show that both model parameters and prediction uncertainty depend
significantly on the composition and number of reference data points.
Accordingly, we suggest that rankings of density functionals based on
performance measures (e.g., the coefficient of correlation, r2, or the
root-mean-square error, RMSE) should not be inferred from a single data set.
This study presents the first statistically rigorous calibration analysis for
theoretical Moessbauer spectroscopy, which is of general applicability for
physico-chemical property models and not restricted to isomer-shift
predictions. We provide the statistically meaningful reference data set MIS39
and a new calibration of the isomer shift based on the PBE0 functional.Comment: 49 pages, 9 figures, 7 table
Sum Rule Approach to the Isoscalar Giant Monopole Resonance in Drip Line Nuclei
Using the density-dependent Hartree-Fock approximation and Skyrme forces
together with the scaling method and constrained Hartree-Fock calculations, we
obtain the average energies of the isoscalar giant monopole resonance. The
calculations are done along several isotopic chains from the proton to the
neutron drip lines. It is found that while approaching the neutron drip line,
the scaled and the constrained energies decrease and the resonance width
increases. Similar but smaller effects arise near the proton drip line,
although only for the lighter isotopic chains. A qualitatively good agreement
is found between our sum rule description and the presently existing random
phase approximation results. The ability of the semiclassical approximations of
the Thomas-Fermi type, which properly describe the average energy of the
isoscalar giant monopole resonance for stable nuclei, to predict average
properties for nuclei near the drip lines is also analyzed. We show that when
hbar corrections are included, the semiclassical estimates reproduce, on
average, the quantal excitation energies of the giant monopole resonance for
nuclei with extreme isospin values.Comment: 31 pages, 12 figures, revtex4; some changes in text and figure
Alignment methods for biased multicanonical sampling
The efficiency of the multicanonical procedure can be significantly improved by applying an additional bias to the numerically generated sample space. However, results obtained by biasing in different sampling regions cannot in general be accurately combined, since their relative normalization coefficient is not known precisely. We demonstrate that for overlapping biasing regions a simple iterative procedure can be employed to determine the required coefficients
Automating first-principles phase diagram calculations
Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented
Gamow-Teller strength distributions for nuclei in pre-supernova stellar cores
Electron-capture and -decay of nuclei in the core of massive stars
play an important role in the stages leading to a type II supernova explosion.
Nuclei in the f-p shell are particularly important for these reactions in the
post Silicon-burning stage of a presupernova star. In this paper, we
characterise the energy distribution of the Gamow-Teller Giant Resonance (GTGR)
for mid-fp-shell nuclei in terms of a few shape parameters, using data obtained
from high energy, forward scattering (p,n) and (n,p) reactions. The energy of
the GTGR centroid is further generalised as function of nuclear
properties like mass number, isospin and other shell model properties of the
nucleus. Since a large fraction of the GT strength lies in the GTGR region, and
the GTGR is accessible for weak transitions taking place at energies relevant
to the cores of presupernova and collapsing stars, our results are relevant to
the study of important -capture and -decay rates of arbitrary,
neutron-rich, f-p shell nuclei in stellar cores. Using the observed GTGR and
Isobaric Analog States (IAS) energy systematics we compare the coupling
coefficients in the Bohr-Mottelson two particle interaction Hamiltonian for
different regions of the Isotope Table.Comment: Revtex, 28 pages +7 figures (PostScript Figures, uuencoded, filename:
Sutfigs.uu). If you have difficulty printing the figures, please contact
[email protected]. Accepted for publication in Phys. Rev. C, Nov 01,
199
Monte Carlo Methods for Equilibrium and Nonequilibrium Problems in Interfacial Electrochemistry
We present a tutorial discussion of Monte Carlo methods for equilibrium and
nonequilibrium problems in interfacial electrochemistry. The discussion is
illustrated with results from simulations of three specific systems: bromine
adsorption on silver (100), underpotential deposition of copper on gold (111),
and electrodeposition of urea on platinum (100).Comment: RevTex, 14 pages, 8 figures. To appear in book _Interfacial
Electrochemisty
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