380,026 research outputs found
Multiscale simulations in simple metals: a density-functional based methodology
We present a formalism for coupling a density functional theory-based quantum
simulation to a classical simulation for the treatment of simple metallic
systems. The formalism is applicable to multiscale simulations in which the
part of the system requiring quantum-mechanical treatment is spatially confined
to a small region. Such situations often arise in physical systems where
chemical interactions in a small region can affect the macroscopic mechanical
properties of a metal. We describe how this coupled treatment can be
accomplished efficiently, and we present a coupled simulation for a bulk
aluminum system.Comment: 15 pages, 7 figure
Simple implementation of complex functionals: scaled selfconsistency
We explore and compare three approximate schemes allowing simple
implementation of complex density functionals by making use of selfconsistent
implementation of simpler functionals: (i) post-LDA evaluation of complex
functionals at the LDA densities (or those of other simple functionals); (ii)
application of a global scaling factor to the potential of the simple
functional; and (iii) application of a local scaling factor to that potential.
Option (i) is a common choice in density-functional calculations. Option (ii)
was recently proposed by Cafiero and Gonzalez. We here put their proposal on a
more rigorous basis, by deriving it, and explaining why it works, directly from
the theorems of density-functional theory. Option (iii) is proposed here for
the first time. We provide detailed comparisons of the three approaches among
each other and with fully selfconsistent implementations for Hartree,
local-density, generalized-gradient, self-interaction corrected, and
meta-generalized-gradient approximations, for atoms, ions, quantum wells and
model Hamiltonians. Scaled approaches turn out to be, on average, better than
post-approaches, and unlike these also provide corrections to eigenvalues and
orbitals. Scaled selfconsistency thus opens the possibility of efficient and
reliable implementation of density functionals of hitherto unprecedented
complexity.Comment: 12 pages, 1 figur
Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics
A variety of researchers have successfully obtained the parameters of low
dimensional diffusion models using the data that comes out of atomistic
simulations. This naturally raises a variety of questions about efficient
estimation, goodness-of-fit tests, and confidence interval estimation. The
first part of this article uses maximum likelihood estimation to obtain the
parameters of a diffusion model from a scalar time series. I address numerical
issues associated with attempting to realize asymptotic statistics results with
moderate sample sizes in the presence of exact and approximated transition
densities. Approximate transition densities are used because the analytic
solution of a transition density associated with a parametric diffusion model
is often unknown.I am primarily interested in how well the deterministic
transition density expansions of Ait-Sahalia capture the curvature of the
transition density in (idealized) situations that occur when one carries out
simulations in the presence of a "glassy" interaction potential. Accurate
approximation of the curvature of the transition density is desirable because
it can be used to quantify the goodness-of-fit of the model and to calculate
asymptotic confidence intervals of the estimated parameters. The second part of
this paper contributes a heuristic estimation technique for approximating a
nonlinear diffusion model. A "global" nonlinear model is obtained by taking a
batch of time series and applying simple local models to portions of the data.
I demonstrate the technique on a diffusion model with a known transition
density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly
shortened
Detection of periodicity in functional time series
We derive several tests for the presence of a periodic component in a time
series of functions. We consider both the traditional setting in which the
periodic functional signal is contaminated by functional white noise, and a
more general setting of a contaminating process which is weakly dependent.
Several forms of the periodic component are considered. Our tests are motivated
by the likelihood principle and fall into two broad categories, which we term
multivariate and fully functional. Overall, for the functional series that
motivate this research, the fully functional tests exhibit a superior balance
of size and power. Asymptotic null distributions of all tests are derived and
their consistency is established. Their finite sample performance is examined
and compared by numerical studies and application to pollution data
Global hybrids from the semiclassical atom theory satisfying the local density linear response
We propose global hybrid approximations of the exchange-correlation (XC)
energy functional which reproduce well the modified fourth-order gradient
expansion of the exchange energy in the semiclassical limit of many-electron
neutral atoms and recover the full local density approximation (LDA) linear
response. These XC functionals represent the hybrid versions of the APBE
functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional
correlation functional which uses the localization concept of the correlation
energy density to improve the compatibility with the Hartree-Fock exchange as
well as the coupling-constant-resolved XC potential energy. Broad energetical
and structural testings, including thermochemistry and geometry, transition
metal complexes, non-covalent interactions, gold clusters and small
gold-molecule interfaces, as well as an analysis of the hybrid parameters, show
that our construction is quite robust. In particular, our testing shows that
the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE,
performs remarkably well for a broad palette of systems and properties, being
generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical
dispersion corrections are also provided.Comment: 12 pages, 4 figure
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