454 research outputs found
Robust non-adiabatic molecular dynamics for metals and insulators
We present a new formulation of the correlated electron-ion dynamics (CEID)
scheme, which systematically improves Ehrenfest dynamics by including quantum
fluctuations around the mean-field atomic trajectories. We show that the method
can simulate models of non-adiabatic electronic transitions, and test it
against exact integration of the time-dependent Schroedinger equation. Unlike
previous formulations of CEID, the accuracy of this scheme depends on a single
tunable parameter which sets the level of atomic fluctuations included. The
convergence to the exact dynamics by increasing the tunable parameter is
demonstrated for a model two level system. This algorithm provides a smooth
description of the non-adiabatic electronic transitions which satisfies the
kinematic constraints (energy and momentum conservation) and preserves quantum
coherence. The applicability of this algorithm to more complex atomic systems
is discussed.Comment: 36 pages, 5 figures. Accepted for publication in Journal of Chemical
Physic
Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested
Inelastic quantum transport: the self-consistent Born approximation and correlated electron-ion dynamics
A dynamical method for inelastic transport simulations in nanostructures is
compared with a steady-state method based on non-equilibrium Green's functions.
A simplified form of the dynamical method produces, in the steady state in the
weak-coupling limit, effective self-energies analogous to those in the Born
Approximation due to electron-phonon coupling. The two methods are then
compared numerically on a resonant system consisting of a linear trimer weakly
embedded between metal electrodes. This system exhibits enhanced heating at
high biases and long phonon equilibration times. Despite the differences in
their formulation, the static and dynamical methods capture local
current-induced heating and inelastic corrections to the current with good
agreement over a wide range of conditions, except in the limit of very high
vibrational excitations, where differences begin to emerge.Comment: 12 pages, 7 figure
Block bond-order potential as a convergent moments-based method
The theory of a novel bond-order potential, which is based on the block
Lanczos algorithm, is presented within an orthogonal tight-binding
representation. The block scheme handles automatically the very different
character of sigma and pi bonds by introducing block elements, which produces
rapid convergence of the energies and forces within insulators, semiconductors,
metals, and molecules. The method gives the first convergent results for
vacancies in semiconductors using a moments-based method with a low number of
moments. Our use of the Lanczos basis simplifies the calculations of the band
energy and forces, which allows the application of the method to the molecular
dynamics simulations of large systems. As an illustration of this convergent
O(N) method we apply the block bond-order potential to the large scale
simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.
The transfer of energy between electrons and ions in solids
In this review we consider those processes in condensed matter that involve
the irreversible flow of energy between electrons and nuclei that follows from
a system being taken out of equilibrium. We survey some of the more important
experimental phenomena associated with these processes, followed by a number of
theoretical techniques for studying them. The techniques considered are those
that can be applied to systems containing many non-equivalent atoms. They
include both perturbative approaches (Fermi's Golden Rule, and non-equilibrium
Green's functions) and molecular dynamics based (the Ehrenfest approximation,
surface hopping, semi-classical gaussian wavefunction methods and correlated
electron-ion dynamics). These methods are described and characterised, with
indications of their relative merits.Comment: LaTeX with IoP style files, 43 pages, 3 figure
Efficient Recursion Method for Inverting Overlap Matrix
A new O(N) algorithm based on a recursion method, in which the computational
effort is proportional to the number of atoms N, is presented for calculating
the inverse of an overlap matrix which is needed in electronic structure
calculations with the the non-orthogonal localized basis set. This efficient
inverting method can be incorporated in several O(N) methods for
diagonalization of a generalized secular equation. By studying convergence
properties of the 1-norm of an error matrix for diamond and fcc Al, this method
is compared to three other O(N) methods (the divide method, Taylor expansion
method, and Hotelling's method) with regard to computational accuracy and
efficiency within the density functional theory. The test calculations show
that the new method is about one-hundred times faster than the divide method in
computational time to achieve the same convergence for both diamond and fcc Al,
while the Taylor expansion method and Hotelling's method suffer from numerical
instabilities in most cases.Comment: 17 pages and 4 figure
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