46,028 research outputs found
Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10,000+ atoms
The recent progress of linear-scaling or O(N) methods in the density
functional theory (DFT) is remarkable. We expect that first-principles
molecular dynamics (FPMD) simulations based on DFT can now treat more realistic
and complex systems using the O(N) technique. However, very few examples of
O(N) FPMD simulations exist so far and the information for the accuracy or
reliability of the simulations is very limited. In this paper, we show that
efficient and robust O(N) FPMD simulations are now possible by the combination
of the extended Lagrangian Born-Oppenheimer molecular dynamics method, which
was recently proposed by Niklasson et al (Phys. Rev. Lett. 100, 123004 (2008)),
and the density matrix method as an O(N) technique. Using our linear-scaling
DFT code Conquest, we investigate the reliable calculation conditions for the
accurate O(N) FPMD and demonstrate that we are now able to do actual and
reliable self-consistent FPMD simulation of a very large system containing
32,768 atoms.Comment: 26 pages, 10 figures, accepted by J. Chem. Theory Compu
Simulating chemistry efficiently on fault-tolerant quantum computers
Quantum computers can in principle simulate quantum physics exponentially
faster than their classical counterparts, but some technical hurdles remain.
Here we consider methods to make proposed chemical simulation algorithms
computationally fast on fault-tolerant quantum computers in the circuit model.
Fault tolerance constrains the choice of available gates, so that arbitrary
gates required for a simulation algorithm must be constructed from sequences of
fundamental operations. We examine techniques for constructing arbitrary gates
which perform substantially faster than circuits based on the conventional
Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf.
Comput.}, \textbf{6}:81, 2006]. For a given approximation error ,
arbitrary single-qubit gates can be produced fault-tolerantly and using a
limited set of gates in time which is or ; with sufficient parallel preparation of ancillas, constant average
depth is possible using a method we call programmable ancilla rotations.
Moreover, we construct and analyze efficient implementations of first- and
second-quantized simulation algorithms using the fault-tolerant arbitrary gates
and other techniques, such as implementing various subroutines in constant
time. A specific example we analyze is the ground-state energy calculation for
Lithium hydride.Comment: 33 pages, 18 figure
Stochastic density functional theory
Linear-scaling implementations of density functional theory (DFT) reach their
intended efficiency regime only when applied to systems having a physical size
larger than the range of their Kohn-Sham density matrix (DM). This causes a
problem since many types of large systems of interest have a rather broad DM
range and are therefore not amenable to analysis using DFT methods. For this
reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM
evaluations, is emerging as an attractive alternative linear-scaling approach.
This review develops a general formulation of sDFT in terms of a
(non)orthogonal basis representation and offers an analysis of the statistical
errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set
implementation of sDFT, applied to water clusters and silicon nanocrystals, it
demonstrates and explains how the standard deviation and the bias depend on the
sampling rate and the system size in various types of calculations. We also
develop basis-set embedded-fragments theory, demonstrating its utility for
reducing the SEs for energy, density of states and nuclear force calculations.
Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU
wall-time linear-scaling. The method parallelizes well over distributed
processors with good scalability and therefore may find use in the upcoming
exascale computing architectures
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 electrons), applicable to
metals and insulators alike. In lieu of explicit diagonalization of the
Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ
a two-level Chebyshev polynomial filter based complementary subspace strategy
to: 1) compute a set of vectors that span the occupied subspace of the
Hamiltonian; 2) reduce subspace diagonalization to just partially occupied
states; and 3) obtain those states in an efficient, scalable manner via an
inner Chebyshev-filter iteration. By reducing the necessary computation to just
partially occupied states, and obtaining these through an inner Chebyshev
iteration, our approach reduces the cost of large metallic calculations
significantly, while eliminating subspace diagonalization for insulating
systems altogether. We describe the implementation of the method within the
framework of the Discontinuous Galerkin (DG) electronic structure method and
show that this results in a computational scheme that can effectively tackle
bulk and nano systems containing tens of thousands of electrons, with chemical
accuracy, within a few minutes or less of wall clock time per SCF iteration on
large-scale computing platforms. We anticipate that our method will be
instrumental in pushing the envelope of large-scale ab initio molecular
dynamics. As a demonstration of this, we simulate a bulk silicon system
containing 8,000 atoms at finite temperature, and obtain an average SCF step
wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2
Network equilibration and first-principles liquid water.
Motivated by the very low diffusivity recently found in ab initio simulations of liquid water, we have studied its dependence with temperature, system size, and duration of the simulations. We use ab initio molecular dynamics (AIMD), following the Born-Oppenheimer forces obtained from density-functional theory (DFT). The linear-scaling capability of our method allows the consideration of larger system sizes (up to 128 molecules in this study), even if the main emphasis of this work is in the time scale. We obtain diffusivities that are substantially lower than the experimental values, in agreement with recent findings using similar methods. A fairly good agreement with D(T) experiments is obtained if the simulation temperature is scaled down by approximately 20%. It is still an open question whether the deviation is due to the limited accuracy of present density functionals or to quantum fluctuations, but neither technical approximations (basis set, localization for linear scaling) nor the system size (down to 32 molecules) deteriorate the DFT description in an appreciable way. We find that the need for long equilibration times is consequence of the slow process of rearranging the H-bond network (at least 20 ps at AIMDs room temperature). The diffusivity is observed to be very directly linked to network imperfection. This link does not appear an artifact of the simulations, but a genuine property of liquid water
Perspectives on the simulation of micro gas and nano liquid flows
Micro- and nano-scale fluid systems can behave very differently from their macro-scale counterparts. Remarkably, there is no sufficiently accurate, computationally efficient, and — most importantly — generally agreed fluid dynamic model that encapsulates all of this important behaviour. The only thing that researchers can agree on is that the conventional Navier-Stokes fluid equations are unable to capture the unique complexity of these often locally non-thermodynamic-equilibrium flows. Here, we outline recent work on developing and exploring new models for these flows, highlighting, in particular, slip flow as a quintessential non-equilibrium (or sub-continuum) phenomenon. We describe the successes and failures of various hydrodynamic and molecular models in capturing the non-equilibrium flow physics in current test applications in micro and nano engineering, including the aerodynamic drag of a sphere in a rarefied gas, and the flow of water along carbon nanotubes
Glass Dynamics at High Strain Rates
We present a shear-transformation-zone (STZ) theoretical analysis of
molecular-dynamics simulations of a rapidly sheared metallic glass. These
simulations are especially revealing because, although they are limited to high
strain rates, they span temperatures ranging from well below to well above the
glass transition. With one important discrepancy, the STZ theory reproduces the
simulation data, including the way in which those data can be made to collapse
onto simple curves by a scaling transformation. The STZ analysis implies that
the system's behavior at high strain rates is controlled primarily by
effective-temperature thermodynamics, as opposed to system-specific details of
the molecular interactions. The discrepancy between theory and simulations
occurs at the lower strain rates for temperatures near the glass transition. We
argue that this discrepancy can be resolved by the same multi-species
generalization of STZ theory that has been proposed recently for understanding
frequency-dependent viscoelastic responses, Stokes-Einstein violations, and
stretched-exponential relaxation in equilibrated glassy materials.Comment: 9 pages, 6 figure
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