3,919 research outputs found
Quantum Monte Carlo Study of High Pressure Solid Molecular Hydrogen
We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground
state phase diagram of solid molecular hydrogen and examine the stability of
the most important insulating phases relative to metallic crystalline molecular
hydrogen. We develop a new method to account for finite-size errors by
combining the use of twist-averaged boundary conditions with corrections
obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional
theory. To study band-gap closure and find the metallization pressure, we
perform accurate quasi-particle many-body calculations using the method.
In the static approximation, our DMC simulations indicate a transition from the
insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa.
The band gap of Cmca-12 closes at roughly the same pressure. In the
dynamic DMC phase diagram, which includes the effects of zero-point energy, the
Cmca-12 structure remains stable up to 430 GPa, well above the pressure at
which the band gap closes. Our results predict that the semimetallic state
observed experimentally at around 360 GPa [Phys. Rev. Lett. {\bf 108}, 146402
(2012)] may correspond to the Cmca-12 structure near the pressure at which the
band gap closes. The dynamic DMC phase diagram indicates that the hexagonal
close packed structure, which has the largest band gap of the
insulating structures considered, is stable up to 220 GPa. This is consistent
with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {\bf 82},
060101(R) (2010)], which also reported a hexagonal close packed arrangement of
hydrogen molecules
{\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm
dense uniform electron gas in the thermodynamic limit. By combining QMC data
with linear response theory we are able to remove finite-size errors from the
potential energy over the entire warm dense regime, overcoming the deficiencies
of the existing finite-size corrections by Brown \emph{et al.}~[PRL
\textbf{110}, 146405 (2013)]. Extensive new QMC results for up to
electrons enable us to compute the potential energy and the
exchange-correlation free energy of the macroscopic electron gas with
an unprecedented accuracy of . A comparison of our new data to the recent parametrization of
by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals
significant deviations to the latter
Accurate exchange-correlation energies for the warm dense electron gas
Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average
-body density matrices for uniform electron gas systems of up to 10
matrix elements via a stochastic solution of the Bloch equation. The results of
these calculations resolve a current debate over the accuracy of the data used
to parametrize finite-temperature density functionals. Exchange-correlation
energies calculated using the real-space restricted path-integral formalism and
the -space configuration path-integral formalism disagree by up to
\% at certain reduced temperatures and densities . Our calculations confirm the accuracy of the configuration
path-integral Monte Carlo results available at high density and bridge the gap
to lower densities, providing trustworthy data in the regime typical of
planetary interiors and solids subject to laser irradiation. We demonstrate
that DMQMC can calculate free energies directly and present exact free energies
for and .Comment: Accepted version: added free energy data and restructured text. Now
includes supplementary materia
Ab-initio solution of the many-electron Schrödinger equation with deep neural networks
Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of wavefunction approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wavefunction Ansatz for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic Neural Network, as a powerful wavefunction Ansatz for many-electron systems. The Fermionic Neural Network is able to achieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods, opening the possibility of accurate direct optimisation of wavefunctions for previously intractable molecules and solids
Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project
The HANDE quantum Monte Carlo project offers accessible stochastic algorithms
for general use for scientists in the field of quantum chemistry. HANDE is an
ambitious and general high-performance code developed by a
geographically-dispersed team with a variety of backgrounds in computational
science. In the course of preparing a public, open-source release, we have
taken this opportunity to step back and look at what we have done and what we
hope to do in the future. We pay particular attention to development processes,
the approach taken to train students joining the project, and how a flat
hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE
The democratic origins of the term "group analysis": Karl Mannheim's "third way" for psychoanalysis and social science.
It is well known that Foulkes acknowledged Karl Mannheim as the
first to use the term ‘group analysis’. However, Mannheim’s work is
otherwise not well known. This article examines the foundations of
Mannheim’s sociological interest in groups using the Frankfurt
School (1929–1933) as a start point through to the brief correspondence
of 1945 between Mannheim and Foulkes (previously
unpublished). It is argued that there is close conjunction between
Mannheim’s and Foulkes’s revision of clinical psychoanalysis along
sociological lines. Current renderings of the Frankfurt School
tradition pay almost exclusive attention to the American connection
(Herbert Marcuse, Eric Fromm, Theodor Adorno and Max Horkheimer)
overlooking the contribution of the English connection through
the work of Mannheim and Foulkes
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