75 research outputs found
Systematic reduction of sign errors in many-body calculations of atoms and molecules
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf
79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an
accurate and robust method for calculating the ground state of atoms and
molecules. By direct comparison with accurate configuration interaction results
for the oxygen atom we show that SHDMC converges systematically towards the
ground-state wave function. We present results for the challenging N
molecule, where the binding energies obtained via both energy minimization and
SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that
SHDMC is robust enough to find the nodal surface for systems at least as large
as C starting from random coefficients. SHDMC is a linear-scaling
method, in the degrees of freedom of the nodes, that systematically reduces the
fermion sign problem.Comment: Final version accepted in Physical Review Letters. The review history
(referees' comments and our replies) is included in the source
Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks
We study the electronic structure of a spherical jellium in the presence of a
central Gaussian impurity. We test how well the resulting inhomogeneity effects
beyond spherical jellium are reproduced by several approximations of density
functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals,
namely local density approximation (LDA), generalized gradient approximation
(GGA), meta-GGA and orbital-dependent hybrid functionals are compared against
our quantum Monte Carlo (QMC) benchmarks. We identify several distinct
transitions in the ground state of the system as the electronic occupation
changes between delocalized and localized states. We examine the parameter
space of realistic densities () and moderate depths of the
Gaussian impurity (). The selected 18 electron system (with closed-shell
ground state) presents transitions while the 30 electron system
(with open-shell ground state) exhibits transitions. For the former
system, the accuracy for the transitions is clearly improving with increasing
sophistication of functionals with meta-GGA and hybrid functionals having only
small deviations from QMC. However, for the latter system, we find much larger
differences for the underlying transitions between our pool of DFT functionals
and QMC. We attribute this failure to treatment of the exact exchange within
these functionals. Additionally, we amplify the inhomogeneity effects by
creating the system with spherical shell which leads to even larger errors in
DFT approximations.Comment: 8 pages, 4 figures, submitted to PRB as a regular article revisited
version after revie
Coherent "metallic" resistance and medium localisation in a disordered 1D insulator
It is believed, that a disordered one-dimensional (1D) wire with coherent
electronic conduction is an insulator with the mean resistance \simeq
e^{2L/\xi} and resistance dispersion \Delta_{\rho} \simeq e^{L/\xi}, where L is
the wire length and \xi is the electron localisation length. Here we show that
this 1D insulator undergoes at full coherence the crossover to a 1D "metal",
caused by thermal smearing and resonant tunnelling. As a result, \Delta_{\rho}
is smaller than unity and tends to be L/\xi - independent, while grows
with L/\xi first nearly linearly and then polynomially, manifesting the
so-called medium localisation.Comment: 4 pages, 4 figures, RevTeX
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer
A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. In this work, we investigate the charge of solvated protons at the Pt(111) | H_2O and Al(111) | H_2O interfaces. Using semi-local density-functional theory as well as hybrid functionals and embedded correlated wavefunction methods as higher-level benchmarks, we show that the effective charge of a solvated proton in the electrochemical double layer or outer Helmholtz plane at all levels of theory is fractional, when the solvated proton and solvent band edges are aligned correctly with the Fermi level of the metal (E_F). The observed fractional charge in the absence of frontier band misalignment arises from a significant overlap between the proton and the electron density from the metal surface, and results in an energetic difference between protons in bulk solution and those in the outer Helmholtz plane
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