47 research outputs found

### Benchmark Quantum Monte Carlo calculations of the ground-state kinetic, interaction, and total energy of the three-dimensional electron gas

We report variational and diffusion Quantum Monte Carlo ground-state energies
of the three-dimensional electron gas using a model periodic Coulomb
interaction and backflow corrections for N=54, 102, 178, and 226 electrons. We
remove finite-size effects by extrapolation and we find lower energies than
previously reported. Using the Hellman-Feynman operator sampling method
introduced in Phys. Rev. Lett. 99, 126406 (2007), we compute accurately, within
the fixed-node pproximation, the separate kinetic and interaction contributions
to the total ground-state energy. The difference between the interaction
energies obtained from the original Slater-determinant nodes and the
backflow-displaced nodes is found to be considerably larger than the difference
between the corresponding kinetic energies

### Hellman-Feynman operator sampling in Diffusion Monte Carlo calculations

Diffusion Monte Carlo (DMC) calculations typically yield highly accurate
results in solid-state and quantum-chemical calculations. However, operators
that do not commute with the Hamiltonian are at best sampled correctly up to
second order in the error of the underlying trial wavefunction, once simple
corrections have been applied. This error is of the same order as that for the
energy in variational calculations. Operators that suffer from these problems
include potential energies and the density. This paper presents a new method,
based on the Hellman-Feynman theorem, for the correct DMC sampling of all
operators diagonal in real space. Our method is easy to implement in any
standard DMC code

### Quantum Monte Carlo modelling of the spherically averaged structure factor of a many-electron system

The interaction and exchange-correlation contributions to the ground-state
energy of an arbitrary many-electron system can be obtained from a spherical
average of the wavevector-dependent diagonal structure factor (SF). We model
the continuous-k spherically averaged SF using quantum Monte Carlo calculations
in finite simulation cells. We thus derive a method that allows to
substantially reduce the troublesome Coulomb finite-size errors that are
usually present in ground-state energy calculations. To demonstrate this, we
perform variational Monte Carlo calculations of the interaction energy of the
homogeneous electron gas. The method is, however, equally applicable to
arbitrary inhomogeneous systems.Comment: 4 pages, 5 figure

### An efficient method for the Quantum Monte Carlo evaluation of the static density-response function of a many-electron system

In a recent Letter we introduced Hellmann-Feynman operator sampling in
diffusion Monte Carlo calculations. Here we derive, by evaluating the second
derivative of the total energy, an efficient method for the calculation of the
static density-response function of a many-electron system. Our analysis of the
effect of the nodes suggests that correlation is described correctly and we
find that the effect of the nodes can be dealt with

### Momentum-space finite-size corrections for Quantum-Monte-Carlo calculations

Extended solids are frequently simulated as finite systems with periodic
boundary conditions, which due to the long-range nature of the Coulomb
interaction may lead to slowly decaying finite- size errors. In the case of
Quantum-Monte-Carlo simulations, which are based on real space, both real-space
and momentum-space solutions to this problem exist. Here, we describe a hybrid
method which using real-space data models the spherically averaged structure
factor in momentum space. We show that (i) by integration our hybrid method
exactly maps onto the real-space model periodic Coulomb-interaction (MPC)
method and (ii) therefore our method combines the best of both worlds
(real-space and momentum-space). One can use known momentum-resolved behavior
to improve convergence where MPC fails (e.g., at surface-like systems). In
contrast to pure momentum-space methods, our method only deals with a simple
single-valued function and, hence, better lends itself to interpolation with
exact small-momentum data as no directional information is needed. By virtue of
integration, the resulting finite-size corrections can be written as an
addition to MPC.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

### First principles simulations of direct coexistence of solid and liquid aluminium

First principles calculations based on density functional theory, with
generalised gradient corrections and ultrasoft pseudopotentials, have been used
to simulate solid and liquid aluminium in direct coexistence at zero pressure.
Simulations have been carried out on systems containing up to 1000 atoms for 15
ps. The points on the melting curve extracted from these simulations are in
very good agreement with previous calculations, which employed the same
electronic structure method but used an approach based on the explicit
calculation of free energies [L. Vo\v{c}adlo and D. Alf\`e, Phys. Rev. B, {\bf
65}, 214105 (2002).]Comment: To appear in Phys. Rev.