6,959 research outputs found
Local-spin-density functional for multideterminant density functional theory
Based on exact limits and quantum Monte Carlo simulations, we obtain, at any
density and spin polarization, an accurate estimate for the energy of a
modified homogeneous electron gas where electrons repel each other only with a
long-range coulombic tail. This allows us to construct an analytic
local-spin-density exchange-correlation functional appropriate to new,
multideterminantal versions of the density functional theory, where quantum
chemistry and approximate exchange-correlation functionals are combined to
optimally describe both long- and short-range electron correlations.Comment: revised version, ti appear in PR
Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
We employ \textit{ab initio} methods of quantum chemistry to investigate
spin-1/2 fermions interacting via a two-body contact potential in a
one-dimensional harmonic trap. The convergence of the total energy with the
size of the one-particle basis set is analytically investigated for the
two-body problem and the same form of the convergence formula is numerically
confirmed to be valid for the many-body case. Benchmark calculations for two to
six fermions with the full configuration interaction method equivalent to the
exact diagonalization approach, and the coupled cluster method including
single, double, triple, and quadruple excitations are presented. The
convergence of the correlation energy with the level of excitations included in
the coupled cluster model is analyzed. The range of the interaction strength
for which single-reference coupled cluster methods work is examined. Next, the
coupled cluster method restricted to single, double, and noniterative triple
excitations, CCSD(T), is employed to study a two-component Fermi gas composed
of 6 to 80 atoms in a one-dimensional harmonic trap. The density profiles of
trapped atomic clouds are also reported. Finally, a comparison with
experimental results for few-fermion systems is presented. Upcoming possible
applications and extensions of the presented approach are discussed.Comment: 25 pages, 12 figures, 1 tabl
Coupled Cluster Channels in the Homogeneous Electron Gas
We discuss diagrammatic modifications to the coupled cluster doubles (CCD)
equations, wherein different groups of terms out of rings, ladders,
crossed-rings and mosaics can be removed to form approximations to the coupled
cluster method, of interest due to their similarity with various types of
random phase approximations. The finite uniform electron gas is benchmarked for
14- and 54-electron systems at the complete basis set limit over a wide density
range and performance of different flavours of CCD are determined. These
results confirm that rings generally overcorrelate and ladders generally
undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We
use a recently developed numerical analysis [J. J. Shepherd and A. Gr\"uneis,
Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods
in the thermodynamic limit. We determine that the mosaics, on forming the
Brueckner Hamltonian, open a gap in the effective one-particle eigenvalues at
the Fermi energy. Numerical evidence is presented which shows that methods
based on this renormalisation have convergent energies in the thermodynamic
limit including mosaic-only CCD, which is just a renormalised MP2. All other
methods including only a single channel, namely ladder-only CCD, ring-only CCD
and crossed-ring-only CCD, appear to yield divergent energies; incorporation of
mosaic terms prevents this from happening.Comment: 9 pages, 4 figures, 1 table. Comments welcome: [email protected]
Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state
Using the finite simulation-cell homogeneous electron gas (HEG) as a model,
we investigate the convergence of the correlation energy to the complete basis
set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple
analytic and numerical results from second-order M{\o}ller-Plesset theory (MP2)
suggest a 1/M decay of the basis-set incompleteness error where M is the number
of plane waves used in the calculation, allowing for straightforward
extrapolation to the CBS limit. As we shall show, the choice of basis set
truncation when constructing many-electron wavefunctions is far from obvious,
and here we propose several alternatives based on the momentum transfer vector,
which greatly improve the rate of convergence. This is demonstrated for a
variety of wavefunction methods, from MP2 to coupled-cluster doubles theory
(CCD) and the random-phase approximation plus second-order screened exchange
(RPA+SOSEX). Finite basis-set energies are presented for these methods and
compared with exact benchmarks. A transformation can map the orbitals of a
general solid state system onto the HEG plane wave basis and thereby allow
application of these methods to more realistic physical problems.Comment: 15 pages, 9 figure
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
We present an investigation into the use of an explicitly correlated plane
wave basis for periodic wavefunction expansions at the level of second-order
M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic
correlation energy with respect to the one-electron basis set is investigated
and compared to conventional MP2 theory in a finite homogeneous electron gas
model. In addition to the widely used Slater-type geminal correlation factor,
we also derive and investigate a novel correlation factor that we term
Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic
results for two electrons in a box and allows for a further improved
convergence of the correlation energies with respect to the employed basis set.
We find the combination of the infinitely delocalized plane waves and local
short-ranged geminals provides a complementary, and rapidly convergent basis
for the description of periodic wavefunctions. We hope that this approach will
expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure
- …