608 research outputs found
Combining Density Functional Theory and Density Matrix Functional Theory
We combine density-functional theory with density-matrix functional theory to
get the best of both worlds. This is achieved by range separation of the
electronic interaction which permits to rigorously combine a short-range
density functional with a long-range density-matrix functional. The short-range
density functional is approximated by the short-range version of the
Perdew-Burke-Ernzerhof functional (srPBE). The long-range density-matrix
functional is approximated by the long-range version of the Buijse-Baerends
functional (lrBB). The obtained srPBE+lrBB method accurately describes both
static and dynamic electron correlation at a computational cost similar to that
of standard density-functional approximations. This is shown for the
dissociation curves of the H, LiH, BH and HF molecules.Comment: 4 pages, 5 figure
Approaching Chemical Accuracy with Quantum Monte Carlo
A quantum Monte Carlo study of the atomization energies for the G2 set of
molecules is presented. Basis size dependence of diffusion Monte Carlo
atomization energies is studied with a single determinant Slater-Jastrow trial
wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the
mean absolute deviation from experimental atomization energies for the G2 set
is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo
improves the agreement between diffusion Monte Carlo and experiment, reducing
the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant
Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete
active space Slater-Jastrow trial wavefunction results in near chemical
accuracy. In this case, the mean absolute deviation from experimental
atomization energies is 1.2 kcal/mol. It is shown from calculations on systems
containing phosphorus that the accuracy can be further improved by employing a
larger active space.Comment: 6 pages, 5 figure
Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations
Molecular calculations in quantum Monte Carlo frequently employ a mixed basis
consisting of contracted and primitive Gaussian functions. While standard basis
sets of varying size and accuracy are available in the literature, we
demonstrate that reoptimizing the primitive function exponents within quantum
Monte Carlo yields more compact basis sets for a given accuracy. Particularly
large gains are achieved for highly excited states. For calculations requiring
non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that
behave as Gaussians at short distances and Slaters at long distances. These
basis functions further improve the energy and fluctuations of the local energy
for a given basis size. Gains achieved by exponent optimization and
Gauss-Slater basis use are exemplified by calculations for the ground state of
carbon, the lowest lying excited states of carbon with , ,
, symmetries, carbon dimer, and naphthalene. Basis size
reduction enables quantum Monte Carlo treatment of larger molecules at high
accuracy.Comment: 8 Pages, 2 Figures, 9 Table
Alleviation of the Fermion-sign problem by optimization of many-body wave functions
We present a simple, robust and highly efficient method for optimizing all
parameters of many-body wave functions in quantum Monte Carlo calculations,
applicable to continuum systems and lattice models. Based on a strong
zero-variance principle, diagonalization of the Hamiltonian matrix in the space
spanned by the wav e function and its derivatives determines the optimal
parameters. It systematically reduces the fixed-node error, as demonstrated by
the calculation of the binding energy of the small but challenging C
molecule to the experimental accuracy of 0.02 eV
Diffuse Neutron Scattering Study of Relaxor Ferroelectric (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3(PZN-xPT)
Diffuse neutron scattering is a valuable tool to obtain information about the
size and orientation of the polar nanoregions that are a characteristic feature
of relaxor ferroelectrics. In this paper, we present new diffuse scattering
results obtained on Pb(Zn1/3Nb2/3)O3 (PZN for short) and
(1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3(PZN-xPT)single crystals (with x=4.5 and 9%),
around various Bragg reflections and along three symmetry directions in the
[100]-[011] zone. Diffuse scattering is observed around reflections with mixed
indices, (100), (011) and (300), and along transverse and diagonal directions
only. No diffuse scattering is found in longitudinal scans. The diffuse
scattering peaks can be fitted well with a Lorentzian function, from which a
correlation length is extracted. The correlation length increases with
decreasing temperatures down to the transition at Tc, first following a
Curie-Weiss law, then departing from it and becoming flat at very low
temperatures. These results are interpreted in terms of three temperature
regions: 1) dynamic polarization fluctuations (i.e. with a finite lifetime) at
high temperatures, 2) static polarization reorientations (condensation of polar
nanoregions) that can still reorient as a unit (relaxor behavior) at
intermediate temperatures and 3) orientational freezing of the polar
nanoregions with random strain fields in pure PZN or a structural phase
transition in PZN-xPT at low temperatures. The addition of PT leads to a
broadening of the diffuse scattering along the diagonal ([111]) relative to the
transverse ([100]) direction, indicating a change in the orientation of the
polar regions. Also, with the addition of PT, the polar nanoregions condense at
a higher temperature above Tc.Comment: AIP 6x9 style files, 9 pages, 5 figures, Conference-Fundamental
Physics of Ferroelectrics 200
The sawtooth chain: From Heisenberg spins to Hubbard electrons
We report on recent studies of the spin-half Heisenberg and the Hubbard model
on the sawtooth chain. For both models we construct a class of exact
eigenstates which are localized due to the frustrating geometry of the lattice
for a certain relation of the exchange (hopping) integrals. Although these
eigenstates differ in details for the two models because of the different
statistics, they share some characteristic features. The localized eigenstates
are highly degenerate and become ground states in high magnetic fields
(Heisenberg model) or at certain electron fillings (Hubbard model),
respectively. They may dominate the low-temperature thermodynamics and lead to
an extra low-temperature maximum in the specific heat. The ground-state
degeneracy can be calculated exactly by a mapping of the manifold of localized
ground states onto a classical hard-dimer problem, and explicit expressions for
thermodynamic quantities can be derived which are valid at low temperatures
near the saturation field for the Heisenberg model or around a certain value of
the chemical potential for the Hubbard model, respectively.Comment: 16 pages, 6 figure, the paper is based on an invited talk on the XXXI
International Workshop on Condensed Matter Theories, Bangkok, Dec 2007;
notation of x-axis in Fig.6 corrected, references update
Bethe-Peierls Approximation for the 2D Random Ising Model
The partition function of the 2d Ising model with random nearest neighbor
coupling is expressed in the dual lattice made of square plaquettes. The dual
model is solved in the the mean field and in different types of Bethe-Peierls
approximations, using the replica method.Comment: Plane TeX file, 21 pages, 5 figures available under request to
[email protected]
Positional, Reorientational and Bond Orientational Order in DNA Mesophases
We investigate the orientational order of transverse polarization vectors of
long, stiff polymer molecules and their coupling to bond orientational and
positional order in high density mesophases. Homogeneous ordering of transverse
polarization vector promotes distortions in the hexatic phase, whereas
inhomogeneous ordering precipitates crystalization of the 2D sections with
different orientations of the transverse polarization vector on each molecule
in the unit cell. We propose possible scenarios for going from the hexatic
phase, through the distorted hexatic phase to the crystalline phase with an
orthorhombic unit cell observed experimentally for the case of DNA.Comment: 4 pages, 2 figure
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