183 research outputs found
Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements
A series of calculations for the first- and second-row post-d elements (Ga-Br
and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo
(AF QMC) method. This method is formulated in a Hilbert space defined by any
chosen one-particle basis, and maps the many-body problem into a linear
combination of independent-particle solutions with external auxiliary fields.
The phase/sign problem is handled approximately by the phaseless formalism
using a trial wave function, which in our calculations was chosen to be the
Hartree-Fock solution. We used the consistent correlated basis sets of Peterson
and coworkers, which employ a small core relativistic pseudopotential. The AF
QMC results are compared with experiment and with those from density-functional
(GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total
energies agree with CCSD(T) to within a few milli-hartrees across the systems
and over several basis sets. The calculated atomic electron affinities,
ionization energies, and spectroscopic properties of dimers are, at large basis
sets, in excellent agreement with experiment.Comment: 10 pages, 2 figures. To be published in Journal of Chemical Physic
Fixed-node diffusion Monte Carlo study of the structures of m-benzyne
Diffusion Monte Carlo (DMC) calculations are performed on the monocyclic and
bicyclic forms of m-benzyne, which are the equilibrium structures at the
CCSD(T) and CCSD levels of coupled cluster theory. We employed
multi-configuration self-consistent field trial wave functions which are
constructed from a carefully selected 8-electrons-in-8-orbitals complete active
space [CAS(8,8)], with CSF coefficients that are reoptimized in the presence of
a Jastrow factor. The DMC calculations show that the monocyclic structure is
lower in energy than the bicyclic structure by 1.9(2) kcal/mole, in excellent
agreement with the best coupled cluster results.Comment: 5 pages, 2 figures. to be published in JC
Bond breaking with auxiliary-field quantum Monte Carlo
Bond stretching mimics different levels of electron correlation and provides
a challenging testbed for approximate many-body computational methods. Using
the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC)
method, we examine bond stretching in the well-studied molecules BH and N,
and in the H chain. To control the sign/phase problem, the phaseless AF
QMC method constrains the paths in the auxiliary-field path integrals with an
approximate phase condition that depends on a trial wave function. With single
Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave
function, the phaseless AF QMC method generally gives better overall accuracy
and a more uniform behavior than the coupled cluster CCSD(T) method in mapping
the potential-energy curve. In both BH and N, we also study the use of
multiple-determinant trial wave functions from multi-configuration
self-consistent-field (MCSCF) calculations. The increase in computational cost
versus the gain in statistical and systematic accuracy are examined. With such
trial wave functions, excellent results are obtained across the entire region
between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC
Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2
The use of an approximate reference state wave function |Phi_r> in electronic
many-body methods can break the spin symmetry of Born-Oppenheimer
spin-independent Hamiltonians. This can result in significant errors,
especially when bonds are stretched or broken. A simple spin-projection method
is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations,
which yields spin-contamination-free results, even with a spin-contaminated
|Phi_r>. The method is applied to the difficult F2 molecule, which is unbound
within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination
causes large systematic errors and long equilibration times in AFQMC in the
intermediate, bond-breaking region. The spin-projection method eliminates these
problems, and delivers an accurate potential energy curve from equilibrium to
the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves
are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are
in excellent agreement with experiment.Comment: 8 pages, 6 figures, submitted to J. Chem. Phy
BEARING CAPACITY OF SQUARE FOOTING ON GEOGRID-REINFORCED LOOSE SAND TO RESIST ECCENTRIC LOAD
This research presents and discuss the results of experimental investigation carried out on geogrids model to study the behavior of geogrid in the loose sandy soil. The effect of location eccentricity, depth of first layer of reinforcement, vertical spacing, number and type of reinforcement layers have been investigated. The results indicated that the percentage of bearing improvement a bout (22 %) at number of reinforced layers N=1 and about (47.5%) at number of reinforced layers N=2 for different Eccentricity values when depth ratio and vertical spacing between layers are (0.5B and 0.75B) respectively
Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model
We have studied quantum-mechanically a system of several small identical
Josephson junctions in a lossless single-mode cavity for different initial
states, under conditions such that the system is at resonance. This system is
analogous to a collection of identical atoms in a cavity, which is described
under appropriate conditions by the Dicke model. We find that our system can be
well approximated by a reduced Hamiltonian consisting of two levels per
junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but
contains an additional term resembling a dipole-dipole interaction between the
junctions. This extra term arises when states outside the degenerate group are
included via degenerate second-order (L\"{o}wdin) perturbation theory. As in
the Dicke model, we find that, when N junctions are present in the cavity, the
oscillation frequency due to the junction-cavity interaction is enhanced by
. The corresponding decrease in the Rabi oscillation period may cause
it to be smaller than the decoherence time due to dissipation, making these
oscillations observable. Finally, we find that the frequency enhancement
survives even if the junctions differ slightly from one another, as expected in
a realistic system.Comment: 11 pages. To be published in Phys. Rev.
Eigenstates of a Small Josephson Junction Coupled to a Resonant Cavity
We carry out a quantum-mechanical analysis of a small Josephson junction
coupled to a single-mode resonant cavity. We find that the eigenstates of the
combined junction-cavity system are strongly entangled only when the gate
voltage applied at one of the superconducting islands is tuned to certain
special values. One such value corresponds to the resonant absorption of a
single photon by Cooper pairs in the junction. Another special value
corresponds to a {\em two-photon} absorption process. Near the single-photon
resonant absorption, the system is accurately described by a simplified model
in which only the lowest two levels of the Josephson junction are retained in
the Hamiltonian matrix. We noticed that this approximation does not work very
well as the number of photons in the resonator increases. Our system shows also
the phenomenon of ``collapse and revival'' under suitable initial conditions,
and our full numerical solution agrees with the two level approximation result.Comment: 7 pages, and 6 figures. To be published in Phys. Rev.
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