137 research outputs found
Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
A simple and stable method for computing accurate expectation values of
observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC)
algorithms is presented. The basic idea consists in replacing the usual
``bare'' estimator associated with the observable by an improved or
``renormalized'' estimator. Using this estimator more accurate averages are
obtained: Not only the statistical fluctuations are reduced but also the
systematic error (bias) associated with the approximate VMC or (fixed-node) DMC
probability densities. It is shown that improved estimators obey a
Zero-Variance Zero-Bias (ZVZB) property similar to the usual Zero-Variance
Zero-Bias property of the energy with the local energy as improved estimator.
Using this property improved estimators can be optimized and the resulting
accuracy on expectation values may reach the remarkable accuracy obtained for
total energies. As an important example, we present the application of our
formalism to the computation of forces in molecular systems. Calculations of
the entire force curve of the H,LiH, and Li molecules are presented.
Spectroscopic constants (equilibrium distance) and (harmonic
frequency) are also computed. The equilibrium distances are obtained with a
relative error smaller than 1%, while the harmonic frequencies are computed
with an error of about 10%
Quantum Monte Carlo calculations of electronic excitation energies: the case of the singlet (CO) transition in acrolein
We report state-of-the-art quantum Monte Carlo calculations of the singlet (CO) vertical excitation energy in the acrolein molecule, extending
the recent study of Bouab\c{c}a {\it et al.} [J. Chem. Phys. {\bf 130}, 114107
(2009)]. We investigate the effect of using a Slater basis set instead of a
Gaussian basis set, and of using state-average versus state-specific
complete-active-space (CAS) wave functions, with or without reoptimization of
the coefficients of the configuration state functions (CSFs) and of the
orbitals in variational Monte Carlo (VMC). It is found that, with the Slater
basis set used here, both state-average and state-specific CAS(6,5) wave
functions give an accurate excitation energy in diffusion Monte Carlo (DMC),
with or without reoptimization of the CSF and orbital coefficients in the
presence of the Jastrow factor. In contrast, the CAS(2,2) wave functions
require reoptimization of the CSF and orbital coefficients to give a good DMC
excitation energy. Our best estimates of the vertical excitation energy are
between 3.86 and 3.89 eV.Comment: 6 pages, 1 figure, 2 tables, to appear in Progress in Theoretical
Chemistry and Physic
Optimization of ground and excited state wavefunctions and van der Waals clusters
A quantum Monte Carlo method is introduced to optimize excited state trial
wavefunctions. The method is applied in a correlation function Monte Carlo
calculation to compute ground and excited state energies of bosonic van der
Waals clusters of upto seven particles. The calculations are performed using
trial wavefunctions with general three-body correlations
Green's Function Monte Carlo for Lattice Fermions: Application to the t-J Model
We develop a general numerical method to study the zero temperature
properties of strongly correlated electron models on large lattices. The
technique, which resembles Green's Function Monte Carlo, projects the ground
state component from a trial wave function with no approximations. We use this
method to determine the phase diagram of the two-dimensional t-J model, using
the Maxwell construction to investigate electronic phase separation. The shell
effects of fermions on finite-sized periodic lattices are minimized by keeping
the number of electrons fixed at a closed-shell configuration and varying the
size of the lattice. Results obtained for various electron numbers
corresponding to different closed-shells indicate that the finite-size effects
in our calculation are small. For any value of interaction strength, we find
that there is always a value of the electron density above which the system can
lower its energy by forming a two-component phase separated state. Our results
are compared with other calculations on the t-J model. We find that the most
accurate results are consistent with phase separation at all interaction
strengths.Comment: 22 pages, 22 figure
Interaction induced delocalisation for two particles in a periodic potential
We consider two interacting particles evolving in a one-dimensional periodic
structure embedded in a magnetic field. We show that the strong localization
induced by the magnetic field for particular values of the flux per unit cell
is destroyed as soon as the particles interact. We study the spectral and the
dynamical aspects of this transition.Comment: 4 pages, 5 EPS figures, minor misprints correcte
Stabilization of d-Band Ferromagnetism by Hybridization with Uncorrelated Bands
We investigate the influence of s-d or p-d hybridization to d-band
ferromagnetism to estimate the importance of hybridization for the magnetic
properties of transition metals. To focus our attention to the interplay
between hybridization and correlation we investigate a simple model system
consisting of two non-degenerated hybridized bands, one strongly correlated,
the other one quasi-free. To solve this extended Hubbard model, we apply simple
approximations, namely SDA and MAA, that, concerning ferromagnetism in the
single-band model, are known to give qualitatively satisfactory results. This
approach allows us to discuss the underlying mechanism, by which d-band
ferromagnetism is influenced by the hybridization on the basis of analytical
expressions. The latter clearly display the order and the functional
dependencies of the important effects. It is found, that spin-dependent
inter-band particle fluctuations cause a spin-dependent band shift and a
spin-dependent band broadening of the Hubbard bands. The shift stabilizes, the
broadening tends to destabilize ferromagnetism. Stabilization requires
relatively high band distances and small hybridization matrix elements.
Super-exchange and RKKY coupling are of minor importance.Comment: 9 pages, 7 figures, accepted for PR
Zero-temperature magnetism in the periodic Anderson model in the limit of large dimensions
We study the magnetism in the periodic Anderson model in the limit of large
dimensions by mapping the lattice problem into an equivalent local impurity
self-consistent model. Through a recently introduced algorithm based on the
exact diagonalization of an effective cluster hamiltonian, we obtain solutions
with and without magnetic order in the half-filled case. We find the exact
AFM-PM phase boundary which is shown to be of order and obeys
We calculate the local staggered moments and the
density of states to gain insights on the behavior of the AFM state as it
evolves from itinerant to a local-moment magnetic regimeComment: 9 pages + 9 figures, to appear in Phys. Rev. B, 1 Sept. 1995 issu
Hydrogel-forming microneedle arrays: Potential for use in minimally-invasive lithium monitoring
AbstractWe describe, for the first time, hydrogel-forming microneedle (s) (MN) arrays for minimally-invasive extraction and quantification of lithium in vitro and in vivo. MN arrays, prepared from aqueous blends of hydrolysed poly(methyl-vinylether-co-maleic anhydride) and crosslinked by poly(ethyleneglycol), imbibed interstitial fluid (ISF) upon skin insertion. Such MN were always removed intact. In vitro, mean detected lithium concentrations showed no significant difference following 30min MN application to excised neonatal porcine skin for lithium citrate concentrations of 0.9 and 2mmol/l. However, after 1h application, the mean lithium concentrations extracted were significantly different, being appropriately concentration-dependent. In vivo, rats were orally dosed with lithium citrate equivalent to 15mg/kg and 30mg/kg lithium carbonate, respectively. MN arrays were applied 1h after dosing and removed 1h later. The two groups, having received different doses, showed no significant difference between lithium concentrations in serum or MN. However, the higher dosed rats demonstrated a lithium concentration extracted from MN arrays equivalent to a mean increase of 22.5% compared to rats which received the lower dose. Hydrogel-forming MN clearly have potential as a minimally-invasive tool for lithium monitoring in outpatient settings. We will now focus on correlation between serum and MN lithium concentrations
Guided random walk calculation of energies and <\sq {r^2} > values of the state of H_2 in a magnetic field
Energies and spatial observables for the state of the hydrogen
molecule in magnetic fields parallel to the proton-proton axis are calculated
with a guided random walk Feynman-Kac algorithm. We demonstrate that the
accuracy of the results and the simplicity of the method may prove it a viable
alternative to large basis set expansions for small molecules in applied
fields.Comment: 10 pages, no figure
- âŠ