621 research outputs found
Efficient Monte Carlo Calculations of the One-Body Density
An alternative Monte Carlo estimator for the one-body density rho(r) is
presented. This estimator has a simple form and can be readily used in any type
of Monte Carlo simulation. Comparisons with the usual regularization of the
delta-function on a grid show that the statistical errors are greatly reduced.
Furthermore, our expression allows accurate calculations of the density at any
point in space, even in the regions never visited during the Monte Carlo
simulation. The method is illustrated with the computation of accurate
Variational Monte Carlo electronic densities for the Helium atom (1D curve) and
for the water dimer (3D grid containing up to 51x51x51=132651 points).Comment: 12 pages with 3 postscript figure
Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions
The potential energy curve of the F molecule is calculated with
Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction
(CI)-type trial wavefunctions. To keep the number of determinants reasonable
(the first and second derivatives of the trial wavefunction need to be
calculated at each step of FN-DMC), the CI expansion is restricted to those
determinants that contribute the most to the total energy. The selection of the
determinants is made using the so-called CIPSI approach (Configuration
Interaction using a Perturbative Selection made Iteratively). Quite remarkably,
the nodes of CIPSI wavefunctions are found to be systematically improved when
increasing the number of selected determinants. To reduce the non-parallelism
error of the potential energy curve a scheme based on the use of a
-dependent number of determinants is introduced. Numerical results show that
improved FN-DMC energy curves for the F molecule are obtained when
employing CIPSI trial wavefunctions. Using the Dunning's cc-pVDZ basis set the
FN-DMC energy curve is of a quality similar to that obtained with FCI/cc-pVQZ.
A key advantage of using selected CI in FN-DMC is the possibility of improving
nodes in a systematic and automatic way without resorting to a preliminary
multi-parameter stochastic optimization of the trial wavefunction performed at
the Variational Monte Carlo level as usually done in FN-DMC.Comment: 16 pages, 15 figure
S12RS SGB No. 11 (Bylaws and RoO)
A BILL
To amend the Senate Rules of Order and the Student Government Bylaw
F11RS SGFB No. 6 (Branch Head Comp)
A FINANCE BILL
To allocate four thousand two hundred seventy two dollars ($4,272.00) from the Student Government Surplus Account to fund computers for Branch Head office
S12RS SGB No. 2 (Org Agenda Bylaws)
A BILL
To amend the Student Government Bylaw
F11RS SGFB No. 1 (Clickers)
A FINANCE BILL
To allocate two thousand two hundred seventh eight dollars and forty five cents ($2,278.45) from the Student Government Surplus Account to fund the acquisition of âclickersâ for the Student Senat
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%
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