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| J. Chem. Phys. 113, 473 (2000). |
Download: PDF |
Ab-initio computation of forces and molecular
spectroscopic constants using planewaves based auxiliary field Monte Carlo with application
to N2
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Roi Baer
Department of Physical Chemistry and the Lise Meitner Minerva-Center for Computational
Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 Israel.
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Abstracts:
Correlated sampling within the Shifted Contour Auxiliary Field Monte Carlo method,
implemented using plane waves and pseudopotentials allows computation of electronic forces
on nuclei, potential energy differences, geometric and vibrotational spectroscopic
constants. This is exemplified on the N2 molecule, where it is demonstrated
that it is possible to compute forces, dissociation energies, bond length parameters and
harmonic frequencies to high precision. |
More details:
The
straightforward way to compute forces is to use a numerical derivative:
 where,
 and
 are,
respectively, the electronic energy and the force component on an atomic nucleus when it
is at position  . When the energy estimators  and
 are
statistically independent, each with statistical error (SE)  , the force estimator SE is
 , and therefore formally infinite. This fact prohibits the
use of Eq. in QMC.
This paper
explores the issue of force, frequency and spectroscopic constants computation using the
Shifted Contour Auxiliary field Monte Carlo method in
its planewaves-pseudopotential implementation
(PW-SCAFMC). We develop a method to execute correlated sampling of electronic energy in different nuclear configurations in such a way that force computations using are possible, without divergence of the variance as
 . This is clearly seen in the Figure above, where the variance of the force on the nuclei of N2
is shown to be largely independent of the size of dx.
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Performance of the method for the N2 bond
Dissociation Energy
The Bond Length
The harmonic frequency
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