1,944 research outputs found
Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals
We describe a method for imposing the correct electron-nucleus (e-n) cusp in
molecular orbitals expanded as a linear combination of (cuspless) Gaussian
basis functions. Enforcing the e-n cusp in trial wave functions is an important
asset in quantum Monte Carlo calculations as it significantly reduces the
variance of the local energy during the Monte Carlo sampling. In the method
presented here, the Gaussian basis set is augmented with a small number of
Slater basis functions. Note that, unlike other e-n cusp correction schemes,
the presence of the Slater function is not limited to the vicinity of the
nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting
Slater basis functions may be self-consistently optimized by diagonalization of
an orbital-dependent effective Fock operator. Illustrative examples are
reported for atoms (\ce{H}, \ce{He} and \ce{Ne}) as well as for a small
molecular system (\ce{BeH2}). For the simple case of the \ce{He} atom, we
observe that, with respect to the cuspless version, the variance is reduced by
one order of magnitude by applying our cusp-corrected scheme.Comment: 23 pages, 5 figure
Jastrow correlation factor for atoms, molecules, and solids
A form of Jastrow factor is introduced for use in quantum Monte Carlo
simulations of finite and periodic systems. Test data are presented for atoms,
molecules, and solids, including both all-electron and pseudopotential atoms.
We demonstrate that our Jastrow factor is able to retrieve a large fraction of
the correlation energy
Ground-state stability and criticality of two-electron atoms with screened Coulomb potentials using the B-splines basis set
We applied the finite-size scaling method using the B-splines basis set to
construct the stability diagram for two-electron atoms with a screened Coulomb
potential. The results of this method for two electron atoms are very accurate
in comparison with previous calculations based on Gaussian, Hylleraas, and
finite-element basis sets. The stability diagram for the screened two-electron
atoms shows three distinct regions: a two-electron region, a one-electron
region, and a zero-electron region, which correspond to stable, ionized and
double ionized atoms. In previous studies, it was difficult to extend the
finite size scaling calculations to large molecules and extended systems
because of the computational cost and the lack of a simple way to increase the
number of Gaussian basis elements in a systematic way. Motivated by recent
studies showing how one can use B-splines to solve Hartree-Fock and Kohn-Sham
equations, this combined finite size scaling using the B-splines basis set,
might provide an effective systematic way to treat criticality of large
molecules and extended systems. As benchmark calculations, the two-electron
systems show the feasibility of this combined approach and provide an accurate
reference for comparison
On Convergence Acceleration of Multipolar and Orthogonal Expansions
Multipolar expansions arise in many branches of the
computational sciences. They are an example of orthogonal expansions.
We present methods for the convergence acceleration of such
expansions. As an example, the computation of the electrostatic potential and its multipolar expansion is treated for the case of a two-center charge
density of exponential-type orbitals. This potential may also be considered as
a special molecular integral, namely as a three-center nuclear attraction
integral. It is shown that in this example, the extrapolation to the limit of the
corresponding expansions via suitable nonlinear sequence transformations leads
to a pronounced convergence acceleration
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