Uniform electron gases. III. Low-density gases on three-dimensional spheres.

@article{Agboola2015UniformEG,
  title={Uniform electron gases. III. Low-density gases on three-dimensional spheres.},
  author={Davids Agboola and Anneke L Knol and Peter M. W. Gill and Pierre-François Loos},
  journal={The Journal of chemical physics},
  year={2015},
  volume={143 8},
  pages={
          084114
        }
}
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor… 

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References

SHOWING 1-10 OF 63 REFERENCES

Generalized local-density approximation and one-dimensional finite uniform electron gases

We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA

Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations

Uniform electron gases. II. The generalized local density approximation in one dimension.

An explicit gLDA functional for the correlation energy of electrons that are confined to a one-dimensional space is presented and its accuracy with LDA, second- and third-order Møller-Plesset perturbation energies, and exact calculations for a variety of inhomogeneous systems are compared.

Correlation energy of two electrons in the high-density limit.

It is conjecture that for large D, the limiting correlation energy E(c) approximately -delta(2)/8 in any confining external potential, where delta = 1/(D-1).

Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs=100–150. We have tested different types of orbital for use in the approximate wave

Hartree-Fock ground state of the three-dimensional electron gas.

Using numerical calculations for finite systems and analytic techniques, this work studies the unrestricted HF ground state of the three-dimensional electron gas and finds broken spin symmetry states with a nearly constant charge density at high density.

Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations

Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a

Ground state of two electrons on a sphere

We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius $R$. We have used electronic structure models ranging from restricted and

Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that
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