Quantum Monte Carlo study of the Ne atom and the Ne+ ion.

We report all-electron and pseudopotential calculations of the ground-state energies of the neutral Ne atom and the Ne(+) ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.

[1]  R. Needs,et al.  Jastrow correlation factor for atoms, molecules, and solids , 2004, 0801.0378.

[2]  M. Requardt,et al.  Poor decay of correlations in inhomogeneous fluids and solids and their relevance for the physics of phase boundaries , 1986 .

[3]  C. Umrigar,et al.  A diffusion Monte Carlo algorithm with very small time-step errors , 1993 .

[4]  D. Ceperley,et al.  Backflow correlations for the electron gas and metallic hydrogen. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Wilson,et al.  Optimized trial wave functions for quantum Monte Carlo calculations. , 1988, Physical review letters.

[6]  Davidson,et al.  Ground-state correlation energies for atomic ions with 3 to 18 electrons. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[7]  R J Needs,et al.  Scheme for adding electron-nucleus cusps to Gaussian orbitals. , 2005, The Journal of chemical physics.

[8]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[9]  Kwon,et al.  Effects of three-body and backflow correlations in the two-dimensional electron gas. , 1993, Physical review. B, Condensed matter.

[10]  S. Fahy,et al.  Optimization of configuration interaction coefficients in multideterminant Jastrow–Slater wave functions , 2002 .

[11]  C. Fischer,et al.  Extension of the HF program to partially filled f-subshells , 1996, physics/0406002.

[12]  Richard Phillips Feynman,et al.  Atomic Theory of the Two-Fluid Model of Liquid Helium , 1954 .

[13]  R. J. Needs,et al.  Variance-minimization scheme for optimizing Jastrow factors , 2005 .

[14]  P. A. Christiansen,et al.  Relativistic effective potentials in quantum Monte Carlo calculations , 1987 .

[15]  Richard Phillips Feynman,et al.  Energy Spectrum of the Excitations in Liquid Helium , 1956 .

[16]  W. Lester,et al.  A soft Hartree–Fock pseudopotential for carbon with application to quantum Monte Carlo , 1998 .

[17]  Claudia Filippi,et al.  Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules , 1996 .

[18]  David M. Ceperley,et al.  Fixed-node quantum Monte Carlo for molecules , 1982 .

[19]  R. Needs,et al.  Quantum Monte Carlo simulations of solids , 2001 .

[20]  D. Ceperley,et al.  Nonlocal pseudopotentials and diffusion Monte Carlo , 1991 .

[21]  James B. Anderson,et al.  Quantum chemistry by random walk. H 2P, H+3D3h1A′1, H23Σ+u, H41Σ+g, Be 1S , 1976 .

[22]  Paul R. C. Kent,et al.  Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions , 1999 .

[23]  Chien-Jung Huang C. J. Umrigar M.P. Nightingale.  Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations , 1997, cond-mat/9703008.

[24]  R J Needs,et al.  Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior. , 2009, The Journal of chemical physics.

[25]  Carlo Pierleoni,et al.  Coupled electron-ion monte carlo calculations of dense metallic hydrogen. , 2004, Physical review letters.

[26]  Optimal orbitals from energy fluctuations in correlated wave functions , 1999, cond-mat/9906305.

[27]  V. Kaufman,et al.  Accurate Ground-Term Combinations in Ne i , 1972 .

[28]  R. Needs,et al.  Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg. , 2005, The Journal of chemical physics.

[29]  R. Martin,et al.  Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study , 1998, cond-mat/9803092.