Accuracy of Electronic Wave Functions in Quantum Monte Carlo: the Effect of High-Order Correlations

Abstract

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 Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based on the theory of invariants is used to compute the high-body correlations. We observe significant improvements in the variational Monte Carlo energy and in the fluctuations of the local energies but not in the fixed-node diffusion Monte Carlo energies. Improvements for the ground states of physical, fermionic atoms are found to be smaller than those for the ground states of fictitious, bosonic atoms, indicating that errors in the nodal surfaces of the fermionic wave functions are a limiting factor.

9 pages, no figures, Latex

Cited by in corpus (22)

• Jastrow correlation factor for atoms, molecules, and solids
• Optimization of quantum Monte Carlo wave functions by energy minimization
• Geminal wavefunctions with Jastrow correlation: a first application to atoms
• Energy and variance optimization of many body wave functions
• All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe
• Vertex corrections in localized and extended systems
• Framework for constructing generic Jastrow correlation factors
• Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon
• Quantum Monte Carlo study of the Ne atom and the Ne+ ion
• Uniform electron gases. I. Electrons on a ring
• A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states
• Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo
• Excited-state diffusion Monte Carlo calculations: a simple and efficient two-determinant ansatz
• Auxiliary-field based trial wave functions in quantum Monte Carlo calculations
• All-electron quantum Monte Carlo with Jastrow single determinant Ansatz: application to the sodium dimer
• Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo
• Nodal surfaces and interdimensional degeneracies
• Jastrow correlation factor for periodic systems
• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• The role of electron correlations in the electronic structure of putative Chern magnet TbMn${}_6$Sn${}_6$
• Three-electron coalescence points in two and three dimensions
• Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals