Continuum variational and diffusion quantum Monte Carlo calculations

Abstract

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

References in corpus (55)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Superfluid Fermi Gases with Large Scattering Length
• Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study
• Correlation energy and spin polarization in the 2D electron gas
• Jastrow correlation factor for atoms, molecules, and solids
• Twist-averaged Boundary Conditions in Continuum Quantum Monte Carlo
• Optimization of quantum Monte Carlo wave functions by energy minimization
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• On the accuracy of DFT exchange-correlation functionals for H bonds in small water clusters II: The water hexamer and van der Waals interactions
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Finite-size errors in continuum quantum Monte Carlo calculations
• Beyond the locality approximation in the standard diffusion Monte Carlo method
• Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg
• Electron Emission from Diamondoids: A Diffusion Quantum Monte Carlo Study
• Excitonic condensation in a symmetric electron-hole bilayer
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior
• The role of electronic correlation in the Si(100) reconstruction: a quantum Monte Carlo study
• Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
• Zero-variance principle for Monte Carlo algorithms
• A variance-minimization scheme for optimizing Jastrow factors
• Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
• Finite-size correction in many-body electronic structure calculations
• Spin Polarization of the Low Density 3D Electron Gas
• Diffusion Monte Carlo with lattice regularization
• Pfaffian pairing and backflow wave functions for electronic structure quantum Monte Carlo methods
• Finite size errors in quantum many-body simulations of extended systems
• Optimization of ground and excited state wavefunctions and van der Waals clusters
• Structural properties and enthalpy of formation of magnesium hydride from quantum Monte Carlo calculations
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Quantum Monte Carlo calculations of H${}_2$ dissociation on Si(001)
• Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon
• Energies of the first row atoms from quantum Monte Carlo
• Polarization Measurements and the Pairing Gap in the Universal Regime
• Symmetry Constraints and Variational Principles in Diffusion Quantum Monte Carlo Calculations of Excited-State Energies
• Correlation Induced Inhomogeneity in Circular Quantum Dots
• The Schottky defect formation energy in MgO calculated by diffusion Monte Carlo
• Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Crossover in Fluid Hydrogen
• Dissociation energy of the water dimer from Quantum Monte Carlo calculations
• Energetics and Dipole Moment of Transition Metal Monoxides by Quantum Monte Carlo
• Excitations in photoactive molecules from quantum Monte Carlo
• All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe
• Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO
• Quantum Monte Carlo study of the Ne atom and the Ne+ ion
• Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas
• Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
• Many-body wavefunctions for normal liquid ${}^3$He
• Diffusion Monte Carlo: Exponential scaling of computational cost for large systems
• Electronic Quantum Monte Carlo Calculations of Atomic Forces, Vibrations, and Anharmonicities
• Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations
• Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials
• Comment on "Quantum Monte Carlo study of the dipole moment of CO" [J. Chem. Phys. 110, 11700 (1999)]
• Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations
• Reply to the Comment on: Quantum Monte Carlo study of the dipole moment of CO [J. Chem. Phys. 110, 11700 (1999)]

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