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.

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Cited by in corpus (59)

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• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
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• Water on hexagonal boron nitride from diffusion Monte Carlo
• Microscopic molecular superfluid response: theory and simulations
• Spicing up continuum solvation models with SaLSA: the spherically-averaged liquid susceptibility ansatz
• Structural Stability and Defect Energetics of ZnO from Diffusion Quantum Monte Carlo
• Shape and Energy Consistent Pseudopotentials for Correlated Electron systems
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• Toward Accurate Adsorption Energetics on Clay Surfaces
• Ground state properties of the one-dimensional electron liquid
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• Diffusion quantum Monte Carlo study of the equation of state and point defects in aluminum
• Diffusion quantum Monte Carlo and GW study of the electronic properties of monolayer and bulk hexagonal boron nitride
• Diamond -> beta-tin phase transition in Si within diffusion quantum Monte Carlo
• Systematic DFT+U and Quantum Monte Carlo benchmark of magnetic two-dimensional (2D) CrX${}_3$ (X = I, Br, Cl, F)
• Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry
• Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets
• Effective-range dependence of resonant Fermi gases
• Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas
• An efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations
• Benchmarking density functional theory on the prediction of antiferromagnetic transition temperatures
• On the Sign Problem of the Fermionic Shadow Wave Function
• Quantum Monte Carlo calculation of the zero-temperature phase diagram of the two-component fermionic hard-core gas in two dimensions
• Equations of state and stability of MgSiO${}_3$ perovskite and post-perovskite phases from quantum Monte Carlo simulations
• The intrinsic ferromagnetism of two-dimensional (2D) MnO${}_2$ revisited: A many-body Quantum Monte Carlo and DFT+U study
• A tail-regression estimator for heavy-tailed distributions of known tail indices and its application to continuum quantum Monte Carlo data
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• Jastrow correlation factor for periodic systems
• High-Pressure Hydrogen Sulfide by Diffusion Quantum Monte Carlo
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• Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers
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• Generalized mean field description of entanglement in dimerized spin systems
• Binding energy of polaronic trions and biexcitons in CsPbBr${}_3$ nanocrystals
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• Diffusion Monte Carlo study of a spin-imbalanced two-dimensional Fermi gas with attractive interactions
• Optimizing Supercell Structures for Heisenberg Exchange Interaction Calculations
• Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian
• Building Materials Genome from Ground-State Configuration to Engineering Advance
• Energetics of H${}_2$ clusters from density functional and coupled cluster theories
• Understanding and eliminating spurious modes in variational Monte Carlo using collective variables
• Fermions with long and finite range interactions on a quantum ring
• Symmetry breaking and restoration on a fermionic quantum ring
• Electronic quantum wires in extended quasiparticle picture
• Quantum Monte Carlo method for metal catalysis: case study of hydrogen production on Pt(111)