Boosting the accuracy and speed of quantum Monte Carlo: size-consistency and time-step

Abstract

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green function to avoid singularities near the nodal surface of the trial wavefunction. We show that these modifications affect the DMC energies in a way that is not size-consistent, resulting in large time-step errors. Building on the modifications of Umrigar {\em et al.} and of DePasquale {\em et al.} we propose a simple Green function modification that restores size-consistency to large values of time-step; substantially reducing the time-step errors. The new algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

References in corpus (19)

• Square ice in graphene nanocapillaries
• Random-phase approximation and its applications in computational chemistry and materials science
• Continuum variational and diffusion quantum Monte Carlo calculations
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Hydrogen bonds and van der Waals forces in ice at ambient and high pressures
• 2D ice from first principles: structures and phase transitions
• Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg
• Norm-conserving Hartree-Fock pseudopotentials and their asymptotic behavior
• An efficient localized basis set for quantum Monte Carlo calculations on condensed matter
• Size-consistent variational approaches to non-local pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited
• Diffusion Monte Carlo with lattice regularization
• Unexpectedly high pressure for molecular dissociation in liquid hydrogen by a reliable electronic simulation
• Water on hexagonal boron nitride from diffusion Monte Carlo
• The effect of electron correlation on the electronic structure and spin-lattice coupling of the high-T${}_c$ cuprates: quantum Monte Carlo calculations
• Ab-initio molecular dynamics simulation of liquid water by Quantum Monte Carlo
• Structural and configurational properties of nanoconfined monolayer ice from first principles
• Benchmarking the performance of Density Functional Theory and Point Charge Force Fields in their Description of sI Methane Hydrate against Diffusion Monte Carlo
• Distinct metallization and atomization transitions in dense liquid hydrogen
• Ab Initio Many-body Study of Cobalt Adatoms Adsorbed on Graphene

Cited by in corpus (36)

• QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids
• Interactions between Large Molecules: Puzzle for Reference Quantum-Mechanical Methods
• On the physisorption of water on graphene: Sub-chemical accuracy from many-body electronic structure methods
• Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
• Fast and accurate quantum Monte Carlo for molecular crystals
• Interaction between water and carbon nanostructures: How good are current density functional approximations?
• TurboRVB: a many-body toolkit for {\it ab initio} electronic simulations by quantum Monte Carlo
• Properties of the water to boron nitride interaction: from zero to two dimensions with benchmark accuracy
• Towards the ground state of molecules via diffusion Monte Carlo on neural networks
• Evidence for Stable Square Ice from Quantum Monte Carlo
• Evidence from quantum Monte Carlo of large gap superfluidity and BCS-BEC crossover in double electron-hole layers
• How strongly do hydrogen and water molecules stick to carbon nanomaterials?
• A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface
• Toward Accurate Adsorption Energetics on Clay Surfaces
• A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: improving reproducibility and reducing the trial-wave-function bias
• Hydration of NH${}_4^{+}$ in Water: Bifurcated Hydrogen Bonding Structures and Fast Rotational Dynamics
• How accurate are simulations and experiments for the lattice energies of molecular crystals?
• DMC-ICE13: ambient and high pressure polymorphs of ice from Diffusion Monte Carlo and Density Functional Theory
• Efficient and accurate description of adsorption in zeolites
• Correlation energies of the high-density spin-polarized electron gas to meV accuracy
• PyQMC: an all-Python real-space quantum Monte Carlo module in PySCF
• Error Cancellation in Diffusion Monte Carlo Calculations of Surface Chemistry
• Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo
• Systematic discrepancies between reference methods for non-covalent interactions within the S66 dataset
• Multi-scale simulation of the adsorption of lithium ion on graphite surface: from Quantum Monte Carlo to Molecular Density Functional Theory
• Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings
• Diffusion Quantum Monte Carlo Study of Martensitic Phase Transition: The Case of Phosphorene
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• An efficient hybrid orbital representation for quantum Monte Carlo calculations
• Reducing the time-step errors in diffusion Monte Carlo
• Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
• On the increase of the melting temperature of water confined in one-dimensional nano-cavities
• A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities
• Energetics of H${}_2$ clusters from density functional and coupled cluster theories
• Quantum Monte Carlo prerequisites for industrial catalysts. Accurately assessing H atom and H${}_2$ physical adsorption energy on Pt(111)
• The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations