Multi-Determinant Wave-functions in Quantum Monte Carlo

Abstract

Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly-correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.

References in corpus (24)

• Twist-averaged Boundary Conditions in Continuum Quantum Monte Carlo
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Optimization of quantum Monte Carlo wave functions by energy minimization
• Path Integral Monte Carlo Calculation of the Deuterium Hugoniot
• 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
• A Constrained Path Quantum Monte Carlo Method for Fermion Ground States
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach
• Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
• Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
• Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
• Approaching Chemical Accuracy with Quantum Monte Carlo
• Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules
• Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules
• Pressure-induced diamond to beta-tin transition in bulk silicon: a near-exact quantum Monte Carlo study
• Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm
• Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states
• Quantum Monte Carlo study of the first-row atoms and ions
• Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets
• Fundamental high pressure calibration from all-electron quantum Monte Carlo calculations
• Systematic reduction of sign errors in many-body calculations of atoms and molecules
• Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudpotentials

Cited by in corpus (46)

• Deep neural network solution of the electronic Schrödinger equation
• 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
• QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
• Shock Response and Phase Transitions of MgO at Planetary Impact Conditions
• Quantum Monte Carlo applied to solids
• Molecular properties by Quantum Monte Carlo: an investigation on the role of the wave function ansatz and the basis set in the water molecule
• Excited State Specific Multi-Slater Jastrow Wave Functions
• Accurate Predictions of Electron Binding Energies of Dipole-Bound Anions via Quantum Monte Carlo Methods
• Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: the Ti${}_4$O${}_7$ Magnéli phase
• Excitation Variance Matching with Limited Configuration Interaction Expansions in Variational Monte Carlo
• Towards DMC accuracy across chemical space with scalable $\Delta$-QML
• Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo
• Assessment of Multireference Approaches to Explicitly Correlated Full Configuration Interaction Quantum Monte Carlo
• Auxiliary-field based trial wave functions in quantum Monte Carlo calculations
• Assessing the Accuracy of the Jastrow Antisymmetrized Geminal Power in the H4 Model System
• All-electron quantum Monte Carlo with Jastrow single determinant Ansatz: application to the sodium dimer
• Towards Quantum Monte Carlo Forces on Heavier Ions: Scaling Properties
• Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo
• Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory
• Variation After Response in Quantum Monte Carlo
• Orbital-dependent backflow wave functions for real-space quantum Monte Carlo
• Equations of state and stability of MgSiO${}_3$ perovskite and post-perovskite phases from quantum Monte Carlo simulations
• Diffusion Monte Carlo Study on Relative Stabilities of Boron Nitride Polymorphs
• A variational Monte Carlo approach for core excitations
• How Large are Nonadiabatic Effects in Atomic and Diatomic Systems?
• TurboGenius: Python suite for high-throughput calculations of ab initio quantum Monte Carlo methods
• Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers
• Calculation of the energies of the multideterminant states of the nitrogen vacancy center in diamond with quantum Monte Carlo
• Towards chemical accuracy using the Jastrow correlated antisymmetrized geminal power ansatz
• Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion
• Fractional charge by fixed-node diffusion Monte Carlo
• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Variational solution of congruent transformed Hamiltonian for many-electron systems using full configuration interaction calculation
• Diffusion Quantum Monte Carlo Study of Martensitic Phase Transition: The Case of Phosphorene
• Floating block method for quantum Monte Carlo simulations
• Basis set incompleteness errors in fixed-node diffusion Monte Carlo calculations on non-covalent interactions
• Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods
• Locality Error Free Effective Core Potentials for 3d Transition Metal Elements Developed for the Diffusion Monte Carlo Method
• Infinite-order diagrammatic summation approach to explicitly correlated congruent transformed Hamiltonian
• Implementing advanced trial wave functions in fermion quantum Monte Carlo via stochastic sampling
• Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
• NNQS-AFQMC: Neural network quantum states enhanced fermionic quantum Monte Carlo
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Making the most of data: Quantum Monte Carlo Post-Analysis Revisited
• Electronic excited states in deep variational Monte Carlo