Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory

Abstract

A hybrid stochastic-deterministic approach for computing the second-order perturbative contribution $E^{(2)}$ within multireference perturbation theory (MRPT) is presented. The idea at the heart of our hybrid scheme --- based on a reformulation of $E^{(2)}$ as a sum of elementary contributions associated with each determinant of the MR wave function --- is to split $E^{(2)}$ into a stochastic and a deterministic part. During the simulation, the stochastic part is gradually reduced by dynamically increasing the deterministic part until one reaches the desired accuracy. In sharp contrast with a purely stochastic MC scheme where the error decreases indefinitely as $t^{-1/2}$ (where $t$ is the computational time), the statistical error in our hybrid algorithm displays a polynomial decay $\sim t^{-n}$ with $n=3-4$ in the examples considered here. If desired, the calculation can be carried on until the stochastic part entirely vanishes. In that case, the exact result is obtained with no error bar and no noticeable computational overhead compared to the fully-deterministic calculation. The method is illustrated on the F${}_2$ and Cr${}_2$ molecules. Even for the largest case corresponding to the Cr${}_2$ molecule treated with the cc-pVQZ basis set, very accurate results are obtained for $E^{(2)}$ for an active space of (28e,176o) and a MR wave function including up to $2\times 10^7$ determinants.

8 pages, 5 figures

References in corpus (5)

• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Stochastic multi-reference perturbation theory with application to linearized coupled cluster method
• Using CIPSI nodes in diffusion Monte Carlo
• A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves

Cited by in corpus (84)

• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids
• Cheap and near exact CASSCF with large active spaces
• Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method
• Reference Energies for Double Excitations
• The Quest For Highly Accurate Excitation Energies: A Computational Perspective
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• CASSCF with Extremely Large Active Spaces using the Adaptive Sampling Configuration Interaction Method
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Excited states using semistochastic heat-bath configuration interaction
• Fast Semistochastic Heat-Bath Configuration Interaction
• Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction
• Selected configuration interaction dressed by perturbation
• Machine Learning Configuration Interaction
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Exotic Molecules and Radicals
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Selected Configuration Interaction in a Basis of Cluster State Tensor Products
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Excitation energies from diffusion Monte Carlo using selected Configuration Interaction nodes
• Chemically Accurate 0-0 Energies with not-so-Accurate Excited State Geometries
• One-step treatment of spin-orbit coupling and electron correlation in large active spaces
• Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach
• Deterministic construction of nodal surfaces within quantum Monte Carlo: the case of FeS
• Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method
• Variational coupled cluster for ground and excited states
• Orbital Optimization in Selected Configuration Interaction Methods
• The performance of CIPSI on the ground state electronic energy of benzene
• Accurate many-body electronic structure near the basis set limit: application to the chromium dimer
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• The Adaptive Shift Method in Full Configuration Interaction Quantum Monte Carlo: Development and Applications
• An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo
• Transcorrelated Density Matrix Renormalization Group
• Accurate full configuration interaction correlation energy estimates for five- and six-membered rings
• Influence of Pseudopotentials on Excitation Energies From Selected Configuration Interaction and Diffusion Monte Carlo
• Reference Energies for Valence Ionizations and Satellite Transitions
• A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4
• How accurate are EOM-CC4 vertical excitation energies?
• Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo
• Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
• Efficient multireference perturbation theory without high-order reduced density matrices
• Reference Energies for Cyclobutadiene: Automerization and Excited States
• SOiCI and iCISO: Combining iterative configuration interaction with spin-orbit coupling in two ways
• Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality
• Is Externally Corrected Coupled Cluster Always Better than the Underlying Truncated Configuration Interaction?
• The QUEST Database of Highly-Accurate Excitation Energies
• Comparing many-body approaches against the helium atom exact solution
• Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
• An efficient stochastic algorithm for the perturbative density matrix renormalization group in large active spaces
• Extension of selected configuration interaction for transcorrelated methods
• High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions: Further Details and Comparisons
• Capturing static and dynamic correlation with $\Delta \text{NO}$-MP2 and $\Delta \text{NO}$-CCSD
• Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference
• Can $GW$ Handle Multireference Systems?
• Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments?
• A Parallel, Distributed Memory Implementation of the Adaptive Sampling Configuration Interaction Method
• Rationale for the Extrapolation Procedure in Selected Configuration Interaction
• Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections
• Stochastic many-body perturbation theory for electron correlation energies
• A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
• Evaluating two-electron-repulsion integrals over arbitrary orbitals using Zero Variance Monte Carlo: Application to Full Configuration Interaction calculations with Slater-type orbitals
• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Unitary Coupled Cluster: Seizing the Quantum Moment
• Selected Configuration Interaction for Resonances
• Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters
• Converging High-Level Coupled-Cluster Energetics via Adaptive Selection of Excitation Manifolds Driven by Moment Expansions
• Compactification of Determinant Expansions via Transcorrelation
• Benchmarking the Semi-Stochastic CC(P;Q) Approach for Singlet-Triplet Gaps in Biradicals
• Specific chemical bond relaxation unravelled by analysis of shake-up satellites in the oxygen single site double core hole spectrum of CO${}_2$
• Complete Active Space Iterative Coupled Cluster Theory
• Critical Limitations in Quantum-Selected Configuration Interaction Methods
• Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals
• PASPT2: a size-extensive and size-consistent partial-active-space multi-state multi-reference second-order perturbation theory for strongly correlated electrons
• Measuring correlated electron motion in atoms with the momentum-balance density
• High-Level Coupled-Cluster Energetics by Merging Moment Expansions with Selected Configuration Interaction
• The Singlet-Triplet Gap of Cyclobutadiene: The CIPSI-Driven CC($P$;$Q$) Study
• Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method
• Near-Exact Nuclear Gradients of Complete Active Space Self-Consistent Field Wave Functions
• Addressing Strong Correlation by Approximate Coupled-Pair Methods with Active-Space and Full Treatments of Three-Body Clusters
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Bicyclic Systems
• Spin-pure Stochastic-CASSCF via GUGA-FCIQMC applied to Iron Sulfur Clusters
• Extension of the CIPSI-Driven CC($P$;$Q$) Approach to Excited Electronic States
• Diffusion Monte Carlo using domains in configuration space
• Double Electron Attachment and Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with Full and Active-Space Treatments of 4-Particle-2-Hole and 4-Hole-2-Particle Excitations and Three-Body Clusters