Excitation energies from diffusion Monte Carlo using selected Configuration Interaction nodes

Abstract

Quantum Monte Carlo (QMC) is a stochastic method which has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that, within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-$\zeta$) basis sets.

arXiv comment8 pages, 3 figures

References in corpus (31)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• Optimization of quantum Monte Carlo wave functions by energy minimization
• Applications of quantum Monte Carlo methods in condensed systems
• Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
• High Accuracy Many-Body Calculational Approaches for Excitations in Molecules
• Excited states using semistochastic heat-bath configuration interaction
• Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
• Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction
• Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions
• Scheme for adding electron-nucleus cusps to Gaussian orbitals
• Symmetry Constraints and Variational Principles in Diffusion Quantum Monte Carlo Calculations of Excited-State Energies
• Excitations in photoactive molecules from quantum Monte Carlo
• Structure of fermion nodes and nodal cells
• Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states
• Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule
• Deterministic construction of nodal surfaces within quantum Monte Carlo: the case of FeS
• Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo
• Spin density distribution in open-shell transition metal systems: A comparative post-Hartree-Fock, Density Functional Theory and quantum Monte Carlo study of the CuCl2 molecule
• Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
• Accurate nonrelativistic ground-state energies of 3d transition metal atoms
• Quantum Monte Carlo with very large multideterminant wavefunctions
• Using CIPSI nodes in diffusion Monte Carlo
• Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond
• Fixed-node errors in quantum Monte Carlo: interplay of electron density and node nonlinearities
• Excitation Variance Matching with Limited Configuration Interaction Expansions in Variational Monte Carlo
• Impact of the Electron Density on the Fixed-Node Errors in Quantum Monte Carlo
• Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo
• Nodal surfaces and interdimensional degeneracies

Cited by in corpus (36)

• Reference Energies for Double Excitations
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
• Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
• Selected configuration interaction dressed by perturbation
• Chemically Accurate 0-0 Energies with not-so-Accurate Excited State Geometries
• Excited states with selected CI-QMC: chemically accurate excitation energies and geometries
• Machine learning configuration interaction for ab initio potential energy curves
• A Density-Based Basis-Set Correction For Wave Function Theory
• The performance of CIPSI on the ground state electronic energy of benzene
• Excited State Specific Multi-Slater Jastrow Wave Functions
• Chemically Accurate Excitation Energies With Small Basis Sets
• Charge density and redox potential of LiNiO2 using ab initio diffusion quantum Monte Carlo
• Accurate full configuration interaction correlation energy estimates for five- and six-membered rings
• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• Reference Energies for Valence Ionizations and Satellite Transitions
• Influence of Pseudopotentials on Excitation Energies From Selected Configuration Interaction and Diffusion Monte Carlo
• Reference Energies for Cyclobutadiene: Automerization and Excited States
• Systematic Comparison and Cross-validation of Fixed-Node Diffusion Monte Carlo and Phaseless Auxiliary-Field Quantum Monte Carlo in Solids
• Towards DMC accuracy across chemical space with scalable $\Delta$-QML
• SOiCI and iCISO: Combining iterative configuration interaction with spin-orbit coupling in two ways
• Excited-state diffusion Monte Carlo calculations: a simple and efficient two-determinant ansatz
• Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Taming the fixed-node error in diffusion Monte Carlo via range separation
• Fully quantum embedding with density functional theory for full configuration interaction quantum Monte Carlo
• Structural, Electronic and Magnetic Properties of Bulk and Epitaxial LaCoO${}_3$ through Diffusion Monte Carlo
• A variational Monte Carlo approach for core excitations
• Spin-adapted selected configuration interaction in a determinant basis
• A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals
• Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification
• Further Development of iCIPT2 for Strongly Correlated Electrons
• Iterative Configuration Interaction with Selection