Compactification of Determinant Expansions via Transcorrelation
arXiv:2405.02640 · doi:10.1063/5.0217650
Abstract
Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.
arXiv comment18 pages, 10 figures (supporting information available)
References in corpus (46)
- Biorthogonal Quantum Mechanics
- Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
- 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
- A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules
- 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
- QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
- The Ground State Electronic Energy of Benzene
- 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
- Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
- Similarity transformation of the electronic Schrödinger equation via Jastrow factorisation
- Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule
- Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime
- Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime
- Full Coupled-Cluster Reduction for Accurate Description of Strong Electron Correlation
- The performance of CIPSI on the ground state electronic energy of benzene
- Towards efficient and accurate \emph{ab initio} solutions to periodic systems via transcorrelation and coupled cluster theory
- Transcorrelated Density Matrix Renormalization Group
- Accurate full configuration interaction correlation energy estimates for five- and six-membered rings
- Reference Energies for Valence Ionizations and Satellite Transitions
- Lie Algebraic Similarity Transformed Hamiltonians for Lattice Model Systems
- Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
- Explicitly correlated electronic structure calculations with transcorrelated matrix product operators
- Correlated Band Structure of a Transition Metal Oxide ZnO Obtained from a Many-Body Wave Function Theory
- xTC: An efficient treatment of three-body interactions in transcorrelated methods
- Eliminating the wave function singularity for ultracold atoms by similarity transformation
- Extension of selected configuration interaction for transcorrelated methods
- A new form of transcorrelated Hamiltonian inspired by range-separated DFT
- Towards near-exact solutions of molecular electronic structure: Full coupled-cluster reduction with a second-order perturbative correction
- High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions: Further Details and Comparisons
- Transcorrelated coupled cluster methods. II. Molecular systems
- Studies on the Transcorrelated Method
- Iterative diagonalization of the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis set: Application to -electron systems with deep core states
- Spin-adapted selected configuration interaction in a determinant basis
- Nonunitary projective transcorrelation theory inspired by the F12 ansatz
- An efficient implementation of Slater-Condon rules
- Rationale for the Extrapolation Procedure in Selected Configuration Interaction
- Converging High-Level Coupled-Cluster Energetics via Adaptive Selection of Excitation Manifolds Driven by Moment Expansions
- TC++: First-principles calculation code for solids using the transcorrelated method
- Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian
- Go Green: Selected Configuration Interaction as a More Sustainable Alternative for High Accuracy