Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Abstract

Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC or connecting second-order perturbation theory to a full-seniority treatment via Padé approximants are better strategies. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.

References in corpus (40)

• Long-range/short-range separation of the electron-electron interaction in density functional theory
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• A natural orbital functional for the many-electron problem
• N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and poly-p-phenylene vinylene oligomer
• Reduced Density Matrix Functional for Many-Electron Systems
• Seniority-based coupled cluster theory
• Efficient description of strongly correlated electrons with mean-field cost
• Global Method for Electron Correlation
• The Delicate Balance of Static and Dynamic Electron Correlation
• Projected seniority-two orbital optimization of the Antisymmetric Product of one-reference orbital Geminal
• Density-Matrix-Power Functional: Performance for Finite Systems and the Homogeneous Electron Gas
• Empirical Functionals for Reduced Density Matrix Functional Theory
• Linearized Coupled Cluster Correction on the Antisymmetric Product of 1 reference orbital Geminals
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Pair extended coupled cluster doubles
• Targeting excited states in all-trans polyenes with electron-pair states
• Variational coupled cluster for ground and excited states
• Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states
• Correlating AGP on a quantum computer
• Targeting doubly-excited states with Equation of Motion Coupled Cluster theory restricted to double excitations
• Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Geminal-Based Configuration Interaction
• Analysis of double hybrid density-functionals along the adiabatic connection
• Correlating the Antisymmetrized Geminal Power Wave Function
• Benchmarking the accuracy of seniority-zero wavefunction methods for non-covalent interactions
• Orbital entanglement and correlation from pCCD-tailored Coupled Cluster wave functions
• Geminal replacement models based on AGP
• Exploring non-linear correlators on AGP
• A functional of the one-body-reduced density matrix derived from the homogeneous electron gas: Performance for finite systems
• Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction
• H${}_4$: A Challenging System For Natural Orbital Functional Approximations
• Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
• Challenges for variational reduced-density-matrix theory with three-particle N-representability conditions
• Capturing static and dynamic correlation with $\Delta \text{NO}$-MP2 and $\Delta \text{NO}$-CCSD
• Projected site-occupation embedding theory
• Active Space Pair 2-Electron Reduced Density Matrix Theory for Strong Correlation
• The seniority quantum number in Tensor Network States
• $\Delta$NO and the complexities of electron correlation in simple hydrogen clusters

Cited by in corpus (10)

• Refining and relating fundamentals of functional theory
• Electron correlation in the Iron(II) Porphyrin by NOF approximations
• Toward more accurate adiabatic connection approach for multireference wave functions
• Outstanding Improvement in Removing the Delocalization Error by Global Natural Orbital Functional
• Numerically Exact Configuration Interaction at Quadrillion-Determinant Scale
• A toolbox of spin-adapted generalized Pauli constraints
• Partial conservation of seniority in semi-magic nuclei
• Spin adaptation of the cumulant expansions of reduced density matrices
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture