Double-hybrid density-functional theory made rigorous

Abstract

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.

References in corpus (6)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Long-range/short-range separation of the electron-electron interaction in density functional theory
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions
• Short-range exchange and correlation energy density functionals: beyond the local density approximation
• Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications

Cited by in corpus (38)

• Empirical Double-Hybrid Density Functional Theory: A 'Third Way' In Between WFT and DFT
• SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters
• Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2 functional
• Rationale for a new class of double-hybrid approximations in density-functional theory
• A multiconfigurational hybrid density-functional theory
• Thermally-assisted-occupation density functional theory with generalized-gradient approximations
• Density Functional Model for Nondynamic and Strong Correlation
• Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes
• A general range-separated double-hybrid density-functional theory
• Rigorous formulation of two-parameter double-hybrid density-functionals
• Restoring size consistency of approximate functionals constructed from the adiabatic connection
• Analysis of double hybrid density-functionals along the adiabatic connection
• Double-hybrid density-functional theory with meta-generalized-gradient approximations
• Strong-interaction limit of an adiabatic connection in Hartree-Fock theory
• Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel
• Towards efficient orbital-dependent density functionals for weak and strong correlation
• Assessment of interaction-strength interpolation formulas for gold and silver clusters
• Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections
• Double hybrid density-functional theory using the Coulomb-attenuating method
• Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method
• Repartitioned Brillouin-Wigner Perturbation Theory with a Size-Consistent Second-Order Correlation Energy
• On the accuracy of the HSE hybrid functional to describe many-electron interactions and charge localization in semiconductors
• Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms
• Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations
• Global hybrids from the semiclassical atom theory satisfying the local density linear response
• Double-hybrid density-functional theory applied to molecular crystals
• Self-consistent range-separated density-functional theory with second-order perturbative correction via the optimized-effective-potential method
• Range-separated double-hybrid density-functional theory applied to periodic systems
• Optimizing the Regularization in Size-Consistent Second-Order Brillouin-Wigner Perturbation Theory
• Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes
• Alternative separation of exchange and correlation energies in range-separated density-functional perturbation theory
• Wave-function inspired density functional applied to the H${}_2$/H${}_2^{+}$ challenge
• Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals
• Improving XYG3-type Doubly Hybrid Approximation using Self-Interaction Corrected SCAN Density and Orbitals via the PZ-SIC Framework: the xDH@SCAN(SIC) Approach
• Simulating one hundred entangled atoms using projected-interacting full configuration interaction wavefunctions corrected by projected density functionals
• Comparing correlation components and approximations in Hartree-Fock and Kohn-Sham theories via an analytical test case study
• Density sensitivity of empirical functionals
• Relativistic density-functional theory based on effective quantum electrodynamics