Analysis of double hybrid density-functionals along the adiabatic connection

Abstract

We present a graphical analysis of the adiabatic connections underlying double-hybrid density-functional methods that employ second-order perturbation theory. Approximate adiabatic connection formulae relevant to the construction of these functionals are derived and compared directly with those calculated using accurate ab initio methods. The discontinuous nature of the approximate adiabatic integrands is emphasized, the discontinuities occurring at interaction strengths which mark the transitions between regions that are: (i) described predominantly by second- order perturbation theory (ii) described by a mixture of density-functional and second-order perturbation theory contributions and (iii) described purely by density-functional theory. Numerical examples are presented for a selection of small molecular systems and van der Waals dimers. The impacts of commonly used approximations in each of the three sections of the adiabatic connection are discussed along with possible routes for the development of improved double-hybrid methodologies.

42 pages, 3 figures

References in corpus (5)

• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Double-hybrid density-functional theory made rigorous
• Long-range-corrected hybrids including RPA correlation
• A multiconfigurational hybrid density-functional theory
• Rigorous formulation of two-parameter double-hybrid density-functionals

Cited by in corpus (5)

• Generalized adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule
• Double-hybrid density-functional theory with meta-generalized-gradient approximations
• Double hybrid density-functional theory using the Coulomb-attenuating method
• Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths
• Alternative separation of exchange and correlation energies in range-separated density-functional perturbation theory