Designing a paradigm for parameter-free double-hybrid density functionals through the adiabatic connection path

Abstract

It is now well established that the double-hybrid (DH) approximations belong to the most accurate methodologies for various properties and electronic structure calculations in the framework of density functional theory (DFT). In this context, we are lately witnessing the blooming of capable DH functionals derived from the adiabatic connection (AC) formalism. In the present work, through the AC path and by using a cubic integrand (CI) function, a novel DH exchange–correlation model is derived. The mixing coefficients are determined based on several well-known limiting conditions and linearly scaled one-parameter DH approximation. Employing the Perdew–Burke–Ernzerhof (PBE) and Tao–Perdew–Staroverov–Scuseria (TPSS) semilocal functionals as exchange and correlation terms in the underlying expression, the two new functionals free of any empirical parameter, CIDH–PBE and CIDH–TPSS, are developed. Using some benchmark sets on a number of different molecular properties including atomization energies, equilibrium geometries, vibrational frequencies, frontier orbital energies, and dipole polarizabilities, the performance of the CIDH models is compared with recently proposed parameterized, parameter-free, and AC-based DHs. Our numerical results show that the CIDH–PBE functional performs slightly better on average than CIDH–TPSS. Moreover, owing to its significant improvement over its parent functional and Møller–Plesset perturbation calculations, and similar or comparable performance compared to other DHs in some cases, CIDH–PBE can be considered as another promising functional for DH computations. On the whole, as evidenced from this study and other recent efforts in this respect, the development of parameter-free DHs from the route of AC has opened a new outlook in the field of DH–DFT, and more investigations in this direction are desirable.