Basis set incompleteness-corrected Random Phase Approximation correlation energy combining ph and pp channels

Random Phase Approximation correlation energy functionals have been developed in the framework of DFT in the particle-hole (ph) and particle-particle (pp) formalisms. We have shown that phRPA offers an appealing way, in terms of accuracy and modest computation cost, for obtaining correlation energy if, instead of a Kohn-Sham determinant, a reference state is described by a multiconfigurational wavefunction [1,2]. It has been revealed that a judicious combination of the ph and pp channels results in achieving good accuracy not only for closed- and open-shell ground states but also for excited states [3].

Unlike local correlation functionals, RPA shares a deficiency of other ab initio methods for electron correlation, namely it converges slowly with the basis set size. By relying on the similarity of the Coulomb electron operator projected on a given finite basis set and a long-range electron interaction in a complete basis set limit, we have constructed a complementary effective short-range operator, which leads to a buildup of the electron cusp. Including this operator in the correlation energy calculations results in the significant reduction of the basis set incompleteness error.

[1] K. Pernal, Phys. Rev. Lett. 9, 5534 (2018)

[2] P. Beran et al., J. Chem. Theory Comput. 17, 7575 (2021)

[3] A. Tucholska, Y. Guo, K. Pernal, J. Phys. Chem. Lett. 15, 12001 (2024)