Benchmark tests and spin adaptation for the particle-particle random phase approximation

Abstract

The particle-particle random phase approximation (pp-RPA) provides an approximation to the correlation energy in DFT via the adiabatic connection (van Aggelen, Yang, and Yang, http://arxiv.org/abs/1306.4957). It has virtually no delocalization error nor static correlation error for single-bond systems. However, with its formal O(N 6 ) scaling, the pp-RPA is computationally expensive. In this paper, we implement a spin-separated and spin-adapted pp-RPA algorithm, which reduces the computational cost by a significant factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database and four test sets for non-bonded interactions (HB6/04, CT7/04, DI6/04 and WI9/04). For the G2/97 database, the pp-RPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particle-hole RPA (ph-RPA) (22.7 kcal/mol). Furthermore, the error in the pp-RPA is nearly constant with the number of atoms in a molecule, while the error in the ph-RPA keeps increasing.For chemical reactions involving typical organic closed-shell molecules, pp-and ph-RPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that pp-RPA gives reliable energies in chemical applications.The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.

Linear-response time-dependent density-functional theory with pairing fields

“…This approximation leads to the working equation of pp-RPA using common DFAs as practiced in Ref. 11,13,16 . Additionally, TDDFT-P allows other pairing matrix dependent functionals E XC [ρ, κ] to be used to calculate N ± 2 excitations in the pp-RPA equation.…”

“…Both the adiabatic and non-adibatic versions of linear-response TDDFT-P are explored. Especially, the adiabatic TDDFT-P justi ed the practice of utilizing orbitals and eigenvalues of common DFAs in pp-RPA equations 11,13,16 . Such an extension enables us to capture e ects beyond mean-eld approximations in N ± 2 excitations, and would also make it possible to capture neutral excitations better by suitable approaches 16,42 .…”

“…Pp-RPA is the rst density-functional approximation (DFA) to satisfy the at-plane condition exactly 11,12 , and outperforms traditional direct particle-hole random phase approximation in many aspects 13 . Theoretical analysis reveals that the correlation energy from pp-RPA with Hartree-Fock references is equivalent to ladder-coupled-cluster doubles 14,15 .…”

Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation

“…This approach is based on the pairing matrix fluctuation, which contains information on two-electron addition and removal processes as well as the ground state correlation energy 38,39 . The pairing matrix fluctuation has been applied to the investigation of Auger Spectroscopy 40,41 .…”

Testing exchange–correlation functionals at fractional electron numbers

“…The "dilemma" of how to define the exchange-correlation potential for fractional N was discussed in early paper [23], while the papers [24,25] represent the most recent investigations related to the fractional-N problem for density functionals. Recently, an orbital functional based on the particle-particle random phase approximation to many-body theory has been shown to exhibit minimal errors for fractional charges and fractional spins and have many promising features [26,27].…”