Resolution of identity approach for the Kohn-Sham correlation energy within exact-exchange random-phase approximation

 P. Bleiziffer, A. Hesselman, A. Gorling, J. Chem. Phys., 136, 134102, (2012)

Hesselman and Gorling recently introduced exact-exchange random phase approximation (EXXRPA) methods. These Kohn Sham (KS) based methods treat the correlation energy via the random phase approximation (RPA) based on TDDFT using the exact frequency-dependent exchange kernel (Mol. Phys. 108, 359 (2010) and PRL 106, 093001 (2011)). Results from these EXXRPA methods for closed shell organic molecules showed results with accuracy on par with CCSD for total energies and slightly less accurate for reaction energies compared to CCSD but better than MP2.

In this paper, the authors report the development and implementation of the resolution of the identity EXXRPA. This results in two new methods: RI-EXXRPA and RI-EXXRPA+. Both methods make use of RI and auxiliary basis sets to reduce the formal scaling from N⁶ to N⁵. The computational speedup allows the inclusion of previously neglected terms giving rise to RI-EXXRPA+.

Results for total energies for 21 molecules show RMSD values of around 10 kcal/mol for RI-EXXRPA and CCSD, and below 10 kcal/mol for RI-EXXRPA+ (using CBS extrapolated CCSD(T) as reference). RMSD for 16 reaction energies gives values around 1.7 kcal/mol compared to 2.5 for MP2 using the same reference. Overall, this proof of principle paper presents two methods that employ RI to reduce the computational scaling. These methods, albeit more computationally costly than conventional DFT, could provide alternatives to post-HF methods using a Kohn-Sham based approach after more extensive testing.