Random Phase Approximation Applied to Many-Body Noncovalent Systems

Abstract

The random phase approximation (RPA) has received a considerable interest in the field of modeling systems where noncovalent interactions are important. Its advantages over widely used density functional theory (DFT) approximations are the exact treatment of exchange and the description of long-range correlation. In this work we address two open questions related to RPA. First, how accurately RPA describes nonadditive interactions encountered in many-body expansion of a binding energy. We consider three-body nonadditive energies in molecular and atomic clusters. Second, how does the accuracy of RPA depend on input provided by different DFT models, without resorting to selfconsistent RPA procedure which is currently impractical for calculations employing periodic boundary conditions. We find that RPA based on the SCAN0 and PBE0 models, i.e., hybrid DFT, achieves an overall accuracy between CCSD and MP3 on a dataset of molecular trimers of Řezáč et al. (J. Chem. Theory. Comput. 2015, 11, 3065) Finally, many-body expansion for molecular clusters and solids often leads to a large number of small contributions that need to be calculated with a high precision. We therefore present a cubic-scaling (or SCF-like) implementation of RPA in atomic basis set, which is designed for calculations with a high numerical precision. rors originating from the exchange functional are on the same order as the errors originating from the missing dispersion energy. [19][20][21] Approximate exchange functionals alone can lead to both strongly overestimated and underestimated noncovalent interactions. 22 For two body systems such issues tend to be masked by adjusting the equilibrium-and short-distance behavior of the dispersion correction. 19 However, the three-body exchange errors cannot be compensated in a similar way by adjusting the pairwise additive dispersion corrections. 19 Overall, the conclusion originating from the existing literature is that no existing semilocal functional can reliably account for many body effects. 21,23 Affordable schemes based on perturbation theory could offer higher and systematically improvable accuracy for calculations of condensed systems compared to standard DFT functionals. 21,[24][25][26][27] Of such schemes, the random phase approximation to the correlation energy (RPA) is promising as it is both compatible with the Hartree-Fock (HF) exchange and it contains terms describing higher-order (nonadditive) correlation effects. 28,29 RPA has been tested for interaction energies of dimers, 30-32 for adsorption, [33][34][35] or for molecular 36-39 and atomic solids 40 and interfaces. 41,42 For the cases involving noncovalent interactions, high accuracy has been achieved with addition of the singles corrections. 43,44 However, its accuracy for predicting nonadditive energies is unknown and this is one of our interests in this work. Moreover, most of the RPA calculations nowadays are performed non-self-consistently, using DFT orbitals and energies in the RPA energy expression. Here we obtain RPA results usi...

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

“…The post-Kohn Sham RPA calculations based on PBE, PBE0, SCAN, and SCAN0 were carried out with the cubic-scaling algorithm described in Ref. 21 and implemented in an inhouse code. The n-body RPA interaction energy can be written down as follows:…”

“…The RPA calculations with PBE, PBE0, SCAN, and SCAN0 orbitals employed the tightest set of numerical precision thresholds defined in Table 1 of Ref. 21. Unless noted otherwise, the RPA correlation energies were extrapolated to the complete basis-set limit with the basis sets AVTZ and AVQZ.…”

“…21 the quadratures are optimized for distribution of orbital energy differences (d ai in Ref. 21) occuring in the full n-body cluster (e.g., a trimer) and all its subsystems. In this work, the quadrature optimization subroutine ignores the high energy differences which occur in the subsystems, but are above the largest occupied-virtual orbital energy difference in the full n-body cluster.…”

“…At the same time, low-scaling implementations promise routine use of RPA for molecular clusters and solids. [15][16][17][18][19][20][21] We have recently shown 21 that three-body RPA nonadditive interactions critically depend on the input DFT orbitals and the use of the renormalized singles energy (RSE). 22,23 For example, RSE qualitatively improves the three-body energies for RPA based on PBE or PBE0 orbitals, but the SCAN-based results are affected less.…”

“…22,23 For example, RSE qualitatively improves the three-body energies for RPA based on PBE or PBE0 orbitals, but the SCAN-based results are affected less. 21 Methane clathrate, modeled either as a finite cluster 24 or as a bulk material, 25 has been found to be a severe test case for widely used theoretical methods. Specifically, it is problematic to obtain accurately the interaction energy of methane molecule with the surrounding water cage.…”