Assessment of random phase approximation with different exchange-correlation functionals for description of binding energies of molecular solids

Abstract

Reliable prediction of the structure and stability of molecular solids is considered one of the important keys to explore the numerous applications of these systems. However, the need to describe reliably electron correlations in solids makes the accurate calculations of their binding energies challenging.

Moreover, the relative energies of different phases or polymorphs of molecular solids are often small, leading to high requirements not only on the accuracy but also on the precision of the numerical set-up. To date, the calculations of binding energies for molecular solids with many atoms can become prohibitively expensive for high levels of theory, such as coupled clusters with singles, doubles, and perturbative triples (CCSD(T)).

In this study, we assess the accuracy of a simpler and computationally cheaper method (random phase approximation (RPA)) based on different exchange-correlation functionals (PBE, SCAN, PBE0, and SCAN0) by comparing with CSD(T) reference data. To do this, we calculated dimer, trimer, and tetramer contributions at the RPA and CCSD(T) levels using many-body expansion (MBE) approach for four crystalline hydrocarbons: ethane, ethylene, and cubic and orthorhombic forms of acetylene.

We find the choice of the DFT functional affects significantly the results of the many-body contributions, but the total binding energies are found to be similar for PBE and SCAN, and for PBE0 and SCAN0. In addition, when Hartree-Fock (HF) exchange is added to PBE and SCAN, the energy changes of all many-body contributions are larger for PBE than for SCAN.

Finally, while the calculations are more computationally expensive for PBE0 and SCAN0 than for PBE and SCAN, the RPA method with renormalized singles energy (RSE) corrections based on PBE and SCAN performs better than that based on PBE0 and SCAN0 for all the considered systems.