Assessment of random phase approximation and second-order Møller–Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene

Abstract

The relative energies of different phases or polymorphs of molecular solids can be small, less than a kiloJoule/mol. Reliable description of such energy differences requires high quality treatment of electron correlations, typically beyond that achievable by routinely applicable density functional theory approximations (DFT). At the same time, high-level wave function theory is currently too computationally expensive. Methods employing intermediate level of approximations, such as Møller-Plesset (MP) perturbation theory and the random-phase approximation (RPA) are potentially useful. However, their development and application for molecular solids has been impeded by the scarcity of necessary benchmark data for these systems. In this work we employ the coupled-clusters method with singles, doubles and perturbative triples (CCSD(T)) to obtain a reference-quality many-body expansion of the binding energy of four crystalline hydrocarbons with a varying π-electron character: ethane, ethene, and cubic and orthorhombic forms of acetylene. The binding energy is resolved into explicit dimer, trimer, and tetramer contributions, which facilitates the analysis of errors in the approximate approaches. With the newly generated benchmark data we test the accuracy of MP2 and non-self-consistent RPA. We find that both of the methods poorly describe the non-additive many-body interactions in closely packed clusters. Using different DFT input states for RPA leads to similar total binding energies, but the many-body components strongly depend on the choice of the exchange-correlation functional.

Post-Kohn–Sham Random-Phase Approximation and Correction Terms in the Expectation-Value Coupled-Cluster Formulation

“…p r sq qs pr (14) To arrive at a useful truncation scheme, we split Γ into the antisymmetrized product of 1-RDMs and the size-extensive remainder, Λ, referred to as the 2-RDM cumulant 34−36 = + qs pr pq rs ps rq qs pr (15) Using the above definitions and Wick's theorem, the complete matrix element of H N on the rhs of eq 12 can be built from the one-particle contributions (17) where δρ is the difference between the fully interacting 1-RDM and the diagonal, noninteracting density matrix, ρ 0 , corresponding to the single determinant…”

“…The RPA response is the central quantity used to formulate the correlation energy approximation via the adiabatic-connection fluctuation–dissipation formula where the integration is over the coupling constant λ and frequency u . It turns out that RPA in eq is enough to capture the essential dispersion forces in many-body noncovalent systems. ,– At long intermolecular distances, the RPA correlation energy correctly reduces to the Casimir–Polder dispersion energy with correlated response functions of the monomers. , χ RPA accounts for the electrodynamic screening in large polarizable noncovalent complexes, which is a neglected effect in, e.g., second-order Møller–Plesset theory. , In molecular crystals and finite clusters, post-KS RPA reproduces the nonadditive many-body effects at a qualitative level, which is beyond the reach of local DFT approximations. – …”

“… 11 , 12 In molecular crystals and finite clusters, post-KS RPA reproduces the nonadditive many-body effects at a qualitative level, which is beyond the reach of local DFT approximations. 13 – 17 …”

Can Spin-Component Scaled MP2 Achieve kJ/mol Accuracy for Cohesive Energies of Molecular Crystals?

“…An alternative to DFT is a wave function-based approach, which naturally includes dispersion interactions at the post-Hartree–Fock (HF) level and is, in principle, systematically improvable. Among such methods, second-order Møller–Plesset perturbation theory (MP2) is the simplest correlation method, and its accuracy can be significantly improved by the separate scaling of the spin components of its correlation energy (at least, for molecules). ,− Despite the increasing use of periodic MP2 due to its relatively low cost, there are few systematic and complete reports on its performance, − especially in the computationally demanding complete basis set (CBS) − limit and thermodynamic limit (TDL). − …”