The nature of three-body interactions in DFT: exchange and polarization effects

We propose a physically motivated decomposition of DFT 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar$_2$-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems range-separated hybrids achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli Blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component although semilocal and global hybrid DFAs appear to imitate it in the short range

Nowe funkcjonały gęstości elektronowej do modelowania układów związanych niekowalencyjnie

The main part of this work deals with the problem of constructing density-functional methods within the realm of hybrid semilocal approximations, that is, within the set of practical electronic-structure methods that can be applied to real-world molecular systems. In a series of works, the author demonstrates the merits of various building blocks of approximate functionals: the kinetic energy dependence of the exchange-correlation functional, dispersion correction, and long-range correction to the DFT exchange energy. The prototype method which includes these elements is the MCS functional; this method is, however, restricted to the description of noncovalent systems. The final and most complete method devised by the author is a scheme for converting an existing exchange functional into its range-separated hybrid variant. The approach is based on the exchange hole of the Becke-Roussel type, which has the exact second-order expansion in the interelectron distance. The LC-PBETPSS functional, which is constructed by applying this scheme, combines the range-separated PBE exchange lifted to the meta-GGA rung and the TPSS correlation. Numerical tests show remarkably robust performance of the method for noncovalent interaction energies, barrier heights, main-group thermochemistry, and excitation energies

Nowe funkcjonały gęstości elektronowej do modelowania układów związanych niekowalencyjnie

Chałasiński, GrzegorzLink archiwalny https://depotuw.ceon.pl/handle/item/192

Random Phase Approximation Applied to Many-Body Noncovalent Systems

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 \v{R}ez\'{a}\v{c} 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

Assessment of random-phase approximation and second order M{\o}ller-Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene

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 M{\o}ller-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 $\pi$-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

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

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH$_4$(H$_2$O)$_{20}$, is a stringent test for approximate methods, including density-functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA). The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of MBE. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the MBE. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.Comment: Data available at https://doi.org/10.5281/zenodo.442967