Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band gap materials. This promise is contingent upon the ability of DFT to predict one-particle states accurately. Unfortunately, approximate functionals fail to align the orbital energies with ionization potentials. We describe a new paradigm for achieving this alignment. In the proposed model, an average electron-exchange hole separation controls the onset of the orbital-dependent exchange in approximate range-separated functionals. The correct description of one-particle states is thus achieved without explicit electron removal or attachment. Extensive numerical tests show that the proposed method provides physically sound orbital gaps and leads to excellent predictions of charge-transfer excitations and other properties critically depending on the tail of the electron density.
The aim of this study is to present a performance test of optimally tuned long-range corrected (LRC) functionals applied to the symmetry-adapted perturbation theory (SAPT). In the present variant, the second-order energy components are evaluated at the coupled level of theory. We demonstrate that the generalized Kohn-Sham (GKS) description of monomers with optimally tuned LRC functionals may be essential for the quality of SAPT interaction energy components. This is connected to the minimization of a many-electron self-interaction error and exemplified by two model systems: polyacetylenes of increasing length and stretching of He 3 (+). Next we provide a comparison of SAPT approaches based on Kohn-Sham and GKS description of the monomers. We show that LRC leads to results better or comparable with the hitherto prevailing asymptotically corrected functionals. Finally, we discuss the advantages and possible limitations of SAPT based on LRC functionals.
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...
Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC n method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, AC n is more efficient than existing ab initio multireference dynamic correlation methods. AC n affords excellent results for singlet–triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.
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