On the top rung of Jacob's ladder of density functional theory: Toward resolving the dilemma of SIE and NCE

Abstract

According to the classification of Jacob's Ladder proposed by Perdew, density functional approximations (DFAs) on the top (fifth) rung add the information of the unoccupied Kohn-Sham orbitals, which hold the promise to enter the heaven of chemical accuracy. In other words, we expect that a much higher accuracy with a broader applicability than the existing DFAs would eventually be achieved on the fifth rung. Nonetheless, Jacob's Ladder itself does not offer a recipe for how to manipulate the unoccupied Kohn-Sham orbitals on the construction of a successful fifth rung DFA. In this article, we briefly review two successful types of the fifth rung DFAs, that is, random-phase approximation (RPA) and doubly hybrid approximation (DHA). The limitations of RPA and DHA will be introduced in the context of the so-called self-interaction error (SIE)/nondynamic correlation error (NCE) dilemma in the world of density functional theory. We propose the development strategy for DHAs to address the general concern about the future of advanced DFAs on the fifth rung. We share our experience here, based on the relevant efforts recently made by the authors and their co-workers, aiming to resolve the SIE/NCE dilemma and to extend the applicability of DHAs from the chemistry of the main group elements to that of the transition metals.

Stability of the polyynic form of C18, C22, C26, and C30nanorings: a challenge tackled by range-separated double-hybrid density functionals

“…The DH models have been introduced and thoroughly tested by several groups in last years, improving the accuracy and range of applications of DFT to those challenging systems for which a GH method was insufficiently accurate. [47][48][49][50][51][52][53][54] More recently, the range-separation strategy was also extended highly successfully to these DH methods, [55][56][57] with different approaches followed to find the optimal value of the o parameter: fitting to large datasets 58,59 or to excited-state energies, 60 or simply by forcing to exactly reproduce the energy of the H atom as a model system free of one-electron self-interaction error. [61][62][63] Another strategy trying to improve the accuracy of a DH functional borrows the scaling of the opposite-and same-spin correlation energies of the PT2 term by a different factor, inspired by the spin-scaling for SCS-MP2, or even neglecting the former contribution, as for SOS-MP2, in analogy with eqn (1).…”

“Dividing and Conquering” and “Caching” in Molecular Modeling

“…Molecular interactions may be accurately described with high level molecular orbital theories (e.g., coupled cluster theory [ 37 , 38 ]) or sophisticated density functionals combined with large basis sets [ 39 , 40 , 41 , 42 , 43 ]. However, such quantum mechanically detailed computation is prohibitively expensive for any realistic complex molecular systems.…”

Theoretical modeling for interfacial catalysis

“…The past decades have witnessed significant progress on computational chemistry which aided in developing new catalysts 16–19 . Especially, with the rapid growth in computer power, parallel algorithm as well as precise theoretical methods, in particular the density functional theory (DFT), detailed information about the active centers, reaction energies, intermediates, transition states, and reaction mechanisms could be provided 20–23 . However, so far much progress has been made by using simple catalyst models, such as extended clean surfaces 24–26 or small clusters 27–29 .…”

“…[16][17][18][19] Especially, with the rapid growth in computer power, parallel algorithm as well as precise theoretical methods, in particular the density functional theory (DFT), detailed information about the active centers, reaction energies, intermediates, transition states, and reaction mechanisms could be provided. [20][21][22][23] However, so far much progress has been made by using simple catalyst models, such as extended clean surfaces [24][25][26] or small clusters. [27][28][29] Although the molecular insights based on these reductionist models have enormously enlarged our knowledge, the predictive ability is usually so limited as these models could not capture the complexity of real catalysts.…”