Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions

Abstract

We present a new class of noninteracting kinetic energy (KE) functionals, derived from the semiclassical-atom theory. These functionals are constructed using the link between exchange and kinetic energies and employ a generalized gradient approximation (GGA) for the enhancement factor, namely, the Perdew-Burke-Ernzerhof (PBE) one. Two of them, named APBEK and revAPBEK, recover in the slowly varying density limit the modified second-order gradient (MGE2) expansion of the KE, which is valid for a neutral atom with a large number of electrons. APBEK contains no empirical parameters, while revAPBEK has one empirical parameter derived from exchange energies, which leads to a higher degree of nonlocality. The other two functionals, APBEKint and revAPBEKint, modify the APBEK and revAPBEK enhancement factors, respectively, to recover the second-order gradient expansion (GE2) of the homogeneous electron gas. We first benchmarked the total KE of atoms/ions and jellium spheres/surfaces: we found that functionals based on the MGE2 are as accurate as the current state-of-the-art KE functionals, containing several empirical parameters. Then, we verified the accuracy of these new functionals in the context of the frozen density embedding (FDE) theory. We benchmarked 20 systems with nonbonded interactions, and we considered embedding errors in the energy and density. We found that all of the PBE-like functionals give accurate and similar embedded densities, but the revAPBEK and revAPBEKint functionals have a significant superior accuracy for the embedded energy, outperforming the current state-of-the-art GGA approaches. While the revAPBEK functional is more accurate than revAPBEKint, APBEKint is better than APBEK. To rationalize this performance, we introduce the reduced-gradient decomposition of the nonadditive kinetic energy, and we discuss how systems with different interactions can be described with the same functional form.

ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order

“…109 This model for the reference energy can still be used to construct a force field for intermolecular Pauli repulsion interactions, provided one uses reasonable GGA approximations for the kinetic, exchange and correlation functionals. 110,111 When a non-neutral reference state is used, this term will also include an important electrostatic contribution.…”

eQE: An open‐source density functional embedding theory code for the condensed phase

“…[54] For these systems, we have demonstrated that eQE reproduces the main features of the structure and dynamics of liquid water at room temperature, provided that an accurate nonadditive kinetic energy functional such as revAPBEK [37] is employed. In general, we obtained good agreement with experiment for the OAO and OAH radial distribution functions, as well as the OAOAO angular distribution function within the first solvation shell.…”

“…[31][32][33] In addition, Turbomole [34] has its own implementation by the Della Sala group. [35][36][37][38][39] We also mention here that other embedding methods, which can be categorized as exact density embedding, exact orbital embedding, or electrostatic embedding, are now found in ADF, [40] MOLPRO, [41][42][43][44][45] Q-Chem, [46,47] CP2K, [48] NWChem, [49] and GAMESS. [50] In this work, we present a novel implementation of the FDE approach that aims at filling the following gap that has persisted over the years, namely, the absence of a code that: (1) has a proven strong parallel efficiency that consistently outperforms semilocal KS-DFT, (2) has the ability to Figure 1 [12] The k-point grids and simulation cells (basis sets) are subsystem-specific, achieving the best performance.…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Moreover, we recall that while in real atoms the electrons far from the nucleus experience a screened nuclear charge so that the corresponding orbitals differ from the hydrogenic ones, for large atoms or very positive ions, this screening effect becomes vanishingly small, and the simple model of hydrogenic orbitals becomes exact [69]. This model system has been largely used in DFT [68,[70][71][72], is very important for semiclassical physics [70,73,74] and has been used as a main reference system in recent GGA functionals [20,55].…”

“…Similar shortcomings as for the XE density near the nucleus affect also many KE functionals at the GGA level [51][52][53][54][55] or at the Laplacian level [56]; for a recent review of semilocal functionals, see [57]. The KE density is usually defined in terms of the KE enhancement factor:…”