The Best DFT Functional Is the Ensemble of Functionals.

The development of better density functional theory (DFT) methods is one of the most active research areas, given the importance of DFT for ubiquitous molecular and materials simulations. However, this research primarily focuses on improving a specific exchange-correlation Kohn-Sham density functional. Here, a robust procedure is proposed for constructing transferable ensembles of density functionals that perform superior to any constituent individual density functional.

A Critical Evaluation of the Hybrid KS DFT Functionals Based on the KS Exchange-Correlation Potentials.

We have developed a critical methodology for the evaluation of the quality of hybrid exchange-correlation (XC) density functional approximations (DFAs) based on very fundamental quantities, i.e., Kohn-Sham (KS) XC potentials, self-consistent electron densities, first ionization potentials (IPs), and total energies.

Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas.

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290.

Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations.

The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.

Self-Consistent Implementation of Kohn-Sham Adiabatic Connection Models with Improved Treatment of the Strong-Interaction Limit.

Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange-correlation functionals. If the exact weak-interaction expansion from the second-order perturbation theory is included, a self-consistent implementation of these functionals is challenging and still absent in the literature. In this work, we fill this gap by presenting a fully self-consistent-field (SCF) implementation of some popular ACM functionals.

Solid-state performance of a meta-GGA screened hybrid density functional constructed from Pauli kinetic enhancement factor dependent semilocal exchange hole.

The semilocal form of an exchange hole is highly useful in developing non-local range-separated hybrid density functionals for finite and extended systems. The way to construct the conventional exact exchange hole model is based on either the Taylor series expansion or the reverse engineering technique from the corresponding exchange energy functional. Although the latter technique is quite popular in the context of generalized gradient approximation (GGA) functionals, the same for the meta-GGA functionals is not so much explored.

Benchmark test of a dispersion corrected revised Tao-Mo semilocal functional for thermochemistry, kinetics, and noncovalent interactions of molecules and solids.

In the density functional theory, dispersion corrected semilocal approximations are often used to benchmark weekly interacting finite and extended systems. Here, the focus is on providing a broad overview of the performance of D3 dispersion corrected revised Tao-Mo (revTM) semilocal functionals [A. Patra et al.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory.

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system.

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···(HO), 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.

Insights from the density functional performance of water and water-solid interactions: SCAN in relation to other meta-GGAs.

Accurate prediction of water properties in its gas and condensed phases, including the interaction of water with surfaces, is of prime importance for many scientific disciplines. However, accurate simulation of all water properties together within semilocal approximations of the density functional theory possesses great challenges. The Strongly Constrained and Appropriately Normed semilocal density functional, which satisfies 17 known exact constraints and includes the intermediate range van der Waals interaction, performs quite well for different properties of water including the correct energy ordering of isomers.

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms.

Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction.

Modified Interaction-Strength Interpolation Method as an Important Step toward Self-Consistent Calculations.

The modified point charge plus continuum (mPC) model [Constantin, L. A.; 2019, 99, 085117] solves the important failures of the original counterpart, namely, the divergences when the reduced gradient of the density is large, such as in the tail of the density and in quasi-dimensional density regimes.

Unveiling the Physics Behind Hybrid Functionals.

We show that accurate exchange-correlation hybrid functionals give very physically optimized effective-correlation potentials, capable of correctly describing the quantum oscillations of atoms and molecules. Based on this analysis and on understanding the error cancellation between semilocal exchange and correlation functionals, we propose a very simple, semilocal correlation potential model compatible with the exact exchange of density functional theory, which performs remarkably well for charge densities and orbital energies.

The ab initio density functional theory applied for spin-polarized calculations.

We have performed a systematic and broad study of the performance of the ab initio OEP2-sc functional for spin-polarized systems, including the computation of ionization potentials and atomization and reaction energies of closed- and open-shell molecules. The results have revealed that, in line with other second-order methods, OEP2-sc can provide accurate results, being competitive to the orbital-optimized MP2 method. Moreover, the analysis of total and relative energies has shown that, unlike the case of double-hybrid functionals, this relatively good performance is not based on an error cancellation effect.

Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method.

We extend the range-separated double-hybrid RSH+MP2 method (Ángyán, J. G.; et al.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation.

We have studied the correlation potentials produced by various adiabatic connection models (ACMs) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials and including most of the physically meaningful features of the accurate reference data.

Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies.

A practical, accurate, and cost- and implementation-free method (ΔMP2-SOS(IP)) for the calculation of vertical ionization potentials is proposed. The simple method is based on a single-step, a diagonal, frequency-independent approximation to the second-order self-energy expression combined with the spin-component-scaled technique. The search for an optimal scaling factor is performed for a set of 50 moderately sized molecules, and the quality of the method is additionally assessed for a benchmark set of 24 organic acceptor molecules.

Approximate solution of coupled cluster equations: application to the coupled cluster doubles method and non-covalent interacting systems.

We have developed a simplified coupled cluster (SCC) methodology, using the basic idea of scaled MP2 methods. The scheme has been applied to the coupled cluster double equations and implemented in three different non-iterative variants. This new method (especially the SCCD[3] variant, which utilizes a spin-resolved formalism) has been found to be very efficient and to yield an accurate approximation of the reference CCD results for both total and interaction energies of different atoms and molecules.

Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals.

The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory.

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method.

We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules.

Accurate Kohn-Sham ionization potentials from scaled-opposite-spin second-order optimized effective potential methods.

One important property of Kohn-Sham (KS) density functional theory is the exact equality of the energy of the highest occupied KS orbital (HOMO) with the negative ionization potential of the system. This exact feature is out of reach for standard density-dependent semilocal functionals. Conversely, accurate results can be obtained using orbital-dependent functionals in the optimized effective potential (OEP) approach.

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations.

Orbital-dependent second-order scaled-opposite-spin correlation functionals in the optimized effective potential method.

The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn-Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite-spin OEP functional [I.

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential.

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I.