Unveiling the Physics Behind Hybrid Functionals

Impact of an Ionic Liquid Solution on Horseradish Peroxidase Activity

Horseradish peroxidase (HRP) is an enzyme that oxidizes pollutants from wastewater. A previous report indicated that peroxidases can have an enhancement in initial enzymatic activity in an aqueous solution of 0.26 M 1-ethyl-3-methylimidazolium ethyl sulfate ([EMIm][EtSO4]) at neutral pH. However, the atomistic details remain elusive. In the enzymatic landscape of HRP, compound II (Cpd II) plays a key role and involves a histidine (H42) residue. Cpd II exists as oxoferryl (2a) or hydroxoferryl (2b(FeIV)) forms, where 2a is the predominantly observed form in experimental studies. Intriguingly, the ferric 2b(FeIII) form seen in synthetic complexes has not been observed in HRP. Here, we have investigated the structure and dynamics of HRP in pure water and aqueous [EMIm][EtSO4] (0.26 M), as well as the reaction mechanism of 2a to 2b conversion using polarizable molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics (QM/MM) calculations. When HRP is solvated in aq [EMIm][EtSO4], the catalytic water displaces, and H42 directly orients over the ferryl moiety, allowing a direct proton transfer (PT) with a significant energy barrier reduction. Conversely, in neat water, the reaction of 2a to 2b follows the previously reported mechanism. We further investigated the deprotonated form of H42. Analysis of the electric fields at the active site indicates that the aq [EMIm][EtSO4] medium facilitates the reaction by providing a more favorable environment compared with the system solvated in neat water. Overall, the atomic level supports the previous experimental observations and underscores the importance of favorable electric fields in the active site to promote catalysis.

Predicting band gaps of ABN3 perovskites: an account from machine learning and first-principle DFT studies

The present paper is primarily focused on predicting the band gaps of nitride perovskites from machine learning (ML) models. The ML models have been framed from the feature descriptors and band gap values of 1563 inorganic nitride perovskites having formation energies <-0.026 eV and band gaps ranging from ∼1.0 to 3.1 eV. Four supervised ML models such as multi-layer perceptron (MLP), gradient boosted decision tree (GBDT), support vector regression (SVR) and random forest regression (RFR) have been considered to predict the band gaps of the said systems. The accuracy of each model has been tested from mean absolute error, root-mean-square error and determination coefficient R2 values. The bivariate plots between the predicted and input band gaps of the compounds for both the training and test datasets have also been estimated. Additionally, two ABN3-type nitride perovskites CeBN3 (B = Mo, W) have been selected and their electronic band structures and optoelectronic properties have been studied from density functional theory (DFT) calculations. The band gap values of the said compounds have been estimated from DFT calculations at PBE, HSE06, G0W0@PBE, G0W0@HSE06 level of theories. The present study will be helpful in exploring the ML models in predicting the band gaps of nitride perovskites which in turn may bear potential applications in photovoltaic cells and optical luminescent devices.

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. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.

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. While using second-order perturbation theory at weak interactions, we have also introduced new generalized gradient approximations (GGAs), beyond the usual point-charge-plus-continuum model, for the first two leading terms at strong interactions, which are crucial to ensure robustness and reliability. We then assess the SCF–ACM functionals for molecular systems and for prototypical strong-correlation problems. We find that they perform well for both the total energy and the electronic density and that the impact of SCF orbitals is directly connected to the accuracy of the ACM functional form. For the H₂ dissociation, the SCF–ACM functionals yield significant improvements with respect to standard functionals also thanks to the use of the new GGAs for the strong-coupling functionals.

A general justification for hybrid functionals in DFT by means of linear response theory

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn-Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy's constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Catalytic properties of the ferryl ion in the solid state: a computational review

This review summarises the last findings in the emerging field of heterogeneous catalytic oxidation of light alkanes by ferryl species supported on solid-state systems such as the conversion of methane into methanol by FeO-MOF74.

A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules

Accurate exchange-correlation (XC) potentials for three-dimensional systems─via solution of the inverse density functional theory (DFT) problem─are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules─dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne─are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10-3-10-2), the model XC potentials have much higher errors of O(10-1-100). Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.

Accurate density functional made more versatile

We propose a one-electron self-interaction-free correlation energy functional compatible with the order-of-limit problem-free Tao-Mo (TM) semilocal functional (regTM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016) and Patra et al., J. Chem. Phys. 153, 184112 (2020)] to be used for general purpose condensed matter physics and quantum chemistry. The assessment of the proposed functional for large classes of condensed matter and chemical systems shows its improvement in most cases compared to the TM functional, e.g., when applied to the relative energy difference of MnO₂ polymorphs. In this respect, the present exchange-correction functional, which incorporates the TM technique of the exchange hole model combined with the slowly varying density correction, can achieve broad applicability, being able to solve difficult solid-state problems.

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, CH₄···(H₂O)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), which uses approximate Kohn-Sham orbitals as its input. 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 the many-body expansion. 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 many-body expansion. 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.

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. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

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

The modified point charge plus continuum (mPC) model [ConstantinL. A.; Phys. Rev. B2019, 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. The mPC allows us to define a modified interaction-strength interpolation (mISI) method inheriting these good features, which are important steps toward the full self-consistent treatment. Here, we provide an assessment of mISI for molecular systems (i.e., considering thermochemistry properties, correlation energies, vertical ionization potentials, and several noncovalent interactions), harmonium atoms, and functional derivatives in the strong-interaction limit. For all our tests, mISI provides a systematic improvement over the original ISI method. Semilocal approximations of the second-order Görling–Levy (GL2) perturbation theory are also considered in the mISI method, showing considerable worsening of the results. Possible further development of mISI is briefly discussed.