Global Hybrids from the Semiclassical Atom Theory Satisfying the Local Density Linear Response

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.

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.

Screened range-separated hybrid by balancing the compact and slowly varying density regimes: Satisfaction of local density linear response

Due to their quantitative accuracy and ability to solve several difficulties, screened range-separated hybrid exchange-correlation functionals are now a standard approach for ab initio simulation of condensed matter systems. However, the screened range-separated hybrid functionals proposed so far are biased either toward compact or slowly varying densities. In this paper, we propose a screened range-separated hybrid functional, named HSEint, which can well describe these density regimes, achieving good accuracy for both molecular and solid-state systems. The semilocal part of the proposed functional is based on the PBEint generalized gradient approximation [E. Fabiano et al., Phys. Rev. B 82, 113104 (2010)], constructed for hybrid interfaces. To improve the functional performance, we employ exact or nearly exact constraints in the construction of range-separated hybrid functional, such as recovering of the local density linear response and semiclassical atom linear response.

DFT Protocol for EPR Prediction of Paramagnetic Cu(II) Complexes and Application to Protein Binding Sites

With the aim to provide a general protocol to interpret electron paramagnetic resonance (EPR) spectra of paramagnetic copper(II) coordination compounds, density functional theory (DFT) calculations of spin Hamiltonian parameters g and A for fourteen Cu(II) complexes with different charges, donor sets, and geometry were carried out using ORCA software. The performance of eleven functionals was tested, and on the basis of the mean absolute percent deviation (MAPD) and standard deviation (SD), the ranking of the functionals for Az is: B3LYP > B3PW91 ~ B3P86 > PBE0 > CAM-B3LYP > TPSSh > BH and HLYP > B2PLYP > MPW1PW91 > ω-B97x-D >> M06; and for gz is: PBE0 > BH and HLYP > B2PLYP > ω-B97x-D > B3PW91~B3LYP~B3P86 > CAM-B3LYP > TPSSh~MPW1PW91 >> M06. With B3LYP the MAPD with respect to A z exp t l is 8.6% with a SD of 4.2%, while with PBE0 the MAPD with respect to g z exp t l is 2.9% with a SD of 1.1%. The results of the validation confirm the fundamental role of the second order spin-orbit contribution to Az. The computational procedure was applied to predict the values of gz and Az of the adducts formed by Cu(II) with albumin and two fragments of prion protein, 106–126 and 180–193.

Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection

Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.