scholarly journals Doubly hybrid density functionals that correctly describe both density and energy for atoms

2018 ◽  
Vol 115 (10) ◽  
pp. 2287-2292 ◽  
Author(s):  
Neil Qiang Su ◽  
Zhenyu Zhu ◽  
Xin Xu
Keyword(s):  
Density Functional ◽  
Second Order ◽  
Density Functionals ◽  
Electron Densities ◽  
Hartree Fock ◽  
Hybrid Functionals ◽  
Jacob's Ladder ◽  
Exact Energy

Recently, it was argued [Medvedev MG, et al. (2017) Science 355:49–52] that the development of density functional approximations (DFAs) is “straying from the path toward the exact functional.” The exact functional should yield both exact energy and density for a system of interest; nevertheless, they found that many heavily fitted functionals for molecular energies actually lead to poor electron densities of atoms. They also observed a trend that, for the nonempirical and few-parameter functionals, densities can be improved as one climbs up the first four rungs of the Jacob’s ladder of DFAs. The XYG3 type of doubly hybrid functionals (xDHs) represents a less-empirical and fewer-parameter functional on the top fifth rung, in which both the Hartree–Fock-like exchange and the second-order perturbative (MP2-like) correlation are hybridized with the low rung functionals. Here, we show that xDHs can well describe both density and energy for the same atomic set of Medvedev et al., showing that the latter trend can well be extended to the top fifth rung.

scholarly journals The crystalline structure of SrRuO3: Application of hybrid scheme to the density functionals revised for solids

2017 ◽  
Vol 57 (2) ◽  
Author(s):  
Šarūnas Masys ◽  
Valdas Jonauskas
Keyword(s):  
Crystalline Structure ◽  
Density Functional ◽  
Theoretical Modelling ◽  
Density Functionals ◽  
Hybrid Scheme ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Hartree Fock ◽  
Hybrid Density Functional ◽  
Theory Scheme

The crystalline structure of ground-state orthorhombic SrRuO3 is reproduced by applying the hybrid density functional theory scheme to the functionals based on the revised generalized-gradient approximations for solidstate calculations. The amount of Hartree–Fock (HF) exchange energy is varied in the range of 5–20% in order to systematically ascertain the optimum value of HF mixing which in turn ensures the best correspondence to the experimental measurements. Such investigation allows one to expand the set of tools that could be used for the efficient theoretical modelling of, for example, only recently stabilized phases of SrRuO3, helping to resolve issues emerging for the experimentalists.

Protonation Effect on C-N Bond Length of Alkylamines Studied by Molecular Orbital Calculations

2000 ◽  
Vol 55 (9-10) ◽  
pp. 769-771 ◽  
Keyword(s):  
Density Functional Theory ◽  
Bond Length ◽  
Molecular Orbital ◽  
Density Functional ◽  
Second Order ◽  
Basis Set ◽  
Molecular Orbital Calculations ◽  
Functional Theory ◽  
Hartree Fock ◽  
Protonation Effect

Abstract Molecular orbital calculations were performed for the six saturated alkylamines (CH3NH2 , (CH3)2 NH, (CH 3)3 N, CH 3CH2NH2 , (CH3)2 CHNH2 , (CH3)3 CNH2), their protonated cations (CH3NH3 + , (CH3)2NH2 + , (CH3)3NH + , CH3CH2NH3 + , (CH3)2CHNH3 + , (CH3)3CNH3+), and (CH3)4 N + using the Hartree-Fock, second-order M0ller-Plesset, and density functional theory methods with the 6-311+G(d,p) basis set. Protonation lengthens the C-N bonds of the amines by 0.05 -0.08 Å and shortens the C-C bonds of CH3CH2NH2, (CH3)2CHNH2 , and (CH3)3CNH2 by ca. 0.01 Å.

scholarly journals How Accurate Are Static Polarizability Predictions from Density Functional Theory? An Assessment over 132 Species at Equilibrium Geometry

2018 ◽  
Author(s):  
Diptarka Hait ◽  
Martin Head-Gordon
Keyword(s):  
Electric Fields ◽  
Density Functional ◽  
Basis Set ◽  
Equilibrium Geometry ◽  
Density Functionals ◽  
Functional Theory ◽  
First Response ◽  
Complete Basis Set ◽  
Complete Basis Set Limit ◽  
Hybrid Functionals

Static polarizabilities are the first response of the electron density to electric fields, and are therefore important for predicting intermolecular and molecule-field interactions. They also offer a global measure of the accuracy of the treatment of excited states by density functionals in a formally exact manner. We have developed a database of benchmark static polarizabilities for 132 small species at equilibrium geometry, using coupled cluster theory through triple excitations (extrapolated to the complete basis set limit), for the purpose of developing and assessing density functionals. The performance of 60 popular and recent functionals are also assessed, which indicates that double hybrid functionals perform the best, having RMS errors in the range of 2.5-3.8% . Many hybrid functionals also give quite reasonable estimates with 4-5% RMSE. A few meta-GGAs like mBEEF and MVS yield performance comparable to hybrids, indicating potential for improved excited state predictions relative to typical local functionals. Some recent functionals however are found to be prone to catastrophic failure (possibly as a consequence of overparameterization), indicating a need for caution in applying these.

scholarly journals Covariant density functional theory: predictive power and first attempts of a microscopic derivation

2018 ◽  
Vol 178 ◽  
pp. 02001
Author(s):  
Peter Ring
Keyword(s):  
Nuclear Matter ◽  
Density Functional ◽  
Predictive Power ◽  
Tensor Force ◽  
Density Functionals ◽  
Functional Theory ◽  
Hartree Fock ◽  
Microscopic Derivation ◽  
Nuclear Systems ◽  
Covariant Density

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

Static- and frequency-dependent NLO properties of dithienothiophene and thienothiophene bridges — A computational investigation

2020 ◽  
Vol 19 (05) ◽  
pp. 2050018
Author(s):  
Sagar B. Yadav ◽  
Nagaiyan Sekar
Keyword(s):  
Density Functional ◽  
Nonlinear Optical ◽  
Chemical Reactivity ◽  
Second Order ◽  
Basis Sets ◽  
Frequency Dependent ◽  
Nlo Properties ◽  
Reactivity Descriptors ◽  
Hartree Fock ◽  
Perturbation Potential

We have explored detailed linear and nonlinear optical properties of push-pull systems bearing thienothiophene and dithienothiophene spacers. By using density functional theory (DFT), frequency-dependent strategies were applied to examine the polarizability ([Formula: see text] and hyperpolarizability ([Formula: see text] and [Formula: see text]. The set of global and range-separated hybrid functionals with different Hartree–Fock (HF) exchange percentage at two basis sets cc-pVDZ and cc-pVTZ were used to evaluate the nonlinear optical (NLO) properties. The observed trends in the absorption maxima supported by perturbation potential analysis; as the absorption maxima increases, the respective amplitude potential decreases. For the investigated compounds, [Formula: see text]-conjugation along with the type of substituted acceptor plays a crucial role in the enhancement of NLO properties. The presence of acceptor group and length of conjugation increase between the D and A group; the first- and second-order intrinsic hyperpolarizability increases, leads to enhanced first- as well as second-order hyperpolarizability. Bond length alternation (BLA)/bond order alteration (BOA) exploration suggested that compounds attain cyanine limit. The trends in NLO properties for investigated compounds are supported by chemical reactivity descriptors, hardness and hyperhardness analysis. The polarizability is linearly correlated with the hyperpolarizability parameters ([Formula: see text] and [Formula: see text] and shows a good regression coefficient by figures of merit analysis.

scholarly journals TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY

2008 ◽  
Vol 22 (14) ◽  
pp. 2225-2239
Author(s):  
TAMÁS GÁL
Keyword(s):  
Density Functional Theory ◽  
Ground State ◽  
Density Functional ◽  
Common Ground ◽  
Particle Density ◽  
Exchange Energy ◽  
Density Functionals ◽  
Simple Derivation ◽  
Functional Theory ◽  
Hartree Fock

Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.

Sign in / Sign up

Export Citation Format

Share Document