General Performance of Density Functionals

Density Functional Theory - Recent Advances, New Perspectives and Applications, 2021

Density Functional Theory (DFT) is a powerful and commonly employed quantum mechanical tool for investigating various aspects of matter. The research in this field ranges from the development of novel analytical approaches focused on the design of precise exchange-correlation functionals to the use of this technique to predict the molecular and electronic configuration of atoms, molecules, complexes, and solids in both gas and solution phases. The history to DFT’s success is the quest for the exchange-correlation functional, which utilizes density to represent advanced many-body phenomena inside one element formalism. If a precise exchange-correlation functional is applied, it may correctly describe the quantum nature of matter. The estimated character of the exchange-correlation functional is the basis for DFT implementation success or failure. Hohenberg-Kohn established that every characteristic of a system in ground state is a unique functional of its density, laying the foundati...

Journal of the American Chemical Society

DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This article explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

Accounts of chemical research, 2008

A lthough density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy "across-theboard" for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06-2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate functional for transition metals and is the only local functional (no Hartree-Fock exchange) with better across-the-board average performance than B3LYP; this is very important because only local functionals are affordable for many demanding applications on very large systems; (d) M06-HF has good performance for valence, Rydberg, and charge transfer excited states with minimal sacrifice of ground-state accuracy. In this Account, we compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases. The tests include barrier heights, conformational energy, and the trend in bond dissociation energies of Grubbs' ruthenium catalysts for olefin metathesis. Based on these tests, we recommend (1) the M06-2X, BMK, and M05-2X functionals for main-group thermochemistry and kinetics, (2) M06-2X and M06 for systems where main-group thermochemistry, kinetics, and noncovalent interactions are all important, (3) M06-L and M06 for transition metal thermochemistry, (4) M06 for problems involving multireference rearrangements or reactions where both organic and transition-metal bonds are formed or broken, (5) M06-2X, M05-2X, M06-HF, M06, and M06-L for the study of noncovalent interactions, (6) M06-HF when the use of full Hartree-Fock exchange is important, for example, to avoid the error of self-interaction at longrange, (7) M06-L when a local functional is required, because a local functional has much lower cost for large systems.

The Journal of Physical Chemistry …, 1997

A comparison is made between traditional quantum chemical approaches to the electron correlation problem and the one taken in density functional theory (DFT). Well-known concepts of DFT, such as the exchangecorrelation energy E xc ) ∫F(r) xc (r) dr and the exchange-correlation potential V xc (r) are related to electron correlation as described in terms of density matrices and the conditional amplitude (Fermi and Coulomb holes). The Kohn-Sham one-electron or orbital model of DFT is contrasted with Hartree-Fock, and the definitions of exchange and correlation in DFT are compared with the traditional ones. The exchangecorrelation energy density xc (r) is decomposed into kinetic and electron-electron potential energy components, and a practical way of calculating these from accurate wave functions is discussed, which offers a route to systematic improvement. V xc (r) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation. X Figure 4. Correlation energy density in He compared to a number of model correlation energy densities: PW, Perdew-Wang; 11 WL, Wilson-Levy; 127 LYP, Lee-Yang-Parr; 8 LW, local Wigner. 126 (a) -F(r) c(r) from r ) 0.0-0.5 bohr. (b) -4π r 2 F(r) c(r) from r ) 0.0-2.0 bohr. Feature Article

A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density functional equation is solved implicitly for the density response, eliminating the instabilities that arise in conventional techniques for simulations of large, metallic or inhomogeneous systems. The auxiliary system is not required to be fermionic, and an example bosonic auxiliary density functional is presented which captures the key aspects of the fermionic Kohn-Sham behaviour. This bosonic auxiliary scheme is shown to provide good performance for a range of bulk materials, and a substantial improvement in the scaling of the calculation with system size for a variety of simulation systems.

2000

This report describes progress made under the CSRF project Current Topics in Density Functional Theory. Density functional theory (DFT) is a technique for computing the energetics of molecules and materials. DFT is unique among atomistic simulation techniques in combining a high accuracy approximation to the quantum mechanics describing the chemical bonding in materials with computationally tractible solutions. This combination makes it particularly important and relevant for Sandia's stockpile stewardship mission, a large part of which involves insuring material performance without nuclear testing. DFT techniques have already made important contributions to Sandia's DP programs. However, to have greater and wider impact at Sandia, DFT techniques need to have increased accuracy, they need to provide this accuracy with increased speed, and they need to have increased range as to the problems and conditions they can contribute to. The goal of this project is to achieve these improvements to DFT.

Journal of Chemical Theory and Computation, 2007

The reliable prediction of molecular properties is a vital task of computational chemistry. In recent years, density functional theory (DFT) has become a popular method for calculating molecular properties for a vast array of systems varying in size from small organic molecules to large biological compounds such as proteins. In this work we assess the ability of many DFT methods to accurately determine atomic and molecular properties for small molecules containing elements commonly found in proteins, DNA, and RNA. These properties include bond lengths, bond angles, ground state vibrational frequencies, electron affinities, ionization potentials, heats of formation, hydrogen bond interaction energies, conformational energies, and reaction barrier heights. Calculations are carried out with the 3-21G*, 6-31G*, 3-21+G*, 6-31+G*, 6-31++G*, cc-pVxZ, and aug-cc-pVxZ (x=D,T) basis sets, while bond distance and bond angle calculations are also done using the cc-pVQZ and aug-cc-pVQZ basis sets. Members of the popular functional classes, namely, LSDA, GGA, meta-GGA, hybrid-GGA, and hybrid-meta-GGA, are considered in this work. For the purpose of comparison, Hartree-Fock (HF) and second order many-body perturbation (MP2) methods are also assessed in terms of their ability to determine these physical properties. Ultimately, it is observed that the split valence bases of the 6-31G variety provide accuracies similar to those of the more computationally expensive Dunning type basis sets. Another conclusion from this survey is that the hybrid-meta-GGA functionals are typically among the most accurate functionals for all of the properties examined in this work.

Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r 1 ,r 2 ,r 3 ,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications: the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.

Springer eBooks, 1998

For the past 30 years density functional theory has been the dominant method for the quantum mechanical simulation of periodic systems. In recent years it has also been adopted by quantum chemists and is now very widely used for the simulation of energy surfaces in molecules. In this lecture we introduce the basic concepts underlying density functional theory and outline the features that have lead to its wide spread adoption. Recent developments in exchange correlation functionals are introduced and the performance of families of functionals reviewed. The lecture is intended for a researcher with little or no experience of quantum mechanical simulations but with a basic (undergraduate) knowledge of quantum mechanics. We hope to provide sufficient background to enable informed judgements on the applicability of a particular implementation of density functional theory to a specific problem in materials simulation. For those who wish to go more deeply into the formalism of density functional theory there are a number of reviews and books aimed at intermediate and advanced levels available in the literature [1,2,3]. Where appropriate source articles are referred to in the text.