Improving Results by Improving Densities: Density-Corrected Density Functional Theory (original) (raw)
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The Elephant in the Room of Density Functional Theory Calculations
Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.
Annals of the New York Academy of Sciences, 2003
A BSTRACT : As molecular electronics advances, efficient and reliable computation procedures are required for the simulation of the atomic structures of actual devices, as well as for the prediction of their electronic properties. Density-functional theory (DFT) has had widespread success throughout chemistry and solid-state physics, and it offers the possibility of fulfilling these roles. In its modern form it is an empirically parameterized approach that cannot be extended toward exact solutions in a prescribed way, ab initio . Thus, it is essential that the weaknesses of the method be identified and likely shortcomings anticipated in advance. We consider four known systematic failures of modern DFT: dispersion, charge transfer, extended conjugation, and bond cleavage. Their ramifications for molecular electronics applications are outlined and we suggest that great care is required when using modern DFT to partition charge flow across electrode-molecule junctions, screen applied electric fields, position molecular orbitals with respect to electrode Fermi energies, and in evaluating the distance dependence of through-molecule conductivity. The causes of these difficulties are traced to errors inherent in the types of density functionals in common use, associated with their inability to treat very long-range electron correlation effects. Heuristic enhancements of modern DFT designed to eliminate individual problems are outlined, as are three new schemes that each represent significant departures from modern DFT implementations designed to provide a priori improvements in at least one and possible all problem areas. Finally, fully semiempirical schemes based on both Hartree-Fock and Kohn-Sham theory are described that, in the short term, offer the means to avoid the inherent problems of modern DFT and, in the long term, offer competitive accuracy at dramatically reduced computational costs.
Density-Corrected DFT Explained: Questions and Answers
Journal of Chemical Theory and Computation, 2022
HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying failures of density functional approximations by separating errors in a functional from errors in its self-consistent (SC) density. Most modern DFT calculations yield highly accurate densities, but important characteristic classes of calculation have large density-driven errors, including reaction barrier heights, electron affinities, radicals and anions in solution, dissociation of heterodimers, and even some torsional barriers. Here, the HF density (if not spin-contaminated) usually yields more accurate and consistent energies than those of the SC density. We use the term DC(HF)-DFT to indicate DC-DFT using HF densities only in such cases. A recent comprehensive study (J. Chem. Theory Comput. 2021, 17, 1368−1379) of HF-DFT led to many unfavorable conclusions. A re-analysis using DC-DFT shows that DC(HF)-DFT substantially improves DFT results precisely when SC densities are flawed.
The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field (CASSCF) methods are deficient in their ability to describe dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we describe the hole-hole Tamm- Dancoff approximated (hh-TDA) density functional theory method, which is closely related to the previously established particle-particle random phase approximation (pp-RPA) and its TDA variant (pp-TDA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical inters...
Density Functional Analysis: The Theory of Density-Corrected DFT
Journal of Chemical Theory and Computation, 2019
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for the analysis of any functional minimization with an approximate functional. We generalize DC-DFT to allow comparison of any two functionals, not just comparison with the exact functional. We introduce a linear interpolation between any two approximations, and use the results to analyze global hybrid density functionals. We define the basins of density-space in which this analysis should apply, and give quantitative criteria for when DC-DFT should apply. We also discuss the effects of strong correlation on density-driven error, utilizing the restricted HF Hubbard dimer as an illustrative example.
CSRF Interim Project Report: Current Topics in Density Functional Theory
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.
OH , F ) : A Surprising Shortcoming of Density Functional Theory
The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R ) Me, Et, i-Pr andt-Bu, and X) H, CH3, OCH3, OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFTand MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of forma...
The Journal of Chemical Physics, 2009
This paper presents an approach for obtaining accurate interaction energies at the DFT level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of eighteen complexes, for which interaction energies were obtained with the B3LYP, PBE and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry.
2015
Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) are powerful methods for solving a variety of problems, including ground state electronic structure, electron dynamics, and the absorbance cross section of molecules and materials. DFT is used to calculate the ground state electron configuration, whereas TDDFT is used to solve for the absorption cross section of excited systems. These techniques are not without their challenges. DFT requires the solution of Kohn-Sham orbitals through the diagonalization of the one electron Hamiltonian, which scales as O(N^3) where N signifies the number of orbitals in a simulation. TDDFT has its challenges as well. Each orbital must be propagated every time step, but since a single TDDFT simulation requires thousands of time steps, it is very costly. In this dissertation, we present methods that were developed to circumvent the limitations of DFT and TDDFT.One method for decreasing the cost of DFT and TDDFT is direc...
A quantum chemical view of density functional theory
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