# How errors in densities contaminate empirical density functionals

@article{Song2020HowEI, title={How errors in densities contaminate empirical density functionals}, author={Suhwan Song and Eunji Sim and Stefan Vuckovic and Kieron Burke}, journal={arXiv: Chemical Physics}, year={2020} }

Empirical fitting of parameters in approximate density functionals is commonplace. Such database fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. Three examples both show the pitfalls and how they can be avoided: Catastrophic failures in a toy example, $H_2^+$ at varying bond lengths, where the standard fitting procedure misses the exact functional; Grimme's D3 fit to noncovalent interactions, which…

## References

SHOWING 1-10 OF 50 REFERENCES

Ions in solution: density corrected density functional theory (DC-DFT).

- ChemistryThe Journal of chemical physics
- 2014

This work discusses how to identify cases where certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities, and how DC-DFT applies more generally.

Quantifying Density Errors in DFT.

- PhysicsThe journal of physical chemistry letters
- 2018

It is shown how to estimate the significance of the density-driven error even when exact densities are unavailable, and in cases with large density errors, the amount of exchange-mixing is often adjusted, but this is unnecessary.

The Importance of Being Self-Consistent

- Physics
- 2016

A recent analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density in density functional theory, yielding insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error.

Density functional theory is straying from the path toward the exact functional

- ChemistryScience
- 2017

The energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals, were found to become closer to the exact ones until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

Improved DFT Potential Energy Surfaces via Improved Densities.

- ChemistryThe journal of physical chemistry letters
- 2015

A simple criterion for when DC-DFT should be more accurate than self-consistent DFT that can be applied for most cases is given and explained and explored more difficult cases, for example, CH(+), where density-corrected DFT results are even better than sophisticated methods like CCSD.

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.

- ChemistryThe Journal of chemical physics
- 2010

The revised DFT-D method is proposed as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

Density functional analysis: The theory of density-corrected DFT.

- ChemistryJournal of chemical theory and computation
- 2019

This paper provides the formal theoretical framework and assumptions for the analysis of any functional minimization with an approximate functional, and generalizes DC-DFT to allow comparison of any two functionals, not just comparison with the exact functional.

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals

- Chemistry
- 2017

ABSTRACT In the past 30 years, Kohn–Sham density functional theory has emerged as the most popular electronic structure method in computational chemistry. To assess the ever-increasing number of…

Generalized Gradient Approximation Made Simple.

- ChemistryPhysical review letters
- 1996

A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

Double-hybrid density-functional theory made rigorous.

- Computer ScienceThe Journal of chemical physics
- 2011

This work provides a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Møller-Plesset correlation with a semilocal exchange-correlation density functional, showing that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.