**Michael G. Medvedev**

A.N. Nesmeyanov Institute of Organoelement Compounds RAS, 119991 Moscow, Russian Federation

N.D. Zelinsky Institute of Organic Chemistry RAS, 119991 Moscow, Russian Federation

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### Abstract

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density (1). For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional.

We have examined the other side of the coin — the energy-minimizing electron densities for atomic species, as produced by more than a hundred DFT functionals (2). Self-consistent electron densities produced by these functionals were compared to the CCSD-full ones by means of three local descriptors: electron density (RHO), its gradient norm (GRD) and its Laplacian (LR); aug-cc-pωCV5Z basis set was used for all calculations.

We have found that, reflecting theoretical advances, DFT functionals’ densities became closer to the CCSD-full ones, until in the early 2000s this trend was reversed by flexible functionals with forms chosen to be suitable for empirical fitting.

During the year 2017 this result was extensively discussed in scientific literature and significantly broadened (3–11).

### References

1. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. *Phys. Rev*. **136**, B864–B871 (1964).

2. M. G. Medvedev, I. S. Bushmarinov, J. Sun, J. P. Perdew, K. A. Lyssenko, Density functional theory is straying from the path toward the exact functional. *Science*. **355**, 49–52 (2017).

3. K. R. Brorsen, Y. Yang, M. V. Pak, S. Hammes-Schiffer, Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated? *J. Phys. Chem. Lett.* **8**, 2076–2081 (2017).

4. T. Gould, What Makes a Density Functional Approximation Good? Insights from the Left Fukui Function. *J. Chem. Theory Comput*. **13**, 2373–2377 (2017).

5. K. P. Kepp, Comment on “Density functional theory is straying from the path toward the exact functional.” *Science* (2017).

6. M. G. Medvedev, I. S. Bushmarinov, J. Sun, J. P. Perdew, K. A. Lyssenko, Response to Comment on “Density functional theory is straying from the path toward the exact functional.” *Science*. **356**, 496–496 (2017).

7. P. Verma, D. G. Truhlar, Can Kohn–Sham density functional theory predict accurate charge distributions for both single-reference and multi-reference molecules? *Phys Chem Chem Phys*. **19**, 12898–12912 (2017).

8. P. D. Mezei, G. I. Csonka, M. Kallay, Electron density errors and density-driven exchange-correlation energy errors in approximate density functional calculations. *J. Chem. Theory Comput.* (2017), doi:10.1021/acs.jctc.7b00550.

9. I. Mayer, I. Pápai, I. Bakó, Á. Nagy, Conceptual Problem with Calculating Electron Densities in Finite Basis Density Functional Theory.* J. Chem. Theory Comput*. (2017), doi:10.1021/acs.jctc.7b00562.

10. D. Hait, M. Head-Gordon, How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values. ArXiv170905075 *Cond-Mat Physicsphysics Physicsquant-Ph* (2017) (available at http://arxiv.org/abs/1709.05075).

11. Y. Wang, X. Wang, D. G. Truhlar, X. He, How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne6+ and Ne8+? *J. Chem. Theory Comput.* (2017), doi:10.1021/acs.jctc.7b00865.