Abstract
We show that using complex, spin-restricted orbitals in Kohn-Sham (KS) density functional theory allows one to access a new class of densities that is not accessible by either spin-restricted (RKS) or spin-unrestricted (UKS) orbitals. We further show that the real part of a complex RKS (CRKS) density matrix can be nonidempotent when the imaginary part of the density matrix is not zero. Using CRKS orbitals shows significant improvements in the triplet-singlet gaps of a benchmark set, called TS12, for well-established, widely used density functionals. Moreover, it was shown that RKS and UKS yield qualitatively wrong charge densities and spin densities, respectively, leading to worse energetics. We demonstrate that representative modern density functionals show surprisingly no improvement even with a qualitatively more accurate density from CRKS orbitals. To this end, our work not only provides a way to escape the symmetry dilemma whenever there exists a CRKS solution, but also suggests a new route to design better approximate density functionals.
| Original language | English |
|---|---|
| Article number | 113001 |
| Journal | Physical Review Letters |
| Volume | 123 |
| Issue number | 11 |
| DOIs | |
| State | Published - Sep 10 2019 |
| Externally published | Yes |
Funding
In this Letter, we showed that it is possible to access a different class of densities that is not possible to obtain within either RKS or UKS. This is achieved by using CRKS to obtain the density. Although the CRKS determinant breaks time-reversal symmetry and complex symmetry, the resulting densities do not exhibit the spatial and spin symmetry breaking associated with RKS and UKS. Furthermore, based on the triplet-singlet test set (TS12), we showed that the CRKS charge densities follow the point group symmetry while RKS does not. This allows CRKS to improve the quantitative accuracy of some XC functionals by a factor of 5. We also showed that the UKS charge density is qualitatively incorrect and the resulting energies are far from chemical accuracy due to spin contamination. Lastly, we note that modern MGGA functionals (SCAN, MN15-L, and B97M-V) do not show any significant improvements even when correct densities from CRKS are used. Even with the exact XC functional, one needs a CRKS determinant to obtain qualitatively correct charge and spin densities for the systems considered here. This Letter suggests that these modern functionals might lack some aspects of the exact XC functional. We hope that our study provides a new class of data that can be used to assess, and possibly inform the design of new approximate XC functionals. The key benefit is a route to escape the symmetry dilemma whenever complex polarization is relevant. The Supplemental Material for this work is available online [43] . This research was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We thank Fionn Malone, Yuezhi Mao, and Narbe Mardirossian for helpful comments. J. L. thanks Soojin Lee for consistent encouragement. This research was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.