5.12.1 Density-Corrected DFT

It is well known that self-interaction error (SIE) in DFT leads to over-delocalization of unpaired spins in open-shell molecules. ²⁵⁵ Cohen A. J., Mori-Sanchez P., Yang W.
Chem. Rev.
(2012), 112, pp. 289. Link This has a variety of deleterious effects, including overstabilization of three-center, two-electron “hemibonds”, ¹⁰⁹⁹ Rana B., Herbert J. M.
J. Phys. Chem. Lett.
(2021), 12, pp. 8053. Link fractional charges in well-separated chemical moieties (i.e., upon dissociation), ¹⁴⁸¹ Zhang Y., Yang W.
J. Chem. Phys.
(1998), 109, pp. 2604. Link ^{, 1143} Ruzsinszky A. et al.
J. Chem. Phys.
(2006), 125, pp. 194112. Link ^{, 856} Mantz Y. A. et al.
J. Phys. Chem. A
(2007), 111, pp. 105. Link and too-low reaction barriers, the latter of which was largely the motivation for the introduction of hybrid density functionals. ⁸³⁷ Lynch B. J., Truhlar D. G.
J. Phys. Chem. A
(2001), 105, pp. 2936. Link ^{, 611} Janesko B. G.
Chem. Soc. Rev.
(2021), 50, pp. 8470. Link Although various ad hoc self-interaction correction schemes have been introduced over the years, none of them is entirely satisfactory. ⁶¹¹ Janesko B. G.
Chem. Soc. Rev.
(2021), 50, pp. 8470. Link Density-corrected (DC-)DFT ¹³⁵³ Vuckovic S. et al.
J. Chem. Theory Comput.
(2019), 15, pp. 6336. Link ^{, 1232} Song S. et al.
J. Chem. Theory Comput.
(2022), 18, pp. 817. Link ^{, 1201} Sim E. et al.
J. Am. Chem. Soc.
(2022), 144, pp. 6625. Link represents a revival of an old idea ⁹⁷⁴ Oliphant N., Bartlett R.
J. Chem. Phys.
(1994), 100, pp. 6550. Link to avoid SIE by evaluating a DFT functional non-self-consistently using self-consistent Hartree-Fock density, which is SIE-free. Self-consistent iterations at the DFT level are avoided as this would re-introduce SIE into the density. If $E_{\text{DFT}}[\rho ]$ represents the user’s chosen density functional and $E_{\text{HF}}[\rho ]$ represents the Hartree-Fock functional, then the DC-DFT energy functional is ¹⁰⁹⁷ Rana B., Beran G. J. O., Herbert J. M.
Mol. Phys.
(2023), 121, pp. e2138789. Link

DC-DFT affords barrier heights that are comparable in accuracy to those obtained with hybrid functionals, even if $E_{\text{DFT}}[\rho ]$ is a semilocal functional. ⁶¹⁰ Janesko B. G., Scuseria G. E.
J. Chem. Phys.
(2008), 128, pp. 244112. Link ^{, 1342} Verma P., Bartlett R. J.
J. Chem. Phys.
(2014), 140, pp. 18A534. Link ^{, 1098} Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275. Link This does not really reduce the cost of hybrid DFT calculations since the Hartree-Fock calculation must be iterated to self-consistency, nevertheless DC-DFT may serve as a useful diagnostic tool. If the DC-DFT result with a given functional is qualitatively different than the self-consistent DFT result with the same functional, then density-driven SIE may be affecting the results. This diagnostic capacity has been used, for example, to detect unrealistic delocalization of polaron (spin) defects in metal oxides. ¹⁰⁹⁸ Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275. Link

Users of Q-Chem’s implementation of DC-DFT are asked to cite Ref.  1098 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275. Link . Analytic energy gradients for DC-DFT are available, ¹⁰⁹⁸ Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275. Link but because the functional $E_{\text{DC-DFT}}$ is not iterated to self-consistency evaluation of the gradient $d{E}_{\text{DC-DFT}}/dx$ requires solution of coupled-perturbed ($Z$-vector) equations, ¹³⁴² Verma P., Bartlett R. J.
J. Chem. Phys.
(2014), 140, pp. 18A534. Link ^{, 1098} Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275. Link which makes the gradient somewhat more expensive than a traditional DFT gradient.

Note:  At present, the coupled-perturbed equtions for DC-DFT are solved in serial, meaning that while the SCF iterations are parallelized the $Z$-vector iterations are not.

To perform a DC-DFT calculation, set use METHOD in the $rem section to select the functional of choice, and also set DC_DFT = TRUE. Note that because $E_{\text{DFT}}[\rho ]$ is never diagonalized, any subsequent properties that are computed at the end of the SCF procedure are based on the Hartree-Fock density. This includes one-particle energy levels, Mulliken charges, multipole moments, etc.