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# 5.12.1 Density-Corrected DFT

(July 14, 2022)

It is well known that self-interaction error (SIE) in DFT leads to over-delocalization of unpaired spins in open-shell molecules. 227 Cohen A. J., Mori-Sanchez P., Yang W.
Chem. Rev.
(2012), 112, pp. 289.
This has a variety of deleterious effects, including overstabilization of three-center, two-electron “hemibonds”, 1003 Rana B., Herbert J. M.
J. Phys. Chem. Lett.
(2021), 12, pp. 8053.
fractional charges in well-separated chemical moieties (i.e., upon dissociation), 1346 Zhang Y., Yang W.
J. Chem. Phys.
(1998), 109, pp. 2604.
, 1044 Ruzsinszky A. et al.
J. Chem. Phys.
(2006), 125, pp. 194112.
and too-low reaction barriers, the latter of which was largely the motivation for the introduction of hybrid density functionals. 762 Lynch B. J., Truhlar D. G.
J. Phys. Chem. A
(2001), 105, pp. 2936.
, 547 Janesko B. G.
Chem. Soc. Rev.
(2021), 50, pp. 8470.
Although various ad hoc self-interaction correction schemes have been introduced over the years, none of them is entirely satisfactory. 547 Janesko B. G.
Chem. Soc. Rev.
(2021), 50, pp. 8470.
Density-corrected (DC-)DFT 1236 Vuckovic S. et al.
J. Chem. Theory Comput.
(2019), 15, pp. 6336.
, 1124 Song S. et al.
J. Chem. Theory Comput.
(2022), 18, pp. 817.
, 1096 Sim E. et al.
J. Am. Chem. Soc.
(2022), 144, pp. 6625.
represents a revival of an old idea 884 Oliphant N., Bartlett R.
J. Chem. Phys.
(1994), 100, pp. 6550.
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

 $E_{\text{DC-DFT}}[\rho]=E_{\text{DFT}}\Big{[}\operatorname*{arg\,min}_{\rho}% \big{(}E_{\text{HF}}[\rho]\big{)}\Big{]}$ (5.73)

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. 546 Janesko B. G., Scuseria G. E.
J. Chem. Phys.
(2008), 128, pp. 244112.
, 1225 Verma P., Bartlett R. J.
J. Chem. Phys.
(2014), 140, pp. 18A534.
, 1002 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275.
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. 1002 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275.

Users of Q-Chem’s implementation of DC-DFT are asked to cite Ref.  1002 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275.
. Analytic energy gradients for DC-DFT are available, 1002 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275.
but because the functional $E_{\text{DC-DFT}}$ is not iterated to self-consistency evaluation of the gradient $dE_{\text{DC-DFT}}/dx$ requires solution of coupled-perturbed ($Z$-vector) equations, 1225 Verma P., Bartlett R. J.
J. Chem. Phys.
(2014), 140, pp. 18A534.
, 1002 Rana B., Coons M. P., Herbert J. M.
J. Phys. Chem. Lett.
(2022), 13, pp. 5275.

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.

DC_DFT

DC_DFT
Controls whether to use DC-DFT.
TYPE:
Boolean
DEFAULT:
FALSE
OPTIONS:
FALSE Do not do DC-DFT. TRUE Iterate the density to self-consistency at the Hartree-Fock level and then perform evaluate $E_{\text{DFT}}[\rho_{\text{HF}}]$ using the functional specified with METHOD.
RECOMMENDATION:
Use if desired. Analytic gradients are available but are a serial bottleneck in the present implementation.