Aiming to study the ground-state properties of large, strongly correlated
systems with minimum computational complexity, Prof. Jeng-Da Chai recently
developed thermally-assisted-occupation density functional theory
(TAO-DFT).^{162} Unlike conventional multi-reference methods, the
computational complexity of TAO-DFT increases very insignificantly with the
size of the active space (*i.e.*, an active space restriction is not needed for
TAO-DFT calculations), and TAO-DFT appears to be very promising for the study
of large poly-radical systems. TAO-DFT is a DFT scheme with fractional orbital
occupations produced by the Fermi-Dirac distribution, controlled by a
fictitious temperature $\theta $, and existing XC functionals (*e.g.*, LDA or
GGAs) can be used in TAO-DFT.^{163} The computational cost of the
method is similar to that of KS-DFT for single-point energy calculations and
analytical nuclear gradients, and reduces to the cost of KS-DFT in the absence
of strong static correlation effects.

There are several *$rem* variables that are used for TAO-DFT.

TAO_DFT

Controls whether to use TAO-DFT.

TYPE:

Boolean

DEFAULT:

false

OPTIONS:

false
Do not use TAO-DFT
true
Use TAO-DFT

RECOMMENDATION:

NONE

TAO_DFT_THETA

The parameter $m$ for the value of the fictitious temperature $\theta =m\times {10}^{-n}{E}_{h}$ in TAO-DFT.

TYPE:

INTEGER

DEFAULT:

7

OPTIONS:

$m$
$in\theta =m\times {10}^{-n}{E}_{h}$, with the other parameter $n$ being set by TAO_DFT_THETA_NDP.

RECOMMENDATION:

NONE

TAO_DFT_THETA_NDP

The parameter $n$ for the value of the fictitious temperature $\theta =m\times {10}^{-n}{E}_{h}$ in TAO-DFT.

TYPE:

INTEGER

DEFAULT:

3

OPTIONS:

$n$
$\theta =m\times {10}^{-n}{E}_{h}$, with the other parameter $m$ being set by TAO_DFT_THETA.

RECOMMENDATION:

NONE

Note that setting TAO_DFT_THETA = 0 recovers ordinary
KS-DFT.^{162} In addition to the XC functional, a functional
${E}_{\theta}[\rho ]$ is needed in TAO-DFT. Currently available in Q-Chem are
an LDA version^{162} (the ETheta_LDA functional) as well as a
version based on the gradient expansion approximation^{163} (GEA)
(ETheta_GEA functional), and the latter may be substituted for the former in
the sample jobs below.

$molecule 0 1 Be $end $rem JOBTYPE sp BASIS 6-31G* EXCHANGE gen TAO_DFT true TAO_DFT_THETA 7 ! default, theta=7 mhartree TAO_DFT_THETA_NDP 3 ! default $end $xc_functional X S 1.0 C PW92 1.0 X ETheta_LDA 1.0 $end

$molecule 0 1 N1 N2 N1 4.5 $end $rem JOBTYPE sp BASIS 6-31G* EXCHANGE gen TAO_DFT true TAO_DFT_THETA 40 ! theta = 40 mhartree TAO_DFT_THETA_NDP 3 $end $xc_functional X PBE 1.0 C PBE 1.0 X ETheta_LDA 1.0 $end

$molecule 0 1 N1 N2 N1 5.0 $end $rem JOBTYPE opt UNRESTRICTED true BASIS 6-31G* EXCHANGE gen TAO_DFT true TAO_DFT_THETA 40 ! theta = 40 mhartrees TAO_DFT_THETA_NDP 3 ! can omit this line SCF_GUESS gwh SCF_GUESS_MIX 3 ! mix in 30% LUMO in alpha to break symmetry GEN_SCFMAN FALSE $end $xc_functional X PBE 1.0 C PBE 1.0 X ETheta_LDA 1.0 $end