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).[Chai(2012)] 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 , and existing XC functionals (*e.g.*, LDA or GGAs) can be used in TAO-DFT.[Chai(2014)] 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

Controls the value of the fictitious temperature in TAO-DFT.

TYPE:

INTEGER

DEFAULT:

7

OPTIONS:

(hartrees), where is the value of TAO_DFT_THETA_NDP

RECOMMENDATION:

NONE

TAO_DFT_THETA_NDP

Controls the value of the fictitious temperature in TAO-DFT.

TYPE:

INTEGER

DEFAULT:

3

OPTIONS:

(hartrees), where is the value of TAO_DFT_THETA

RECOMMENDATION:

NONE

Note that setting TAO_DFT_THETA = 0 recovers ordinary KS-DFT.[Chai(2012)] In addition to the XC functional, a functional is needed in TAO-DFT. Currently available in Q-Chem are an LDA version[Chai(2012)] (the ETheta_LDA functional) as well as a version based on the gradient expansion approximation[Chai(2014)] (GEA) (ETheta_GEA functional), and the latter may be substituted for the former in the sample jobs below.

**Example 5.63** TAO-LDA calculation on Be atom

$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

**Example 5.64** TAO-PBE, spin-restricted calculation on stretched N

$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

**Example 5.65** TAO-PBE, spin-unrestricted calculation on stretched N

$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