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).186 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., LDA186, GGAs187 or global hybrid GGAs188) can be used in TAO-DFT. 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
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
TAO_DFT_THETA
The parameter (the mantissa) for the value of the fictitious temperature in TAO-DFT.
TYPE:
INTEGER
DEFAULT:
7
OPTIONS:
Customize the mantissa for the fictitious temperature.
RECOMMENDATION:
NONE
TAO_DFT_THETA_NDP
TAO_DFT_THETA_NDP
The parameter (the exponent) for the value of the fictitious temperature in TAO-DFT.
TYPE:
INTEGER
DEFAULT:
3
OPTIONS:
Customize the exponential power for the fictitious temperature.
RECOMMENDATION:
NONE
Note that setting TAO_DFT_THETA = 0 recovers ordinary KS-DFT.186 In addition to the XC functional, a functional is needed in TAO-DFT. Currently available in Q-Chem are an LDA version186 (the ETheta_LDA functional) as well as a version based on the gradient expansion approximation187 (GEA) (the ETheta_GEA functional), and the latter may be substituted for the former in the sample jobs below. Furthermore, a functional is also needed in TAO-DFT for global hybrid GGAs. Currently available in Q-CHEM is an LDA version (the EThetaX_LDA functional).188
Example 5.24 TAO-LDA calculation on Be atom
$molecule 0 1 Be $end $rem 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 5.25 TAO-PBE, spin-restricted calculation on stretched N
$molecule 0 1 N1 N2 N1 4.5 $end $rem 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 5.26 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 $end $xc_functional X PBE 1.0 C PBE 1.0 X ETheta_LDA 1.0 $end
Example 5.27 TAO-PBE0 calculation on H molecule
$molecule 0 1 H1 H2 H1 1.00 $end $rem JOBTYPE opt UNRESTRICTED true BASIS 6-31G* EXCHANGE gen TAO_DFT true TAO_DFT_THETA 20 ! theta = 20 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 $end $xc_functional X ETheta_LDA 1.00 X EThetaX_LDA 0.25 X HF 0.25 X PBE 0.75 C PBE 1.00 $end
Example 5.28 TAO-B3LYP calculation on H molecule
$molecule 0 1 H1 H2 H1 1.00 $end $rem JOBTYPE opt UNRESTRICTED true BASIS 6-31G* EXCHANGE gen TAO_DFT true TAO_DFT_THETA 174 ! theta = 17.4 mhartrees TAO_DFT_THETA_NDP 4 SCF_GUESS gwh SCF_GUESS_MIX 3 ! mix in 30% LUMO in alpha to break symmetry $end $xc_functional X ETheta_LDA 1.00 X EThetaX_LDA 0.20 X HF 0.20 X Slater 0.08 X Becke88 0.72 C LYP 0.81 C VWN1RPA 0.19 $end