5.12 Thermally-Assisted-Occupation Density Functional Theory (TAO-DFT)

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).¹⁶³ 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.¹⁶⁴ 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.

Note that setting TAO_DFT_THETA = 0 recovers ordinary KS-DFT.¹⁶³ In addition to the XC functional, a functional $E_{\theta }[\rho ]$ is needed in TAO-DFT. Currently available in Q-Chem are an LDA version¹⁶³ (the ETheta_LDA functional) as well as a version based on the gradient expansion approximation¹⁶⁴ (GEA) (ETheta_GEA functional), and the latter may be substituted for the former in the sample jobs below.