Thermally-assisted-occupation density functional theory with generalized-gradient approximations

Abstract

We extend the recently proposed thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] to generalized-gradient approximation (GGA) exchange-correlation density functionals. Relative to our previous TAO-LDA (i.e., the local density approximation to TAO-DFT), the resulting TAO-GGAs are significantly superior for a wide range of applications, such as thermochemistry, kinetics, and reaction energies. For noncovalent interactions, TAO-GGAs with empirical dispersion corrections are shown to yield excellent performance. Due to their computational efficiency for systems with strong static correlation effects, TAO-LDA and TAO-GGAs are applied to study the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy) of acenes with different number of linearly fused benzene rings (up to 100), which is very challenging for conventional electronic structure methods. The ground states of acenes are shown to be singlets for all the chain lengths studied here. With the increase of acene length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy (i.e., a measure of polyradical character) increase monotonically.

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

“…In TAO-DFT [20,21], the representation of the ground-state density from the exact theory (see Eq. (1)) has been highlighted.…”

“…Nonetheless, owing to the inappropriate treatment of nonlocal XC effects [12,13], KS-DFAs can perform very poorly in situations where the self-interaction error (SIE) [12][13][14][15], noncovalent interaction error (NCIE) [16][17][18], or static correlation error (SCE) [12,[19][20][21][22] is pronounced. Over the years, considerable efforts have been made to resolve the qualitative failures of KS-DFAs at a reasonable computational cost.…”

“…In spite of their computational efficiency, KS-DFAs, hybrid functionals, and double-hybrid functionals can perform very poorly for systems with strong static correlation effects (i.e., multi-reference systems) [12,[19][20][21][22]. Within KS-DFT, fully nonlocal XC functionals, such as those based on the random phase approximation (RPA), may be adopted for a reliably accurate description of strong static correlation effects.…”

“…To reduce the SCE problems with low computational complexity, we have recently developed thermally-assisted-occupation density functional theory (TAO-DFT) [20,21], an efficient electronic structure method for studying the ground-state properties of very large systems (e.g., containing up to a few thousand electrons) with strong static correlation effects [45][46][47][48]. Unlike finite-temperature DFT [49], TAO-DFT is developed for ground-state systems at zero temperature.…”

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

“…Alternatively, KS-DFT may also be combined with symmetry-adapted perturbation theory (SAPT) [96][97][98][99][100][101][102][103][104] to yield accurate results for noncovalent interactions [105][106][107][108][109][110][111]. In addition, to properly describe strong static correlation, it could be essential to develop a combined LC hybrid scheme with random phase approximations (RPAs) [25,[112][113][114] for small-to medium-sized systems or with thermally-assisted-occupation density functional theory (TAO-DFT) [115][116][117] for large-sized systems.…”