Electronic Properties of Cyclacenes from TAO-DFT.

Chun-Shian Wu,Pei-Yin Lee,Jeng-Da Chai

doi:10.1038/srep37249

Abstract

Owing to the presence of strong static correlation effects, accurate prediction of the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and real-space representation of active orbitals) of cyclacenes with n fused benzene rings (n = 4–100) has posed a great challenge to traditional electronic structure methods. To meet the challenge, we study these properties using our newly developed thermally-assisted-occupation density functional theory (TAO-DFT), a very efficient method for the study of large systems with strong static correlation effects. Besides, to examine the role of cyclic topology, the electronic properties of cyclacenes are also compared with those of acenes. Similar to acenes, the ground states of cyclacenes are singlets for all the cases studied. In contrast to acenes, the electronic properties of cyclacenes, however, exhibit oscillatory behavior (for n ≤ 30) in the approach to the corresponding properties of acenes with increasing number of benzene rings. On the basis of the calculated orbitals and their occupation numbers, the larger cyclacenes are shown to exhibit increasing polyradical character in their ground states, with the active orbitals being mainly localized at the peripheral carbon atoms.

Highlights

Owing to the presence of strong static correlation effects, accurate prediction of the electronic properties of cyclacenes with n fused benzene rings (n = 4–100) has posed a great challenge to traditional electronic structure methods
The amplitudes of the even-odd oscillations are considerably larger for Kohn-Sham density functional theory (KS-DFT) with the XC functionals, which are closely related to the degree of spin contamination
The larger fraction of Hartree-Fock (HF) exchange adopted in the XC functional in KS-DFT, the higher the degree of spin contamination for systems with strong static correlation effects

Summary

Computational Details

All calculations are performed with a development version of Q-Chem 4.060, using the 6–31 G(d) basis set with the fine grid EML (75, 302), consisting of 75 Euler-Maclaurin radial grid points and 302 Lebedev angular grid points. Results are calculated using KS-LDA (i.e., KS-DFT with the LDA XC density functional29,30) and TAO-LDA (i.e., TAO-DFT with the LDA XC density functional and the LDA θ-dependent density functional EθLDA (see Eq (41) of ref. The ground state of n-cyclacene/n-acene (n = 4–100) is obtained by performing spin-unrestricted KS-LDA and TAO-LDA calculations for the lowest singlet and triplet energies of n-cyclacene/n-acene on the respective geometries that were fully optimized at the same level of theory. The singlet-triplet energy (ST) gap of n-cyclacene/n-acene is calculated as (ET −ES), the energy difference between the lowest triplet (T) and singlet (S) states of n-cyclacene/n-acene

Results and Discussion

Conclusions

Additional Information