Structure of [18]Annulene Revisited: Challenges for Computing Benzenoid Systems

For cyclic conjugated structures, erratic computational results have been obtained with Hartree–Fock (HF) molecular orbital (MO) methods as well as density functional theory (DFT) with large HF-exchange contributions. In this work, the reasons for this unreliability are explored. Extensive computations on [18]annulene and related compounds highlight the pitfalls to be avoided and the due diligence required for such computational investigations. In particular, a careful examination of the MO singlet-stability eigenvalues is recommended. The appearance of negative eigenvalues is not (necessarily) problematic, but near-zero (positive or negative) eigenvalues can lead to dramatic errors in vibrational frequencies and related properties. DFT approaches with a lower HF admixture generally appear more robust in this regard for the description of benzenoid structures, although they may exaggerate the tendency toward planarity and C–C bond-equalization. For the iconic [18]annulene, the results support a nonplanar equilibrium structure. The density-fitted frozen natural orbital coupled-cluster singles and doubles with perturbative triples [DF-FNO CCSD(T)] method of electron correlation with an aug-pVQZ/aug-pVTZ basis set places the C2 global minimum 1.1 kcal mol–1 below the D6h stationary point.


SI Table of Contents
Table S1: Comparison of DF-FNO and conventional CC results for 1.
Table S5:Total CC energies for conformations of 1 for Table 3.
Table S6:Total DF-FNO CC energies for 1 for Table 4.
Table S14: Details of stability analyses for structures 2-6.Table S15: Total energies from stability analyses of 1.

S6
Table S7: Geometries (Ångstroms) and energies (au) for 1 for Table  Table S14.Overview of stability analyses and key vibrational frequencies of other benzenoid systems 2-6 at different levels of theory.

Figure S1 :
Figure S1: Dependence of the force constant for the b 2u imaginary frequency of 1 on a uniform C-C bond elongation.

Figure S2 :
Figure S2: Dependence of the excitation energy for the lowest singlet excited state of 1 on a uniform C-C bond elongation.

Figure S1 .
Figure S1.Dependence of the force constant for the b2u imaginary frequency on a uniform CC bond elongation computed at BHHLYP/6-311+G(d,p)).

Figure S2 .
Figure S2.Dependence of the excitation energy for the lowest singlet excited state on a uniform CC bond elongation computed at BHHLYP/6-311+G(d,p).

Table S3 :
Vibrational frequencies of D 6h -1 a Relative energies in kcal mol −1 from CCSD(T) single-

Table S13 .
Overview of stability analyses, and key vibrational frequencies for various structures of[18]annulene at different levels of theory D3h converges to D6h [c] At OLYP/6-311+G(d,p) D3d converges to D6h and Ci to D3d, while no anomalies can be found for C2, D3d, D3h.[e] The Ci symmetric structure converges at CCSD/DZ to C1, at MP2/cc-pVDZ to D3d, at BHLYP/6-311+G(d,p) to D6h, and at HF with different basis sets to D6h.

Table S15 .
Total energies from stability analyses of 1.