Vibrational frequencies and determination of stability of aromatic molecules

After the vibrational frequencies of 66 benzene, naphthalene, anthracene, biphenylene, acenaphthylene molecules and their derivatives are computed by 7 ab initio methods [i.e., HF, MP2, MP2(Full), MP3, CISD, QCISD and CCSD], 7 density functional theory (DFT) methods (i.e., B3LYP, B3P86, LSDA, HCTH, M06, B97D and mPW2PLYPD) and 20 popular basis sets (i.e., 18 k-nlmG type basis sets, cc-pVDZ and aug-cc-pVDZ), it is found that no imaginary frequency appears only for 10 molecules and imaginary frequencies appear for 1365 method/basis sets. The percentages of the numbers of imaginary frequencies relative to their total computed method/basis sets for the 7 DFT methods, HF method and MP2 method are 7.01%, 7.34%, and 36.38%, respectively. The results of the 16 substituted arenes containing methyl or ammonium group computed by all the methods except mPW2PLYPD are very unreliable, but the results of the other molecules computed by the DFT and HF methods are very reliable when determined from the criterion that the percentage of imaginary frequency which will exclude the stability of a computed molecule is negligible. When 45 heterocyclic aromatic compounds and their derivatives are similarly computed, the percentages of imaginary frequencies of the DFT methods, HF method, and MP2 method are 2.11%, 2.78%, and 27.44%, respectively. Imaginary frequencies do not disappear when the experimental structure of benzene is used to compute or when the planar or nonplanar optimized structures of benzene and toluene are used to compute. Moreover, when benzene and toluene are computed by more than one hundred methods and more than one hundred basis sets, their percentage of imaginary frequencies is also as high as 18.18%. Then the ab initio and DFT methods are not always reliable or suitable for computing frequencies, and the viewpoint that benzene and other arenes are nonplanar is at least not completely correct.