Coupled-cluster connected quadruples and quintuples corrections to the harmonic vibrational frequencies and equilibrium bond distances of HF, N(2), F(2), and CO.

Using the coupled-cluster method, we have examined the contributions from the connected quadruple and quintuple virtual excitations to the harmonic vibrational frequencies and equilibrium bond distances of HF, N(2), F(2), and CO. Whereas the largest quadruples contributions are -18.8 cm(-1) to the harmonic frequency of N(2) and 0.43 pm to the bond distance of F(2), the largest quintuples contributions are -3.9 cm(-1) to the harmonic frequency of N(2) and 0.03 pm to the bond distances of N(2) and F(2). As we improve the description by going from the coupled-cluster singles-and-doubles model with a perturbative triples correction [CCSD(T)] to the coupled-cluster singles-doubles-triples-and-quadruples model, the mean and maximum absolute errors in the calculated frequencies relative to experiment are reduced from 11.3 and 15.8 cm(-1), respectively, to 3.2 and 4.7 cm(-1); for the bond distances, the mean and maximum absolute errors are reduced from 0.16 and 0.47 pm, respectively, to 0.04 and 0.13 pm. The calculations presented here confirm previous observations that, to some extent, the relatively small errors in the CCSD(T) equilibrium bond distances and harmonic frequencies arise from a cancellation of errors in the approximate (perturbative) treatment of the connected triples and the neglect of higher-order connected excitations. Further inclusion of quintuples contributions, relativistic corrections, and adiabatic corrections reduces the mean and maximum absolute errors to 1.1 and 2.3 cm(-1), respectively, for the harmonic frequencies and to 0.02 and 0.05 pm, respectively, for the bond distances.