Coarctate and Möbius: The Helical Orbitals of Allene and Other Cumulenes.

As brought to the attention of the community by Hendon et al. and noted by previous workers, the π orbitals of the equilibrium geometry odd-carbon (even number of double bonds = n) [n]cumulenes may be written in either rectilinear or helical form. We trace the origins and detailed composition of the helical orbitals of cumulenes, which emerge in the simplest Hückel model and are not much modified in advanced computations. For the α,ω-disubstituted even [n]cumulenes, the helical representation is obligatory as the symmetry is reduced from D2d to C2. A relationship is apparent between these helical orbitals of the even [n]cumulenes, seen as a Herges coarctate system, and the corresponding Möbius cyclic polyene orbitals. The twist of the orbitals varies in interesting ways along the helix, and so does the contribution of the component atomic orbitals. Though the electronic structures of even [n]cumulenes and Möbius cyclopolyenes are closely related, they differ for higher n in intriguing ways; these are linked to the constrained rotation of the basis orbitals along the helical twist itinerary. Relations are constructed between the level patterns of the π-systems of even [n]cumulenes and ideas of Hückel and Möbius aromaticity.

Benchmarking second order methods for the calculation of vertical electronic excitation energies: valence and Rydberg states in polycyclic aromatic hydrocarbons.

The performance of the six second order linear response methods RPA(D), SOPPA, SOPPA(CCSD), CIS(D), CC2, and CCSD, which include either noniterative or iterative doubles contributions, has been studied in calculations of vertical excitation energies. The benchmark set consisted of 39 valence and 76 Rydberg states of benzene and five polycyclic aromatic hydrocarbons. As reference values we have used the results of the corresponding calculations with the third order method CCSDR(3), which includes noniterative triples contributions. In addition we have also carried out equivalent calculations at the level of the random phase approximation as well as with the configuration interaction singles and multireference configuration interaction singles and doubles methods.

Two-photon absorption cross sections: an investigation of the accuracy of calculated absolute and relative values.

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple zeta level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.