Electronic structure, bonding, spectra, and linear and nonlinear electric properties of Ti@C28

The potential energy surface (PES) of Ti@C(28) has been revisited, and the stationary points have been carefully characterized. In particular, the C(2v) symmetry structure considered previously turns out to be a transition state lying 2.3 kcal/mol above the ground state of C(3v) symmetry at the MP2/6-31G(d) level. A large binding energy of 181.3 kcal/mol is found at the ROMP2/6-31G(d) level. Topological analysis of the generalized Ti@C(28) density reveals four bond paths between Ti and carbon atoms of the host. The character of all four contacts corresponds to a partially covalent closed shell interaction. UV-vis, IR, and Raman spectra are calculated and compared with C(28)H(4). The dipole moment and the static electronic and double harmonic vibrational (hyper)polarizabilities have been obtained. Distortion of the fullerene cage due to encapsulation leads to nonzero diagonal components of the electronic first hyperpolarizability β, and to an increase in the diagonal components of the electronic polarizability α and second hyperpolarizability γ. However, introduction of the Ti atom causes a comparable or larger reduction in most cases due to localized bonding interactions. At the double harmonic level, the average vibrational β is much larger than its electronic counterpart, but the opposite is true for α and for the contribution to γ that has been calculated. There is also a very large anharmonic (nuclear relaxation) contribution to β which results from a shallow PES with four minima separated by very low barriers. Thus, the vibrational γ (and α) may, likewise, become much larger when anharmonicity is taken into account.