Electronic Structure, Bonding, Spectra, and Linear and Nonlinear Electric Properties of Ti@C₂₈

Abstract

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.

Ab initio infrared vibrational modes for neutral and charged small fullerenes (C 20 , C 24 , C 26 , C 28 , C 30 and C 60 )

“…Comparing our C 4− 28 result with previous calculations for Ti@C 28 shows qualitatively good agreement [48], with strong peaks for Ti@C 28 reported at 1357/1396 cm −1 , and several bands around 780-830 cm −1 . This peak splitting compared with our results comes from symmetry breaking by the Ti atom, which displaces from the cage centre towards one of the triplet-pentagon centred carbon atoms.…”

Evaluation of the nonlinear optical properties for an expanded porphyrin Hückel-Möbius aromaticity switch

“…can be considered as high NLOP values. 40,41,43 For instance, theγ obtained in this work are one order of magnitude larger than our results obtained for the Hückel and Möbius conformers for the bianthraquinodimethane modified [16] annulene. 16 It is important to remark that large differences ofγ between the Hückel and Möbius conformers are obtained, the maximum difference is 1 × 10 6 a.u.…”

“…37 It is well established that diffuse and polarization functions are required for a quantitative description of both the electronic and vibrational (hyper)polarizabilities of medium size organic molecules. 32,[38][39][40][41] Nevertheless, it has also been found in the past that the 6-31G basis set is adequate to obtain qualitative results, and many previous theoretical investigations of NLOP have used it. 31,36,39,40,42 In Tables II and III, one can see that the increment of basis set from 6-31G to 6-311G(d) does not provoke a large variation of α e and γ e values (lie in the 2%-32% range).…”

Vibrational optical activity of chiral carbon nanoclusters treated by a generalized π-electron method

“…As of yet, C 28 has been characterized only in its chemically stabilized derivatives, e.g., Ti@C 28 . 106,107 As confirmed by several theoretical studies, 83,[105][106][107][108][109][110][111][112] the most stable isomer of C 28 has a quintuplet ground state and a geometry of T d symmetry, with four non-adjacent hexagons. The ground state of the less stable isomer, D 2 -C 28 (characterized by two edge-sharing hexagon pairs) has a singlet ground state.…”