Fullerenes vibrational properties

Kuzmany H, Winter J (2000) Vibrational properties of fullerenes and fullerides. In Andreoni W (ed) The physics of fullerenes and related materials. World Scientific, Singapore, p 208 Kuzmany H, Winkler R, Pichler (1995) J Phys Condens Matter 7 6601... 

Yamawaki, H., Yoshida, M., Kakadate, Y, Usuba, S., Yokoi, H., Fujiwara, S., Aoki, K., Ruoff, R., Malhorta, R., and Lorents, D.C. 1993. Infrared study of vibrational property and polymerization of fullerene C q and C,-, under pressure. Journal of Physical Chemistry 97, 11161-11163. 

In Ref. [76] the electronic and vibrational NR properties of the endohedral fullerene Sc2 C7o were reported at the HF level with the 6-31+G basis set for C, while Sc was treated by an Stuttgardt-Dresden ECP [77] with 11 valence electrons. The optimized geometry was of D2h symmetry, and only the properties along the D2 axis, on which the two Sc atoms are located, were computed. The results are shown in Table 5.26. The vibrational properties were calculated using FlCs. Similarly as found for the Li C6o fullerenes, the vibrational NR contribution to the static ot was very small compared to the electronic contribution. Due to heavy computational cost, for y only the vibrational contribution to the EFISH... 

In fullerene anions C%q, the n electrons outside closed shells occupy /lu triplet electronic states. Jahn-Teller (JT) coupling between these states and 5-fold h-type vibrations has important consequences for many properties of the fullerene anions. It is therefore important to understand the JT effect experienced by these ions from a theoretical point of view. We will study the cases of n = 2 and 4, where the lowest adiabatic potential energy surface is found to consist of a two-dimensional trough in linear coupling. The motion of the system therefore consists of vibrations in three directions across the trough and pseudo-rotations in two directions around the trough. Analytical expressions for states of the system that reflect this motion are obtained and the resultant energies determined. 

The symmetry of many molecules and especially of crystals is immediately obvious. Benzene has a six-fold symmetry axis and is planar, buckminsterfullerene (or just fullerene or footballene) contains 60 carbon atoms, regularly arranged in six- and five-membered rings with the same symmetry (point group //,) as that of the Platonic bodies pentagon dodecahedron and icosahedron (Fig. 2.7-1). Most crystals exhibit macroscopically visible symmetry axes and planes. In order to utilize the symmetry of molecules and crystals for vibrational spectroscopy, the symmetry properties have to be defined conveniently. 

The nature of the lowest-lying excited states of the fullerenes has been difficult to identify with much certainty. From Shpol skii-type luminescence spectra recorded at 1.5 K it has been concluded that the first-excited singlet state in C70 is of A 2 character. The origins of the lowest energy transitions in Ceo, namely Si(T]g) and S2(Gg), have been assigned on the basis of fluorescence and excitation spectra, supported by theoretical calculations. " The luminescence properties and relaxation dynamics of single crystals of Qo have been described while related measurements have been made for solid films of Ceo " Similar studies have reported the luminescence spectral properties of 50 trapped inside the cavities of NiY zeolites. An analysis of the fine structure of electron-vibrational spectra has been made for 50 and its derivatives in a solid toluene matrix. The rate of triplet energy transfer between fullerenes in toluene solution has been measured as a function of temperature and used to derive thermodynamic parameters for the transfer process. ... 

Based on the results of calculations of the vibrational spectrum it is possible to estimate the influence of fullerene defects on the properties of the superconductive phase. As was mentioned above, Tc is proportional to the logarithmic average of normal vibrational modes. Because considered defects only locally distort the structure of the Ceo shell, in the first approximation it is possible to consider coupling constants unchanged and therefore the exp(-l/A,) component as a constant. 

Since their discovery, fullerenes and their derivatives have been the subject of very extensive research. One of the topics investigated intensively are the linear and nonlinear optical (NLO) properties, owing to a variety of possible applications. Here we review some of the recent work of our group in this area, which is concerned with the ab-initio calculation of molecular NLO properties of two different kinds of fullerene derivatives, a) substituted 1,2-dihydro fullerenes and b) fullerenes endohedrally doped with atoms or small molecules. Apart from the purely electronic response, we also focus on the vibrational contributions to the NLO response, that is, to the response of the nuclei to the external electric fields. 

Two main aspects of the present contribution can be generalized and formulated as follows. Firstly, we compute both electronic (Sect. 3.2.2) and vibrational (Sect. 3.2.4) contributions to (hyper)polarizability. Thus, we explore the limitations of the currently available computational procedures. Secondly, we associate the linear and nonlinear optical properties of investigated organofullerenes with their electronic structure (Sect. 3.2.3). The purpose of the analysis of the relations between NLO properties and structure of organofullerenes is to make a basis for further rational design of new [60]fullerene derivatives suitable for photonic applications. 

As concerns endohedral fullerenes in general, some calculations of their polarizabilities have been reported, usually employing DPT methods [10-15], but reports on vibrational polarizabilities are rare. We mention here the work of Pederson et al. [16], who computed the vibrational polarizabiUty of Kr C6o, as well as of Ceo itself, in the lowest-order of perturbation theory (double-harmonic approximation). At that level, these contributions were found to be very small compared with the electronic property. 

In this section we present the nuclear relaxation (NR) contributions to the vibrational (hyper)polarizabilities of Li C6o and [Li C6o]. As previously stated our treatment requires a geometry optimization in the presence of a finite field. A problem can arise when there are multiple minima on the PES separated by low energy barriers. The finite field method works satisfactorily in that event as long as the field-dependent optimized structure corresponds to the same minimum as the field-free optimized structure. This was the case in previous work on ammonia [42], which has a double minimum potential. However, it is sometimes not the case for the endohedral fullerenes considered here, especially Li C6o- In fact, we were unable to determine the NR contribution in the x direction, i.e. perpendicular to the symmetry plane, for that molecule. It was possible to obtain based on the alternative analytical formulation [32-34], utilizing field-free dipole (first) derivatives and the Hessian. The analytical polarizability components in the other two directions were, then, used to confirm the values of the corresponding finite field method for those properties. 

We have computed both electronic and NR vibrational contributions to the (hyper) polarizabilities of the prototype endohedral fullereneLi C60 and its cation. A number of these properties were obtained for the first time. In other cases our results differ quite signicantly from those previously determined using more approximate approaches. The latter include the static electronic properties calculated by Campbell et al. [5, 6], Although, for the cation, there is a large difference between our values of the static vibrational conffibution to a and those reported by Whitehouse and... 

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