![[Equation 1 - Musgrave and Pople potential]](E1.gif)
Philosophical Magazine Letters, 65(6), 291-298 (1992)
We now want to investigate which vibratory modes will couple most strongly to this distortion. This will be important in the application of the Bardeen-Cooper-Schrieffer theory of superconductivity. The technique adopted here (Jones and Sayyash 1986; Jones 1988, 1989) is to generate the dynamical matrix of the molecule from that of a small patch of four atoms on the surface of the molecule (fig. 1) which is treated with a very large basis set and the remaining atoms with a much smaller basis. The atoms in the patch and their neighbours are then allowed to move until the forces on them vanish.
We now use a wave-function basis consisting of four s- and p- Gaussian functions with independent exponents (i.e. 16 orbitals per atom) on the central 4 atoms of the patch. The remaining atoms were treated with a fixed linear combination of these four functions with the coefficients of the fit determined from the free atom. The charge density was fitted to Gaussian s-like functions with 5 independent exponents per atom. In addition, bond centred s- and p- Gaussian orbitals were placed at the centres of 9 innermost bonds. Tests with larger bases showed little change to the structure found below.
The starting structure possessed bond lengths of 1.42 Å. The forces on the inner 9 atoms were evaluated and these atoms moved by a conjugate gradient scheme until they vanished. The bond lengths of the central atom were then 1.37 and 1.43 Å, slightly smaller than those deduced above.
The second derivatives of the energy were then evaluated between the inner 4 atoms. These were used in two ways: firstly, we fitted them to the derivatives of the potential of Musgrave and Pople (1962) where the potential for atom i is
Here 
and 
are the changes in the length of the i-j bond and angle between the i-j and i-k bond, respectively. The sum is over the nearest neighbour atoms only. Table 1 gives the coefficients 
, 
, 
, 
and 
. This potential was used to generate the dynamical matrix of C60 and the resulting 174 non-zero modes are given in table 2.
Secondly, we used the symmetry of the icosahedral molecule to generate all the derivatives from a set calculated by the ab initio method. These involved the derivative on the central atom, between it and two nearest neighbours and between two pairs of next-nearest neighbours. These were used directly to determine the modes also given in table 2. The symmetries of the normal modes were assigned by comparing with the normal modes given by Weeks and Harter (1989).
[Abstract] [Introduction] [Method] [Vibrational modes] [Conclusions] [Acknowledgements] [References] [Table 1] [Table 2] [Table 3] [Table 4] [Figure 1] [Figure 2]
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