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SUMMARY:Variational calculations of monoatomic endofullerenes - Kripa Panc
 hagnula\, University of Cambridge
DTSTART:20220202T143000Z
DTEND:20220202T150000Z
UID:TALK168671@talks.cam.ac.uk
CONTACT:Lisa Masters
DESCRIPTION:Endohedral fullerenes are an example of non-bonded complexes w
 hose properties are dominated by strong quantum effects. Following the wor
 k of Bacanu et al.\, and Bacic and Mandziuk\, He@C60 and Ne@C70 were studi
 ed. These systems exhibit quantisation of translational energies due to pa
 rticle in a box type effects\, and symmetry breaking lifting the degenerac
 y of energy levels. The energies\, wavefunctions and spectra calculated ve
 ry closely match the previously seen results.\nFor He@C60 the potential wa
 s assumed to be radially symmetric and constructed from R2\, R4 and R6 ter
 ms. This was then used to construct the Hamiltonian matrix in the finite b
 asis representation which was diagonalised to calculate the translational 
 and rotational energy levels with fundamental frequencies of 217.9 cm^-1 a
 nd 96.7 cm^-1 respectively. These were used to plot two low temperature pr
 edicted rotational infrared spectra which closely matched the experimental
  spectra. The wavefunctions show a strong resemblance to hydrogenic atomic
  orbitals because of the imposed spherical symmetry.\nFor Ne@C70\, the sph
 erical symmetry was broken by elongation of the fullerene along the now un
 ique z axis. The potential was taken to be a pairwise Lennard-Jones summat
 ion over atoms which could be modelled as a one dimensional anharmonic osc
 illator along the z direction\, and a two dimensional isotropic anharmonic
  oscillator in the xy plane. The Hamiltonian matrix was constructed in the
  discrete variable representation and its eigenvalues calculated. The pres
 ence of an\nanisotropic direction lifted the (2l +1)-fold degeneracies int
 o only singly and doubly degenerate states indexed by the angular momentum
  quantum number for the two-dimensional oscillator. The fundamental freque
 ncies for the z and xy planes were found to be 9.92 cm^-1 and 54.73 cm^-1 
 respectively. While the wavefunctions do not have an intuitive analogue as
  for He@C60\, they show a very simple and regular structure linked with th
 e quantum number assignments.
LOCATION:via zoom 
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