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CATEGORIES:Theory - Chemistry Research Interest Group
SUMMARY:Variational calculations of monoatomic endofullere
nes - Kripa Panchagnula\, University of Cambridge
DTSTART;TZID=Europe/London:20220202T143000
DTEND;TZID=Europe/London:20220202T150000
UID:TALK168671AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/168671
DESCRIPTION:Endohedral fullerenes are an example of non-bonded
complexes whose properties are dominated by stron
g quantum effects. Following the work of Bacanu et
al.\, and Bacic and Mandziuk\, He@C60 and Ne@C70
were studied. These systems exhibit quantisation o
f translational energies due to particle in a box
type effects\, and symmetry breaking lifting the d
egeneracy of energy levels. The energies\, wavefun
ctions and spectra calculated very closely match t
he previously seen results.\nFor He@C60 the potent
ial was assumed to be radially symmetric and const
ructed from R2\, R4 and R6 terms. This was then us
ed to construct the Hamiltonian matrix in the fini
te basis representation which was diagonalised to
calculate the translational and rotational energy
levels with fundamental frequencies of 217.9 cm^-1
and 96.7 cm^-1 respectively. These were used to p
lot two low temperature predicted rotational infra
red spectra which closely matched the experimental
spectra. The wavefunctions show a strong resembla
nce to hydrogenic atomic orbitals because of the i
mposed spherical symmetry.\nFor Ne@C70\, the spher
ical symmetry was broken by elongation of the full
erene along the now unique z axis. The potential w
as taken to be a pairwise Lennard-Jones summation
over atoms which could be modelled as a one dimens
ional anharmonic oscillator along the z direction\
, and a two dimensional isotropic anharmonic oscil
lator in the xy plane. The Hamiltonian matrix was
constructed in the discrete variable representatio
n and its eigenvalues calculated. The presence of
an\nanisotropic direction lifted the (2l +1)-fold
degeneracies into only singly and doubly degenerat
e states indexed by the angular momentum quantum n
umber for the two-dimensional oscillator. The fund
amental frequencies for the z and xy planes were f
ound 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 the quantum numb
er assignments.
LOCATION:via zoom
CONTACT:Lisa Masters
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