Buckminsterfullerene
Eine Geodätische Kuppel von Richard Buckminster Fuller, die Biosphère, Ile Ste-Hélène, Montreal.
T3g
T3u
reduction of the 180 x 180 matrix of coordinates on each carbon atom givesΓred = 2(Ag), 1(Au), 4(T1g), 5(T1u), 4(T3g), 5(T3u), 6(Gg), 6(Gu), 8(Hg), and 7(Hu)
subtract translation and rotation, remains 46 frequencies - clearly quite a number of silent ones !which ones are infrared, which ones Raman active ? 2(Ag), 1(Au), 4(T1g), 5(T1u), 4(T3g), 5(T3u), 6(Gg), 6(Gu), 8(Hg), and 7(Hu) R IR R
IR spectrum
Raman spectrum
Optical phonon modes in solid and doped C60, P. C. Eklund al., J. Phys. Chern. Solids 53, 1391-1413. (1992)
solid state effects
isotope effects
ligand substitution
methane CH4active modes
IR 2(T2) Raman A1, E, 2T2
deuterated methane CH3D C3vactive modes
CH4 CH3D CH2D2
IR 2T2 3A1,3E 4A1.2B1,2B2
Raman A1,E, T2 3A1, 3E 4A1,A2,2B1,2B2
transition metal complexes
in a spherical field, all d orbitals would increase in energy together - no term splitting
in an octahedral field, energies of eg state increases and that of t2g decreases, maintaining the overall center of gravity of the d state energy
magnitude of splitting (d0 or 10Dq) depends on metal ion and ligand nature
material from R.L.Carter, Molecular Symmetry and Group Theory, Wiley 1998 Chapter 7
Jahn-Teller effect in octahedral transition metal complexes
For any nonlinear molecular system in a degenerate electronic state a distortion will occur so as to lower the symmetry and remove the degeneracy.
A degenerate state results whenever the electrons can be distributed in two or more ways among degenerate orbitals. This is a different meaning from degeneracy of irreducible representations or atomic levels, since it involves the actual occupancy
example: a) ground state is a single d electron (d1) level ; can be distributed in any of the three t2g orbitals - triply degenerate!b) d2 equally degeneratec) d3 is nondegenerate, full t2g orbital...
eg
t2g
d1 d2 d3
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