...the bible...1945

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

filling of levels - Hund’s rules

eg

t2g

d1 d2 d3 d4high spin

d5high spin

d5low spin

d6high spin

d6low spin

d7high spin

d7low spin

d8 d9 d10d4low spin

3 3 0 2 3 30 3 0 3 2 0 02

tetragonal distortion